%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW317+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.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 1.61s 2.46s
% Output   : Proof 1.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW317+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.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 22:43:18 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.61/2.46  
% 1.61/2.46  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.61/2.46  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.61/2.46  %-----------------------------------------------------
% 1.61/2.46  ncf(matrix, plain, [(52063 ^ _779530) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), c_Hoare__Mirabelle_Otriple_Otriple(t_a, v_P, c_Com_Ocom_OSKIP, v_P)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))], (2 ^ _779530) ^ [_779560] : [-(_779560 = _779560)], (4 ^ _779530) ^ [_779583, _779585] : [_779585 = _779583, -(_779583 = _779585)], (10 ^ _779530) ^ [_779656, _779658, _779660] : [-(_779660 = _779656), _779660 = _779658, _779658 = _779656], (20 ^ _779530) ^ [_779793, _779795, _779797, _779799, _779801, _779803, _779805, _779807, _779809, _779811, _779813, _779815] : [-(c_Predicate_Oinv__imagep(_779813, _779809, _779805, _779801, _779797, _779793)), c_Predicate_Oinv__imagep(_779815, _779811, _779807, _779803, _779799, _779795), _779815 = _779813, _779811 = _779809, _779807 = _779805, _779803 = _779801, _779799 = _779797, _779795 = _779793], (50 ^ _779530) ^ [_780338, _780340, _780342, _780344, _780346, _780348, _780350, _780352, _780354, _780356, _780358, _780360] : [-(c_Nitpick_Ofold__graph_H(_780358, _780354, _780350, _780346, _780342, _780338)), c_Nitpick_Ofold__graph_H(_780360, _780356, _780352, _780348, _780344, _780340), _780360 = _780358, _780356 = _780354, _780352 = _780350, _780348 = _780346, _780344 = _780342, _780340 = _780338], (80 ^ _779530) ^ [_780883, _780885, _780887, _780889, _780891, _780893, _780895, _780897] : [-(c_Partial__Function_Omk__less(_780895, _780891, _780887, _780883)), c_Partial__Function_Omk__less(_780897, _780893, _780889, _780885), _780897 = _780895, _780893 = _780891, _780889 = _780887, _780885 = _780883], (102 ^ _779530) ^ [_781236, _781238, _781240, _781242, _781244, _781246] : [-(c_Orderings_Oorder__class_Ostrict__mono(_781244, _781240, _781236)), c_Orderings_Oorder__class_Ostrict__mono(_781246, _781242, _781238), _781246 = _781244, _781242 = _781240, _781238 = _781236], (120 ^ _779530) ^ [_781505, _781507, _781509, _781511, _781513, _781515, _781517, _781519] : [-(c_Finite__Set_Ofolding__idem(_781517, _781513, _781509, _781505)), c_Finite__Set_Ofolding__idem(_781519, _781515, _781511, _781507), _781519 = _781517, _781515 = _781513, _781511 = _781509, _781507 = _781505], (142 ^ _779530) ^ [_781858, _781860, _781862, _781864, _781866, _781868, _781870, _781872, _781874, _781876, _781878, _781880] : [-(c_Equiv__Relations_Ocongruent2(_781878, _781874, _781870, _781866, _781862, _781858)), c_Equiv__Relations_Ocongruent2(_781880, _781876, _781872, _781868, _781864, _781860), _781880 = _781878, _781876 = _781874, _781872 = _781870, _781868 = _781866, _781864 = _781862, _781860 = _781858], (172 ^ _779530) ^ [_782403, _782405, _782407, _782409] : [-(c_Nitpick_Orefl_H(_782407, _782403)), c_Nitpick_Orefl_H(_782409, _782405), _782409 = _782407, _782405 = _782403], (186 ^ _779530) ^ [_782596, _782598, _782600, _782602, _782604, _782606, _782608, _782610, _782612, _782614] : [-(c_Finite__Set_Ofolding__image(_782612, _782608, _782604, _782600, _782596)), c_Finite__Set_Ofolding__image(_782614, _782610, _782606, _782602, _782598), _782614 = _782612, _782610 = _782608, _782606 = _782604, _782602 = _782600, _782598 = _782596], (212 ^ _779530) ^ [_783041, _783043, _783045, _783047, _783049, _783051, _783053, _783055, _783057, _783059] : [-(c_Big__Operators_Ocomm__monoid__big(_783057, _783053, _783049, _783045, _783041)), c_Big__Operators_Ocomm__monoid__big(_783059, _783055, _783051, _783047, _783043), _783059 = _783057, _783055 = _783053, _783051 = _783049, _783047 = _783045, _783043 = _783041], (238 ^ _779530) ^ [_783486, _783488, _783490, _783492] : [-(c_Equiv__Relations_Oequivp(_783490, _783486)), c_Equiv__Relations_Oequivp(_783492, _783488), _783492 = _783490, _783488 = _783486], (252 ^ _779530) ^ [_783679, _783681, _783683, _783685, _783687, _783689, _783691, _783693] : [-(c_Natural_Oevaln(_783691, _783687, _783683, _783679)), c_Natural_Oevaln(_783693, _783689, _783685, _783681), _783693 = _783691, _783689 = _783687, _783685 = _783683, _783681 = _783679], (274 ^ _779530) ^ [_784032, _784034, _784036, _784038, _784040, _784042] : [-(c_Orderings_Oorder__class_Omono(_784040, _784036, _784032)), c_Orderings_Oorder__class_Omono(_784042, _784038, _784034), _784042 = _784040, _784038 = _784036, _784034 = _784032], (292 ^ _779530) ^ [_784301, _784303, _784305, _784307] : [-(c_Int_Oiszero(_784305, _784301)), c_Int_Oiszero(_784307, _784303), _784307 = _784305, _784303 = _784301], (306 ^ _779530) ^ [_784494, _784496] : [-(class_Rings_Odivision__ring__inverse__zero(_784494)), _784496 = _784494, class_Rings_Odivision__ring__inverse__zero(_784496)], (316 ^ _779530) ^ [_784619, _784621] : [-(class_Rings_Odivision__ring(_784619)), _784621 = _784619, class_Rings_Odivision__ring(_784621)], (326 ^ _779530) ^ [_784744, _784746] : [-(class_Fields_Ofield__inverse__zero(_784744)), _784746 = _784744, class_Fields_Ofield__inverse__zero(_784746)], (336 ^ _779530) ^ [_784869, _784871] : [-(class_Fields_Ofield(_784869)), _784871 = _784869, class_Fields_Ofield(_784871)], (346 ^ _779530) ^ [_784994, _784996] : [-(c_Nat__Transfer_Ois__nat(_784994)), _784996 = _784994, c_Nat__Transfer_Ois__nat(_784996)], (356 ^ _779530) ^ [_785119, _785121] : [-(class_Fields_Olinordered__field(_785119)), _785121 = _785119, class_Fields_Olinordered__field(_785121)], (366 ^ _779530) ^ [_785244, _785246] : [-(class_Fields_Olinordered__field__inverse__zero(_785244)), _785246 = _785244, class_Fields_Olinordered__field__inverse__zero(_785246)], (376 ^ _779530) ^ [_785369, _785371, _785373, _785375, _785377, _785379, _785381, _785383] : [-(c_Wellfounded_Omax__extp(_785381, _785377, _785373, _785369)), c_Wellfounded_Omax__extp(_785383, _785379, _785375, _785371), _785383 = _785381, _785379 = _785377, _785375 = _785373, _785371 = _785369], (398 ^ _779530) ^ [_785722, _785724, _785726, _785728, _785730, _785732, _785734, _785736, _785738, _785740, _785742, _785744, _785746, _785748] : [-(c_Predicate_Opred__comp(_785746, _785742, _785738, _785734, _785730, _785726, _785722)), c_Predicate_Opred__comp(_785748, _785744, _785740, _785736, _785732, _785728, _785724), _785748 = _785746, _785744 = _785742, _785740 = _785738, _785736 = _785734, _785732 = _785730, _785728 = _785726, _785724 = _785722], (432 ^ _779530) ^ [_786375, _786377, _786379, _786381] : [-(c_FunDef_Oreduction__pair(_786379, _786375)), c_FunDef_Oreduction__pair(_786381, _786377), _786381 = _786379, _786377 = _786375], (446 ^ _779530) ^ [_786568, _786570, _786572, _786574] : [-(c_Predicate_Oreflp(_786572, _786568)), c_Predicate_Oreflp(_786574, _786570), _786574 = _786572, _786570 = _786568], (460 ^ _779530) ^ [_786761, _786763, _786765, _786767, _786769, _786771] : [-(c_Big__Operators_Osemilattice__big(_786769, _786765, _786761)), c_Big__Operators_Osemilattice__big(_786771, _786767, _786763), _786771 = _786769, _786767 = _786765, _786763 = _786761], (478 ^ _779530) ^ [_787030, _787032, _787034, _787036] : [-(c_Nitpick_Owf_H(_787034, _787030)), c_Nitpick_Owf_H(_787036, _787032), _787036 = _787034, _787032 = _787030], (492 ^ _779530) ^ [_787223, _787225] : [-(c_Nitpick_Ounknown(_787223)), _787225 = _787223, c_Nitpick_Ounknown(_787225)], (502 ^ _779530) ^ [_787348, _787350, _787352, _787354, _787356, _787358, _787360, _787362, _787364, _787366, _787368, _787370] : [-(c_Finite__Set_Ofolding__image__simple(_787368, _787364, _787360, _787356, _787352, _787348)), c_Finite__Set_Ofolding__image__simple(_787370, _787366, _787362, _787358, _787354, _787350), _787370 = _787368, _787366 = _787364, _787362 = _787360, _787358 = _787356, _787354 = _787352, _787350 = _787348], (532 ^ _779530) ^ [_787893, _787895, _787897, _787899, _787901, _787903, _787905, _787907] : [-(c_Equiv__Relations_Ocongruent(_787905, _787901, _787897, _787893)), c_Equiv__Relations_Ocongruent(_787907, _787903, _787899, _787895), _787907 = _787905, _787903 = _787901, _787899 = _787897, _787895 = _787893], (554 ^ _779530) ^ [_788246, _788248, _788250, _788252, _788254, _788256] : [-(c_Hoare__Mirabelle_Ohoare__valids(_788254, _788250, _788246)), c_Hoare__Mirabelle_Ohoare__valids(_788256, _788252, _788248), _788256 = _788254, _788252 = _788250, _788248 = _788246], (572 ^ _779530) ^ [_788515, _788517, _788519, _788521, _788523, _788525] : [-(c_Hoare__Mirabelle_Otriple__valid(_788523, _788519, _788515)), c_Hoare__Mirabelle_Otriple__valid(_788525, _788521, _788517), _788525 = _788523, _788521 = _788519, _788517 = _788515], (590 ^ _779530) ^ [_788784, _788786] : [-(c_Nat__Transfer_Onat__set(_788784)), _788786 = _788784, c_Nat__Transfer_Onat__set(_788786)], (600 ^ _779530) ^ [_788909, _788911, _788913, _788915, _788917, _788919] : [-(c_Enum_Oall__n__lists(_788917, _788913, _788909)), c_Enum_Oall__n__lists(_788919, _788915, _788911), _788919 = _788917, _788915 = _788913, _788911 = _788909], (618 ^ _779530) ^ [_789178, _789180, _789182, _789184, _789186, _789188] : [-(c_Enum_Oex__n__lists(_789186, _789182, _789178)), c_Enum_Oex__n__lists(_789188, _789184, _789180), _789188 = _789186, _789184 = _789182, _789180 = _789178], (636 ^ _779530) ^ [_789447, _789449, _789451, _789453, _789455, _789457, _789459, _789461] : [-(c_List_Olistrelp(_789459, _789455, _789451, _789447)), c_List_Olistrelp(_789461, _789457, _789453, _789449), _789461 = _789459, _789457 = _789455, _789453 = _789451, _789449 = _789447], (658 ^ _779530) ^ [_789800, _789802] : [-(c_List_Onat__list(_789800)), _789802 = _789800, c_List_Onat__list(_789802)], (668 ^ _779530) ^ [_789925, _789927, _789929, _789931, _789933, _789935, _789937, _789939] : [-(c_Fun_Oinj__on(_789937, _789933, _789929, _789925)), c_Fun_Oinj__on(_789939, _789935, _789931, _789927), _789939 = _789937, _789935 = _789933, _789931 = _789929, _789927 = _789925], (690 ^ _779530) ^ [_790278, _790280, _790282, _790284] : [-(c_Wellfounded_OwfP(_790282, _790278)), c_Wellfounded_OwfP(_790284, _790280), _790284 = _790282, _790280 = _790278], (704 ^ _779530) ^ [_790471, _790473, _790475, _790477, _790479, _790481, _790483, _790485, _790487, _790489] : [-(c_List_Olist__all2(_790487, _790483, _790479, _790475, _790471)), c_List_Olist__all2(_790489, _790485, _790481, _790477, _790473), _790489 = _790487, _790485 = _790483, _790481 = _790479, _790477 = _790475, _790473 = _790471], (730 ^ _779530) ^ [_790916, _790918, _790920, _790922] : [-(c_List_Olinorder__class_Osorted(_790920, _790916)), c_List_Olinorder__class_Osorted(_790922, _790918), _790922 = _790920, _790918 = _790916], (744 ^ _779530) ^ [_791109, _791111, _791113, _791115, _791117, _791119] : [-(c_List_Olist__ex(_791117, _791113, _791109)), c_List_Olist__ex(_791119, _791115, _791111), _791119 = _791117, _791115 = _791113, _791111 = _791109], (762 ^ _779530) ^ [_791378, _791380, _791382, _791384, _791386, _791388, _791390, _791392, _791394, _791396] : [-(c_Typedef_Otype__definition(_791394, _791390, _791386, _791382, _791378)), c_Typedef_Otype__definition(_791396, _791392, _791388, _791384, _791380), _791396 = _791394, _791392 = _791390, _791388 = _791386, _791384 = _791382, _791380 = _791378], (788 ^ _779530) ^ [_791823, _791825, _791827, _791829] : [-(c_Relation_Oirrefl(_791827, _791823)), c_Relation_Oirrefl(_791829, _791825), _791829 = _791827, _791825 = _791823], (802 ^ _779530) ^ [_792016, _792018, _792020, _792022, _792024, _792026] : [-(c_Relation_Orefl__on(_792024, _792020, _792016)), c_Relation_Orefl__on(_792026, _792022, _792018), _792026 = _792024, _792022 = _792020, _792018 = _792016], (820 ^ _779530) ^ [_792285, _792287, _792289, _792291, _792293, _792295] : [-(c_Equiv__Relations_Oequiv(_792293, _792289, _792285)), c_Equiv__Relations_Oequiv(_792295, _792291, _792287), _792295 = _792293, _792291 = _792289, _792287 = _792285], (838 ^ _779530) ^ [_792554, _792556, _792558, _792560, _792562, _792564] : [-(c_Relation_Ototal__on(_792562, _792558, _792554)), c_Relation_Ototal__on(_792564, _792560, _792556), _792564 = _792562, _792560 = _792558, _792556 = _792554], (856 ^ _779530) ^ [_792823, _792825, _792827, _792829] : [-(c_Wellfounded_Oacyclic(_792827, _792823)), c_Wellfounded_Oacyclic(_792829, _792825), _792829 = _792827, _792825 = _792823], (870 ^ _779530) ^ [_793016, _793018, _793020, _793022, _793024, _793026] : [-(c_Relation_Osingle__valued(_793024, _793020, _793016)), c_Relation_Osingle__valued(_793026, _793022, _793018), _793026 = _793024, _793022 = _793020, _793018 = _793016], (888 ^ _779530) ^ [_793285, _793287, _793289, _793291, _793293, _793295, _793297, _793299] : [-(c_Finite__Set_Ofolding(_793297, _793293, _793289, _793285)), c_Finite__Set_Ofolding(_793299, _793295, _793291, _793287), _793299 = _793297, _793295 = _793293, _793291 = _793289, _793287 = _793285], (910 ^ _779530) ^ [_793638, _793640, _793642, _793644, _793646, _793648] : [-(c_Finite__Set_Ofolding__one__idem(_793646, _793642, _793638)), c_Finite__Set_Ofolding__one__idem(_793648, _793644, _793640), _793648 = _793646, _793644 = _793642, _793640 = _793638], (928 ^ _779530) ^ [_793907, _793909, _793911, _793913, _793915, _793917] : [-(c_Finite__Set_Ofun__left__comm__idem(_793915, _793911, _793907)), c_Finite__Set_Ofun__left__comm__idem(_793917, _793913, _793909), _793917 = _793915, _793913 = _793911, _793909 = _793907], (946 ^ _779530) ^ [_794176, _794178] : [-(class_Lattices_Oab__semigroup__idem__mult(_794176)), _794178 = _794176, class_Lattices_Oab__semigroup__idem__mult(_794178)], (956 ^ _779530) ^ [_794301, _794303, _794305, _794307, _794309, _794311] : [-(c_Finite__Set_Ofolding__one(_794309, _794305, _794301)), c_Finite__Set_Ofolding__one(_794311, _794307, _794303), _794311 = _794309, _794307 = _794305, _794303 = _794301], (974 ^ _779530) ^ [_794570, _794572, _794574, _794576, _794578, _794580] : [-(c_Finite__Set_Ofun__left__comm(_794578, _794574, _794570)), c_Finite__Set_Ofun__left__comm(_794580, _794576, _794572), _794580 = _794578, _794576 = _794574, _794572 = _794570], (992 ^ _779530) ^ [_794839, _794841, _794843, _794845] : [-(c_Wellfounded_Owf(_794843, _794839)), c_Wellfounded_Owf(_794845, _794841), _794845 = _794843, _794841 = _794839], (1006 ^ _779530) ^ [_795032, _795034, _795036, _795038, _795040, _795042, _795044, _795046, _795048, _795050, _795052, _795054] : [-(c_Finite__Set_Ofolding__image__simple__idem(_795052, _795048, _795044, _795040, _795036, _795032)), c_Finite__Set_Ofolding__image__simple__idem(_795054, _795050, _795046, _795042, _795038, _795034), _795054 = _795052, _795050 = _795048, _795046 = _795044, _795042 = _795040, _795038 = _795036, _795034 = _795032], (1036 ^ _779530) ^ [_795577, _795579] : [-(class_Rings_Oinverse(_795577)), _795579 = _795577, class_Rings_Oinverse(_795579)], (1046 ^ _779530) ^ [_795702, _795704, _795706, _795708, _795710, _795712] : [-(c_Nitpick_Oless__frac(_795710, _795706, _795702)), c_Nitpick_Oless__frac(_795712, _795708, _795704), _795712 = _795710, _795708 = _795706, _795704 = _795702], (1064 ^ _779530) ^ [_795971, _795973, _795975, _795977, _795979, _795981] : [-(c_Nitpick_Oless__eq__frac(_795979, _795975, _795971)), c_Nitpick_Oless__eq__frac(_795981, _795977, _795973), _795981 = _795979, _795977 = _795975, _795973 = _795971], (1082 ^ _779530) ^ [_796240, _796242, _796244, _796246, _796248, _796250] : [-(c_List_Olist__all(_796248, _796244, _796240)), c_List_Olist__all(_796250, _796246, _796242), _796250 = _796248, _796246 = _796244, _796242 = _796240], (1100 ^ _779530) ^ [_796509, _796511, _796513, _796515, _796517, _796519] : [-(c_List_Olist__ex1(_796517, _796513, _796509)), c_List_Olist__ex1(_796519, _796515, _796511), _796519 = _796517, _796515 = _796513, _796511 = _796509], (1118 ^ _779530) ^ [_796778, _796780, _796782, _796784] : [-(c_FunDef_Ois__measure(_796782, _796778)), c_FunDef_Ois__measure(_796784, _796780), _796784 = _796782, _796780 = _796778], (1132 ^ _779530) ^ [_796971, _796973, _796975, _796977, _796979, _796981, _796983, _796985] : [-(c_Nat__Transfer_Otransfer__morphism(_796983, _796979, _796975, _796971)), c_Nat__Transfer_Otransfer__morphism(_796985, _796981, _796977, _796973), _796985 = _796983, _796981 = _796979, _796977 = _796975, _796973 = _796971], (1154 ^ _779530) ^ [_797324, _797326] : [-(class_Lattices_Obounded__lattice(_797324)), _797326 = _797324, class_Lattices_Obounded__lattice(_797326)], (1164 ^ _779530) ^ [_797449, _797451] : [-(class_Rings_Olinordered__semiring__1__strict(_797449)), _797451 = _797449, class_Rings_Olinordered__semiring__1__strict(_797451)], (1174 ^ _779530) ^ [_797574, _797576] : [-(class_Groups_Oordered__ab__group__add__abs(_797574)), _797576 = _797574, class_Groups_Oordered__ab__group__add__abs(_797576)], (1184 ^ _779530) ^ [_797699, _797701] : [-(class_Groups_Olinordered__ab__group__add(_797699)), _797701 = _797699, class_Groups_Olinordered__ab__group__add(_797701)], (1194 ^ _779530) ^ [_797824, _797826] : [-(class_Rings_Oring__1__no__zero__divisors(_797824)), _797826 = _797824, class_Rings_Oring__1__no__zero__divisors(_797826)], (1204 ^ _779530) ^ [_797949, _797951] : [-(class_Rings_Olinordered__ring__strict(_797949)), _797951 = _797949, class_Rings_Olinordered__ring__strict(_797951)], (1214 ^ _779530) ^ [_798074, _798076] : [-(class_Rings_Oring__no__zero__divisors(_798074)), _798076 = _798074, class_Rings_Oring__no__zero__divisors(_798076)], (1224 ^ _779530) ^ [_798199, _798201] : [-(class_Rings_Olinordered__semiring__1(_798199)), _798201 = _798199, class_Rings_Olinordered__semiring__1(_798201)], (1234 ^ _779530) ^ [_798324, _798326] : [-(class_Groups_Oordered__ab__group__add(_798324)), _798326 = _798324, class_Groups_Oordered__ab__group__add(_798326)], (1244 ^ _779530) ^ [_798449, _798451] : [-(class_Rings_Oordered__ring__abs(_798449)), _798451 = _798449, class_Rings_Oordered__ring__abs(_798451)], (1254 ^ _779530) ^ [_798574, _798576] : [-(class_Rings_Olinordered__ring(_798574)), _798576 = _798574, class_Rings_Olinordered__ring(_798576)], (1264 ^ _779530) ^ [_798699, _798701] : [-(class_Rings_Olinordered__idom(_798699)), _798701 = _798699, class_Rings_Olinordered__idom(_798701)], (1274 ^ _779530) ^ [_798824, _798826] : [-(class_Groups_Oab__group__add(_798824)), _798826 = _798824, class_Groups_Oab__group__add(_798826)], (1284 ^ _779530) ^ [_798949, _798951] : [-(class_Rings_Oordered__ring(_798949)), _798951 = _798949, class_Rings_Oordered__ring(_798951)], (1294 ^ _779530) ^ [_799074, _799076] : [-(class_Rings_Ocomm__ring__1(_799074)), _799076 = _799074, class_Rings_Ocomm__ring__1(_799076)], (1304 ^ _779530) ^ [_799199, _799201] : [-(class_Groups_Ogroup__add(_799199)), _799201 = _799199, class_Groups_Ogroup__add(_799201)], (1314 ^ _779530) ^ [_799324, _799326] : [-(class_Divides_Oring__div(_799324)), _799326 = _799324, class_Divides_Oring__div(_799326)], (1324 ^ _779530) ^ [_799449, _799451] : [-(class_Int_Oring__char__0(_799449)), _799451 = _799449, class_Int_Oring__char__0(_799451)], (1334 ^ _779530) ^ [_799574, _799576] : [-(class_Int_Onumber__ring(_799574)), _799576 = _799574, class_Int_Onumber__ring(_799576)], (1344 ^ _779530) ^ [_799699, _799701] : [-(class_Groups_Osgn__if(_799699)), _799701 = _799699, class_Groups_Osgn__if(_799701)], (1354 ^ _779530) ^ [_799824, _799826] : [-(class_Groups_Oabs__if(_799824)), _799826 = _799824, class_Groups_Oabs__if(_799826)], (1364 ^ _779530) ^ [_799949, _799951] : [-(class_Rings_Oring__1(_799949)), _799951 = _799949, class_Rings_Oring__1(_799951)], (1374 ^ _779530) ^ [_800074, _800076] : [-(class_Rings_Oring(_800074)), _800076 = _800074, class_Rings_Oring(_800076)], (1384 ^ _779530) ^ [_800199, _800201] : [-(class_Rings_Oidom(_800199)), _800201 = _800199, class_Rings_Oidom(_800201)], (1394 ^ _779530) ^ [_800324, _800326] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800324)), _800326 = _800324, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800326)], (1404 ^ _779530) ^ [_800449, _800451] : [-(class_Orderings_Owellorder(_800449)), _800451 = _800449, class_Orderings_Owellorder(_800451)], (1414 ^ _779530) ^ [_800574, _800576] : [-(class_Complete__Lattice_Ocomplete__lattice(_800574)), _800576 = _800574, class_Complete__Lattice_Ocomplete__lattice(_800576)], (1424 ^ _779530) ^ [_800699, _800701] : [-(class_Lattices_Obounded__lattice__top(_800699)), _800701 = _800699, class_Lattices_Obounded__lattice__top(_800701)], (1434 ^ _779530) ^ [_800824, _800826] : [-(class_Lattices_Obounded__lattice__bot(_800824)), _800826 = _800824, class_Lattices_Obounded__lattice__bot(_800826)], (1444 ^ _779530) ^ [_800949, _800951] : [-(class_Lattices_Osemilattice__sup(_800949)), _800951 = _800949, class_Lattices_Osemilattice__sup(_800951)], (1454 ^ _779530) ^ [_801074, _801076] : [-(class_Lattices_Osemilattice__inf(_801074)), _801076 = _801074, class_Lattices_Osemilattice__inf(_801076)], (1464 ^ _779530) ^ [_801199, _801201] : [-(class_Lattices_Odistrib__lattice(_801199)), _801201 = _801199, class_Lattices_Odistrib__lattice(_801201)], (1474 ^ _779530) ^ [_801324, _801326] : [-(class_Lattices_Oboolean__algebra(_801324)), _801326 = _801324, class_Lattices_Oboolean__algebra(_801326)], (1484 ^ _779530) ^ [_801449, _801451] : [-(class_Lattices_Olattice(_801449)), _801451 = _801449, class_Lattices_Olattice(_801451)], (1494 ^ _779530) ^ [_801574, _801576] : [-(class_Orderings_Otop(_801574)), _801576 = _801574, class_Orderings_Otop(_801576)], (1504 ^ _779530) ^ [_801699, _801701] : [-(class_Orderings_Obot(_801699)), _801701 = _801699, class_Orderings_Obot(_801701)], (1514 ^ _779530) ^ [_801824, _801826] : [-(class_Groups_Ouminus(_801824)), _801826 = _801824, class_Groups_Ouminus(_801826)], (1524 ^ _779530) ^ [_801949, _801951] : [-(class_Finite__Set_Ofinite(_801949)), _801951 = _801949, class_Finite__Set_Ofinite(_801951)], (1534 ^ _779530) ^ [_802074, _802076] : [-(class_Smallcheck_Osmall(_802074)), _802076 = _802074, class_Smallcheck_Osmall(_802076)], (1544 ^ _779530) ^ [_802199, _802201] : [-(class_Enum_Oenum(_802199)), _802201 = _802199, class_Enum_Oenum(_802201)], (1554 ^ _779530) ^ [_802324, _802326] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_802324)), _802326 = _802324, class_Groups_Oordered__cancel__ab__semigroup__add(_802326)], (1564 ^ _779530) ^ [_802449, _802451] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_802449)), _802451 = _802449, class_Groups_Oordered__ab__semigroup__add__imp__le(_802451)], (1574 ^ _779530) ^ [_802574, _802576] : [-(class_Rings_Olinordered__comm__semiring__strict(_802574)), _802576 = _802574, class_Rings_Olinordered__comm__semiring__strict(_802576)], (1584 ^ _779530) ^ [_802699, _802701] : [-(class_Groups_Olinordered__ab__semigroup__add(_802699)), _802701 = _802699, class_Groups_Olinordered__ab__semigroup__add(_802701)], (1594 ^ _779530) ^ [_802824, _802826] : [-(class_Rings_Olinordered__semiring__strict(_802824)), _802826 = _802824, class_Rings_Olinordered__semiring__strict(_802826)], (1604 ^ _779530) ^ [_802949, _802951] : [-(class_Groups_Oordered__ab__semigroup__add(_802949)), _802951 = _802949, class_Groups_Oordered__ab__semigroup__add(_802951)], (1614 ^ _779530) ^ [_803074, _803076] : [-(class_Groups_Oordered__comm__monoid__add(_803074)), _803076 = _803074, class_Groups_Oordered__comm__monoid__add(_803076)], (1624 ^ _779530) ^ [_803199, _803201] : [-(class_Groups_Ocancel__ab__semigroup__add(_803199)), _803201 = _803199, class_Groups_Ocancel__ab__semigroup__add(_803201)], (1634 ^ _779530) ^ [_803324, _803326] : [-(class_Rings_Oordered__cancel__semiring(_803324)), _803326 = _803324, class_Rings_Oordered__cancel__semiring(_803326)], (1644 ^ _779530) ^ [_803449, _803451] : [-(class_Rings_Oordered__comm__semiring(_803449)), _803451 = _803449, class_Rings_Oordered__comm__semiring(_803451)], (1654 ^ _779530) ^ [_803574, _803576] : [-(class_Groups_Ocancel__semigroup__add(_803574)), _803576 = _803574, class_Groups_Ocancel__semigroup__add(_803576)], (1664 ^ _779530) ^ [_803699, _803701] : [-(class_Rings_Olinordered__semiring(_803699)), _803701 = _803699, class_Rings_Olinordered__semiring(_803701)], (1674 ^ _779530) ^ [_803824, _803826] : [-(class_Rings_Olinordered__semidom(_803824)), _803826 = _803824, class_Rings_Olinordered__semidom(_803826)], (1684 ^ _779530) ^ [_803949, _803951] : [-(class_Groups_Oab__semigroup__mult(_803949)), _803951 = _803949, class_Groups_Oab__semigroup__mult(_803951)], (1694 ^ _779530) ^ [_804074, _804076] : [-(class_Groups_Ocomm__monoid__mult(_804074)), _804076 = _804074, class_Groups_Ocomm__monoid__mult(_804076)], (1704 ^ _779530) ^ [_804199, _804201] : [-(class_Groups_Oab__semigroup__add(_804199)), _804201 = _804199, class_Groups_Oab__semigroup__add(_804201)], (1714 ^ _779530) ^ [_804324, _804326] : [-(class_Rings_Oordered__semiring(_804324)), _804326 = _804324, class_Rings_Oordered__semiring(_804326)], (1724 ^ _779530) ^ [_804449, _804451] : [-(class_Rings_Ono__zero__divisors(_804449)), _804451 = _804449, class_Rings_Ono__zero__divisors(_804451)], (1734 ^ _779530) ^ [_804574, _804576] : [-(class_Groups_Ocomm__monoid__add(_804574)), _804576 = _804574, class_Groups_Ocomm__monoid__add(_804576)], (1744 ^ _779530) ^ [_804699, _804701] : [-(class_Rings_Ocomm__semiring__1(_804699)), _804701 = _804699, class_Rings_Ocomm__semiring__1(_804701)], (1754 ^ _779530) ^ [_804824, _804826] : [-(class_Groups_Osemigroup__add(_804824)), _804826 = _804824, class_Groups_Osemigroup__add(_804826)], (1764 ^ _779530) ^ [_804949, _804951] : [-(class_Divides_Osemiring__div(_804949)), _804951 = _804949, class_Divides_Osemiring__div(_804951)], (1774 ^ _779530) ^ [_805074, _805076] : [-(class_Rings_Ocomm__semiring(_805074)), _805076 = _805074, class_Rings_Ocomm__semiring(_805076)], (1784 ^ _779530) ^ [_805199, _805201] : [-(class_Nat_Osemiring__char__0(_805199)), _805201 = _805199, class_Nat_Osemiring__char__0(_805201)], (1794 ^ _779530) ^ [_805324, _805326] : [-(class_Rings_Ozero__neq__one(_805324)), _805326 = _805324, class_Rings_Ozero__neq__one(_805326)], (1804 ^ _779530) ^ [_805449, _805451] : [-(class_Orderings_Opreorder(_805449)), _805451 = _805449, class_Orderings_Opreorder(_805451)], (1814 ^ _779530) ^ [_805574, _805576] : [-(class_Orderings_Olinorder(_805574)), _805576 = _805574, class_Orderings_Olinorder(_805576)], (1824 ^ _779530) ^ [_805699, _805701] : [-(class_Groups_Omonoid__mult(_805699)), _805701 = _805699, class_Groups_Omonoid__mult(_805701)], (1834 ^ _779530) ^ [_805824, _805826] : [-(class_Groups_Omonoid__add(_805824)), _805826 = _805824, class_Groups_Omonoid__add(_805826)], (1844 ^ _779530) ^ [_805949, _805951] : [-(class_Rings_Osemiring__1(_805949)), _805951 = _805949, class_Rings_Osemiring__1(_805951)], (1854 ^ _779530) ^ [_806074, _806076] : [-(class_Rings_Osemiring__0(_806074)), _806076 = _806074, class_Rings_Osemiring__0(_806076)], (1864 ^ _779530) ^ [_806199, _806201] : [-(class_Rings_Omult__zero(_806199)), _806201 = _806199, class_Rings_Omult__zero(_806201)], (1874 ^ _779530) ^ [_806324, _806326] : [-(class_Orderings_Oorder(_806324)), _806326 = _806324, class_Orderings_Oorder(_806326)], (1884 ^ _779530) ^ [_806449, _806451] : [-(class_Rings_Osemiring(_806449)), _806451 = _806449, class_Rings_Osemiring(_806451)], (1894 ^ _779530) ^ [_806574, _806576] : [-(class_Orderings_Oord(_806574)), _806576 = _806574, class_Orderings_Oord(_806576)], (1904 ^ _779530) ^ [_806699, _806701] : [-(class_Groups_Ominus(_806699)), _806701 = _806699, class_Groups_Ominus(_806701)], (1914 ^ _779530) ^ [_806824, _806826] : [-(class_Power_Opower(_806824)), _806826 = _806824, class_Power_Opower(_806826)], (1924 ^ _779530) ^ [_806949, _806951] : [-(class_Groups_Ozero(_806949)), _806951 = _806949, class_Groups_Ozero(_806951)], (1934 ^ _779530) ^ [_807074, _807076] : [-(class_Int_Onumber(_807074)), _807076 = _807074, class_Int_Onumber(_807076)], (1944 ^ _779530) ^ [_807199, _807201] : [-(class_Groups_Oone(_807199)), _807201 = _807199, class_Groups_Oone(_807201)], (1954 ^ _779530) ^ [_807324, _807326] : [-(class_HOL_Oequal(_807324)), _807326 = _807324, class_HOL_Oequal(_807326)], (1964 ^ _779530) ^ [_807449, _807451] : [-(class_Nat_Osize(_807449)), _807451 = _807449, class_Nat_Osize(_807451)], (1974 ^ _779530) ^ [_807574, _807576] : [-(hBOOL(_807574)), _807576 = _807574, hBOOL(_807576)], (1984 ^ _779530) ^ [_807695, _807697, _807699, _807701, _807703, _807705] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807703, _807699, _807695)), c_Hoare__Mirabelle_Ohoare__derivs(_807705, _807701, _807697), _807705 = _807703, _807701 = _807699, _807697 = _807695], (2002 ^ _779530) ^ [_808747, _808749, _808751, _808753, _808755, _808757, _808759, _808761] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808761, _808757, _808753, _808749) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808759, _808755, _808751, _808747)), _808761 = _808759, _808757 = _808755, _808753 = _808751, _808749 = _808747], (2020 ^ _779530) ^ [_809048, _809050, _809052, _809054, _809056, _809058, _809060, _809062] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_809062, _809058, _809054, _809050) = c_Hoare__Mirabelle_Otriple_Otriple__case(_809060, _809056, _809052, _809048)), _809062 = _809060, _809058 = _809056, _809054 = _809052, _809050 = _809048], (2038 ^ _779530) ^ [_809349, _809351, _809353, _809355, _809357, _809359] : [-(c_Hoare__Mirabelle_Opeek__and(_809359, _809355, _809351) = c_Hoare__Mirabelle_Opeek__and(_809357, _809353, _809349)), _809359 = _809357, _809355 = _809353, _809351 = _809349], (2052 ^ _779530) ^ [_809570, _809572, _809574, _809576] : [-(c_Enum_Oenum__the(_809576, _809572) = c_Enum_Oenum__the(_809574, _809570)), _809576 = _809574, _809572 = _809570], (2062 ^ _779530) ^ [_809719, _809721, _809723, _809725, _809727, _809729, _809731, _809733, _809735, _809737, _809739, _809741, _809743, _809745, _809747, _809749, _809751, _809753, _809755, _809757] : [-(c_Com_Ocom_Ocom__case(_809757, _809753, _809749, _809745, _809741, _809737, _809733, _809729, _809725, _809721) = c_Com_Ocom_Ocom__case(_809755, _809751, _809747, _809743, _809739, _809735, _809731, _809727, _809723, _809719)), _809757 = _809755, _809753 = _809751, _809749 = _809747, _809745 = _809743, _809741 = _809739, _809737 = _809735, _809733 = _809731, _809729 = _809727, _809725 = _809723, _809721 = _809719], (2104 ^ _779530) ^ [_810668, _810670] : [_810670 = _810668, -(c_Hoare__Mirabelle_OMGT(_810670) = c_Hoare__Mirabelle_OMGT(_810668))], (2110 ^ _779530) ^ [_810753, _810755, _810757, _810759] : [-(c_Natural_Ogetlocs(_810759, _810755) = c_Natural_Ogetlocs(_810757, _810753)), _810759 = _810757, _810755 = _810753], (2120 ^ _779530) ^ [_810902, _810904, _810906, _810908, _810910, _810912, _810914, _810916] : [-(c_Com_Ovname_Ovname__case(_810916, _810912, _810908, _810904) = c_Com_Ovname_Ovname__case(_810914, _810910, _810906, _810902)), _810916 = _810914, _810912 = _810910, _810908 = _810906, _810904 = _810902], (2138 ^ _779530) ^ [_811203, _811205, _811207, _811209, _811211, _811213, _811215, _811217] : [-(c_Com_Ovname_Ovname__rec(_811217, _811213, _811209, _811205) = c_Com_Ovname_Ovname__rec(_811215, _811211, _811207, _811203)), _811217 = _811215, _811213 = _811211, _811209 = _811207, _811205 = _811203], (2156 ^ _779530) ^ [_811504, _811506] : [_811506 = _811504, -(c_Natural_Oevalc(_811506) = c_Natural_Oevalc(_811504))], (2162 ^ _779530) ^ [_811589, _811591, _811593, _811595, _811597, _811599] : [-(c_Partial__Function_Oflat__lub(_811599, _811595, _811591) = c_Partial__Function_Oflat__lub(_811597, _811593, _811589)), _811599 = _811597, _811595 = _811593, _811591 = _811589], (2176 ^ _779530) ^ [_811810, _811812, _811814, _811816] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_811816, _811812) = c_Inductive_Ocomplete__lattice__class_Ogfp(_811814, _811810)), _811816 = _811814, _811812 = _811810], (2186 ^ _779530) ^ [_811959, _811961, _811963, _811965, _811967, _811969, _811971, _811973, _811975, _811977] : [-(c_Fun_Ooverride__on(_811977, _811973, _811969, _811965, _811961) = c_Fun_Ooverride__on(_811975, _811971, _811967, _811963, _811959)), _811977 = _811975, _811973 = _811971, _811969 = _811967, _811965 = _811963, _811961 = _811959], (2208 ^ _779530) ^ [_812348, _812350, _812352, _812354, _812356, _812358] : [-(c_SetInterval_Oord_OatMost(_812358, _812354, _812350) = c_SetInterval_Oord_OatMost(_812356, _812352, _812348)), _812358 = _812356, _812354 = _812352, _812350 = _812348], (2222 ^ _779530) ^ [_812569, _812571, _812573, _812575, _812577, _812579] : [-(c_SetInterval_Oord_OatLeast(_812579, _812575, _812571) = c_SetInterval_Oord_OatLeast(_812577, _812573, _812569)), _812579 = _812577, _812575 = _812573, _812571 = _812569], (2236 ^ _779530) ^ [_812790, _812792, _812794, _812796, _812798, _812800] : [-(c_SetInterval_Oord_OlessThan(_812800, _812796, _812792) = c_SetInterval_Oord_OlessThan(_812798, _812794, _812790)), _812800 = _812798, _812796 = _812794, _812792 = _812790], (2250 ^ _779530) ^ [_813011, _813013, _813015, _813017, _813019, _813021] : [-(c_SetInterval_Oord_OgreaterThan(_813021, _813017, _813013) = c_SetInterval_Oord_OgreaterThan(_813019, _813015, _813011)), _813021 = _813019, _813017 = _813015, _813013 = _813011], (2264 ^ _779530) ^ [_813232, _813234, _813236, _813238, _813240, _813242, _813244, _813246] : [-(c_SetInterval_Oord_OatLeastAtMost(_813246, _813242, _813238, _813234) = c_SetInterval_Oord_OatLeastAtMost(_813244, _813240, _813236, _813232)), _813246 = _813244, _813242 = _813240, _813238 = _813236, _813234 = _813232], (2282 ^ _779530) ^ [_813533, _813535, _813537, _813539, _813541, _813543, _813545, _813547] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_813547, _813543, _813539, _813535) = c_SetInterval_Oord_OgreaterThanLessThan(_813545, _813541, _813537, _813533)), _813547 = _813545, _813543 = _813541, _813539 = _813537, _813535 = _813533], (2300 ^ _779530) ^ [_813834, _813836, _813838, _813840, _813842, _813844, _813846, _813848, _813850, _813852] : [-(c_SetInterval_Oord_OatLeastLessThan(_813852, _813848, _813844, _813840, _813836) = c_SetInterval_Oord_OatLeastLessThan(_813850, _813846, _813842, _813838, _813834)), _813852 = _813850, _813848 = _813846, _813844 = _813842, _813840 = _813838, _813836 = _813834], (2322 ^ _779530) ^ [_814223, _814225, _814227, _814229] : [-(c_Option_Oset(_814229, _814225) = c_Option_Oset(_814227, _814223)), _814229 = _814227, _814225 = _814223], (2332 ^ _779530) ^ [_814372, _814374, _814376, _814378, _814380, _814382, _814384, _814386, _814388, _814390] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_814390, _814386, _814382, _814378, _814374) = c_SetInterval_Oord_OgreaterThanAtMost(_814388, _814384, _814380, _814376, _814372)), _814390 = _814388, _814386 = _814384, _814382 = _814380, _814378 = _814376, _814374 = _814372], (2354 ^ _779530) ^ [_814761, _814763, _814765, _814767, _814769, _814771, _814773, _814775] : [-(c_Fun_Othe__inv__into(_814775, _814771, _814767, _814763) = c_Fun_Othe__inv__into(_814773, _814769, _814765, _814761)), _814775 = _814773, _814771 = _814769, _814767 = _814765, _814763 = _814761], (2372 ^ _779530) ^ [_815062, _815064, _815066, _815068, _815070, _815072] : [-(c_Smallcheck_Oorelse(_815072, _815068, _815064) = c_Smallcheck_Oorelse(_815070, _815066, _815062)), _815072 = _815070, _815068 = _815066, _815064 = _815062], (2386 ^ _779530) ^ [_815283, _815285, _815287, _815289, _815291, _815293, _815295, _815297, _815299, _815301, _815303, _815305] : [-(c_Map_Omap__comp(_815305, _815301, _815297, _815293, _815289, _815285) = c_Map_Omap__comp(_815303, _815299, _815295, _815291, _815287, _815283)), _815305 = _815303, _815301 = _815299, _815297 = _815295, _815293 = _815291, _815289 = _815287, _815285 = _815283], (2412 ^ _779530) ^ [_815768, _815770, _815772, _815774] : [-(c_Orderings_Oord__class_OLeast(_815774, _815770) = c_Orderings_Oord__class_OLeast(_815772, _815768)), _815774 = _815772, _815770 = _815768], (2422 ^ _779530) ^ [_815917, _815919, _815921, _815923, _815925, _815927] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_815927, _815923, _815919) = c_Hoare__Mirabelle_Otriple_Otriple__size(_815925, _815921, _815917)), _815927 = _815925, _815923 = _815921, _815919 = _815917], (2436 ^ _779530) ^ [_816138, _816140] : [_816140 = _816138, -(c_Com_Ovname_Ovname__size(_816140) = c_Com_Ovname_Ovname__size(_816138))], (2442 ^ _779530) ^ [_816223, _816225] : [_816225 = _816223, -(c_Com_Ovname_OGlb(_816225) = c_Com_Ovname_OGlb(_816223))], (2448 ^ _779530) ^ [_816308, _816310] : [_816310 = _816308, -(c_Com_Ovname_OLoc(_816310) = c_Com_Ovname_OLoc(_816308))], (2454 ^ _779530) ^ [_816393, _816395, _816397, _816399, _816401, _816403] : [-(c_Option_Ooption_Ooption__size(_816403, _816399, _816395) = c_Option_Ooption_Ooption__size(_816401, _816397, _816393)), _816403 = _816401, _816399 = _816397, _816395 = _816393], (2468 ^ _779530) ^ [_816614, _816616] : [_816616 = _816614, -(c_Com_Ocom_Ocom__size(_816616) = c_Com_Ocom_Ocom__size(_816614))], (2474 ^ _779530) ^ [_816699, _816701, _816703, _816705, _816707, _816709, _816711, _816713] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_816713, _816709, _816705, _816701) = c_Nat_Osemiring__1__class_Oof__nat__aux(_816711, _816707, _816703, _816699)), _816713 = _816711, _816709 = _816707, _816705 = _816703, _816701 = _816699], (2492 ^ _779530) ^ [_817000, _817002] : [_817002 = _817000, -(c_Nat_Onat_Onat__size(_817002) = c_Nat_Onat_Onat__size(_817000))], (2498 ^ _779530) ^ [_817085, _817087, _817089, _817091, _817093, _817095, _817097, _817099] : [-(c_Sum__Type_OPlus(_817099, _817095, _817091, _817087) = c_Sum__Type_OPlus(_817097, _817093, _817089, _817085)), _817099 = _817097, _817095 = _817093, _817091 = _817089, _817087 = _817085], (2516 ^ _779530) ^ [_817386, _817388, _817390, _817392, _817394, _817396] : [-(c_Power_Opower_Opower(_817396, _817392, _817388) = c_Power_Opower_Opower(_817394, _817390, _817386)), _817396 = _817394, _817392 = _817390, _817388 = _817386], (2530 ^ _779530) ^ [_817607, _817609, _817611, _817613] : [-(c_Com_Ocom_OSemi(_817613, _817609) = c_Com_Ocom_OSemi(_817611, _817607)), _817613 = _817611, _817609 = _817607], (2540 ^ _779530) ^ [_817756, _817758, _817760, _817762] : [-(c_Com_Ocom_OAss(_817762, _817758) = c_Com_Ocom_OAss(_817760, _817756)), _817762 = _817760, _817758 = _817756], (2550 ^ _779530) ^ [_817905, _817907, _817909, _817911] : [-(c_Com_Ocom_OWhile(_817911, _817907) = c_Com_Ocom_OWhile(_817909, _817905)), _817911 = _817909, _817907 = _817905], (2560 ^ _779530) ^ [_818054, _818056, _818058, _818060, _818062, _818064] : [-(c_Com_Ocom_OCond(_818064, _818060, _818056) = c_Com_Ocom_OCond(_818062, _818058, _818054)), _818064 = _818062, _818060 = _818058, _818056 = _818054], (2574 ^ _779530) ^ [_818275, _818277, _818279, _818281, _818283, _818285] : [-(c_Com_Ocom_OLocal(_818285, _818281, _818277) = c_Com_Ocom_OLocal(_818283, _818279, _818275)), _818285 = _818283, _818281 = _818279, _818277 = _818275], (2588 ^ _779530) ^ [_818496, _818498, _818500, _818502] : [-(c_SMT_Oz3div(_818502, _818498) = c_SMT_Oz3div(_818500, _818496)), _818502 = _818500, _818498 = _818496], (2598 ^ _779530) ^ [_818645, _818647, _818649, _818651] : [-(c_Orderings_Oord_Omax(_818651, _818647) = c_Orderings_Oord_Omax(_818649, _818645)), _818651 = _818649, _818647 = _818645], (2608 ^ _779530) ^ [_818794, _818796, _818798, _818800] : [-(c_Orderings_Oord_Omin(_818800, _818796) = c_Orderings_Oord_Omin(_818798, _818794)), _818800 = _818798, _818796 = _818794], (2618 ^ _779530) ^ [_818943, _818945, _818947, _818949] : [-(c_SMT_Oz3mod(_818949, _818945) = c_SMT_Oz3mod(_818947, _818943)), _818949 = _818947, _818945 = _818943], (2628 ^ _779530) ^ [_819092, _819094, _819096, _819098, _819100, _819102, _819104, _819106] : [-(c_Nitpick_Oprod(_819106, _819102, _819098, _819094) = c_Nitpick_Oprod(_819104, _819100, _819096, _819092)), _819106 = _819104, _819102 = _819100, _819098 = _819096, _819094 = _819092], (2646 ^ _779530) ^ [_819393, _819395, _819397, _819399, _819401, _819403, _819405, _819407, _819409, _819411] : [-(c_Product__Type_Oprod_Oprod__rec(_819411, _819407, _819403, _819399, _819395) = c_Product__Type_Oprod_Oprod__rec(_819409, _819405, _819401, _819397, _819393)), _819411 = _819409, _819407 = _819405, _819403 = _819401, _819399 = _819397, _819395 = _819393], (2668 ^ _779530) ^ [_819782, _819784, _819786, _819788] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819788, _819784) = c_Inductive_Ocomplete__lattice__class_Olfp(_819786, _819782)), _819788 = _819786, _819784 = _819782], (2678 ^ _779530) ^ [_819931, _819933, _819935, _819937] : [-(c_Divides_Odivmod__int__rel(_819937, _819933) = c_Divides_Odivmod__int__rel(_819935, _819931)), _819937 = _819935, _819933 = _819931], (2688 ^ _779530) ^ [_820080, _820082, _820084, _820086, _820088, _820090, _820092, _820094, _820096, _820098] : [-(c_Product__Type_Oprod_Oprod__size(_820098, _820094, _820090, _820086, _820082) = c_Product__Type_Oprod_Oprod__size(_820096, _820092, _820088, _820084, _820080)), _820098 = _820096, _820094 = _820092, _820090 = _820088, _820086 = _820084, _820082 = _820080], (2710 ^ _779530) ^ [_820469, _820471, _820473, _820475] : [-(c_Divides_Odivmod__nat(_820475, _820471) = c_Divides_Odivmod__nat(_820473, _820469)), _820475 = _820473, _820471 = _820469], (2720 ^ _779530) ^ [_820618, _820620, _820622, _820624] : [-(c_Divides_Odivmod__nat__rel(_820624, _820620) = c_Divides_Odivmod__nat__rel(_820622, _820618)), _820624 = _820622, _820620 = _820618], (2730 ^ _779530) ^ [_820767, _820769, _820771, _820773] : [-(c_Int_Onat__aux(_820773, _820769) = c_Int_Onat__aux(_820771, _820767)), _820773 = _820771, _820769 = _820767], (2740 ^ _779530) ^ [_820916, _820918, _820920, _820922] : [-(c_Set_Othe__elem(_820922, _820918) = c_Set_Othe__elem(_820920, _820916)), _820922 = _820920, _820918 = _820916], (2750 ^ _779530) ^ [_821065, _821067] : [_821067 = _821065, -(c_Int_Oring__1__class_OInts(_821067) = c_Int_Oring__1__class_OInts(_821065))], (2756 ^ _779530) ^ [_821150, _821152] : [_821152 = _821150, -(c_Divides_Oadjust(_821152) = c_Divides_Oadjust(_821150))], (2762 ^ _779530) ^ [_821235, _821237, _821239, _821241] : [-(c_Divides_OnegDivAlg(_821241, _821237) = c_Divides_OnegDivAlg(_821239, _821235)), _821241 = _821239, _821237 = _821235], (2772 ^ _779530) ^ [_821384, _821386, _821388, _821390] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_821390, _821386) = c_Code__Numeral_Odiv__mod__code__numeral(_821388, _821384)), _821390 = _821388, _821386 = _821384], (2782 ^ _779530) ^ [_821533, _821535, _821537, _821539, _821541, _821543] : [-(c_Smallcheck_Osmall_H(_821543, _821539, _821535) = c_Smallcheck_Osmall_H(_821541, _821537, _821533)), _821543 = _821541, _821539 = _821537, _821535 = _821533], (2796 ^ _779530) ^ [_821754, _821756] : [_821756 = _821754, -(c_Smallcheck_Osmall__class_Osmall(_821756) = c_Smallcheck_Osmall__class_Osmall(_821754))], (2802 ^ _779530) ^ [_821839, _821841] : [_821841 = _821839, -(c_Int_Osucc(_821841) = c_Int_Osucc(_821839))], (2808 ^ _779530) ^ [_821924, _821926] : [_821926 = _821924, -(c_Int_Opred(_821926) = c_Int_Opred(_821924))], (2814 ^ _779530) ^ [_822009, _822011, _822013, _822015, _822017, _822019] : [-(c_Nat_Onat_Onat__rec(_822019, _822015, _822011) = c_Nat_Onat_Onat__rec(_822017, _822013, _822009)), _822019 = _822017, _822015 = _822013, _822011 = _822009], (2828 ^ _779530) ^ [_822230, _822232, _822234, _822236, _822238, _822240] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_822240, _822236, _822232) = c_Smallcheck_Ofull__small__class_Ofull__small(_822238, _822234, _822230)), _822240 = _822238, _822236 = _822234, _822232 = _822230], (2842 ^ _779530) ^ [_822451, _822453, _822455, _822457, _822459, _822461] : [-(c_Smallcheck_Ofull__small_H(_822461, _822457, _822453) = c_Smallcheck_Ofull__small_H(_822459, _822455, _822451)), _822461 = _822459, _822457 = _822455, _822453 = _822451], (2856 ^ _779530) ^ [_822672, _822674, _822676, _822678] : [-(c_Nat__Transfer_Otsub(_822678, _822674) = c_Nat__Transfer_Otsub(_822676, _822672)), _822678 = _822676, _822674 = _822672], (2866 ^ _779530) ^ [_822821, _822823] : [_822823 = _822821, -(c_Nat_Osemiring__1__class_ONats(_822823) = c_Nat_Osemiring__1__class_ONats(_822821))], (2872 ^ _779530) ^ [_822906, _822908] : [_822908 = _822906, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_822908) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_822906))], (2878 ^ _779530) ^ [_822991, _822993, _822995, _822997] : [-(c_FunDef_Orp__inv__image(_822997, _822993) = c_FunDef_Orp__inv__image(_822995, _822991)), _822997 = _822995, _822993 = _822991], (2888 ^ _779530) ^ [_823140, _823142] : [_823142 = _823140, -(c_SetInterval_Oord__class_OatLeast(_823142) = c_SetInterval_Oord__class_OatLeast(_823140))], (2894 ^ _779530) ^ [_823225, _823227, _823229, _823231, _823233, _823235, _823237, _823239] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_823239, _823235, _823231, _823227) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_823237, _823233, _823229, _823225)), _823239 = _823237, _823235 = _823233, _823231 = _823229, _823227 = _823225], (2912 ^ _779530) ^ [_823526, _823528, _823530, _823532] : [-(c_Divides_Odivmod__int(_823532, _823528) = c_Divides_Odivmod__int(_823530, _823526)), _823532 = _823530, _823528 = _823526], (2922 ^ _779530) ^ [_823675, _823677, _823679, _823681] : [-(c_Groups_Osgn__class_Osgn(_823681, _823677) = c_Groups_Osgn__class_Osgn(_823679, _823675)), _823681 = _823679, _823677 = _823675], (2932 ^ _779530) ^ [_823824, _823826, _823828, _823830] : [-(c_Divides_Opdivmod(_823830, _823826) = c_Divides_Opdivmod(_823828, _823824)), _823830 = _823828, _823826 = _823824], (2942 ^ _779530) ^ [_823973, _823975, _823977, _823979] : [-(c_Divides_OposDivAlg(_823979, _823975) = c_Divides_OposDivAlg(_823977, _823973)), _823979 = _823977, _823975 = _823973], (2952 ^ _779530) ^ [_824122, _824124, _824126, _824128] : [-(c_Nitpick_Onat__gcd(_824128, _824124) = c_Nitpick_Onat__gcd(_824126, _824122)), _824128 = _824126, _824124 = _824122], (2962 ^ _779530) ^ [_824271, _824273, _824275, _824277] : [-(c_Nitpick_Onat__lcm(_824277, _824273) = c_Nitpick_Onat__lcm(_824275, _824271)), _824277 = _824275, _824273 = _824271], (2972 ^ _779530) ^ [_824420, _824422] : [_824422 = _824420, -(c_Wellfounded_Omeasure(_824422) = c_Wellfounded_Omeasure(_824420))], (2978 ^ _779530) ^ [_824505, _824507, _824509, _824511] : [-(c_Wellfounded_Omin__ext(_824511, _824507) = c_Wellfounded_Omin__ext(_824509, _824505)), _824511 = _824509, _824507 = _824505], (2988 ^ _779530) ^ [_824654, _824656] : [_824656 = _824654, -(c_Wellfounded_Ofinite__psubset(_824656) = c_Wellfounded_Ofinite__psubset(_824654))], (2994 ^ _779530) ^ [_824739, _824741, _824743, _824745, _824747, _824749] : [-(c_Wellfounded_Omlex__prod(_824749, _824745, _824741) = c_Wellfounded_Omlex__prod(_824747, _824743, _824739)), _824749 = _824747, _824745 = _824743, _824741 = _824739], (3008 ^ _779530) ^ [_824960, _824962] : [_824962 = _824960, -(c_Int_Oint__ge__less__than2(_824962) = c_Int_Oint__ge__less__than2(_824960))], (3014 ^ _779530) ^ [_825045, _825047] : [_825047 = _825045, -(c_Int_Oint__ge__less__than(_825047) = c_Int_Oint__ge__less__than(_825045))], (3020 ^ _779530) ^ [_825130, _825132, _825134, _825136, _825138, _825140, _825142, _825144] : [-(c_Recdef_Osame__fst(_825144, _825140, _825136, _825132) = c_Recdef_Osame__fst(_825142, _825138, _825134, _825130)), _825144 = _825142, _825140 = _825138, _825136 = _825134, _825132 = _825130], (3038 ^ _779530) ^ [_825431, _825433] : [_825433 = _825431, -(c_Nitpick_Ozero__frac(_825433) = c_Nitpick_Ozero__frac(_825431))], (3044 ^ _779530) ^ [_825516, _825518] : [_825518 = _825516, -(c_Nitpick_Oone__frac(_825518) = c_Nitpick_Oone__frac(_825516))], (3050 ^ _779530) ^ [_825601, _825603, _825605, _825607] : [-(c_Nitpick_Onumber__of__frac(_825607, _825603) = c_Nitpick_Onumber__of__frac(_825605, _825601)), _825607 = _825605, _825603 = _825601], (3060 ^ _779530) ^ [_825750, _825752, _825754, _825756] : [-(c_Nitpick_Onorm__frac(_825756, _825752) = c_Nitpick_Onorm__frac(_825754, _825750)), _825756 = _825754, _825752 = _825750], (3070 ^ _779530) ^ [_825899, _825901, _825903, _825905, _825907, _825909, _825911, _825913] : [-(c_Product__Type_Oapsnd(_825913, _825909, _825905, _825901) = c_Product__Type_Oapsnd(_825911, _825907, _825903, _825899)), _825913 = _825911, _825909 = _825907, _825905 = _825903, _825901 = _825899], (3088 ^ _779530) ^ [_826200, _826202, _826204, _826206, _826208, _826210, _826212, _826214] : [-(c_Product__Type_Oapfst(_826214, _826210, _826206, _826202) = c_Product__Type_Oapfst(_826212, _826208, _826204, _826200)), _826214 = _826212, _826210 = _826208, _826206 = _826204, _826202 = _826200], (3106 ^ _779530) ^ [_826501, _826503, _826505, _826507, _826509, _826511] : [-(c_Finite__Set_Ofold1Set(_826511, _826507, _826503) = c_Finite__Set_Ofold1Set(_826509, _826505, _826501)), _826511 = _826509, _826507 = _826505, _826503 = _826501], (3120 ^ _779530) ^ [_826722, _826724, _826726, _826728, _826730, _826732] : [-(c_FunDef_Oin__rel(_826732, _826728, _826724) = c_FunDef_Oin__rel(_826730, _826726, _826722)), _826732 = _826730, _826728 = _826726, _826724 = _826722], (3134 ^ _779530) ^ [_826943, _826945, _826947, _826949] : [-(c_Predicate_OPowp(_826949, _826945) = c_Predicate_OPowp(_826947, _826943)), _826949 = _826947, _826945 = _826943], (3144 ^ _779530) ^ [_827092, _827094, _827096, _827098] : [-(c_Option_Omap(_827098, _827094) = c_Option_Omap(_827096, _827092)), _827098 = _827096, _827094 = _827092], (3154 ^ _779530) ^ [_827241, _827243, _827245, _827247, _827249, _827251] : [-(c_Map_Oran(_827251, _827247, _827243) = c_Map_Oran(_827249, _827245, _827241)), _827251 = _827249, _827247 = _827245, _827243 = _827241], (3168 ^ _779530) ^ [_827462, _827464, _827466, _827468, _827470, _827472, _827474, _827476, _827478, _827480, _827482, _827484] : [-(c_Product__Type_Omap__pair(_827484, _827480, _827476, _827472, _827468, _827464) = c_Product__Type_Omap__pair(_827482, _827478, _827474, _827470, _827466, _827462)), _827484 = _827482, _827480 = _827478, _827476 = _827474, _827472 = _827470, _827468 = _827466, _827464 = _827462], (3194 ^ _779530) ^ [_827947, _827949, _827951, _827953] : [-(c_List_Olexn(_827953, _827949) = c_List_Olexn(_827951, _827947)), _827953 = _827951, _827949 = _827947], (3204 ^ _779530) ^ [_828096, _828098, _828100, _828102] : [-(c_List_Olenlex(_828102, _828098) = c_List_Olenlex(_828100, _828096)), _828102 = _828100, _828098 = _828096], (3214 ^ _779530) ^ [_828245, _828247, _828249, _828251, _828253, _828255, _828257, _828259] : [-(c_Wellfounded_Olex__prod(_828259, _828255, _828251, _828247) = c_Wellfounded_Olex__prod(_828257, _828253, _828249, _828245)), _828259 = _828257, _828255 = _828253, _828251 = _828249, _828247 = _828245], (3232 ^ _779530) ^ [_828546, _828548] : [_828548 = _828546, -(c_Power_Opower__class_Opower(_828548) = c_Power_Opower__class_Opower(_828546))], (3238 ^ _779530) ^ [_828631, _828633] : [_828633 = _828631, -(c_Enum_Oenum__class_Oenum__all(_828633) = c_Enum_Oenum__class_Oenum__all(_828631))], (3244 ^ _779530) ^ [_828716, _828718] : [_828718 = _828716, -(c_Enum_Oenum__class_Oenum__ex(_828718) = c_Enum_Oenum__class_Oenum__ex(_828716))], (3250 ^ _779530) ^ [_828801, _828803, _828805, _828807, _828809, _828811, _828813, _828815] : [-(c_Map_Orestrict__map(_828815, _828811, _828807, _828803) = c_Map_Orestrict__map(_828813, _828809, _828805, _828801)), _828815 = _828813, _828811 = _828809, _828807 = _828805, _828803 = _828801], (3268 ^ _779530) ^ [_829102, _829104] : [_829104 = _829102, -(c_Equiv__Relations_Oquotient(_829104) = c_Equiv__Relations_Oquotient(_829102))], (3274 ^ _779530) ^ [_829187, _829189, _829191, _829193, _829195, _829197, _829199, _829201] : [-(c_Nitpick_Osetsum_H(_829201, _829197, _829193, _829189) = c_Nitpick_Osetsum_H(_829199, _829195, _829191, _829187)), _829201 = _829199, _829197 = _829195, _829193 = _829191, _829189 = _829187], (3292 ^ _779530) ^ [_829488, _829490, _829492, _829494] : [-(c_Nitpick_Ocard_H(_829494, _829490) = c_Nitpick_Ocard_H(_829492, _829488)), _829494 = _829492, _829490 = _829488], (3302 ^ _779530) ^ [_829637, _829639, _829641, _829643] : [-(c_Hilbert__Choice_OEps(_829643, _829639) = c_Hilbert__Choice_OEps(_829641, _829637)), _829643 = _829641, _829639 = _829637], (3312 ^ _779530) ^ [_829786, _829788] : [_829788 = _829786, -(c_Option_Othe(_829788) = c_Option_Othe(_829786))], (3318 ^ _779530) ^ [_829871, _829873, _829875, _829877, _829879, _829881, _829883, _829885] : [-(c_List_Omap__filter(_829885, _829881, _829877, _829873) = c_List_Omap__filter(_829883, _829879, _829875, _829871)), _829885 = _829883, _829881 = _829879, _829877 = _829875, _829873 = _829871], (3336 ^ _779530) ^ [_830172, _830174, _830176, _830178, _830180, _830182] : [-(c_List_Olist_Olist__size(_830182, _830178, _830174) = c_List_Olist_Olist__size(_830180, _830176, _830172)), _830182 = _830180, _830178 = _830176, _830174 = _830172], (3350 ^ _779530) ^ [_830393, _830395, _830397, _830399, _830401, _830403] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_830403, _830399, _830395) = c_SetInterval_Oord__class_OatLeastAtMost(_830401, _830397, _830393)), _830403 = _830401, _830399 = _830397, _830395 = _830393], (3364 ^ _779530) ^ [_830614, _830616] : [_830616 = _830614, -(c_SetInterval_Oord__class_OlessThan(_830616) = c_SetInterval_Oord__class_OlessThan(_830614))], (3370 ^ _779530) ^ [_830699, _830701, _830703, _830705, _830707, _830709] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830709, _830705, _830701) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830707, _830703, _830699)), _830709 = _830707, _830705 = _830703, _830701 = _830699], (3384 ^ _779530) ^ [_830920, _830922, _830924, _830926, _830928, _830930] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_830930, _830926, _830922) = c_SetInterval_Oord__class_OgreaterThanLessThan(_830928, _830924, _830920)), _830930 = _830928, _830926 = _830924, _830922 = _830920], (3398 ^ _779530) ^ [_831141, _831143] : [_831143 = _831141, -(c_SetInterval_Oord__class_OatMost(_831143) = c_SetInterval_Oord__class_OatMost(_831141))], (3404 ^ _779530) ^ [_831226, _831228, _831230, _831232, _831234, _831236] : [-(c_List_Oset__Cons(_831236, _831232, _831228) = c_List_Oset__Cons(_831234, _831230, _831226)), _831236 = _831234, _831232 = _831230, _831228 = _831226], (3418 ^ _779530) ^ [_831447, _831449, _831451, _831453] : [-(c_List_Olistset(_831453, _831449) = c_List_Olistset(_831451, _831447)), _831453 = _831451, _831449 = _831447], (3428 ^ _779530) ^ [_831596, _831598, _831600, _831602] : [-(c_Enum_Osublists(_831602, _831598) = c_Enum_Osublists(_831600, _831596)), _831602 = _831600, _831598 = _831596], (3438 ^ _779530) ^ [_831745, _831747, _831749, _831751, _831753, _831755, _831757, _831759] : [-(c_Enum_Oproduct(_831759, _831755, _831751, _831747) = c_Enum_Oproduct(_831757, _831753, _831749, _831745)), _831759 = _831757, _831755 = _831753, _831751 = _831749, _831747 = _831745], (3456 ^ _779530) ^ [_832046, _832048, _832050, _832052, _832054, _832056] : [-(c_List_Osublist(_832056, _832052, _832048) = c_List_Osublist(_832054, _832050, _832046)), _832056 = _832054, _832052 = _832050, _832048 = _832046], (3470 ^ _779530) ^ [_832267, _832269] : [_832269 = _832267, -(c_List_Oreturn__list(_832269) = c_List_Oreturn__list(_832267))], (3476 ^ _779530) ^ [_832352, _832354] : [_832354 = _832352, -(c_List_Oembed__list(_832354) = c_List_Oembed__list(_832352))], (3482 ^ _779530) ^ [_832437, _832439] : [_832439 = _832437, -(c_If(_832439) = c_If(_832437))], (3488 ^ _779530) ^ [_832522, _832524, _832526, _832528, _832530, _832532] : [-(c_List_Opartition(_832532, _832528, _832524) = c_List_Opartition(_832530, _832526, _832522)), _832532 = _832530, _832528 = _832526, _832524 = _832522], (3502 ^ _779530) ^ [_832743, _832745, _832747, _832749] : [-(c_Wellfounded_Oaccp(_832749, _832745) = c_Wellfounded_Oaccp(_832747, _832743)), _832749 = _832747, _832745 = _832743], (3512 ^ _779530) ^ [_832892, _832894] : [_832894 = _832892, -(c_List_Otranspose__rel(_832894) = c_List_Otranspose__rel(_832892))], (3518 ^ _779530) ^ [_832977, _832979, _832981, _832983, _832985, _832987, _832989, _832991] : [-(c_Nat_Onat_Onat__case(_832991, _832987, _832983, _832979) = c_Nat_Onat_Onat__case(_832989, _832985, _832981, _832977)), _832991 = _832989, _832987 = _832985, _832983 = _832981, _832979 = _832977], (3536 ^ _779530) ^ [_833278, _833280, _833282, _833284, _833286, _833288] : [-(c_Enum_On__lists(_833288, _833284, _833280) = c_Enum_On__lists(_833286, _833282, _833278)), _833288 = _833286, _833284 = _833282, _833280 = _833278], (3550 ^ _779530) ^ [_833499, _833501, _833503, _833505, _833507, _833509, _833511, _833513] : [-(c_List_Olist_Olist__case(_833513, _833509, _833505, _833501) = c_List_Olist_Olist__case(_833511, _833507, _833503, _833499)), _833513 = _833511, _833509 = _833507, _833505 = _833503, _833501 = _833499], (3568 ^ _779530) ^ [_833800, _833802, _833804, _833806] : [-(c_Fun_Ofun__upd(_833806, _833802) = c_Fun_Ofun__upd(_833804, _833800)), _833806 = _833804, _833802 = _833800], (3578 ^ _779530) ^ [_833949, _833951, _833953, _833955] : [-(c_List_Oupto(_833955, _833951) = c_List_Oupto(_833953, _833949)), _833955 = _833953, _833951 = _833949], (3588 ^ _779530) ^ [_834098, _834100, _834102, _834104, _834106, _834108, _834110, _834112, _834114, _834116] : [-(c_List_Olinorder__class_Oinsort__insert__key(_834116, _834112, _834108, _834104, _834100) = c_List_Olinorder__class_Oinsort__insert__key(_834114, _834110, _834106, _834102, _834098)), _834116 = _834114, _834112 = _834110, _834108 = _834106, _834104 = _834102, _834100 = _834098], (3610 ^ _779530) ^ [_834487, _834489, _834491, _834493, _834495, _834497, _834499, _834501, _834503, _834505] : [-(c_List_Ofoldr(_834505, _834501, _834497, _834493, _834489) = c_List_Ofoldr(_834503, _834499, _834495, _834491, _834487)), _834505 = _834503, _834501 = _834499, _834497 = _834495, _834493 = _834491, _834489 = _834487], (3632 ^ _779530) ^ [_834876, _834878, _834880, _834882] : [-(c_List_Otranspose(_834882, _834878) = c_List_Otranspose(_834880, _834876)), _834882 = _834880, _834878 = _834876], (3642 ^ _779530) ^ [_835025, _835027, _835029, _835031, _835033, _835035, _835037, _835039, _835041, _835043] : [-(c_Map_Omap__upds(_835043, _835039, _835035, _835031, _835027) = c_Map_Omap__upds(_835041, _835037, _835033, _835029, _835025)), _835043 = _835041, _835039 = _835037, _835035 = _835033, _835031 = _835029, _835027 = _835025], (3664 ^ _779530) ^ [_835414, _835416, _835418, _835420, _835422, _835424, _835426, _835428] : [-(c_Map_Omap__add(_835428, _835424, _835420, _835416) = c_Map_Omap__add(_835426, _835422, _835418, _835414)), _835428 = _835426, _835424 = _835422, _835420 = _835418, _835416 = _835414], (3682 ^ _779530) ^ [_835715, _835717] : [_835717 = _835715, -(c_List_Otl(_835717) = c_List_Otl(_835715))], (3688 ^ _779530) ^ [_835800, _835802, _835804, _835806] : [-(c_List_Olexord(_835806, _835802) = c_List_Olexord(_835804, _835800)), _835806 = _835804, _835802 = _835800], (3698 ^ _779530) ^ [_835949, _835951, _835953, _835955] : [-(c_List_Olinorder__class_Osorted__list__of__set(_835955, _835951) = c_List_Olinorder__class_Osorted__list__of__set(_835953, _835949)), _835955 = _835953, _835951 = _835949], (3708 ^ _779530) ^ [_836098, _836100, _836102, _836104, _836106, _836108, _836110, _836112] : [-(c_List_Olinorder__class_Osort__key(_836112, _836108, _836104, _836100) = c_List_Olinorder__class_Osort__key(_836110, _836106, _836102, _836098)), _836112 = _836110, _836108 = _836106, _836104 = _836102, _836100 = _836098], (3726 ^ _779530) ^ [_836399, _836401] : [_836401 = _836399, -(c_List_Ohd(_836401) = c_List_Ohd(_836399))], (3732 ^ _779530) ^ [_836484, _836486, _836488, _836490] : [-(c_List_Oupt(_836490, _836486) = c_List_Oupt(_836488, _836484)), _836490 = _836488, _836486 = _836484], (3742 ^ _779530) ^ [_836633, _836635, _836637, _836639] : [-(c_List_Obutlast(_836639, _836635) = c_List_Obutlast(_836637, _836633)), _836639 = _836637, _836635 = _836633], (3752 ^ _779530) ^ [_836782, _836784, _836786, _836788] : [-(c_List_Olast(_836788, _836784) = c_List_Olast(_836786, _836782)), _836788 = _836786, _836784 = _836782], (3762 ^ _779530) ^ [_836931, _836933] : [_836933 = _836931, -(c_Set_OBall(_836933) = c_Set_OBall(_836931))], (3768 ^ _779530) ^ [_837016, _837018] : [_837018 = _837016, -(c_Set_OPow(_837018) = c_Set_OPow(_837016))], (3774 ^ _779530) ^ [_837101, _837103, _837105, _837107, _837109, _837111] : [-(c_Set_Ovimage(_837111, _837107, _837103) = c_Set_Ovimage(_837109, _837105, _837101)), _837111 = _837109, _837107 = _837105, _837103 = _837101], (3788 ^ _779530) ^ [_837322, _837324] : [_837324 = _837322, -(c_SetInterval_Oord__class_OgreaterThan(_837324) = c_SetInterval_Oord__class_OgreaterThan(_837322))], (3794 ^ _779530) ^ [_837407, _837409, _837411, _837413] : [-(c_List_Olistsp(_837413, _837409) = c_List_Olistsp(_837411, _837407)), _837413 = _837411, _837409 = _837407], (3804 ^ _779530) ^ [_837556, _837558, _837560, _837562] : [-(c_List_Olists(_837562, _837558) = c_List_Olists(_837560, _837556)), _837562 = _837560, _837558 = _837556], (3814 ^ _779530) ^ [_837705, _837707, _837709, _837711, _837713, _837715] : [-(c_Set_Oimage(_837715, _837711, _837707) = c_Set_Oimage(_837713, _837709, _837705)), _837715 = _837713, _837711 = _837709, _837707 = _837705], (3828 ^ _779530) ^ [_837926, _837928] : [_837928 = _837926, -(c_HOL_OAll(_837928) = c_HOL_OAll(_837926))], (3834 ^ _779530) ^ [_838011, _838013] : [_838013 = _838011, -(c_List_Odrop(_838013) = c_List_Odrop(_838011))], (3840 ^ _779530) ^ [_838096, _838098, _838100, _838102] : [-(c_List_Olist__update(_838102, _838098) = c_List_Olist__update(_838100, _838096)), _838102 = _838100, _838098 = _838096], (3850 ^ _779530) ^ [_838245, _838247, _838249, _838251, _838253, _838255] : [-(c_List_Oremove1(_838255, _838251, _838247) = c_List_Oremove1(_838253, _838249, _838245)), _838255 = _838253, _838251 = _838249, _838247 = _838245], (3864 ^ _779530) ^ [_838466, _838468, _838470, _838472] : [-(c_List_OremoveAll(_838472, _838468) = c_List_OremoveAll(_838470, _838466)), _838472 = _838470, _838468 = _838466], (3874 ^ _779530) ^ [_838615, _838617, _838619, _838621, _838623, _838625] : [-(c_List_Oinsert(_838625, _838621, _838617) = c_List_Oinsert(_838623, _838619, _838615)), _838625 = _838623, _838621 = _838619, _838617 = _838615], (3888 ^ _779530) ^ [_838836, _838838, _838840, _838842, _838844, _838846, _838848, _838850] : [-(c_List_Omaps(_838850, _838846, _838842, _838838) = c_List_Omaps(_838848, _838844, _838840, _838836)), _838850 = _838848, _838846 = _838844, _838842 = _838840, _838838 = _838836], (3906 ^ _779530) ^ [_839137, _839139, _839141, _839143] : [-(c_List_Oconcat(_839143, _839139) = c_List_Oconcat(_839141, _839137)), _839143 = _839141, _839139 = _839137], (3916 ^ _779530) ^ [_839286, _839288, _839290, _839292] : [-(c_List_Olex(_839292, _839288) = c_List_Olex(_839290, _839286)), _839292 = _839290, _839288 = _839286], (3926 ^ _779530) ^ [_839435, _839437, _839439, _839441] : [-(c_List_Omeasures(_839441, _839437) = c_List_Omeasures(_839439, _839435)), _839441 = _839439, _839437 = _839435], (3936 ^ _779530) ^ [_839584, _839586] : [_839586 = _839584, -(c_List_Otake(_839586) = c_List_Otake(_839584))], (3942 ^ _779530) ^ [_839669, _839671, _839673, _839675] : [-(c_List_Ozip(_839675, _839671) = c_List_Ozip(_839673, _839669)), _839675 = _839673, _839671 = _839669], (3952 ^ _779530) ^ [_839818, _839820, _839822, _839824] : [-(c_Map_Omap__of(_839824, _839820) = c_Map_Omap__of(_839822, _839818)), _839824 = _839822, _839820 = _839818], (3962 ^ _779530) ^ [_839967, _839969, _839971, _839973, _839975, _839977] : [-(c_Predicate_ODomainP(_839977, _839973, _839969) = c_Predicate_ODomainP(_839975, _839971, _839967)), _839977 = _839975, _839973 = _839971, _839969 = _839967], (3976 ^ _779530) ^ [_840188, _840190, _840192, _840194, _840196, _840198] : [-(c_Predicate_ORangeP(_840198, _840194, _840190) = c_Predicate_ORangeP(_840196, _840192, _840188)), _840198 = _840196, _840194 = _840192, _840190 = _840188], (3990 ^ _779530) ^ [_840409, _840411, _840413, _840415, _840417, _840419] : [-(c_List_OdropWhile(_840419, _840415, _840411) = c_List_OdropWhile(_840417, _840413, _840409)), _840419 = _840417, _840415 = _840413, _840411 = _840409], (4004 ^ _779530) ^ [_840630, _840632, _840634, _840636, _840638, _840640] : [-(c_Map_Odom(_840640, _840636, _840632) = c_Map_Odom(_840638, _840634, _840630)), _840640 = _840638, _840636 = _840634, _840632 = _840630], (4018 ^ _779530) ^ [_840851, _840853] : [_840853 = _840851, -(c_List_Odistinct(_840853) = c_List_Odistinct(_840851))], (4024 ^ _779530) ^ [_840936, _840938, _840940, _840942, _840944, _840946] : [-(c_List_OtakeWhile(_840946, _840942, _840938) = c_List_OtakeWhile(_840944, _840940, _840936)), _840946 = _840944, _840942 = _840940, _840938 = _840936], (4038 ^ _779530) ^ [_841157, _841159] : [_841159 = _841157, -(c_Finite__Set_Ocard(_841159) = c_Finite__Set_Ocard(_841157))], (4044 ^ _779530) ^ [_841242, _841244, _841246, _841248] : [-(c_Wellfounded_Omax__ext(_841248, _841244) = c_Wellfounded_Omax__ext(_841246, _841242)), _841248 = _841246, _841244 = _841242], (4054 ^ _779530) ^ [_841391, _841393, _841395, _841397, _841399, _841401, _841403, _841405] : [-(c_Random_Oiterate(_841405, _841401, _841397, _841393) = c_Random_Oiterate(_841403, _841399, _841395, _841391)), _841405 = _841403, _841401 = _841399, _841397 = _841395, _841393 = _841391], (4072 ^ _779530) ^ [_841692, _841694, _841696, _841698] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_841698, _841694) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_841696, _841692)), _841698 = _841696, _841694 = _841692], (4082 ^ _779530) ^ [_841841, _841843, _841845, _841847] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_841847, _841843) = c_SetInterval_Oord__class_OatLeastLessThan(_841845, _841841)), _841847 = _841845, _841843 = _841841], (4092 ^ _779530) ^ [_841990, _841992, _841994, _841996] : [-(c_Random_Olog(_841996, _841992) = c_Random_Olog(_841994, _841990)), _841996 = _841994, _841992 = _841990], (4102 ^ _779530) ^ [_842139, _842141, _842143, _842145, _842147, _842149] : [-(c_Random_Ominus__shift(_842149, _842145, _842141) = c_Random_Ominus__shift(_842147, _842143, _842139)), _842149 = _842147, _842145 = _842143, _842141 = _842139], (4116 ^ _779530) ^ [_842360, _842362, _842364, _842366] : [-(c_Random_Oinc__shift(_842366, _842362) = c_Random_Oinc__shift(_842364, _842360)), _842366 = _842364, _842362 = _842360], (4126 ^ _779530) ^ [_842509, _842511, _842513, _842515] : [-(c_List_Ofilter(_842515, _842511) = c_List_Ofilter(_842513, _842509)), _842515 = _842513, _842511 = _842509], (4136 ^ _779530) ^ [_842658, _842660, _842662, _842664] : [-(c_Random_Oselect__weight(_842664, _842660) = c_Random_Oselect__weight(_842662, _842658)), _842664 = _842662, _842660 = _842658], (4146 ^ _779530) ^ [_842807, _842809] : [_842809 = _842807, -(c_List_Omonoid__add__class_Olistsum(_842809) = c_List_Omonoid__add__class_Olistsum(_842807))], (4152 ^ _779530) ^ [_842892, _842894, _842896, _842898] : [-(c_Random_Opick(_842898, _842894) = c_Random_Opick(_842896, _842892)), _842898 = _842896, _842894 = _842892], (4162 ^ _779530) ^ [_843041, _843043, _843045, _843047] : [-(c_List_Omap(_843047, _843043) = c_List_Omap(_843045, _843041)), _843047 = _843045, _843043 = _843041], (4172 ^ _779530) ^ [_843190, _843192, _843194, _843196] : [-(c_Random_Oselect(_843196, _843192) = c_Random_Oselect(_843194, _843190)), _843196 = _843194, _843192 = _843190], (4182 ^ _779530) ^ [_843339, _843341, _843343, _843345, _843347, _843349, _843351, _843353] : [-(c_Product__Type_Oscomp(_843353, _843349, _843345, _843341) = c_Product__Type_Oscomp(_843351, _843347, _843343, _843339)), _843353 = _843351, _843349 = _843347, _843345 = _843343, _843341 = _843339], (4200 ^ _779530) ^ [_843640, _843642] : [_843642 = _843640, -(c_Random_Orange(_843642) = c_Random_Orange(_843640))], (4206 ^ _779530) ^ [_843725, _843727, _843729, _843731] : [-(c_Code__Numeral_Onat__of__aux(_843731, _843727) = c_Code__Numeral_Onat__of__aux(_843729, _843725)), _843731 = _843729, _843727 = _843725], (4216 ^ _779530) ^ [_843874, _843876] : [_843876 = _843874, -(c_Code__Numeral_OSuc__code__numeral(_843876) = c_Code__Numeral_OSuc__code__numeral(_843874))], (4222 ^ _779530) ^ [_843959, _843961] : [_843961 = _843959, -(c_Lazy__Sequence_Ohb__not__seq(_843961) = c_Lazy__Sequence_Ohb__not__seq(_843959))], (4228 ^ _779530) ^ [_844044, _844046, _844048, _844050] : [-(c_Wellfounded_Oacc(_844050, _844046) = c_Wellfounded_Oacc(_844048, _844044)), _844050 = _844048, _844046 = _844044], (4238 ^ _779530) ^ [_844193, _844195, _844197, _844199] : [-(c_List_Olistrel(_844199, _844195) = c_List_Olistrel(_844197, _844193)), _844199 = _844197, _844195 = _844193], (4248 ^ _779530) ^ [_844342, _844344] : [_844344 = _844342, -(c_HOL_OEx(_844344) = c_HOL_OEx(_844342))], (4254 ^ _779530) ^ [_844427, _844429, _844431, _844433] : [-(c_Product__Type_OSigma(_844433, _844429) = c_Product__Type_OSigma(_844431, _844427)), _844433 = _844431, _844429 = _844427], (4264 ^ _779530) ^ [_844576, _844578, _844580, _844582] : [-(c_Relation_Oinv__image(_844582, _844578) = c_Relation_Oinv__image(_844580, _844576)), _844582 = _844580, _844578 = _844576], (4274 ^ _779530) ^ [_844725, _844727] : [_844727 = _844725, -(c_Relation_OField(_844727) = c_Relation_OField(_844725))], (4280 ^ _779530) ^ [_844810, _844812, _844814, _844816] : [-(c_List_Olistrel1(_844816, _844812) = c_List_Olistrel1(_844814, _844810)), _844816 = _844814, _844812 = _844810], (4290 ^ _779530) ^ [_844959, _844961, _844963, _844965] : [-(c_Relation_ORange(_844965, _844961) = c_Relation_ORange(_844963, _844959)), _844965 = _844963, _844961 = _844959], (4300 ^ _779530) ^ [_845108, _845110, _845112, _845114] : [-(c_Relation_ODomain(_845114, _845110) = c_Relation_ODomain(_845112, _845108)), _845114 = _845112, _845110 = _845108], (4310 ^ _779530) ^ [_845257, _845259, _845261, _845263] : [-(c_Relation_OId__on(_845263, _845259) = c_Relation_OId__on(_845261, _845257)), _845263 = _845261, _845259 = _845257], (4320 ^ _779530) ^ [_845406, _845408, _845410, _845412, _845414, _845416] : [-(c_Relation_OImage(_845416, _845412, _845408) = c_Relation_OImage(_845414, _845410, _845406)), _845416 = _845414, _845412 = _845410, _845408 = _845406], (4334 ^ _779530) ^ [_845627, _845629] : [_845629 = _845627, -(c_Fun_Oid(_845629) = c_Fun_Oid(_845627))], (4340 ^ _779530) ^ [_845712, _845714] : [_845714 = _845712, -(c_Nat_Ofunpow(_845714) = c_Nat_Ofunpow(_845712))], (4346 ^ _779530) ^ [_845797, _845799, _845801, _845803] : [-(c_List_Orotate(_845803, _845799) = c_List_Orotate(_845801, _845797)), _845803 = _845801, _845799 = _845797], (4356 ^ _779530) ^ [_845946, _845948] : [_845948 = _845946, -(c_List_Orotate1(_845948) = c_List_Orotate1(_845946))], (4362 ^ _779530) ^ [_846031, _846033, _846035, _846037, _846039, _846041, _846043, _846045] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_846045, _846041, _846037, _846033) = c_New__Random__Sequence_Opos__not__random__dseq(_846043, _846039, _846035, _846031)), _846045 = _846043, _846041 = _846039, _846037 = _846035, _846033 = _846031], (4380 ^ _779530) ^ [_846332, _846334] : [_846334 = _846332, -(c_New__DSequence_Opos__not__seq(_846334) = c_New__DSequence_Opos__not__seq(_846332))], (4386 ^ _779530) ^ [_846417, _846419, _846421, _846423] : [-(c_Nat_Ocompow(_846423, _846419) = c_Nat_Ocompow(_846421, _846417)), _846423 = _846421, _846419 = _846417], (4396 ^ _779530) ^ [_846566, _846568, _846570, _846572] : [-(c_Transitive__Closure_Otrancl(_846572, _846568) = c_Transitive__Closure_Otrancl(_846570, _846566)), _846572 = _846570, _846568 = _846566], (4406 ^ _779530) ^ [_846715, _846717, _846719, _846721] : [-(c_Transitive__Closure_Ortrancl(_846721, _846717) = c_Transitive__Closure_Ortrancl(_846719, _846715)), _846721 = _846719, _846717 = _846715], (4416 ^ _779530) ^ [_846864, _846866] : [_846866 = _846864, -(c_Relation_OId(_846866) = c_Relation_OId(_846864))], (4422 ^ _779530) ^ [_846949, _846951, _846953, _846955] : [-(c_HOL_OThe(_846955, _846951) = c_HOL_OThe(_846953, _846949)), _846955 = _846953, _846951 = _846949], (4432 ^ _779530) ^ [_847098, _847100, _847102, _847104, _847106, _847108] : [-(c_Finite__Set_Ofold__image(_847108, _847104, _847100) = c_Finite__Set_Ofold__image(_847106, _847102, _847098)), _847108 = _847106, _847104 = _847102, _847100 = _847098], (4446 ^ _779530) ^ [_847319, _847321, _847323, _847325] : [-(c_Complete__Lattice_OInf__class_OInf(_847325, _847321) = c_Complete__Lattice_OInf__class_OInf(_847323, _847319)), _847325 = _847323, _847321 = _847319], (4456 ^ _779530) ^ [_847468, _847470, _847472, _847474, _847476, _847478] : [-(c_Big__Operators_Olattice_OInf__fin(_847478, _847474, _847470) = c_Big__Operators_Olattice_OInf__fin(_847476, _847472, _847468)), _847478 = _847476, _847474 = _847472, _847470 = _847468], (4470 ^ _779530) ^ [_847689, _847691, _847693, _847695, _847697, _847699] : [-(c_Big__Operators_Olattice_OSup__fin(_847699, _847695, _847691) = c_Big__Operators_Olattice_OSup__fin(_847697, _847693, _847689)), _847699 = _847697, _847695 = _847693, _847691 = _847689], (4484 ^ _779530) ^ [_847910, _847912, _847914, _847916] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_847916, _847912) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_847914, _847910)), _847916 = _847914, _847912 = _847910], (4494 ^ _779530) ^ [_848059, _848061, _848063, _848065] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_848065, _848061) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_848063, _848059)), _848065 = _848063, _848061 = _848059], (4504 ^ _779530) ^ [_848208, _848210] : [_848210 = _848208, -(c_Orderings_Otop__class_Otop(_848210) = c_Orderings_Otop__class_Otop(_848208))], (4510 ^ _779530) ^ [_848293, _848295, _848297, _848299] : [-(c_Finite__Set_Ofold1(_848299, _848295) = c_Finite__Set_Ofold1(_848297, _848293)), _848299 = _848297, _848295 = _848293], (4520 ^ _779530) ^ [_848442, _848444, _848446, _848448] : [-(c_Big__Operators_Olattice__class_OSup__fin(_848448, _848444) = c_Big__Operators_Olattice__class_OSup__fin(_848446, _848442)), _848448 = _848446, _848444 = _848442], (4530 ^ _779530) ^ [_848591, _848593, _848595, _848597] : [-(c_Big__Operators_Olattice__class_OInf__fin(_848597, _848593) = c_Big__Operators_Olattice__class_OInf__fin(_848595, _848591)), _848597 = _848595, _848593 = _848591], (4540 ^ _779530) ^ [_848740, _848742, _848744, _848746] : [-(c_Big__Operators_Olinorder__class_OMin(_848746, _848742) = c_Big__Operators_Olinorder__class_OMin(_848744, _848740)), _848746 = _848744, _848742 = _848740], (4550 ^ _779530) ^ [_848889, _848891, _848893, _848895] : [-(c_Big__Operators_Olinorder__class_OMax(_848895, _848891) = c_Big__Operators_Olinorder__class_OMax(_848893, _848889)), _848895 = _848893, _848891 = _848889], (4560 ^ _779530) ^ [_849038, _849040, _849042, _849044, _849046, _849048] : [-(c_List_Olinorder__class_Oinsort__key(_849048, _849044, _849040) = c_List_Olinorder__class_Oinsort__key(_849046, _849042, _849038)), _849048 = _849046, _849044 = _849042, _849040 = _849038], (4574 ^ _779530) ^ [_849259, _849261, _849263, _849265, _849267, _849269, _849271, _849273] : [-(c_List_Ofoldl(_849273, _849269, _849265, _849261) = c_List_Ofoldl(_849271, _849267, _849263, _849259)), _849273 = _849271, _849269 = _849267, _849265 = _849263, _849261 = _849259], (4592 ^ _779530) ^ [_849560, _849562, _849564, _849566] : [-(c_List_Oremdups(_849566, _849562) = c_List_Oremdups(_849564, _849560)), _849566 = _849564, _849562 = _849560], (4602 ^ _779530) ^ [_849709, _849711, _849713, _849715, _849717, _849719, _849721, _849723, _849725, _849727] : [-(c_Finite__Set_Ofold__graph(_849727, _849723, _849719, _849715, _849711) = c_Finite__Set_Ofold__graph(_849725, _849721, _849717, _849713, _849709)), _849727 = _849725, _849723 = _849721, _849719 = _849717, _849715 = _849713, _849711 = _849709], (4624 ^ _779530) ^ [_850098, _850100] : [_850100 = _850098, -(c_Orderings_Oord__class_Omax(_850100) = c_Orderings_Oord__class_Omax(_850098))], (4630 ^ _779530) ^ [_850183, _850185] : [_850185 = _850183, -(c_Orderings_Oord__class_Omin(_850185) = c_Orderings_Oord__class_Omin(_850183))], (4636 ^ _779530) ^ [_850268, _850270] : [_850270 = _850268, -(c_Lattices_Osemilattice__inf__class_Oinf(_850270) = c_Lattices_Osemilattice__inf__class_Oinf(_850268))], (4642 ^ _779530) ^ [_850353, _850355, _850357, _850359, _850361, _850363] : [-(c_Finite__Set_Ofold(_850363, _850359, _850355) = c_Finite__Set_Ofold(_850361, _850357, _850353)), _850363 = _850361, _850359 = _850357, _850355 = _850353], (4656 ^ _779530) ^ [_850574, _850576, _850578, _850580, _850582, _850584] : [-(c_Divides_Odiv__class_Omod(_850584, _850580, _850576) = c_Divides_Odiv__class_Omod(_850582, _850578, _850574)), _850584 = _850582, _850580 = _850578, _850576 = _850574], (4670 ^ _779530) ^ [_850795, _850797] : [_850797 = _850795, -(c_Lattices_Osemilattice__sup__class_Osup(_850797) = c_Lattices_Osemilattice__sup__class_Osup(_850795))], (4676 ^ _779530) ^ [_850880, _850882, _850884, _850886] : [-(c_Complete__Lattice_OSup__class_OSup(_850886, _850882) = c_Complete__Lattice_OSup__class_OSup(_850884, _850880)), _850886 = _850884, _850882 = _850880], (4686 ^ _779530) ^ [_851029, _851031, _851033, _851035, _851037, _851039, _851041, _851043, _851045, _851047] : [-(c_Option_Ooption_Ooption__rec(_851047, _851043, _851039, _851035, _851031) = c_Option_Ooption_Ooption__rec(_851045, _851041, _851037, _851033, _851029)), _851047 = _851045, _851043 = _851041, _851039 = _851037, _851035 = _851033, _851031 = _851029], (4708 ^ _779530) ^ [_851418, _851420] : [_851420 = _851418, -(c_Option_Ooption_ONone(_851420) = c_Option_Ooption_ONone(_851418))], (4714 ^ _779530) ^ [_851503, _851505, _851507, _851509] : [-(c_Relation_Oconverse(_851509, _851505) = c_Relation_Oconverse(_851507, _851503)), _851509 = _851507, _851505 = _851503], (4724 ^ _779530) ^ [_851652, _851654, _851656, _851658, _851660, _851662] : [-(c_Relation_Orel__comp(_851662, _851658, _851654) = c_Relation_Orel__comp(_851660, _851656, _851652)), _851662 = _851660, _851658 = _851656, _851654 = _851652], (4738 ^ _779530) ^ [_851873, _851875, _851877, _851879] : [-(c_HOL_OLet(_851879, _851875) = c_HOL_OLet(_851877, _851873)), _851879 = _851877, _851875 = _851873], (4748 ^ _779530) ^ [_852022, _852024, _852026, _852028] : [-(c_Nitpick_Oint__lcm(_852028, _852024) = c_Nitpick_Oint__lcm(_852026, _852022)), _852028 = _852026, _852024 = _852022], (4758 ^ _779530) ^ [_852171, _852173] : [_852173 = _852171, -(c_Divides_Odiv__class_Odiv(_852173) = c_Divides_Odiv__class_Odiv(_852171))], (4764 ^ _779530) ^ [_852256, _852258, _852260, _852262, _852264, _852266] : [-(c_Nitpick_Otimes__frac(_852266, _852262, _852258) = c_Nitpick_Otimes__frac(_852264, _852260, _852256)), _852266 = _852264, _852262 = _852260, _852258 = _852256], (4778 ^ _779530) ^ [_852477, _852479] : [_852479 = _852477, -(c_Groups_Otimes__class_Otimes(_852479) = c_Groups_Otimes__class_Otimes(_852477))], (4784 ^ _779530) ^ [_852562, _852564, _852566, _852568, _852570, _852572] : [-(c_Nitpick_Oof__frac(_852572, _852568, _852564) = c_Nitpick_Oof__frac(_852570, _852566, _852562)), _852572 = _852570, _852568 = _852566, _852564 = _852562], (4798 ^ _779530) ^ [_852783, _852785] : [_852785 = _852783, -(c_Rings_Oinverse__class_Odivide(_852785) = c_Rings_Oinverse__class_Odivide(_852783))], (4804 ^ _779530) ^ [_852868, _852870] : [_852870 = _852868, -(c_Int_Oring__1__class_Oof__int(_852870) = c_Int_Oring__1__class_Oof__int(_852868))], (4810 ^ _779530) ^ [_852953, _852955, _852957, _852959] : [-(c_Nitpick_Oinverse__frac(_852959, _852955) = c_Nitpick_Oinverse__frac(_852957, _852953)), _852959 = _852957, _852955 = _852953], (4820 ^ _779530) ^ [_853102, _853104] : [_853104 = _853102, -(c_Nitpick_Ofrac(_853104) = c_Nitpick_Ofrac(_853102))], (4826 ^ _779530) ^ [_853187, _853189, _853191, _853193] : [-(c_Nitpick_OAbs__Frac(_853193, _853189) = c_Nitpick_OAbs__Frac(_853191, _853187)), _853193 = _853191, _853189 = _853187], (4836 ^ _779530) ^ [_853336, _853338] : [_853338 = _853336, -(c_Groups_Ouminus__class_Ouminus(_853338) = c_Groups_Ouminus__class_Ouminus(_853336))], (4842 ^ _779530) ^ [_853421, _853423, _853425, _853427, _853429, _853431] : [-(c_Nitpick_Oplus__frac(_853431, _853427, _853423) = c_Nitpick_Oplus__frac(_853429, _853425, _853421)), _853431 = _853429, _853427 = _853425, _853423 = _853421], (4856 ^ _779530) ^ [_853642, _853644, _853646, _853648] : [-(c_Nitpick_Ouminus__frac(_853648, _853644) = c_Nitpick_Ouminus__frac(_853646, _853642)), _853648 = _853646, _853644 = _853642], (4866 ^ _779530) ^ [_853791, _853793] : [_853793 = _853791, -(c_Nitpick_Odenom(_853793) = c_Nitpick_Odenom(_853791))], (4872 ^ _779530) ^ [_853876, _853878] : [_853878 = _853876, -(c_Nitpick_Onum(_853878) = c_Nitpick_Onum(_853876))], (4878 ^ _779530) ^ [_853961, _853963] : [_853963 = _853961, -(c_Nitpick_ORep__Frac(_853963) = c_Nitpick_ORep__Frac(_853961))], (4884 ^ _779530) ^ [_854046, _854048] : [_854048 = _854046, -(c_Orderings_Oord__class_Oless(_854048) = c_Orderings_Oord__class_Oless(_854046))], (4890 ^ _779530) ^ [_854131, _854133] : [_854133 = _854131, -(c_List_Onth(_854133) = c_List_Onth(_854131))], (4896 ^ _779530) ^ [_854216, _854218] : [_854218 = _854216, -(c_List_Oappend(_854218) = c_List_Oappend(_854216))], (4902 ^ _779530) ^ [_854301, _854303] : [_854303 = _854301, -(c_List_Orev(_854303) = c_List_Orev(_854301))], (4908 ^ _779530) ^ [_854386, _854388, _854390, _854392, _854394, _854396] : [-(c_Product__Type_Ointernal__split(_854396, _854392, _854388) = c_Product__Type_Ointernal__split(_854394, _854390, _854386)), _854396 = _854394, _854392 = _854390, _854388 = _854386], (4922 ^ _779530) ^ [_854607, _854609] : [_854609 = _854607, -(c_List_Olist_OCons(_854609) = c_List_Olist_OCons(_854607))], (4928 ^ _779530) ^ [_854692, _854694, _854696, _854698] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_854698, _854694) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_854696, _854692)), _854698 = _854696, _854694 = _854692], (4938 ^ _779530) ^ [_854841, _854843] : [_854843 = _854841, -(c_List_Olist_ONil(_854843) = c_List_Olist_ONil(_854841))], (4944 ^ _779530) ^ [_854926, _854928] : [_854928 = _854926, -(c_HOL_Obool_Obool__size(_854928) = c_HOL_Obool_Obool__size(_854926))], (4950 ^ _779530) ^ [_855011, _855013] : [_855013 = _855011, -(c_Set_OCollect(_855013) = c_Set_OCollect(_855011))], (4956 ^ _779530) ^ [_855096, _855098] : [_855098 = _855096, -(c_Finite__Set_Ofinite(_855098) = c_Finite__Set_Ofinite(_855096))], (4962 ^ _779530) ^ [_855181, _855183] : [_855183 = _855181, -(c_Groups_Oabs__class_Oabs(_855183) = c_Groups_Oabs__class_Oabs(_855181))], (4968 ^ _779530) ^ [_855266, _855268] : [_855268 = _855266, -(c_member(_855268) = c_member(_855266))], (4974 ^ _779530) ^ [_855351, _855353] : [_855353 = _855351, -(c_List_Oset(_855353) = c_List_Oset(_855351))], (4980 ^ _779530) ^ [_855436, _855438] : [_855438 = _855436, -(c_Enum_Oenum__class_Oenum(_855438) = c_Enum_Oenum__class_Oenum(_855436))], (4986 ^ _779530) ^ [_855521, _855523, _855525, _855527] : [-(c_Product__Type_Ofst(_855527, _855523) = c_Product__Type_Ofst(_855525, _855521)), _855527 = _855525, _855523 = _855521], (4996 ^ _779530) ^ [_855670, _855672, _855674, _855676] : [-(c_Product__Type_Osnd(_855676, _855672) = c_Product__Type_Osnd(_855674, _855670)), _855676 = _855674, _855672 = _855670], (5006 ^ _779530) ^ [_855819, _855821] : [_855821 = _855819, -(c_Nat_Osemiring__1__class_Oof__nat(_855821) = c_Nat_Osemiring__1__class_Oof__nat(_855819))], (5012 ^ _779530) ^ [_855904, _855906] : [_855906 = _855904, -(c_Lazy__Sequence_Ohit__bound(_855906) = c_Lazy__Sequence_Ohit__bound(_855904))], (5018 ^ _779530) ^ [_855989, _855991] : [_855991 = _855989, -(c_Int_Onumber__class_Onumber__of(_855991) = c_Int_Onumber__class_Onumber__of(_855989))], (5024 ^ _779530) ^ [_856074, _856076] : [_856076 = _856074, -(c_Int_OBit0(_856076) = c_Int_OBit0(_856074))], (5030 ^ _779530) ^ [_856159, _856161] : [_856161 = _856159, -(c_Int_OBit1(_856161) = c_Int_OBit1(_856159))], (5036 ^ _779530) ^ [_856244, _856246, _856248, _856250, _856252, _856254, _856256, _856258, _856260, _856262, _856264, _856266, _856268, _856270] : [-(c_New__Random__Sequence_Oneg__decr__bind(_856270, _856266, _856262, _856258, _856254, _856250, _856246) = c_New__Random__Sequence_Oneg__decr__bind(_856268, _856264, _856260, _856256, _856252, _856248, _856244)), _856270 = _856268, _856266 = _856264, _856262 = _856260, _856258 = _856256, _856254 = _856252, _856250 = _856248, _856246 = _856244], (5066 ^ _779530) ^ [_856833, _856835, _856837, _856839, _856841, _856843, _856845, _856847] : [-(c_New__DSequence_Oneg__decr__bind(_856847, _856843, _856839, _856835) = c_New__DSequence_Oneg__decr__bind(_856845, _856841, _856837, _856833)), _856847 = _856845, _856843 = _856841, _856839 = _856837, _856835 = _856833], (5084 ^ _779530) ^ [_857134, _857136, _857138, _857140, _857142, _857144, _857146, _857148] : [-(c_Lazy__Sequence_Ohb__bind(_857148, _857144, _857140, _857136) = c_Lazy__Sequence_Ohb__bind(_857146, _857142, _857138, _857134)), _857148 = _857146, _857144 = _857142, _857140 = _857138, _857136 = _857134], (5102 ^ _779530) ^ [_857435, _857437] : [_857437 = _857435, -(c_HOL_Oequal__class_Oequal(_857437) = c_HOL_Oequal__class_Oequal(_857435))], (5108 ^ _779530) ^ [_857520, _857522, _857524, _857526, _857528, _857530, _857532, _857534] : [-(c_New__DSequence_Oneg__bind(_857534, _857530, _857526, _857522) = c_New__DSequence_Oneg__bind(_857532, _857528, _857524, _857520)), _857534 = _857532, _857530 = _857528, _857526 = _857524, _857522 = _857520], (5126 ^ _779530) ^ [_857821, _857823, _857825, _857827, _857829, _857831, _857833, _857835] : [-(c_Option_Ooption_Ooption__case(_857835, _857831, _857827, _857823) = c_Option_Ooption_Ooption__case(_857833, _857829, _857825, _857821)), _857835 = _857833, _857831 = _857829, _857827 = _857825, _857823 = _857821], (5144 ^ _779530) ^ [_858122, _858124, _858126, _858128, _858130, _858132] : [-(c_Product__Type_Oprod_Oprod__case(_858132, _858128, _858124) = c_Product__Type_Oprod_Oprod__case(_858130, _858126, _858122)), _858132 = _858130, _858128 = _858126, _858124 = _858122], (5158 ^ _779530) ^ [_858343, _858345] : [_858345 = _858343, -(c_Lazy__Sequence_Oyieldn(_858345) = c_Lazy__Sequence_Oyieldn(_858343))], (5164 ^ _779530) ^ [_858428, _858430, _858432, _858434, _858436, _858438] : [-(c_Lazy__Sequence_Oanamorph(_858438, _858434, _858430) = c_Lazy__Sequence_Oanamorph(_858436, _858432, _858428)), _858438 = _858436, _858434 = _858432, _858430 = _858428], (5178 ^ _779530) ^ [_858649, _858651, _858653, _858655] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_858655, _858651) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_858653, _858649)), _858655 = _858653, _858651 = _858649], (5188 ^ _779530) ^ [_858798, _858800, _858802, _858804, _858806, _858808, _858810, _858812, _858814, _858816] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_858816, _858812, _858808, _858804, _858800) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_858814, _858810, _858806, _858802, _858798)), _858816 = _858814, _858812 = _858810, _858808 = _858806, _858804 = _858802, _858800 = _858798], (5210 ^ _779530) ^ [_859187, _859189] : [_859189 = _859187, -(c_Lazy__Sequence_Oyield(_859189) = c_Lazy__Sequence_Oyield(_859187))], (5216 ^ _779530) ^ [_859272, _859274] : [_859274 = _859272, -(c_Option_Ooption_OSome(_859274) = c_Option_Ooption_OSome(_859272))], (5222 ^ _779530) ^ [_859357, _859359, _859361, _859363] : [-(c_Product__Type_OPair(_859363, _859359) = c_Product__Type_OPair(_859361, _859357)), _859363 = _859361, _859359 = _859357], (5232 ^ _779530) ^ [_859506, _859508, _859510, _859512, _859514, _859516] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_859516, _859512, _859508) = c_Lazy__Sequence_Olazy__sequence_OInsert(_859514, _859510, _859506)), _859516 = _859514, _859512 = _859510, _859508 = _859506], (5246 ^ _779530) ^ [_859727, _859729] : [_859729 = _859727, -(c_Groups_Oplus__class_Oplus(_859729) = c_Groups_Oplus__class_Oplus(_859727))], (5252 ^ _779530) ^ [_859812, _859814] : [_859814 = _859812, -(c_Nat_Osize__class_Osize(_859814) = c_Nat_Osize__class_Osize(_859812))], (5258 ^ _779530) ^ [_859897, _859899, _859901, _859903, _859905, _859907, _859909, _859911] : [-(c_New__Random__Sequence_Oneg__map(_859911, _859907, _859903, _859899) = c_New__Random__Sequence_Oneg__map(_859909, _859905, _859901, _859897)), _859911 = _859909, _859907 = _859905, _859903 = _859901, _859899 = _859897], (5276 ^ _779530) ^ [_860198, _860200, _860202, _860204, _860206, _860208, _860210, _860212] : [-(c_New__Random__Sequence_Oneg__bind(_860212, _860208, _860204, _860200) = c_New__Random__Sequence_Oneg__bind(_860210, _860206, _860202, _860198)), _860212 = _860210, _860208 = _860206, _860204 = _860202, _860200 = _860198], (5294 ^ _779530) ^ [_860499, _860501, _860503, _860505, _860507, _860509, _860511, _860513] : [-(c_Fun_Ocomp(_860513, _860509, _860505, _860501) = c_Fun_Ocomp(_860511, _860507, _860503, _860499)), _860513 = _860511, _860509 = _860507, _860505 = _860503, _860501 = _860499], (5312 ^ _779530) ^ [_860800, _860802] : [_860802 = _860800, -(c_New__Random__Sequence_Oneg__single(_860802) = c_New__Random__Sequence_Oneg__single(_860800))], (5318 ^ _779530) ^ [_860885, _860887] : [_860887 = _860885, -(c_Lazy__Sequence_Oempty(_860887) = c_Lazy__Sequence_Oempty(_860885))], (5324 ^ _779530) ^ [_860970, _860972] : [_860972 = _860970, -(c_Groups_Ozero__class_Ozero(_860972) = c_Groups_Ozero__class_Ozero(_860970))], (5330 ^ _779530) ^ [_861055, _861057, _861059, _861061, _861063, _861065, _861067, _861069] : [-(c_Lazy__Sequence_Obind(_861069, _861065, _861061, _861057) = c_Lazy__Sequence_Obind(_861067, _861063, _861059, _861055)), _861069 = _861067, _861065 = _861063, _861061 = _861059, _861057 = _861055], (5348 ^ _779530) ^ [_861356, _861358] : [_861358 = _861356, -(c_Groups_Ominus__class_Ominus(_861358) = c_Groups_Ominus__class_Ominus(_861356))], (5354 ^ _779530) ^ [_861441, _861443] : [_861443 = _861441, -(c_Groups_Oone__class_Oone(_861443) = c_Groups_Oone__class_Oone(_861441))], (5360 ^ _779530) ^ [_861526, _861528, _861530, _861532, _861534, _861536, _861538, _861540, _861542, _861544, _861546, _861548, _861550, _861552] : [-(c_New__Random__Sequence_Opos__decr__bind(_861552, _861548, _861544, _861540, _861536, _861532, _861528) = c_New__Random__Sequence_Opos__decr__bind(_861550, _861546, _861542, _861538, _861534, _861530, _861526)), _861552 = _861550, _861548 = _861546, _861544 = _861542, _861540 = _861538, _861536 = _861534, _861532 = _861530, _861528 = _861526], (5390 ^ _779530) ^ [_862115, _862117, _862119, _862121, _862123, _862125, _862127, _862129] : [-(c_New__DSequence_Opos__decr__bind(_862129, _862125, _862121, _862117) = c_New__DSequence_Opos__decr__bind(_862127, _862123, _862119, _862115)), _862129 = _862127, _862125 = _862123, _862121 = _862119, _862117 = _862115], (5408 ^ _779530) ^ [_862416, _862418] : [_862418 = _862416, -(tc_List_Olist(_862418) = tc_List_Olist(_862416))], (5414 ^ _779530) ^ [_862501, _862503, _862505, _862507] : [-(tc_sum(_862507, _862503) = tc_sum(_862505, _862501)), _862507 = _862505, _862503 = _862501], (5424 ^ _779530) ^ [_862650, _862652] : [_862652 = _862650, -(tc_Option_Ooption(_862652) = tc_Option_Ooption(_862650))], (5430 ^ _779530) ^ [_862735, _862737, _862739, _862741] : [-(tc_prod(_862741, _862737) = tc_prod(_862739, _862735)), _862741 = _862739, _862737 = _862735], (5440 ^ _779530) ^ [_862884, _862886] : [_862886 = _862884, -(tc_Lazy__Sequence_Olazy__sequence(_862886) = tc_Lazy__Sequence_Olazy__sequence(_862884))], (5446 ^ _779530) ^ [_862969, _862971] : [_862971 = _862969, -(c_COMBI(_862971) = c_COMBI(_862969))], (5452 ^ _779530) ^ [_863054, _863056, _863058, _863060] : [-(c_COMBK(_863060, _863056) = c_COMBK(_863058, _863054)), _863060 = _863058, _863056 = _863054], (5462 ^ _779530) ^ [_863203, _863205, _863207, _863209, _863211, _863213] : [-(c_COMBB(_863213, _863209, _863205) = c_COMBB(_863211, _863207, _863203)), _863213 = _863211, _863209 = _863207, _863205 = _863203], (5476 ^ _779530) ^ [_863424, _863426, _863428, _863430, _863432, _863434] : [-(c_COMBC(_863434, _863430, _863426) = c_COMBC(_863432, _863428, _863424)), _863434 = _863432, _863430 = _863428, _863426 = _863424], (5490 ^ _779530) ^ [_863645, _863647, _863649, _863651, _863653, _863655] : [-(c_COMBS(_863655, _863651, _863647) = c_COMBS(_863653, _863649, _863645)), _863655 = _863653, _863651 = _863649, _863647 = _863645], (5504 ^ _779530) ^ [_863866, _863868] : [_863868 = _863866, -(c_Orderings_Oord__class_Oless__eq(_863868) = c_Orderings_Oord__class_Oless__eq(_863866))], (5510 ^ _779530) ^ [_863951, _863953, _863955, _863957] : [-(hAPP(_863957, _863953) = hAPP(_863955, _863951)), _863957 = _863955, _863953 = _863951], (5520 ^ _779530) ^ [_864100, _864102] : [_864102 = _864100, -(c_Set_Oinsert(_864102) = c_Set_Oinsert(_864100))], (5526 ^ _779530) ^ [_864185, _864187, _864189, _864191, _864193, _864195, _864197, _864199] : [-(c_Hoare__Mirabelle_Otriple_Otriple(_864199, _864195, _864191, _864187) = c_Hoare__Mirabelle_Otriple_Otriple(_864197, _864193, _864189, _864185)), _864199 = _864197, _864195 = _864193, _864191 = _864189, _864187 = _864185], (5544 ^ _779530) ^ [_864486, _864488] : [_864488 = _864486, -(c_Orderings_Obot__class_Obot(_864488) = c_Orderings_Obot__class_Obot(_864486))], (5560 ^ _779530) ^ [_864716, _864718] : [_864718 = _864716, -(tc_Hoare__Mirabelle_Otriple(_864718) = tc_Hoare__Mirabelle_Otriple(_864716))], (5550 ^ _779530) ^ [_864571, _864573, _864575, _864577] : [-(tc_fun(_864577, _864573) = tc_fun(_864575, _864571)), _864577 = _864575, _864573 = _864571], (5566 ^ _779530) ^ [_867459, _867461] : [hAPP(_867459, 5567 ^ [_867459, _867461]) = hAPP(_867461, 5567 ^ [_867459, _867461]), -(_867459 = _867461)], (5573 ^ _779530) ^ [_867585, _867587] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867585, _867587, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867585), tc_HOL_Obool))))], (5575 ^ _779530) ^ [_867618, _867620, _867622] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867618, _867620, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867618)), c_Hoare__Mirabelle_Otriple_Otriple(_867618, _867622, c_Com_Ocom_OSKIP, _867622)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867618), tc_HOL_Obool)))))], (5577 ^ _779530) ^ [_867668, _867670] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867668, _867670, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867668), tc_HOL_Obool))))], (5579 ^ _779530) ^ [_867701, _867703, _867705] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867701, _867703, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867701)), c_Hoare__Mirabelle_Otriple_Otriple(_867701, _867705, c_Com_Ocom_OSKIP, _867705)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867701), tc_HOL_Obool)))))], (5581 ^ _779530) ^ [_867781, _867783, _867785, _867787, _867789, _867791, _867793] : [c_Hoare__Mirabelle_Otriple_Otriple(_867781, _867783, _867785, _867787) = c_Hoare__Mirabelle_Otriple_Otriple(_867781, _867789, _867791, _867793), 5584 ^ _779530 : [(5585 ^ _779530) ^ [] : [-(_867783 = _867789)], (5587 ^ _779530) ^ [] : [-(_867785 = _867791)], (5589 ^ _779530) ^ [] : [-(_867787 = _867793)]]], (5591 ^ _779530) ^ [_867934, _867936, _867938, _867940, _867942, _867944, _867946] : [-(c_Hoare__Mirabelle_Otriple_Otriple(_867934, _867936, _867938, _867940) = c_Hoare__Mirabelle_Otriple_Otriple(_867934, _867942, _867944, _867946)), _867936 = _867942, _867938 = _867944, _867940 = _867946], (5605 ^ _779530) ^ [_868167, _868169, _868171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_868167), tc_HOL_Obool)), _868169), _868171)), -(c_Hoare__Mirabelle_Ohoare__derivs(_868167, _868171, _868169))], (5611 ^ _779530) ^ [_868272, _868274, _868276, _868278] : [c_Hoare__Mirabelle_Ohoare__derivs(_868272, _868274, _868276), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_868272), tc_HOL_Obool)), _868278), _868276)), -(c_Hoare__Mirabelle_Ohoare__derivs(_868272, _868274, _868278))], (5621 ^ _779530) ^ [_868437, _868439, _868441, _868443] : [c_Hoare__Mirabelle_Ohoare__derivs(_868437, _868439, _868441), c_Hoare__Mirabelle_Ohoare__derivs(_868437, _868443, _868439), -(c_Hoare__Mirabelle_Ohoare__derivs(_868437, _868443, _868441))], (5631 ^ _779530) ^ [_868580, _868582, _868584, _868586] : [c_Hoare__Mirabelle_Ohoare__derivs(_868580, _868582, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_868580)), _868584), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_868580), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_868580, _868582, _868586), -(c_Hoare__Mirabelle_Ohoare__derivs(_868580, _868582, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_868580)), _868584), _868586)))], (5641 ^ _779530) ^ [_868777, _868779] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868777, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_868777, tc_HOL_Obool))), _868779)))], (5643 ^ _779530) ^ [_868817, _868819, _868821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868817, tc_HOL_Obool)), _868819), hAPP(hAPP(c_Set_Oinsert(_868817), _868821), c_Orderings_Obot__class_Obot(tc_fun(_868817, tc_HOL_Obool))))), -(_868819 = c_Orderings_Obot__class_Obot(tc_fun(_868817, tc_HOL_Obool))), -(_868819 = hAPP(hAPP(c_Set_Oinsert(_868817), _868821), c_Orderings_Obot__class_Obot(tc_fun(_868817, tc_HOL_Obool))))], (5653 ^ _779530) ^ [_868991, _868993, _868995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868991, tc_HOL_Obool)), _868993), _868995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868991, tc_HOL_Obool)), _868995), _868993)), -(_868993 = _868995)], (5663 ^ _779530) ^ [_869164, _869166] : [class_Orderings_Opreorder(_869164), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_869164), _869166), _869166)))], (5669 ^ _779530) ^ [_869253, _869255, _869257] : [class_Orderings_Obot(_869253), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_869255, _869253)), _869257) = c_Orderings_Obot__class_Obot(_869253))], (5675 ^ _779530) ^ [_869350, _869352, _869354, _869356, _869358, _869360] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_869350, _869352, _869354, c_Hoare__Mirabelle_Otriple_Otriple(_869350, _869356, _869358, _869360)) = hAPP(hAPP(hAPP(_869354, _869356), _869358), _869360))], (5677 ^ _779530) ^ [_869402, _869404, _869406, _869408, _869410, _869412] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_869402, _869404, _869406, c_Hoare__Mirabelle_Otriple_Otriple(_869402, _869408, _869410, _869412)) = hAPP(hAPP(hAPP(_869406, _869408), _869410), _869412))], (5679 ^ _779530) ^ [_869454, _869456, _869458] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869454, tc_HOL_Obool)), _869456), hAPP(hAPP(c_Set_Oinsert(_869454), _869458), _869456))))], (5681 ^ _779530) ^ [_869499, _869501, _869503, _869505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869499, tc_HOL_Obool)), _869501), _869503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869499, tc_HOL_Obool)), _869501), hAPP(hAPP(c_Set_Oinsert(_869499), _869505), _869503))))], (5687 ^ _779530) ^ [_869636, _869638, _869640, _869642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869636, tc_HOL_Obool)), _869638), _869640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869636, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_869636), _869642), _869638)), hAPP(hAPP(c_Set_Oinsert(_869636), _869642), _869640))))], (5693 ^ _779530) ^ [_869804, _869806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869804, tc_HOL_Obool)), _869806), c_Orderings_Obot__class_Obot(tc_fun(_869804, tc_HOL_Obool)))), -(_869806 = c_Orderings_Obot__class_Obot(tc_fun(_869804, tc_HOL_Obool)))], (5699 ^ _779530) ^ [_869917, _869919] : [_869919 = c_Orderings_Obot__class_Obot(tc_fun(_869917, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869917, tc_HOL_Obool)), _869919), c_Orderings_Obot__class_Obot(tc_fun(_869917, tc_HOL_Obool)))))], (5705 ^ _779530) ^ [_870051, _870053, _870055] : [c_Orderings_Obot__class_Obot(tc_fun(_870051, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_870051), _870053), _870055)], (5707 ^ _779530) ^ [_870091, _870093, _870095] : [class_Orderings_Olinorder(_870091), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870091), _870093), _870095))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870091), _870095), _870093)))], (5717 ^ _779530) ^ [_870211, _870213, _870215, _870217] : [class_Orderings_Oorder(_870211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870211), _870213), _870215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870211), _870217), _870213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870211), _870217), _870215)))], (5731 ^ _779530) ^ [_870444, _870446, _870448] : [class_Orderings_Oorder(_870444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870444), _870446), _870448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870444), _870448), _870446)), -(_870448 = _870446)], (5745 ^ _779530) ^ [_870657, _870659, _870661, _870663] : [class_Orderings_Opreorder(_870657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870657), _870659), _870661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870657), _870661), _870663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870657), _870659), _870663)))], (5759 ^ _779530) ^ [_870890, _870892, _870894] : [class_Orderings_Oorder(_870890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870890), _870892), _870894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_870890), _870894), _870892)), -(_870892 = _870894)], (5773 ^ _779530) ^ [_871103, _871105, _871107, _871109] : [class_Orderings_Oorder(_871103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871103), _871105), _871107)), _871105 = _871109, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871103), _871109), _871107)))], (5787 ^ _779530) ^ [_871322, _871324, _871326, _871328] : [class_Orderings_Oord(_871322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871322), _871324), _871326)), _871326 = _871328, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871322), _871324), _871328)))], (5801 ^ _779530) ^ [_871541, _871543, _871545, _871547] : [class_Orderings_Oorder(_871541), _871543 = _871545, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871541), _871547), _871545)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871541), _871547), _871543)))], (5815 ^ _779530) ^ [_871760, _871762, _871764, _871766] : [class_Orderings_Oord(_871760), _871762 = _871764, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871760), _871764), _871766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871760), _871762), _871766)))], (5829 ^ _779530) ^ [_871979, _871981, _871983] : [class_Orderings_Oorder(_871979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871979), _871981), _871983)), 5836 ^ _779530 : [(5837 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871979), _871983), _871981)), -(_871983 = _871981)], (5843 ^ _779530) ^ [] : [_871983 = _871981, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_871979), _871983), _871981)))]]], (5849 ^ _779530) ^ [_872279, _872281, _872283] : [class_Orderings_Opreorder(_872279), _872281 = _872283, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872279), _872281), _872283)))], (5859 ^ _779530) ^ [_872424, _872426, _872428] : [class_Orderings_Oorder(_872424), 5862 ^ _779530 : [(5863 ^ _779530) ^ [] : [_872426 = _872428, 5866 ^ _779530 : [(5867 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872424), _872426), _872428)))], (5869 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872424), _872428), _872426)))]]], (5871 ^ _779530) ^ [] : [-(_872426 = _872428), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872424), _872426), _872428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872424), _872428), _872426))]]], (5881 ^ _779530) ^ [_872751, _872753, _872755] : [class_Orderings_Olinorder(_872751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872751), _872753), _872755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872751), _872755), _872753)))], (5901 ^ _779530) ^ [_873004, _873006, _873008, _873010] : [5902 ^ _779530 : [(5903 ^ _779530) ^ [] : [_873006 = _873010], (5905 ^ _779530) ^ [] : [hBOOL(hAPP(_873008, _873010))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_873004), _873006), _873008), _873010)))], (5891 ^ _779530) ^ [_872890, _872892, _872894, _872896] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872890), _872892), _872894), _872896)), -(_872892 = _872896), -(hBOOL(hAPP(_872894, _872896)))], (5909 ^ _779530) ^ [_873149, _873151, _873153, _873155] : [-(hAPP(hAPP(c_Set_Oinsert(_873149), _873151), hAPP(hAPP(c_Set_Oinsert(_873149), _873153), _873155)) = hAPP(hAPP(c_Set_Oinsert(_873149), _873153), hAPP(hAPP(c_Set_Oinsert(_873149), _873151), _873155)))], (5911 ^ _779530) ^ [_873210, _873212, _873214] : [-(hAPP(hAPP(c_Set_Oinsert(_873210), _873212), hAPP(hAPP(c_Set_Oinsert(_873210), _873212), _873214)) = hAPP(hAPP(c_Set_Oinsert(_873210), _873212), _873214))], (5913 ^ _779530) ^ [_873261, _873263, _873265] : [_873261 = _873263, 5916 ^ _779530 : [(5917 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873265, tc_HOL_Obool)), _873261), _873263)))], (5919 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873265, tc_HOL_Obool)), _873263), _873261)))]]], (5921 ^ _779530) ^ [_873410, _873412, _873414, _873416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873410, tc_HOL_Obool)), _873412), _873414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873410, tc_HOL_Obool)), _873414), _873416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873410, tc_HOL_Obool)), _873412), _873416)))], (5931 ^ _779530) ^ [_873607, _873609, _873611] : [_873607 = _873609, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873611, tc_HOL_Obool)), _873609), _873607)))], (5937 ^ _779530) ^ [_873706, _873708, _873710] : [_873706 = _873708, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873710, tc_HOL_Obool)), _873706), _873708)))], (5943 ^ _779530) ^ [_873823, _873825, _873827] : [_873823 = _873825, 5946 ^ _779530 : [(5947 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873827, tc_HOL_Obool)), _873823), _873825)))], (5949 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873827, tc_HOL_Obool)), _873825), _873823)))]]], (5951 ^ _779530) ^ [_873964, _873966, _873968] : [-(_873964 = _873966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873968, tc_HOL_Obool)), _873964), _873966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873968, tc_HOL_Obool)), _873966), _873964))], (5961 ^ _779530) ^ [_874139, _874141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874139, tc_HOL_Obool)), _874141), _874141)))], (5963 ^ _779530) ^ [_874174, _874176] : [class_Orderings_Obot(_874174), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874174), c_Orderings_Obot__class_Obot(_874174)), _874176)))], (5969 ^ _779530) ^ [_874267, _874269, _874271, _874273, _874275] : [class_Orderings_Oord(_874267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874269, _874267)), _874271), _874273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874267), hAPP(_874271, _874275)), hAPP(_874273, _874275))))], (5979 ^ _779530) ^ [_874452, _874454, _874456, _874458, _874460] : [class_Orderings_Oord(_874452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874454, _874452)), _874456), _874458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874452), hAPP(_874456, _874460)), hAPP(_874458, _874460))))], (5989 ^ _779530) ^ [_874637, _874639, _874641, _874643] : [class_Orderings_Oord(_874637), 5992 ^ _779530 : [(5993 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874639, _874637)), _874641), _874643)), 5996 ^ _779530 : [(5997 ^ _779530) ^ [_874794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874637), hAPP(_874641, _874794)), hAPP(_874643, _874794))))]]], (5999 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874637), hAPP(_874641, 6000 ^ [_874637, _874639, _874641, _874643])), hAPP(_874643, 6000 ^ [_874637, _874639, _874641, _874643]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874639, _874637)), _874641), _874643)))]]], (6006 ^ _779530) ^ [_874983, _874985, _874987] : [class_Orderings_Obot(_874983), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_874985, _874983)), _874987) = c_Orderings_Obot__class_Obot(_874983))], (6012 ^ _779530) ^ [_875080, _875082, _875084] : [hAPP(hAPP(c_Set_Oinsert(_875080), _875082), c_Orderings_Obot__class_Obot(tc_fun(_875080, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_875080), _875084), c_Orderings_Obot__class_Obot(tc_fun(_875080, tc_HOL_Obool))), -(_875082 = _875084)], (6018 ^ _779530) ^ [_875235, _875237, _875239, _875241, _875243] : [hAPP(hAPP(c_Set_Oinsert(_875235), _875237), hAPP(hAPP(c_Set_Oinsert(_875235), _875239), c_Orderings_Obot__class_Obot(tc_fun(_875235, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_875235), _875241), hAPP(hAPP(c_Set_Oinsert(_875235), _875243), c_Orderings_Obot__class_Obot(tc_fun(_875235, tc_HOL_Obool)))), 6023 ^ _779530 : [(6024 ^ _779530) ^ [] : [-(_875237 = _875241)], (6026 ^ _779530) ^ [] : [-(_875239 = _875243)]], 6027 ^ _779530 : [(6028 ^ _779530) ^ [] : [-(_875237 = _875243)], (6030 ^ _779530) ^ [] : [-(_875239 = _875241)]]], (6032 ^ _779530) ^ [_875497, _875499, _875501, _875503, _875505] : [-(hAPP(hAPP(c_Set_Oinsert(_875497), _875499), hAPP(hAPP(c_Set_Oinsert(_875497), _875501), c_Orderings_Obot__class_Obot(tc_fun(_875497, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_875497), _875503), hAPP(hAPP(c_Set_Oinsert(_875497), _875505), c_Orderings_Obot__class_Obot(tc_fun(_875497, tc_HOL_Obool))))), 6033 ^ _779530 : [(6034 ^ _779530) ^ [] : [_875499 = _875503, _875501 = _875505], (6040 ^ _779530) ^ [] : [_875499 = _875505, _875501 = _875503]]], (6048 ^ _779530) ^ [_875828, _875830, _875832] : [hAPP(hAPP(c_Set_Oinsert(_875828), _875830), _875832) = c_Orderings_Obot__class_Obot(tc_fun(_875828, tc_HOL_Obool))], (6050 ^ _779530) ^ [_875868, _875870] : [-(c_Set_Othe__elem(_875868, hAPP(hAPP(c_Set_Oinsert(_875868), _875870), c_Orderings_Obot__class_Obot(tc_fun(_875868, tc_HOL_Obool)))) = _875870)], (6052 ^ _779530) ^ [_875909, _875911, _875913, _875915, _875917] : [6055 ^ _779530 : [(6056 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_875909, 6053 ^ [_875909, _875911, _875913, _875915, _875917]), 6054 ^ [_875909, _875911, _875913, _875915, _875917])))], (6058 ^ _779530) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_875911, _875913, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_875911)), c_Hoare__Mirabelle_Otriple_Otriple(_875911, hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _875911), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 6054 ^ [_875909, _875911, _875913, _875915, _875917])), _875915, hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _875911), hAPP(_875917, 6053 ^ [_875909, _875911, _875913, _875915, _875917])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_875911), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_875911, _875913, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_875911)), c_Hoare__Mirabelle_Otriple_Otriple(_875911, _875909, _875915, _875917)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_875911), tc_HOL_Obool)))))], (6062 ^ _779530) ^ [_876301, _876303, _876305, _876307, _876309, _876311] : [c_Hoare__Mirabelle_Ohoare__derivs(_876301, _876303, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876301)), c_Hoare__Mirabelle_Otriple_Otriple(_876301, _876305, _876307, _876309)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876301), tc_HOL_Obool)))), 6069 ^ _779530 : [(6070 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_876311, 6067 ^ [_876301, _876303, _876305, _876307, _876309, _876311]), 6068 ^ [_876301, _876303, _876305, _876307, _876309, _876311])))], (6072 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_876305, 6067 ^ [_876301, _876303, _876305, _876307, _876309, _876311]), 6068 ^ [_876301, _876303, _876305, _876307, _876309, _876311]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_876301, _876303, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876301)), c_Hoare__Mirabelle_Otriple_Otriple(_876301, _876311, _876307, _876309)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876301), tc_HOL_Obool)))))], (6076 ^ _779530) ^ [_876706, _876708, _876710, _876712, _876714, _876716] : [c_Hoare__Mirabelle_Ohoare__derivs(_876706, _876708, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876706)), c_Hoare__Mirabelle_Otriple_Otriple(_876706, _876710, _876712, _876714)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876706), tc_HOL_Obool)))), 6083 ^ _779530 : [(6084 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_876714, 6081 ^ [_876706, _876708, _876710, _876712, _876714, _876716]), 6082 ^ [_876706, _876708, _876710, _876712, _876714, _876716])))], (6086 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_876716, 6081 ^ [_876706, _876708, _876710, _876712, _876714, _876716]), 6082 ^ [_876706, _876708, _876710, _876712, _876714, _876716]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_876706, _876708, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_876706)), c_Hoare__Mirabelle_Otriple_Otriple(_876706, _876710, _876712, _876716)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_876706), tc_HOL_Obool)))))], (6090 ^ _779530) ^ [_877111, _877113, _877115, _877117, _877119, _877121, _877123] : [c_Hoare__Mirabelle_Ohoare__derivs(_877111, _877113, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877111)), c_Hoare__Mirabelle_Otriple_Otriple(_877111, _877115, _877117, _877119)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877111), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_877111, _877113, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877111)), c_Hoare__Mirabelle_Otriple_Otriple(_877111, _877119, _877121, _877123)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877111), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_877111, _877113, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877111)), c_Hoare__Mirabelle_Otriple_Otriple(_877111, _877115, c_Com_Ocom_OSemi(_877117, _877121), _877123)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877111), tc_HOL_Obool)))))], (6100 ^ _779530) ^ [_877404, _877406, _877408, _877410, _877412] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_877404, _877406, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877404)), c_Hoare__Mirabelle_Otriple_Otriple(_877404, hAPP(hAPP(c_COMBC(_877404, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _877404), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _877404), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _877408))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _877410)), c_Com_Ocom_OWhile(_877410, _877412), _877408)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877404), tc_HOL_Obool)))))], (6102 ^ _779530) ^ [_877494, _877496, _877498, _877500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877494, tc_HOL_Obool)), _877496), _877498)), hBOOL(hAPP(_877496, _877500)), -(hBOOL(hAPP(_877498, _877500)))], (6112 ^ _779530) ^ [_877659, _877661, _877663, _877665] : [hBOOL(hAPP(_877659, _877661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877663, tc_HOL_Obool)), _877659), _877665)), -(hBOOL(hAPP(_877665, _877661)))], (6122 ^ _779530) ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836] : [c_Hoare__Mirabelle_Ohoare__derivs(_877824, _877826, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877824)), c_Hoare__Mirabelle_Otriple_Otriple(_877824, _877828, _877830, _877832)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877824), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_877824, _877826, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_877824)), c_Hoare__Mirabelle_Otriple_Otriple(_877824, _877834, _877830, _877836)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877824), tc_HOL_Obool))))), 6129 ^ _779530 : [(6130 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_877834, 6127 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836]), 6128 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836])))], (6139 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_877836, 6127 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836]), 6131 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836]))], (6133 ^ _779530) ^ [_878280] : [hBOOL(hAPP(hAPP(_877828, _878280), 6128 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836])), -(hBOOL(hAPP(hAPP(_877832, _878280), 6131 ^ [_877824, _877826, _877828, _877830, _877832, _877834, _877836])))]]], (6143 ^ _779530) ^ [_878571, _878573, _878575, _878577, _878579] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_878571, _878573, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_878571)), c_Hoare__Mirabelle_Otriple_Otriple(_878571, hAPP(hAPP(c_COMBC(_878571, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _878571), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _878575)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _878577)), _878579)), c_Com_Ocom_OAss(_878577, _878579), _878575)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_878571), tc_HOL_Obool)))))], (6145 ^ _779530) ^ [_878657, _878659, _878661, _878663, _878665] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_878657, _878659, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_878657)), c_Hoare__Mirabelle_Otriple_Otriple(_878657, hAPP(hAPP(c_COMBC(_878657, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _878657), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _878661)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _878663)), _878665)), c_Com_Ocom_OAss(_878663, _878665), _878661)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_878657), tc_HOL_Obool)))))], (6147 ^ _779530) ^ [_878743, _878745, _878747, _878749] : [class_Orderings_Oorder(_878743), class_Enum_Oenum(_878745), 6154 ^ _779530 : [(6155 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878745, _878743)), _878747), _878749)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878745), hAPP(hAPP(c_COMBS(_878745, _878743, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878743, tc_fun(_878743, tc_HOL_Obool), _878745), c_Orderings_Oord__class_Oless__eq(_878743)), _878747)), _878749))))], (6161 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878745), hAPP(hAPP(c_COMBS(_878745, _878743, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878743, tc_fun(_878743, tc_HOL_Obool), _878745), c_Orderings_Oord__class_Oless__eq(_878743)), _878747)), _878749))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878745, _878743)), _878747), _878749)))]]], (6167 ^ _779530) ^ [_879133, _879135] : [class_Enum_Oenum(_879133), 6170 ^ _779530 : [(6171 ^ _779530) ^ [] : [hBOOL(hAPP(_879135, 6172 ^ [_879133, _879135])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_879133), _879135)))], (6178 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_879133), _879135)), 6181 ^ _779530 : [(6182 ^ _779530) ^ [_879351] : [-(hBOOL(hAPP(_879135, _879351)))]]]]], (6184 ^ _779530) ^ [_879386, _879388] : [class_Enum_Oenum(_879386), 6187 ^ _779530 : [(6188 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_879386), _879388)), 6191 ^ _779530 : [(6192 ^ _779530) ^ [_879512] : [-(hBOOL(hAPP(_879388, _879512)))]]], (6194 ^ _779530) ^ [] : [hBOOL(hAPP(_879388, 6195 ^ [_879386, _879388])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_879386), _879388)))]]], (6201 ^ _779530) ^ [_879651, _879653] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_879651, _879653)], (6203 ^ _779530) ^ [_879691, _879693] : [c_Com_Ocom_OSemi(_879691, _879693) = c_Com_Ocom_OSKIP], (6205 ^ _779530) ^ [_879731, _879733] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_879731, _879733)], (6207 ^ _779530) ^ [_879771, _879773] : [c_Com_Ocom_OAss(_879771, _879773) = c_Com_Ocom_OSKIP], (6209 ^ _779530) ^ [_879817, _879819, _879821, _879823] : [c_Com_Ocom_OSemi(_879817, _879819) = c_Com_Ocom_OAss(_879821, _879823)], (6211 ^ _779530) ^ [_879870, _879872, _879874, _879876] : [c_Com_Ocom_OAss(_879870, _879872) = c_Com_Ocom_OSemi(_879874, _879876)], (6213 ^ _779530) ^ [_879917, _879919] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_879917, _879919)], (6215 ^ _779530) ^ [_879957, _879959] : [c_Com_Ocom_OWhile(_879957, _879959) = c_Com_Ocom_OSKIP], (6217 ^ _779530) ^ [_880003, _880005, _880007, _880009] : [c_Com_Ocom_OWhile(_880003, _880005) = c_Com_Ocom_OSemi(_880007, _880009)], (6219 ^ _779530) ^ [_880056, _880058, _880060, _880062] : [c_Com_Ocom_OSemi(_880056, _880058) = c_Com_Ocom_OWhile(_880060, _880062)], (6221 ^ _779530) ^ [_880109, _880111, _880113, _880115] : [c_Com_Ocom_OWhile(_880109, _880111) = c_Com_Ocom_OAss(_880113, _880115)], (6223 ^ _779530) ^ [_880162, _880164, _880166, _880168] : [c_Com_Ocom_OAss(_880162, _880164) = c_Com_Ocom_OWhile(_880166, _880168)], (6225 ^ _779530) ^ [_880218, _880220, _880222, _880224] : [c_Com_Ocom_OWhile(_880218, _880220) = c_Com_Ocom_OWhile(_880222, _880224), 6228 ^ _779530 : [(6229 ^ _779530) ^ [] : [-(_880218 = _880222)], (6231 ^ _779530) ^ [] : [-(_880220 = _880224)]]], (6233 ^ _779530) ^ [_880333, _880335, _880337, _880339] : [-(c_Com_Ocom_OWhile(_880333, _880335) = c_Com_Ocom_OWhile(_880337, _880339)), _880333 = _880337, _880335 = _880339], (6243 ^ _779530) ^ [_880505, _880507, _880509, _880511] : [c_Com_Ocom_OAss(_880505, _880507) = c_Com_Ocom_OAss(_880509, _880511), 6246 ^ _779530 : [(6247 ^ _779530) ^ [] : [-(_880505 = _880509)], (6249 ^ _779530) ^ [] : [-(_880507 = _880511)]]], (6251 ^ _779530) ^ [_880620, _880622, _880624, _880626] : [-(c_Com_Ocom_OAss(_880620, _880622) = c_Com_Ocom_OAss(_880624, _880626)), _880620 = _880624, _880622 = _880626], (6261 ^ _779530) ^ [_880792, _880794, _880796, _880798] : [c_Com_Ocom_OSemi(_880792, _880794) = c_Com_Ocom_OSemi(_880796, _880798), 6264 ^ _779530 : [(6265 ^ _779530) ^ [] : [-(_880792 = _880796)], (6267 ^ _779530) ^ [] : [-(_880794 = _880798)]]], (6269 ^ _779530) ^ [_880907, _880909, _880911, _880913] : [-(c_Com_Ocom_OSemi(_880907, _880909) = c_Com_Ocom_OSemi(_880911, _880913)), _880907 = _880911, _880909 = _880913], (6279 ^ _779530) ^ [_881058, _881060] : [-(c_Set_Othe__elem(_881058, _881060) = c_HOL_OThe(_881058, hAPP(hAPP(c_COMBB(tc_fun(_881058, tc_HOL_Obool), tc_HOL_Obool, _881058), hAPP(c_fequal, _881060)), hAPP(hAPP(c_COMBC(_881058, tc_fun(_881058, tc_HOL_Obool), tc_fun(_881058, tc_HOL_Obool)), c_Set_Oinsert(_881058)), c_Orderings_Obot__class_Obot(tc_fun(_881058, tc_HOL_Obool))))))], (6281 ^ _779530) ^ [_881128, _881130, _881132, _881134, _881136] : [c_Hoare__Mirabelle_Ohoare__derivs(_881128, _881130, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881128)), c_Hoare__Mirabelle_Otriple_Otriple(_881128, c_Hoare__Mirabelle_Opeek__and(_881128, _881132, _881134), _881136, _881132)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881128), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_881128, _881130, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881128)), c_Hoare__Mirabelle_Otriple_Otriple(_881128, _881132, c_Com_Ocom_OWhile(_881134, _881136), c_Hoare__Mirabelle_Opeek__and(_881128, _881132, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _881134)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881128), tc_HOL_Obool)))))], (6287 ^ _779530) ^ [_881331, _881333, _881335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881331, tc_HOL_Obool)), _881333), _881335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_881331, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_881331, _881333)), c_Predicate_OPowp(_881331, _881335))))], (6293 ^ _779530) ^ [_881468, _881470, _881472] : [class_Orderings_Owellorder(_881468), hBOOL(hAPP(_881470, _881472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881468), c_Orderings_Oord__class_OLeast(_881468, _881470)), _881472)))], (6303 ^ _779530) ^ [_881623, _881625, _881627, _881629] : [class_Orderings_Oord(_881623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881623), hAPP(_881625, 6308 ^ [_881623, _881625, _881627, _881629])), hAPP(_881627, 6308 ^ [_881623, _881625, _881627, _881629]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881629, _881623)), _881625), _881627)))], (6314 ^ _779530) ^ [_881887, _881889, _881891, _881893, _881895, _881897] : [c_Predicate_Oinv__imagep(_881887, _881889, _881891, _881893, _881895, _881897), -(hBOOL(hAPP(hAPP(_881891, hAPP(_881893, _881895)), hAPP(_881893, _881897))))], (6320 ^ _779530) ^ [_881998, _882000, _882002, _882004, _882006, _882008] : [hBOOL(hAPP(hAPP(_882002, hAPP(_882004, _882006)), hAPP(_882004, _882008))), -(c_Predicate_Oinv__imagep(_881998, _882000, _882002, _882004, _882006, _882008))], (6326 ^ _779530) ^ [_882115, _882117, _882119, _882121, _882123, _882125, _882127, _882129, _882131] : [-(c_Com_Ocom_Ocom__case(_882115, _882117, _882119, _882121, _882123, _882125, _882127, _882129, _882131, c_Com_Ocom_OSKIP) = _882117)], (6328 ^ _779530) ^ [_882165, _882167, _882169, _882171, _882173, _882175, _882177, _882179, _882181, _882183, _882185] : [-(c_Com_Ocom_Ocom__case(_882165, _882167, _882169, _882171, _882173, _882175, _882177, _882179, _882181, c_Com_Ocom_OSemi(_882183, _882185)) = hAPP(hAPP(_882173, _882183), _882185))], (6330 ^ _779530) ^ [_882228, _882230, _882232, _882234, _882236, _882238, _882240, _882242, _882244, _882246, _882248] : [-(c_Com_Ocom_Ocom__case(_882228, _882230, _882232, _882234, _882236, _882238, _882240, _882242, _882244, c_Com_Ocom_OAss(_882246, _882248)) = hAPP(hAPP(_882232, _882246), _882248))], (6332 ^ _779530) ^ [_882291, _882293, _882295, _882297, _882299] : [class_Orderings_Oorder(_882291), class_Orderings_Olinorder(_882293), c_Orderings_Oorder__class_Ostrict__mono(_882293, _882291, _882295), 6343 ^ _779530 : [(6344 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882291), hAPP(_882295, _882297)), hAPP(_882295, _882299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882293), _882297), _882299)))], (6350 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882293), _882297), _882299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882291), hAPP(_882295, _882297)), hAPP(_882295, _882299))))]]], (6356 ^ _779530) ^ [_882692, _882694, _882696, _882698, _882700, _882702, _882704, _882706, _882708, _882710, _882712] : [-(c_Com_Ocom_Ocom__case(_882692, _882694, _882696, _882698, _882700, _882702, _882704, _882706, _882708, c_Com_Ocom_OWhile(_882710, _882712)) = hAPP(hAPP(_882704, _882710), _882712))], (6358 ^ _779530) ^ [_882755, _882757, _882759, _882761, _882763, _882765, _882767, _882769] : [c_Hoare__Mirabelle_Ohoare__derivs(_882755, _882757, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_882755)), c_Hoare__Mirabelle_Otriple_Otriple(_882755, _882759, _882761, hAPP(hAPP(c_COMBC(_882755, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _882755), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _882763)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_882765))), c_Natural_Ogetlocs(_882767, _882765))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_882755), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_882755, _882757, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_882755)), c_Hoare__Mirabelle_Otriple_Otriple(_882755, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _882755), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _882767)))), hAPP(hAPP(c_COMBC(_882755, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _882755), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _882759)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_882765))), _882769))), c_Com_Ocom_OLocal(_882765, _882769, _882761), _882763)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_882755), tc_HOL_Obool)))))], (6364 ^ _779530) ^ [_883127, _883129] : [c_Com_Ovname_OLoc(_883127) = c_Com_Ovname_OLoc(_883129), -(_883127 = _883129)], (6370 ^ _779530) ^ [_883208, _883210] : [_883208 = _883210, -(c_Com_Ovname_OLoc(_883208) = c_Com_Ovname_OLoc(_883210))], (6376 ^ _779530) ^ [_883322, _883324, _883326, _883328, _883330, _883332] : [c_Com_Ocom_OLocal(_883322, _883324, _883326) = c_Com_Ocom_OLocal(_883328, _883330, _883332), 6379 ^ _779530 : [(6380 ^ _779530) ^ [] : [-(_883322 = _883328)], (6382 ^ _779530) ^ [] : [-(_883324 = _883330)], (6384 ^ _779530) ^ [] : [-(_883326 = _883332)]]], (6386 ^ _779530) ^ [_883469, _883471, _883473, _883475, _883477, _883479] : [-(c_Com_Ocom_OLocal(_883469, _883471, _883473) = c_Com_Ocom_OLocal(_883475, _883477, _883479)), _883469 = _883475, _883471 = _883477, _883473 = _883479], (6400 ^ _779530) ^ [_883692, _883694, _883696, _883698, _883700, _883702, _883704, _883706, _883708, _883710, _883712, _883714] : [-(c_Com_Ocom_Ocom__case(_883692, _883694, _883696, _883698, _883700, _883702, _883704, _883706, _883708, c_Com_Ocom_OLocal(_883710, _883712, _883714)) = hAPP(hAPP(hAPP(_883698, _883710), _883712), _883714))], (6402 ^ _779530) ^ [_883761, _883763] : [class_Orderings_Owellorder(_883761), 6407 ^ _779530 : [(6408 ^ _779530) ^ [_883855] : [hBOOL(hAPP(_883763, _883855))]], -(hBOOL(hAPP(_883763, c_Orderings_Oord__class_OLeast(_883761, _883763))))], (6412 ^ _779530) ^ [_883915, _883917, _883919, _883921, _883923] : [class_Orderings_Oorder(_883915), class_Orderings_Olinorder(_883917), c_Orderings_Oorder__class_Ostrict__mono(_883917, _883915, _883919), 6423 ^ _779530 : [(6424 ^ _779530) ^ [] : [hAPP(_883919, _883921) = hAPP(_883919, _883923), -(_883921 = _883923)], (6430 ^ _779530) ^ [] : [_883921 = _883923, -(hAPP(_883919, _883921) = hAPP(_883919, _883923))]]], (6436 ^ _779530) ^ [_884274, _884276, _884278] : [class_Orderings_Owellorder(_884274), hBOOL(hAPP(_884276, _884278)), -(hBOOL(hAPP(_884276, c_Orderings_Oord__class_OLeast(_884274, _884276))))], (6446 ^ _779530) ^ [_884446, _884448, _884450, _884452, _884454, _884456] : [c_Predicate_Oinv__imagep(_884446, _884448, _884450, _884452, _884454, _884456), -(hBOOL(hAPP(hAPP(_884450, hAPP(_884452, _884454)), hAPP(_884452, _884456))))], (6452 ^ _779530) ^ [_884557, _884559, _884561, _884563, _884565, _884567] : [hBOOL(hAPP(hAPP(_884561, hAPP(_884563, _884565)), hAPP(_884563, _884567))), -(c_Predicate_Oinv__imagep(_884557, _884559, _884561, _884563, _884565, _884567))], (6458 ^ _779530) ^ [_884698, _884700, _884702, _884704, _884706] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_884698, _884700, _884702), _884704), _884706)), 6461 ^ _779530 : [(6462 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_884700, _884704), _884706)))], (6464 ^ _779530) ^ [] : [-(hBOOL(hAPP(_884702, _884706)))]]], (6466 ^ _779530) ^ [_884835, _884837, _884839, _884841, _884843] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_884835, _884837, _884839), _884841), _884843))), hBOOL(hAPP(hAPP(_884837, _884841), _884843)), hBOOL(hAPP(_884839, _884843))], (6476 ^ _779530) ^ [_885031, _885033, _885035, _885037, _885039] : [c_Com_Ocom_OLocal(_885031, _885033, _885035) = c_Com_Ocom_OWhile(_885037, _885039)], (6478 ^ _779530) ^ [_885090, _885092, _885094, _885096, _885098] : [c_Com_Ocom_OWhile(_885090, _885092) = c_Com_Ocom_OLocal(_885094, _885096, _885098)], (6480 ^ _779530) ^ [_885149, _885151, _885153, _885155, _885157] : [c_Com_Ocom_OLocal(_885149, _885151, _885153) = c_Com_Ocom_OAss(_885155, _885157)], (6482 ^ _779530) ^ [_885208, _885210, _885212, _885214, _885216] : [c_Com_Ocom_OAss(_885208, _885210) = c_Com_Ocom_OLocal(_885212, _885214, _885216)], (6484 ^ _779530) ^ [_885267, _885269, _885271, _885273, _885275] : [c_Com_Ocom_OLocal(_885267, _885269, _885271) = c_Com_Ocom_OSemi(_885273, _885275)], (6486 ^ _779530) ^ [_885326, _885328, _885330, _885332, _885334] : [c_Com_Ocom_OSemi(_885326, _885328) = c_Com_Ocom_OLocal(_885330, _885332, _885334)], (6488 ^ _779530) ^ [_885379, _885381, _885383] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_885379, _885381, _885383)], (6490 ^ _779530) ^ [_885425, _885427, _885429] : [c_Com_Ocom_OLocal(_885425, _885427, _885429) = c_Com_Ocom_OSKIP], (6492 ^ _779530) ^ [_885456, _885458, _885460, _885462, _885464, _885466, _885468] : [c_Hoare__Mirabelle_Ohoare__derivs(_885456, _885458, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885456)), c_Hoare__Mirabelle_Otriple_Otriple(_885456, c_Hoare__Mirabelle_Opeek__and(_885456, _885460, _885462), _885464, _885466)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_885456), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_885456, _885458, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885456)), c_Hoare__Mirabelle_Otriple_Otriple(_885456, c_Hoare__Mirabelle_Opeek__and(_885456, _885460, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _885462)), _885468, _885466)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_885456), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_885456, _885458, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_885456)), c_Hoare__Mirabelle_Otriple_Otriple(_885456, _885460, c_Com_Ocom_OCond(_885462, _885464, _885468), _885466)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_885456), tc_HOL_Obool)))))], (6502 ^ _779530) ^ [_885773, _885775] : [-(c_Enum_Oenum__the(_885773, _885775) = c_HOL_OThe(_885773, _885775))], (6504 ^ _779530) ^ [_885804, _885806] : [-(c_HOL_OThe(_885804, hAPP(hAPP(c_COMBC(_885804, _885804, tc_HOL_Obool), c_fequal), _885806)) = _885806)], (6506 ^ _779530) ^ [_885842, _885844] : [-(c_HOL_OThe(_885842, hAPP(c_fequal, _885844)) = _885844)], (6508 ^ _779530) ^ [_885873, _885875, _885877, _885879] : [-(c_Com_Ovname_Ovname__rec(_885873, _885875, _885877, c_Com_Ovname_OLoc(_885879)) = hAPP(_885877, _885879))], (6510 ^ _779530) ^ [_885912, _885914, _885916, _885918] : [-(c_Com_Ovname_Ovname__case(_885912, _885914, _885916, c_Com_Ovname_OLoc(_885918)) = hAPP(_885916, _885918))], (6512 ^ _779530) ^ [_885951, _885953, _885955, _885957, _885959, _885961] : [-(hAPP(hAPP(c_Fun_Ocomp(_885951, _885953, _885955, hAPP(c_COMBK(_885953, _885951), _885957)), _885959), _885961) = _885957)], (6514 ^ _779530) ^ [_886001, _886003, _886005, _886007, _886009, _886011] : [-(hAPP(hAPP(c_Fun_Ocomp(_886001, _886003, _886005, _886007), _886009), _886011) = hAPP(_886007, hAPP(_886009, _886011)))], (6516 ^ _779530) ^ [_886051, _886053, _886055, _886057, _886059] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886051), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886053), c_Com_Ovname_OLoc(_886055)), hAPP(_886057, _886053))), _886059)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_886055, _886057, _886051)), _886053), hAPP(hAPP(hAPP(c_Natural_Oupdate, _886059), c_Com_Ovname_OLoc(_886055)), c_Natural_Ogetlocs(_886053, _886055)))))], (6522 ^ _779530) ^ [_886226, _886228, _886230, _886232, _886234, _886236] : [c_Natural_Oevaln(_886226, hAPP(hAPP(hAPP(c_Natural_Oupdate, _886228), c_Com_Ovname_OLoc(_886230)), hAPP(_886232, _886228)), _886234, _886236), -(c_Natural_Oevaln(c_Com_Ocom_OLocal(_886230, _886232, _886226), _886228, _886234, hAPP(hAPP(hAPP(c_Natural_Oupdate, _886236), c_Com_Ovname_OLoc(_886230)), c_Natural_Ogetlocs(_886228, _886230))))], (6528 ^ _779530) ^ [_886383, _886385, _886387, _886389, _886391, _886393, _886395, _886397] : [hAPP(c_Fun_Ocomp(_886383, _886385, _886387, _886389), _886391) = hAPP(c_Fun_Ocomp(_886393, _886385, _886387, _886395), _886397), 6531 ^ _779530 : [(6532 ^ _779530) ^ [_886498] : [-(hAPP(_886389, hAPP(_886391, _886498)) = hAPP(_886395, hAPP(_886397, _886498)))]]], (6534 ^ _779530) ^ [_886533, _886535, _886537, _886539] : [-(hBOOL(hAPP(_886533, _886535))), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886533, _886537), _886535, _886539, _886535))], (6540 ^ _779530) ^ [_886580, _886582, _886584, _886586, _886588, _886590] : [hBOOL(hAPP(_886580, _886582)), c_Natural_Oevaln(_886584, _886582, _886586, _886588), c_Natural_Oevaln(c_Com_Ocom_OWhile(_886580, _886584), _886588, _886586, _886590), -(c_Natural_Oevaln(c_Com_Ocom_OWhile(_886580, _886584), _886582, _886586, _886590))], (6554 ^ _779530) ^ [_886809, _886811, _886813] : [-(hBOOL(hAPP(_886809, _886811))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_886809, _886813)), _886811), _886811)))], (6560 ^ _779530) ^ [_886859, _886861, _886863, _886865, _886867] : [hBOOL(hAPP(_886859, _886861)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_886863), _886861), _886865)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_886859, _886863)), _886865), _886867)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_886859, _886863)), _886861), _886867)))], (6574 ^ _779530) ^ [_887115, _887117, _887119, _887121, _887123, _887125] : [-(hBOOL(hAPP(_887115, _887117))), c_Natural_Oevaln(_887119, _887117, _887121, _887123), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_887115, _887125, _887119), _887117, _887121, _887123))], (6584 ^ _779530) ^ [_887276, _887278, _887280, _887282, _887284, _887286] : [hBOOL(hAPP(_887276, _887278)), c_Natural_Oevaln(_887280, _887278, _887282, _887284), -(c_Natural_Oevaln(c_Com_Ocom_OCond(_887276, _887280, _887286), _887278, _887282, _887284))], (6594 ^ _779530) ^ [_887441, _887443, _887445, _887447, _887449, _887451] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_887441, _887443, _887445), _887447, _887449, _887451), 6599 ^ _779530 : [(6600 ^ _779530) ^ [] : [-(hBOOL(hAPP(_887441, _887447)))], (6602 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_887443, _887447, _887449, _887451))]], 6603 ^ _779530 : [(6604 ^ _779530) ^ [] : [hBOOL(hAPP(_887441, _887447))], (6606 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_887445, _887447, _887449, _887451))]]], (6608 ^ _779530) ^ [_887682, _887684, _887686, _887688, _887690] : [-(hBOOL(hAPP(_887682, _887684))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887686), _887684), _887688)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_887682, _887690, _887686)), _887684), _887688)))], (6618 ^ _779530) ^ [_887859, _887861, _887863, _887865, _887867] : [hBOOL(hAPP(_887859, _887861)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_887863), _887861), _887865)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_887859, _887863, _887867)), _887861), _887865)))], (6628 ^ _779530) ^ [_888040, _888042, _888044, _888046, _888048] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_888040, _888042, _888044)), _888046), _888048)), 6633 ^ _779530 : [(6634 ^ _779530) ^ [] : [-(hBOOL(hAPP(_888040, _888046)))], (6636 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888042), _888046), _888048)))]], 6637 ^ _779530 : [(6638 ^ _779530) ^ [] : [hBOOL(hAPP(_888040, _888046))], (6640 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888044), _888046), _888048)))]]], (6642 ^ _779530) ^ [_888308, _888310, _888312, _888314, _888316, _888318] : [c_Natural_Oevaln(_888308, _888310, _888312, _888314), c_Natural_Oevaln(_888316, _888314, _888312, _888318), -(c_Natural_Oevaln(c_Com_Ocom_OSemi(_888308, _888316), _888310, _888312, _888318))], (6652 ^ _779530) ^ [_888471, _888473, _888475] : [c_Natural_Oevaln(c_Com_Ocom_OSKIP, _888471, _888473, _888475), -(_888475 = _888471)], (6658 ^ _779530) ^ [_888554, _888556] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _888554, _888556, _888554))], (6660 ^ _779530) ^ [_888581, _888583, _888585, _888587, _888589] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888581), _888583), _888585)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888587), _888585), _888589)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_888581, _888587)), _888583), _888589)))], (6670 ^ _779530) ^ [_888770, _888772] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _888770), _888772)), -(_888772 = _888770)], (6676 ^ _779530) ^ [_888857] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _888857), _888857)))], (6678 ^ _779530) ^ [_888885, _888887, _888889, _888891] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_888885, _888887), _888889, _888891, hAPP(hAPP(hAPP(c_Natural_Oupdate, _888889), _888885), hAPP(_888887, _888889))))], (6680 ^ _779530) ^ [_888931, _888933, _888935, _888937, _888939] : [c_Natural_Oevaln(c_Com_Ocom_OAss(_888931, _888933), _888935, _888937, _888939), -(_888939 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _888935), _888931), hAPP(_888933, _888935)))], (6686 ^ _779530) ^ [_889048, _889050, _889052] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_889048, _889050)), _889052), hAPP(hAPP(hAPP(c_Natural_Oupdate, _889052), _889048), hAPP(_889050, _889052)))))], (6688 ^ _779530) ^ [_889097, _889099, _889101, _889103] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_889097, _889099)), _889101), _889103)), -(_889103 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _889101), _889097), hAPP(_889099, _889101)))], (6694 ^ _779530) ^ [_889222, _889224, _889226, _889228, _889230] : [c_Natural_Oevaln(_889222, _889224, _889226, _889228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889226), _889230)), -(c_Natural_Oevaln(_889222, _889224, _889230, _889228))], (6704 ^ _779530) ^ [_889399, _889401, _889403] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889399), _889401), _889403)), -(c_Natural_Oevaln(_889399, _889401, 6707 ^ [_889399, _889401, _889403], _889403))], (6711 ^ _779530) ^ [_889506, _889508, _889510] : [6712 ^ _779530 : [(6713 ^ _779530) ^ [_889556] : [c_Natural_Oevaln(_889506, _889508, _889556, _889510)]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889506), _889508), _889510)))], (6717 ^ _779530) ^ [_889642, _889644, _889646, _889648, _889650] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889642, _889644, _889646)), _889648), _889650)), 6722 ^ _779530 : [(6723 ^ _779530) ^ [] : [-(hBOOL(hAPP(_889642, _889648)))], (6725 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889644), _889648), _889650)))]], 6726 ^ _779530 : [(6727 ^ _779530) ^ [] : [hBOOL(hAPP(_889642, _889648))], (6729 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889646), _889648), _889650)))]]], (6731 ^ _779530) ^ [_889900, _889902, _889904, _889906, _889908] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_889900, _889902, _889904)), _889906), _889908))), 6732 ^ _779530 : [(6733 ^ _779530) ^ [] : [hBOOL(hAPP(_889900, _889906)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889902), _889906), _889908))], (6739 ^ _779530) ^ [] : [-(hBOOL(hAPP(_889900, _889906))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889904), _889906), _889908))]]], (6747 ^ _779530) ^ [_890217, _890219, _890221, _890223, _890225] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_890217, _890219, _890221)), _890223), _890225)), 6752 ^ _779530 : [(6753 ^ _779530) ^ [] : [-(hBOOL(hAPP(_890217, _890223)))], (6755 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890219), _890223), _890225)))]], 6756 ^ _779530 : [(6757 ^ _779530) ^ [] : [hBOOL(hAPP(_890217, _890223))], (6759 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890221), _890223), _890225)))]]], (6761 ^ _779530) ^ [_890475, _890477, _890479, _890481, _890483] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_890475, _890477, _890479)), _890481), _890483))), 6762 ^ _779530 : [(6763 ^ _779530) ^ [] : [hBOOL(hAPP(_890475, _890481)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890477), _890481), _890483))], (6769 ^ _779530) ^ [] : [-(hBOOL(hAPP(_890475, _890481))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890479), _890481), _890483))]]], (6777 ^ _779530) ^ [_890795, _890797, _890799, _890801, _890803, _890805] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_890795, _890797, _890799), _890801, _890803, _890805), 6782 ^ _779530 : [(6783 ^ _779530) ^ [] : [-(hBOOL(hAPP(_890795, _890801)))], (6785 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_890797, _890801, _890803, _890805))]], 6786 ^ _779530 : [(6787 ^ _779530) ^ [] : [hBOOL(hAPP(_890795, _890801))], (6789 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_890799, _890801, _890803, _890805))]]], (6791 ^ _779530) ^ [_891027, _891029, _891031, _891033, _891035, _891037] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_891027, _891029, _891031), _891033, _891035, _891037)), 6792 ^ _779530 : [(6793 ^ _779530) ^ [] : [hBOOL(hAPP(_891027, _891033)), c_Natural_Oevaln(_891029, _891033, _891035, _891037)], (6799 ^ _779530) ^ [] : [-(hBOOL(hAPP(_891027, _891033))), c_Natural_Oevaln(_891031, _891033, _891035, _891037)]]], (6807 ^ _779530) ^ [_891323, _891325, _891327, _891329, _891331, _891333] : [c_Natural_Oevaln(c_Com_Ocom_OCond(_891323, _891325, _891327), _891329, _891331, _891333), 6812 ^ _779530 : [(6813 ^ _779530) ^ [] : [-(hBOOL(hAPP(_891323, _891329)))], (6815 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_891325, _891329, _891331, _891333))]], 6816 ^ _779530 : [(6817 ^ _779530) ^ [] : [hBOOL(hAPP(_891323, _891329))], (6819 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_891327, _891329, _891331, _891333))]]], (6821 ^ _779530) ^ [_891555, _891557, _891559, _891561, _891563, _891565] : [-(c_Natural_Oevaln(c_Com_Ocom_OCond(_891555, _891557, _891559), _891561, _891563, _891565)), 6822 ^ _779530 : [(6823 ^ _779530) ^ [] : [hBOOL(hAPP(_891555, _891561)), c_Natural_Oevaln(_891557, _891561, _891563, _891565)], (6829 ^ _779530) ^ [] : [-(hBOOL(hAPP(_891555, _891561))), c_Natural_Oevaln(_891559, _891561, _891563, _891565)]]], (6837 ^ _779530) ^ [_891824, _891826, _891828, _891830] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891824), _891826), _891828)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891824), _891826), _891830)), -(_891830 = _891828)], (6847 ^ _779530) ^ [_891989, _891991, _891993, _891995] : [c_Natural_Oevaln(_891989, _891991, _891993, _891995), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_891989), _891991), _891995)))], (6853 ^ _779530) ^ [_892115, _892117, _892119, _892121, _892123, _892125] : [c_Com_Ocom_OCond(_892115, _892117, _892119) = c_Com_Ocom_OCond(_892121, _892123, _892125), 6856 ^ _779530 : [(6857 ^ _779530) ^ [] : [-(_892115 = _892121)], (6859 ^ _779530) ^ [] : [-(_892117 = _892123)], (6861 ^ _779530) ^ [] : [-(_892119 = _892125)]]], (6863 ^ _779530) ^ [_892262, _892264, _892266, _892268, _892270, _892272] : [-(c_Com_Ocom_OCond(_892262, _892264, _892266) = c_Com_Ocom_OCond(_892268, _892270, _892272)), _892262 = _892268, _892264 = _892270, _892266 = _892272], (6877 ^ _779530) ^ [_892506, _892508, _892510, _892512] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_892506, _892508), _892510, _892512, _892510), hBOOL(hAPP(_892506, _892510)), 6885 ^ _779530 : [(6886 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_892508, _892510, _892512, 6884 ^ [_892506, _892508, _892510, _892512]))], (6888 ^ _779530) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_892506, _892508), 6884 ^ [_892506, _892508, _892510, _892512], _892512, _892510))]]], (6890 ^ _779530) ^ [_892720, _892722, _892724, _892726] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_892720, _892722), _892724, _892726, _892724)), 6891 ^ _779530 : [(6892 ^ _779530) ^ [] : [-(hBOOL(hAPP(_892720, _892724)))], (6894 ^ _779530) ^ [_892807] : [c_Natural_Oevaln(_892722, _892724, _892726, _892807), c_Natural_Oevaln(c_Com_Ocom_OWhile(_892720, _892722), _892807, _892726, _892724)]]], (6902 ^ _779530) ^ [_892964, _892966, _892968, _892970, _892972] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_892964, _892966), _892968, _892970, _892972), 6907 ^ _779530 : [(6908 ^ _779530) ^ [] : [-(_892972 = _892968)], (6910 ^ _779530) ^ [] : [hBOOL(hAPP(_892964, _892968))]], 6911 ^ _779530 : [(6912 ^ _779530) ^ [] : [-(hBOOL(hAPP(_892964, _892968)))], (6915 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_892966, _892968, _892970, 6913 ^ [_892964, _892966, _892968, _892970, _892972]))], (6917 ^ _779530) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_892964, _892966), 6913 ^ [_892964, _892966, _892968, _892970, _892972], _892970, _892972))]]], (6919 ^ _779530) ^ [_893249, _893251, _893253, _893255, _893257] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_893249, _893251), _893253, _893255, _893257)), 6920 ^ _779530 : [(6921 ^ _779530) ^ [] : [_893257 = _893253, -(hBOOL(hAPP(_893249, _893253)))], (6927 ^ _779530) ^ [] : [hBOOL(hAPP(_893249, _893253)), 6930 ^ _779530 : [(6931 ^ _779530) ^ [_893459] : [c_Natural_Oevaln(_893251, _893253, _893255, _893459), c_Natural_Oevaln(c_Com_Ocom_OWhile(_893249, _893251), _893459, _893255, _893257)]]]]], (6939 ^ _779530) ^ [_893616, _893618, _893620] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893616, _893618)), _893620), _893620)), hBOOL(hAPP(_893616, _893620)), 6947 ^ _779530 : [(6948 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893618), _893620), 6946 ^ [_893616, _893618, _893620])))], (6950 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893616, _893618)), 6946 ^ [_893616, _893618, _893620]), _893620)))]]], (6952 ^ _779530) ^ [_893852, _893854, _893856] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893852, _893854)), _893856), _893856))), 6953 ^ _779530 : [(6954 ^ _779530) ^ [] : [-(hBOOL(hAPP(_893852, _893856)))], (6956 ^ _779530) ^ [_893952] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893854), _893856), _893952)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_893852, _893854)), _893952), _893856))]]], (6964 ^ _779530) ^ [_894129, _894131, _894133, _894135] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_894129, _894131)), _894133), _894135)), 6969 ^ _779530 : [(6970 ^ _779530) ^ [] : [-(_894135 = _894133)], (6972 ^ _779530) ^ [] : [hBOOL(hAPP(_894129, _894133))]], 6973 ^ _779530 : [(6974 ^ _779530) ^ [] : [-(hBOOL(hAPP(_894129, _894133)))], (6977 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894131), _894133), 6975 ^ [_894129, _894131, _894133, _894135])))], (6979 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_894129, _894131)), 6975 ^ [_894129, _894131, _894133, _894135]), _894135)))]]], (6981 ^ _779530) ^ [_894436, _894438, _894440, _894442] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_894436, _894438)), _894440), _894442))), 6982 ^ _779530 : [(6983 ^ _779530) ^ [] : [_894442 = _894440, -(hBOOL(hAPP(_894436, _894440)))], (6989 ^ _779530) ^ [] : [hBOOL(hAPP(_894436, _894440)), 6992 ^ _779530 : [(6993 ^ _779530) ^ [_894655] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_894438), _894440), _894655)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_894436, _894438)), _894655), _894442))]]]]], (7001 ^ _779530) ^ [_894841, _894843, _894845, _894847, _894849] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_894841, _894843), _894845, _894847, _894849), 7005 ^ _779530 : [(7006 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_894841, _894845, _894847, 7004 ^ [_894841, _894843, _894845, _894847, _894849]))], (7008 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_894843, 7004 ^ [_894841, _894843, _894845, _894847, _894849], _894847, _894849))]]], (7010 ^ _779530) ^ [_894995, _894997, _894999, _895001, _895003] : [-(c_Natural_Oevaln(c_Com_Ocom_OSemi(_894995, _894997), _894999, _895001, _895003)), 7011 ^ _779530 : [(7012 ^ _779530) ^ [_895050] : [c_Natural_Oevaln(_894995, _894999, _895001, _895050), c_Natural_Oevaln(_894997, _895050, _895001, _895003)]]], (7020 ^ _779530) ^ [_895177, _895179] : [-(c_Natural_Oevaln(c_Com_Ocom_OSKIP, _895177, _895179, _895177))], (7022 ^ _779530) ^ [_895225, _895227, _895229, _895231] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_895225, _895227)), _895229), _895231)), 7026 ^ _779530 : [(7027 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895225), _895229), 7025 ^ [_895225, _895227, _895229, _895231])))], (7029 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895227), 7025 ^ [_895225, _895227, _895229, _895231]), _895231)))]]], (7031 ^ _779530) ^ [_895403, _895405, _895407, _895409] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_895403, _895405)), _895407), _895409))), 7032 ^ _779530 : [(7033 ^ _779530) ^ [_895471] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895403), _895407), _895471)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_895405), _895471), _895409))]]], (7041 ^ _779530) ^ [_895621] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _895621), _895621)))], (7043 ^ _779530) ^ [_895670, _895672, _895674, _895676, _895678] : [c_Com_Ocom_OWhile(_895670, _895672) = c_Com_Ocom_OCond(_895674, _895676, _895678)], (7045 ^ _779530) ^ [_895729, _895731, _895733, _895735, _895737] : [c_Com_Ocom_OCond(_895729, _895731, _895733) = c_Com_Ocom_OWhile(_895735, _895737)], (7047 ^ _779530) ^ [_895767, _895769, _895771, _895773] : [-(c_Natural_Oevaln(c_Com_Ocom_OAss(_895767, _895769), _895771, _895773, hAPP(hAPP(hAPP(c_Natural_Oupdate, _895771), _895767), hAPP(_895769, _895771))))], (7049 ^ _779530) ^ [_895834, _895836, _895838, _895840, _895842] : [c_Com_Ocom_OAss(_895834, _895836) = c_Com_Ocom_OCond(_895838, _895840, _895842)], (7051 ^ _779530) ^ [_895893, _895895, _895897, _895899, _895901] : [c_Com_Ocom_OCond(_895893, _895895, _895897) = c_Com_Ocom_OAss(_895899, _895901)], (7053 ^ _779530) ^ [_895952, _895954, _895956, _895958, _895960] : [c_Com_Ocom_OSemi(_895952, _895954) = c_Com_Ocom_OCond(_895956, _895958, _895960)], (7055 ^ _779530) ^ [_896011, _896013, _896015, _896017, _896019] : [c_Com_Ocom_OCond(_896011, _896013, _896015) = c_Com_Ocom_OSemi(_896017, _896019)], (7057 ^ _779530) ^ [_896073, _896075, _896077, _896079, _896081, _896083] : [c_Com_Ocom_OLocal(_896073, _896075, _896077) = c_Com_Ocom_OCond(_896079, _896081, _896083)], (7059 ^ _779530) ^ [_896138, _896140, _896142, _896144, _896146, _896148] : [c_Com_Ocom_OCond(_896138, _896140, _896142) = c_Com_Ocom_OLocal(_896144, _896146, _896148)], (7061 ^ _779530) ^ [_896194, _896196, _896198] : [c_Com_Ocom_OCond(_896194, _896196, _896198) = c_Com_Ocom_OSKIP], (7063 ^ _779530) ^ [_896240, _896242, _896244] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_896240, _896242, _896244)], (7065 ^ _779530) ^ [_896271, _896273, _896275] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_896271, _896273)), _896275), hAPP(hAPP(hAPP(c_Natural_Oupdate, _896275), _896271), hAPP(_896273, _896275)))))], (7067 ^ _779530) ^ [_896320, _896322, _896324, _896326, _896328, _896330, _896332, _896334, _896336, _896338, _896340, _896342] : [-(c_Com_Ocom_Ocom__case(_896320, _896322, _896324, _896326, _896328, _896330, _896332, _896334, _896336, c_Com_Ocom_OCond(_896338, _896340, _896342)) = hAPP(hAPP(hAPP(_896330, _896338), _896340), _896342))], (7069 ^ _779530) ^ [_896416, _896418, _896420, _896422, _896424, _896426] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_896416, _896418, _896420), _896422, _896424, hAPP(hAPP(hAPP(c_Natural_Oupdate, _896426), c_Com_Ovname_OLoc(_896416)), c_Natural_Ogetlocs(_896422, _896416))), 7073 ^ _779530 : [(7074 ^ _779530) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _896426), c_Com_Ovname_OLoc(_896416)), c_Natural_Ogetlocs(_896422, _896416)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 7072 ^ [_896416, _896418, _896420, _896422, _896424, _896426]), c_Com_Ovname_OLoc(_896416)), c_Natural_Ogetlocs(_896422, _896416)))], (7076 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_896420, hAPP(hAPP(hAPP(c_Natural_Oupdate, _896422), c_Com_Ovname_OLoc(_896416)), hAPP(_896418, _896422)), _896424, 7072 ^ [_896416, _896418, _896420, _896422, _896424, _896426]))]]], (7078 ^ _779530) ^ [_896686, _896688, _896690, _896692, _896694, _896696] : [-(c_Natural_Oevaln(c_Com_Ocom_OLocal(_896686, _896688, _896690), _896692, _896694, hAPP(hAPP(hAPP(c_Natural_Oupdate, _896696), c_Com_Ovname_OLoc(_896686)), c_Natural_Ogetlocs(_896692, _896686)))), 7079 ^ _779530 : [(7080 ^ _779530) ^ [_896798] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _896696), c_Com_Ovname_OLoc(_896686)), c_Natural_Ogetlocs(_896692, _896686)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _896798), c_Com_Ovname_OLoc(_896686)), c_Natural_Ogetlocs(_896692, _896686)), c_Natural_Oevaln(_896690, hAPP(hAPP(hAPP(c_Natural_Oupdate, _896692), c_Com_Ovname_OLoc(_896686)), hAPP(_896688, _896692)), _896694, _896798)]]], (7088 ^ _779530) ^ [_897046, _897048, _897050, _897052, _897054] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_897046, _897048, _897050)), _897052), hAPP(hAPP(hAPP(c_Natural_Oupdate, _897054), c_Com_Ovname_OLoc(_897046)), c_Natural_Ogetlocs(_897052, _897046)))), 7092 ^ _779530 : [(7093 ^ _779530) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _897054), c_Com_Ovname_OLoc(_897046)), c_Natural_Ogetlocs(_897052, _897046)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 7091 ^ [_897046, _897048, _897050, _897052, _897054]), c_Com_Ovname_OLoc(_897046)), c_Natural_Ogetlocs(_897052, _897046)))], (7095 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_897050), hAPP(hAPP(hAPP(c_Natural_Oupdate, _897052), c_Com_Ovname_OLoc(_897046)), hAPP(_897048, _897052))), 7091 ^ [_897046, _897048, _897050, _897052, _897054])))]]], (7097 ^ _779530) ^ [_897330, _897332, _897334, _897336, _897338] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_897330, _897332, _897334)), _897336), hAPP(hAPP(hAPP(c_Natural_Oupdate, _897338), c_Com_Ovname_OLoc(_897330)), c_Natural_Ogetlocs(_897336, _897330))))), 7098 ^ _779530 : [(7099 ^ _779530) ^ [_897450] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _897338), c_Com_Ovname_OLoc(_897330)), c_Natural_Ogetlocs(_897336, _897330)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _897450), c_Com_Ovname_OLoc(_897330)), c_Natural_Ogetlocs(_897336, _897330)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_897334), hAPP(hAPP(hAPP(c_Natural_Oupdate, _897336), c_Com_Ovname_OLoc(_897330)), hAPP(_897332, _897336))), _897450))]]], (7107 ^ _779530) ^ [_897687, _897689, _897691, _897693, _897695, _897697, _897699] : [-(hAPP(c_Fun_Ocomp(_897687, _897689, _897691, _897693), hAPP(c_Fun_Ocomp(_897695, _897687, _897691, _897697), _897699)) = hAPP(c_Fun_Ocomp(_897695, _897689, _897691, hAPP(c_Fun_Ocomp(_897687, _897689, _897695, _897693), _897697)), _897699))], (7109 ^ _779530) ^ [_897754, _897756, _897758, _897760, _897762, _897764] : [-(hAPP(hAPP(c_Fun_Ocomp(_897754, _897756, _897758, _897760), _897762), _897764) = hAPP(_897760, hAPP(_897762, _897764)))], (7111 ^ _779530) ^ [_897804, _897806, _897808, _897810, _897812, _897814, _897816] : [hAPP(c_Fun_Ocomp(_897804, _897806, _897808, _897810), _897812) = _897814, -(hAPP(_897810, hAPP(_897812, _897816)) = hAPP(_897814, _897816))], (7117 ^ _779530) ^ [_897925, _897927, _897929, _897931, _897933, _897935, _897937, _897939, _897941] : [hAPP(c_Fun_Ocomp(_897925, _897927, _897929, _897931), _897933) = hAPP(c_Fun_Ocomp(_897935, _897927, _897929, _897937), _897939), -(hAPP(_897931, hAPP(_897933, _897941)) = hAPP(_897937, hAPP(_897939, _897941)))], (7123 ^ _779530) ^ [_898072] : [-(c_Hoare__Mirabelle_OMGT(_898072) = c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate, c_fequal, _898072, c_Natural_Oevalc(_898072)))], (7125 ^ _779530) ^ [_898104, _898106, _898108, _898110, _898112] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_898104, _898106, _898108)), _898110), _898112)), 7129 ^ _779530 : [(7130 ^ _779530) ^ [] : [-(_898112 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 7128 ^ [_898104, _898106, _898108, _898110, _898112]), c_Com_Ovname_OLoc(_898104)), c_Natural_Ogetlocs(_898110, _898104)))], (7132 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_898108), hAPP(hAPP(hAPP(c_Natural_Oupdate, _898110), c_Com_Ovname_OLoc(_898104)), hAPP(_898106, _898110))), 7128 ^ [_898104, _898106, _898108, _898110, _898112])))]]], (7134 ^ _779530) ^ [_898340, _898342, _898344, _898346, _898348, _898350] : [c_Natural_Oevaln(c_Com_Ocom_OLocal(_898340, _898342, _898344), _898346, _898348, _898350), 7138 ^ _779530 : [(7139 ^ _779530) ^ [] : [-(_898350 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 7137 ^ [_898340, _898342, _898344, _898346, _898348, _898350]), c_Com_Ovname_OLoc(_898340)), c_Natural_Ogetlocs(_898346, _898340)))], (7141 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_898344, hAPP(hAPP(hAPP(c_Natural_Oupdate, _898346), c_Com_Ovname_OLoc(_898340)), hAPP(_898342, _898346)), _898348, 7137 ^ [_898340, _898342, _898344, _898346, _898348, _898350]))]]], (7143 ^ _779530) ^ [_898562, _898564, _898566, _898568] : [-(c_Com_Ovname_Ovname__case(_898562, _898564, _898566, c_Com_Ovname_OGlb(_898568)) = hAPP(_898564, _898568))], (7145 ^ _779530) ^ [_898601, _898603, _898605, _898607] : [-(c_Com_Ovname_Ovname__rec(_898601, _898603, _898605, c_Com_Ovname_OGlb(_898607)) = hAPP(_898603, _898607))], (7161 ^ _779530) ^ [_898970, _898972, _898974, _898976, _898978] : [7164 ^ _779530 : [(7165 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_898974, 7162 ^ [_898970, _898972, _898974, _898976, _898978]), 7163 ^ [_898970, _898972, _898974, _898976, _898978])))], (7168 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_898976, 7163 ^ [_898970, _898972, _898974, _898976, _898978], _898972, 7166 ^ [_898970, _898972, _898974, _898976, _898978]))], (7170 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_898978, 7162 ^ [_898970, _898972, _898974, _898976, _898978]), 7166 ^ [_898970, _898972, _898974, _898976, _898978]))]], -(c_Hoare__Mirabelle_Otriple__valid(_898970, _898972, c_Hoare__Mirabelle_Otriple_Otriple(_898970, _898974, _898976, _898978)))], (7147 ^ _779530) ^ [_898664, _898666, _898668, _898670, _898672] : [c_Hoare__Mirabelle_Otriple__valid(_898664, _898666, c_Hoare__Mirabelle_Otriple_Otriple(_898664, _898668, _898670, _898672)), 7150 ^ _779530 : [(7151 ^ _779530) ^ [_898773, _898775] : [hBOOL(hAPP(hAPP(_898668, _898775), _898773)), 7154 ^ _779530 : [(7155 ^ _779530) ^ [_898863] : [c_Natural_Oevaln(_898670, _898773, _898666, _898863), -(hBOOL(hAPP(hAPP(_898672, _898775), _898863)))]]]]], (7174 ^ _779530) ^ [_899339, _899341, _899343, _899345] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_899339, _899341)), _899343), _899345)), 7178 ^ _779530 : [(7179 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899339), _899343), 7177 ^ [_899339, _899341, _899343, _899345])))], (7181 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899341), 7177 ^ [_899339, _899341, _899343, _899345]), _899345)))]]], (7183 ^ _779530) ^ [_899525, _899527, _899529, _899531, _899533] : [c_Natural_Oevaln(c_Com_Ocom_OSemi(_899525, _899527), _899529, _899531, _899533), 7187 ^ _779530 : [(7188 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_899525, _899529, _899531, 7186 ^ [_899525, _899527, _899529, _899531, _899533]))], (7190 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_899527, 7186 ^ [_899525, _899527, _899529, _899531, _899533], _899531, _899533))]]], (7192 ^ _779530) ^ [_899687, _899689, _899691, _899693, _899695, _899697, _899699, _899701, _899703, _899705, _899707] : [hAPP(_899687, hAPP(_899689, _899691)) = hAPP(_899693, hAPP(_899695, _899697)), -(hAPP(hAPP(c_Fun_Ocomp(_899699, _899701, _899703, _899687), _899689), _899691) = hAPP(hAPP(c_Fun_Ocomp(_899705, _899701, _899707, _899693), _899695), _899697))], (7198 ^ _779530) ^ [_899850, _899852, _899854, _899856] : [-(c_Fun_Ooverride__on(_899850, _899852, _899854, _899856, c_Orderings_Obot__class_Obot(tc_fun(_899850, tc_HOL_Obool))) = _899854)], (7200 ^ _779530) ^ [_899890, _899892, _899894, _899896] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_899890, _899892)), _899894), _899896)), 7205 ^ _779530 : [(7206 ^ _779530) ^ [] : [-(_899896 = _899894)], (7208 ^ _779530) ^ [] : [hBOOL(hAPP(_899890, _899894))]], 7209 ^ _779530 : [(7210 ^ _779530) ^ [] : [-(hBOOL(hAPP(_899890, _899894)))], (7213 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_899892), _899894), 7211 ^ [_899890, _899892, _899894, _899896])))], (7215 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_899890, _899892)), 7211 ^ [_899890, _899892, _899894, _899896]), _899896)))]]], (7217 ^ _779530) ^ [_900218, _900220] : [c_Com_Ovname_OGlb(_900218) = c_Com_Ovname_OGlb(_900220), -(_900218 = _900220)], (7223 ^ _779530) ^ [_900299, _900301] : [_900299 = _900301, -(c_Com_Ovname_OGlb(_900299) = c_Com_Ovname_OGlb(_900301))], (7229 ^ _779530) ^ [_900398, _900400] : [c_Com_Ovname_OGlb(_900398) = c_Com_Ovname_OLoc(_900400)], (7231 ^ _779530) ^ [_900439, _900441] : [c_Com_Ovname_OLoc(_900439) = c_Com_Ovname_OGlb(_900441)], (7233 ^ _779530) ^ [_900468] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900468), _900468)))], (7235 ^ _779530) ^ [_900492, _900494] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900492), _900494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900494), _900492)))], (7241 ^ _779530) ^ [_900538, _900540] : [_900538 = _900540, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900538), _900540)))], (7247 ^ _779530) ^ [_900625, _900627, _900629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900625), _900627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900627), _900629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900625), _900629)))], (7257 ^ _779530) ^ [_900788, _900790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900788), _900790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _900790), _900788)), -(_900788 = _900790)], (7267 ^ _779530) ^ [_900937, _900939, _900941, _900943, _900945] : [c_Natural_Oevaln(c_Com_Ocom_OWhile(_900937, _900939), _900941, _900943, _900945), 7272 ^ _779530 : [(7273 ^ _779530) ^ [] : [-(_900945 = _900941)], (7275 ^ _779530) ^ [] : [hBOOL(hAPP(_900937, _900941))]], 7276 ^ _779530 : [(7277 ^ _779530) ^ [] : [-(hBOOL(hAPP(_900937, _900941)))], (7280 ^ _779530) ^ [] : [-(c_Natural_Oevaln(_900939, _900941, _900943, 7278 ^ [_900937, _900939, _900941, _900943, _900945]))], (7282 ^ _779530) ^ [] : [-(c_Natural_Oevaln(c_Com_Ocom_OWhile(_900937, _900939), 7278 ^ [_900937, _900939, _900941, _900943, _900945], _900943, _900945))]]], (7284 ^ _779530) ^ [_901228, _901230, _901232] : [class_Orderings_Oorder(_901228), hBOOL(hAPP(_901230, _901232)), 7294 ^ _779530 : [(7295 ^ _779530) ^ [] : [-(hBOOL(hAPP(_901230, 7293 ^ [_901228, _901230, _901232])))], (7297 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901228), _901232), 7293 ^ [_901228, _901230, _901232]))]], -(c_Orderings_Oord__class_OLeast(_901228, _901230) = _901232)], (7301 ^ _779530) ^ [_901517, _901519, _901521] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_901517), _901519), _901521)), -(c_Natural_Oevaln(_901517, _901519, 7304 ^ [_901517, _901519, _901521], _901521))], (7308 ^ _779530) ^ [_901628, _901630, _901632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901628, tc_HOL_Obool)), _901630), _901632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_901628, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_901628), _901630)), hAPP(c_Set_OPow(_901628), _901632))))], (7314 ^ _779530) ^ [_901773, _901775, _901777] : [hBOOL(hAPP(_901773, _901775)), 7320 ^ _779530 : [(7321 ^ _779530) ^ [] : [-(hBOOL(hAPP(_901773, 7319 ^ [_901773, _901775, _901777])))], (7323 ^ _779530) ^ [] : [7319 ^ [_901773, _901775, _901777] = _901775]], -(c_HOL_OThe(_901777, _901773) = _901775)], (7327 ^ _779530) ^ [_901989, _901991] : [-(hAPP(c_Set_OCollect(_901989), hAPP(c_fequal, _901991)) = hAPP(hAPP(c_Set_Oinsert(_901989), _901991), c_Orderings_Obot__class_Obot(tc_fun(_901989, tc_HOL_Obool))))], (7329 ^ _779530) ^ [_902035, _902037] : [-(hAPP(c_Set_OCollect(_902035), _902037) = _902037)], (7331 ^ _779530) ^ [_902077, _902079] : [hAPP(c_Set_OPow(_902077), _902079) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_902077, tc_HOL_Obool), tc_HOL_Obool))], (7333 ^ _779530) ^ [_902115, _902117] : [-(hAPP(c_Set_OPow(_902115), _902117) = hAPP(c_Set_OCollect(tc_fun(_902115, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_902115, tc_HOL_Obool), tc_fun(_902115, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_902115, tc_HOL_Obool))), _902117)))], (7335 ^ _779530) ^ [_902189, _902191] : [hAPP(c_Set_OCollect(_902189), _902191) = c_Orderings_Obot__class_Obot(tc_fun(_902189, tc_HOL_Obool)), 7338 ^ _779530 : [(7339 ^ _779530) ^ [_902274] : [hBOOL(hAPP(_902191, _902274))]]], (7341 ^ _779530) ^ [_902297, _902299] : [-(hBOOL(hAPP(_902299, 7342 ^ [_902297, _902299]))), -(hAPP(c_Set_OCollect(_902297), _902299) = c_Orderings_Obot__class_Obot(tc_fun(_902297, tc_HOL_Obool)))], (7348 ^ _779530) ^ [_902369, _902371] : [c_Orderings_Obot__class_Obot(tc_fun(_902369, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_902369), _902371), 7351 ^ _779530 : [(7352 ^ _779530) ^ [_902454] : [hBOOL(hAPP(_902371, _902454))]]], (7354 ^ _779530) ^ [_902477, _902479] : [-(hBOOL(hAPP(_902479, 7355 ^ [_902477, _902479]))), -(c_Orderings_Obot__class_Obot(tc_fun(_902477, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_902477), _902479))], (7361 ^ _779530) ^ [_902534] : [-(hAPP(c_Set_OPow(_902534), c_Orderings_Obot__class_Obot(tc_fun(_902534, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_902534, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_902534, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_902534, tc_HOL_Obool), tc_HOL_Obool))))], (7363 ^ _779530) ^ [_902591] : [-(c_Orderings_Obot__class_Obot(tc_fun(_902591, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_902591), hAPP(c_COMBK(tc_HOL_Obool, _902591), c_fFalse)))], (7365 ^ _779530) ^ [_902630, _902632, _902634] : [-(hAPP(hAPP(c_Set_Oinsert(_902630), _902632), hAPP(c_Set_OCollect(_902630), _902634)) = hAPP(c_Set_OCollect(_902630), hAPP(hAPP(c_COMBS(_902630, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _902630), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _902630), c_fNot), hAPP(hAPP(c_COMBC(_902630, _902630, tc_HOL_Obool), c_fequal), _902632)))), _902634)))], (7367 ^ _779530) ^ [_902727, _902729, _902731] : [hBOOL(hAPP(_902727, _902729)), -(hAPP(c_Set_OCollect(_902731), hAPP(hAPP(c_COMBS(_902731, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _902731), c_fconj), hAPP(hAPP(c_COMBC(_902731, _902731, tc_HOL_Obool), c_fequal), _902729))), _902727)) = hAPP(hAPP(c_Set_Oinsert(_902731), _902729), c_Orderings_Obot__class_Obot(tc_fun(_902731, tc_HOL_Obool))))], (7373 ^ _779530) ^ [_902900, _902902, _902904] : [-(hBOOL(hAPP(_902900, _902902))), -(hAPP(c_Set_OCollect(_902904), hAPP(hAPP(c_COMBS(_902904, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _902904), c_fconj), hAPP(hAPP(c_COMBC(_902904, _902904, tc_HOL_Obool), c_fequal), _902902))), _902900)) = c_Orderings_Obot__class_Obot(tc_fun(_902904, tc_HOL_Obool)))], (7379 ^ _779530) ^ [_902994, _902996, _902998] : [hBOOL(hAPP(_902994, _902996)), -(hAPP(c_Set_OCollect(_902998), hAPP(hAPP(c_COMBS(_902998, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _902998), c_fconj), hAPP(c_fequal, _902996))), _902994)) = hAPP(hAPP(c_Set_Oinsert(_902998), _902996), c_Orderings_Obot__class_Obot(tc_fun(_902998, tc_HOL_Obool))))], (7385 ^ _779530) ^ [_903153, _903155, _903157] : [-(hBOOL(hAPP(_903153, _903155))), -(hAPP(c_Set_OCollect(_903157), hAPP(hAPP(c_COMBS(_903157, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _903157), c_fconj), hAPP(c_fequal, _903155))), _903153)) = c_Orderings_Obot__class_Obot(tc_fun(_903157, tc_HOL_Obool)))], (7391 ^ _779530) ^ [_903228, _903230] : [-(hAPP(c_Set_OCollect(_903228), hAPP(hAPP(c_COMBC(_903228, _903228, tc_HOL_Obool), c_fequal), _903230)) = hAPP(hAPP(c_Set_Oinsert(_903228), _903230), c_Orderings_Obot__class_Obot(tc_fun(_903228, tc_HOL_Obool))))], (7393 ^ _779530) ^ [_903281, _903283, _903285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903281, tc_HOL_Obool)), _903283), _903285)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_903281, tc_HOL_Obool)), _903283), hAPP(c_Set_OPow(_903281), _903285))))], (7399 ^ _779530) ^ [_903410, _903412, _903414] : [7401 ^ _779530 : [(7402 ^ _779530) ^ [] : [-(hBOOL(hAPP(_903410, 7400 ^ [_903410, _903412, _903414])))], (7404 ^ _779530) ^ [] : [hBOOL(hAPP(_903412, 7400 ^ [_903410, _903412, _903414]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903414, tc_HOL_Obool)), hAPP(c_Set_OCollect(_903414), _903410)), hAPP(c_Set_OCollect(_903414), _903412))))], (7408 ^ _779530) ^ [_903608, _903610, _903612] : [-(hAPP(hAPP(c_Set_Oinsert(_903608), _903610), _903612) = hAPP(c_Set_OCollect(_903608), hAPP(hAPP(c_COMBS(_903608, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _903608), c_fdisj), hAPP(hAPP(c_COMBC(_903608, _903608, tc_HOL_Obool), c_fequal), _903610))), hAPP(hAPP(c_COMBC(_903608, tc_fun(_903608, tc_HOL_Obool), tc_HOL_Obool), c_member(_903608)), _903612))))], (7410 ^ _779530) ^ [_903693, _903695, _903697] : [-(hAPP(hAPP(c_Set_Oinsert(_903693), _903695), _903697) = hAPP(c_Set_OCollect(_903693), hAPP(hAPP(c_COMBS(_903693, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _903693), c_fdisj), hAPP(hAPP(c_COMBC(_903693, _903693, tc_HOL_Obool), c_fequal), _903695))), hAPP(hAPP(c_COMBC(_903693, tc_fun(_903693, tc_HOL_Obool), tc_HOL_Obool), c_member(_903693)), _903697))))], (7412 ^ _779530) ^ [_903778, _903780, _903782] : [-(hAPP(hAPP(c_Set_Oinsert(_903778), _903780), _903782) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903778, tc_HOL_Obool)), hAPP(c_Set_OCollect(_903778), hAPP(hAPP(c_COMBC(_903778, _903778, tc_HOL_Obool), c_fequal), _903780))), _903782))], (7414 ^ _779530) ^ [_903857, _903859, _903861] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_903857, tc_HOL_Obool)), _903859), hAPP(c_Set_OPow(_903857), _903861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903857, tc_HOL_Obool)), _903859), _903861)))], (7420 ^ _779530) ^ [_903982, _903984, _903986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903982, tc_HOL_Obool)), _903984), _903986)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_903982, tc_HOL_Obool)), _903984), hAPP(c_Set_OPow(_903982), _903986))))], (7426 ^ _779530) ^ [_904113, _904115, _904117] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_904113, tc_HOL_Obool)), _904115), hAPP(c_Set_OPow(_904113), _904117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904113, tc_HOL_Obool)), _904115), _904117)))], (7432 ^ _779530) ^ [_904242, _904244] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_904242, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_904242, tc_HOL_Obool))), hAPP(c_Set_OPow(_904242), _904244))))], (7434 ^ _779530) ^ [_904302, _904304, _904306, _904308] : [_904302 = c_Orderings_Obot__class_Obot(tc_fun(_904304, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_904304, _904306, hAPP(c_COMBK(_904306, _904304), _904308)), _904302) = c_Orderings_Obot__class_Obot(tc_fun(_904306, tc_HOL_Obool)))], (7440 ^ _779530) ^ [_904423, _904425, _904427, _904429] : [-(_904423 = c_Orderings_Obot__class_Obot(tc_fun(_904425, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_904425, _904427, hAPP(c_COMBK(_904427, _904425), _904429)), _904423) = hAPP(hAPP(c_Set_Oinsert(_904427), _904429), c_Orderings_Obot__class_Obot(tc_fun(_904427, tc_HOL_Obool))))], (7446 ^ _779530) ^ [_904496, _904498, _904500] : [class_Orderings_Oorder(_904496), class_Orderings_Oorder(_904498), c_Orderings_Oorder__class_Ostrict__mono(_904498, _904496, _904500), -(c_Orderings_Oorder__class_Omono(_904498, _904496, _904500))], (7460 ^ _779530) ^ [_904684, _904686, _904688, _904690] : [-(hBOOL(hAPP(hAPP(c_member(_904684), _904686), _904688))), 7463 ^ _779530 : [(7464 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904684, tc_HOL_Obool)), _904688), hAPP(hAPP(c_Set_Oinsert(_904684), _904686), _904690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904684, tc_HOL_Obool)), _904688), _904690)))], (7470 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904684, tc_HOL_Obool)), _904688), _904690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904684, tc_HOL_Obool)), _904688), hAPP(hAPP(c_Set_Oinsert(_904684), _904686), _904690))))]]], (7476 ^ _779530) ^ [_904992, _904994, _904996, _904998] : [_904992 = _904994, 7481 ^ _779530 : [(7482 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_904996), _904998), _904992)))], (7484 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_904996), _904998), _904994)))]], 7485 ^ _779530 : [(7486 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_904996), _904998), _904992))], (7488 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_904996), _904998), _904994))]]], (7490 ^ _779530) ^ [_905255, _905257, _905259, _905261] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905255, tc_HOL_Obool)), _905257), _905259), _905261)), -(hBOOL(hAPP(_905257, _905261))), -(hBOOL(hAPP(_905259, _905261)))], (7500 ^ _779530) ^ [_905385, _905387, _905389, _905391] : [7501 ^ _779530 : [(7502 ^ _779530) ^ [] : [hBOOL(hAPP(_905385, _905387))], (7504 ^ _779530) ^ [] : [hBOOL(hAPP(_905389, _905387))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905391, tc_HOL_Obool)), _905389), _905385), _905387)))], (7508 ^ _779530) ^ [_905552, _905554] : [hBOOL(hAPP(hAPP(c_member(_905552), _905554), c_Orderings_Obot__class_Obot(tc_fun(_905552, tc_HOL_Obool))))], (7510 ^ _779530) ^ [_905589, _905591, _905593, _905595] : [hBOOL(hAPP(hAPP(c_member(_905589), _905591), hAPP(hAPP(c_Set_Oinsert(_905589), _905593), _905595))), -(_905591 = _905593), -(hBOOL(hAPP(hAPP(c_member(_905589), _905591), _905595)))], (7520 ^ _779530) ^ [_905729, _905731, _905733, _905735] : [7521 ^ _779530 : [(7522 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_905729), _905731), _905733))], (7524 ^ _779530) ^ [] : [_905731 = _905735]], -(hBOOL(hAPP(hAPP(c_member(_905729), _905731), hAPP(hAPP(c_Set_Oinsert(_905729), _905735), _905733))))], (7528 ^ _779530) ^ [_905894, _905896, _905898, _905900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905894, tc_HOL_Obool)), _905896), _905898)), hBOOL(hAPP(hAPP(c_member(_905894), _905900), _905896)), -(hBOOL(hAPP(hAPP(c_member(_905894), _905900), _905898)))], (7538 ^ _779530) ^ [_906079, _906081, _906083, _906085, _906087, _906089] : [_906079 = hAPP(_906081, _906083), hBOOL(hAPP(hAPP(c_member(_906085), _906083), _906087)), -(hBOOL(hAPP(hAPP(c_member(_906089), _906079), hAPP(c_Set_Oimage(_906085, _906089, _906081), _906087))))], (7548 ^ _779530) ^ [_906272, _906274, _906276, _906278] : [hBOOL(hAPP(hAPP(c_member(_906272), _906274), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906272, tc_HOL_Obool)), _906276), _906278))), -(hBOOL(hAPP(hAPP(c_member(_906272), _906274), _906276))), -(hBOOL(hAPP(hAPP(c_member(_906272), _906274), _906278)))], (7558 ^ _779530) ^ [_906432, _906434, _906436, _906438] : [7559 ^ _779530 : [(7560 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_906432), _906434), _906436))], (7562 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_906432), _906434), _906438))]], -(hBOOL(hAPP(hAPP(c_member(_906432), _906434), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906432, tc_HOL_Obool)), _906438), _906436))))], (7566 ^ _779530) ^ [_906617, _906619, _906621] : [hBOOL(hAPP(_906617, _906619)), -(hBOOL(hAPP(hAPP(c_member(_906621), _906619), hAPP(c_Set_OCollect(_906621), _906617))))], (7572 ^ _779530) ^ [_906724, _906726] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906724, tc_HOL_Obool)), _906726), _906726) = _906726)], (7574 ^ _779530) ^ [_906778, _906780, _906782] : [hBOOL(hAPP(hAPP(c_member(_906778), _906780), _906782)), -(hBOOL(hAPP(_906782, _906780)))], (7580 ^ _779530) ^ [_906871, _906873, _906875] : [hBOOL(hAPP(_906875, _906873)), -(hBOOL(hAPP(hAPP(c_member(_906871), _906873), _906875)))], (7586 ^ _779530) ^ [_906970, _906972, _906974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906970, tc_HOL_Obool)), _906972), _906974) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_906970, tc_HOL_Obool)), _906974), _906972))], (7588 ^ _779530) ^ [_907019, _907021, _907023] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907019, tc_HOL_Obool)), _907021), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907019, tc_HOL_Obool)), _907021), _907023)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907019, tc_HOL_Obool)), _907021), _907023))], (7590 ^ _779530) ^ [_907103, _907105, _907107, _907109, _907111] : [hBOOL(hAPP(hAPP(c_member(_907103), _907105), hAPP(c_Set_Oimage(_907107, _907103, _907109), _907111))), 7594 ^ _779530 : [(7595 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907107), 7593 ^ [_907103, _907105, _907107, _907109, _907111]), _907111)))], (7597 ^ _779530) ^ [] : [-(_907105 = hAPP(_907109, 7593 ^ [_907103, _907105, _907107, _907109, _907111]))]]], (7599 ^ _779530) ^ [_907287, _907289, _907291, _907293, _907295] : [-(hBOOL(hAPP(hAPP(c_member(_907287), _907289), hAPP(c_Set_Oimage(_907291, _907287, _907293), _907295)))), 7600 ^ _779530 : [(7601 ^ _779530) ^ [_907357] : [hBOOL(hAPP(hAPP(c_member(_907291), _907357), _907295)), _907289 = hAPP(_907293, _907357)]]], (7609 ^ _779530) ^ [_907505, _907507, _907509, _907511] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907505, tc_HOL_Obool)), _907507), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907505, tc_HOL_Obool)), _907509), _907511)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907505, tc_HOL_Obool)), _907509), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907505, tc_HOL_Obool)), _907507), _907511)))], (7611 ^ _779530) ^ [_907578, _907580, _907582, _907584, _907586] : [-(hAPP(c_Set_Oimage(_907578, _907580, _907582), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907578, tc_HOL_Obool)), _907584), _907586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907580, tc_HOL_Obool)), hAPP(c_Set_Oimage(_907578, _907580, _907582), _907584)), hAPP(c_Set_Oimage(_907578, _907580, _907582), _907586)))], (7623 ^ _779530) ^ [_907827, _907829, _907831, _907833] : [7624 ^ _779530 : [(7625 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907827), _907829), _907831))], (7627 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907827), _907829), _907833))]], -(hBOOL(hAPP(hAPP(c_member(_907827), _907829), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907827, tc_HOL_Obool)), _907831), _907833))))], (7613 ^ _779530) ^ [_907673, _907675, _907677, _907679] : [hBOOL(hAPP(hAPP(c_member(_907673), _907675), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907673, tc_HOL_Obool)), _907677), _907679))), -(hBOOL(hAPP(hAPP(c_member(_907673), _907675), _907677))), -(hBOOL(hAPP(hAPP(c_member(_907673), _907675), _907679)))], (7631 ^ _779530) ^ [_908012, _908014, _908016, _908018] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908012, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908012, tc_HOL_Obool)), _908014), _908016)), _908018) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908012, tc_HOL_Obool)), _908014), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908012, tc_HOL_Obool)), _908016), _908018)))], (7633 ^ _779530) ^ [_908106, _908108, _908110, _908112] : [7634 ^ _779530 : [(7635 ^ _779530) ^ [_908216] : [hBOOL(hAPP(hAPP(c_member(_908106), _908216), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908106, tc_HOL_Obool)), _908108), _908110))), hBOOL(hAPP(_908112, _908216))]], 7643 ^ _779530 : [(7644 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908106), 7642 ^ [_908106, _908108, _908110, _908112]), _908108)))], (7646 ^ _779530) ^ [] : [-(hBOOL(hAPP(_908112, 7642 ^ [_908106, _908108, _908110, _908112])))]], 7648 ^ _779530 : [(7649 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908106), 7647 ^ [_908106, _908108, _908110, _908112]), _908110)))], (7651 ^ _779530) ^ [] : [-(hBOOL(hAPP(_908112, 7647 ^ [_908106, _908108, _908110, _908112])))]]], (7653 ^ _779530) ^ [_908505, _908507, _908509, _908511] : [7667 ^ _779530 : [(7668 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908505), 7666 ^ [_908505, _908507, _908509, _908511]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908505, tc_HOL_Obool)), _908507), _908509))))], (7670 ^ _779530) ^ [] : [-(hBOOL(hAPP(_908511, 7666 ^ [_908505, _908507, _908509, _908511])))]], 7654 ^ _779530 : [(7655 ^ _779530) ^ [_908618] : [hBOOL(hAPP(hAPP(c_member(_908505), _908618), _908507)), hBOOL(hAPP(_908511, _908618))], (7661 ^ _779530) ^ [_908714] : [hBOOL(hAPP(hAPP(c_member(_908505), _908714), _908509)), hBOOL(hAPP(_908511, _908714))]]], (7691 ^ _779530) ^ [_909351, _909353, _909355, _909357] : [7695 ^ _779530 : [(7696 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909351), 7694 ^ [_909351, _909353, _909355, _909357]), _909353)))], (7698 ^ _779530) ^ [] : [hBOOL(hAPP(_909357, 7694 ^ [_909351, _909353, _909355, _909357]))]], 7700 ^ _779530 : [(7701 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_909351), 7699 ^ [_909351, _909353, _909355, _909357]), _909355)))], (7703 ^ _779530) ^ [] : [hBOOL(hAPP(_909357, 7699 ^ [_909351, _909353, _909355, _909357]))]], 7704 ^ _779530 : [(7705 ^ _779530) ^ [_909684] : [hBOOL(hAPP(hAPP(c_member(_909351), _909684), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909351, tc_HOL_Obool)), _909353), _909355))), -(hBOOL(hAPP(_909357, _909684)))]]], (7672 ^ _779530) ^ [_908929, _908931, _908933, _908935] : [7674 ^ _779530 : [(7675 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_908929), 7673 ^ [_908929, _908931, _908933, _908935]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_908929, tc_HOL_Obool)), _908931), _908933))))], (7677 ^ _779530) ^ [] : [hBOOL(hAPP(_908935, 7673 ^ [_908929, _908931, _908933, _908935]))]], 7678 ^ _779530 : [(7679 ^ _779530) ^ [_909149] : [hBOOL(hAPP(hAPP(c_member(_908929), _909149), _908931)), -(hBOOL(hAPP(_908935, _909149)))], (7685 ^ _779530) ^ [_909246] : [hBOOL(hAPP(hAPP(c_member(_908929), _909246), _908933)), -(hBOOL(hAPP(_908935, _909246)))]]], (7711 ^ _779530) ^ [_909815, _909817, _909819, _909821] : [hBOOL(hAPP(hAPP(c_member(_909815), _909817), _909819)), -(hBOOL(hAPP(hAPP(c_member(_909815), _909817), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909815, tc_HOL_Obool)), _909819), _909821))))], (7717 ^ _779530) ^ [_909946, _909948, _909950, _909952] : [hBOOL(hAPP(hAPP(c_member(_909946), _909948), _909950)), -(hBOOL(hAPP(hAPP(c_member(_909946), _909948), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_909946, tc_HOL_Obool)), _909952), _909950))))], (7723 ^ _779530) ^ [_910077, _910079, _910081, _910083, _910085] : [hBOOL(hAPP(hAPP(c_member(_910077), _910079), _910081)), -(hBOOL(hAPP(hAPP(c_member(_910083), hAPP(_910085, _910079)), hAPP(c_Set_Oimage(_910077, _910083, _910085), _910081))))], (7729 ^ _779530) ^ [_910208, _910210, _910212, _910214] : [_910208 = _910210, 7732 ^ _779530 : [(7733 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910212), _910214), _910208)), -(hBOOL(hAPP(hAPP(c_member(_910212), _910214), _910210)))], (7739 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910212), _910214), _910210)), -(hBOOL(hAPP(hAPP(c_member(_910212), _910214), _910208)))]]], (7745 ^ _779530) ^ [_910469, _910471, _910473, _910475] : [_910469 = _910471, 7748 ^ _779530 : [(7749 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910473), _910469), _910475)), -(hBOOL(hAPP(hAPP(c_member(_910473), _910471), _910475)))], (7755 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910473), _910471), _910475)), -(hBOOL(hAPP(hAPP(c_member(_910473), _910469), _910475)))]]], (7761 ^ _779530) ^ [_910730, _910732, _910734, _910736] : [_910730 = _910732, hBOOL(hAPP(hAPP(c_member(_910734), _910732), _910736)), -(hBOOL(hAPP(hAPP(c_member(_910734), _910730), _910736)))], (7771 ^ _779530) ^ [_910895, _910897, _910899, _910901, _910903, _910905] : [hBOOL(hAPP(hAPP(c_member(_910895), _910897), _910899)), _910901 = hAPP(_910903, _910897), -(hBOOL(hAPP(hAPP(c_member(_910905), _910901), hAPP(c_Set_Oimage(_910895, _910905, _910903), _910899))))], (7781 ^ _779530) ^ [_911106, _911108, _911110] : [hBOOL(hAPP(hAPP(c_member(_911106), _911108), hAPP(c_fequal, _911110))), -(_911108 = _911110)], (7787 ^ _779530) ^ [_911201, _911203, _911205] : [_911203 = _911205, -(hBOOL(hAPP(hAPP(c_member(_911201), _911203), hAPP(c_fequal, _911205))))], (7793 ^ _779530) ^ [_911323, _911325, _911327, _911329] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911323, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_911323, tc_fun(_911323, tc_HOL_Obool), tc_HOL_Obool), c_member(_911323)), _911325)), hAPP(hAPP(c_COMBC(_911323, tc_fun(_911323, tc_HOL_Obool), tc_HOL_Obool), c_member(_911323)), _911327)), _911329)), -(hBOOL(hAPP(hAPP(c_member(_911323), _911329), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911323, tc_HOL_Obool)), _911325), _911327))))], (7799 ^ _779530) ^ [_911522, _911524, _911526, _911528] : [hBOOL(hAPP(hAPP(c_member(_911522), _911528), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911522, tc_HOL_Obool)), _911524), _911526))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911522, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_911522, tc_fun(_911522, tc_HOL_Obool), tc_HOL_Obool), c_member(_911522)), _911524)), hAPP(hAPP(c_COMBC(_911522, tc_fun(_911522, tc_HOL_Obool), tc_HOL_Obool), c_member(_911522)), _911526)), _911528)))], (7805 ^ _779530) ^ [_911727, _911729, _911731, _911733] : [hBOOL(hAPP(_911727, _911729)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911731, tc_HOL_Obool)), _911727), _911733), _911729)))], (7811 ^ _779530) ^ [_911838, _911840, _911842, _911844] : [hBOOL(hAPP(_911838, _911840)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_911842, tc_HOL_Obool)), _911844), _911838), _911840)))], (7817 ^ _779530) ^ [_911949, _911951, _911953, _911955, _911957] : [hBOOL(hAPP(hAPP(c_member(_911949), _911951), _911953)), -(hAPP(hAPP(c_Set_Oinsert(_911955), hAPP(_911957, _911951)), hAPP(c_Set_Oimage(_911949, _911955, _911957), _911953)) = hAPP(c_Set_Oimage(_911949, _911955, _911957), _911953))], (7823 ^ _779530) ^ [_912096, _912098, _912100, _912102, _912104, _912106] : [-(hAPP(c_Set_Oimage(_912096, _912098, _912100), hAPP(c_Set_Oimage(_912102, _912096, _912104), _912106)) = hAPP(c_Set_Oimage(_912102, _912098, hAPP(hAPP(c_COMBB(_912096, _912098, _912102), _912100), _912104)), _912106))], (7825 ^ _779530) ^ [_912160, _912162] : [-(hAPP(c_Set_Oimage(_912160, _912160, c_COMBI(_912160)), _912162) = _912162)], (7827 ^ _779530) ^ [_912194, _912196, _912198, _912200, _912202] : [hAPP(c_Set_Oimage(_912194, _912196, _912198), _912200) = _912202, -(hAPP(c_Set_Oimage(tc_fun(_912194, tc_HOL_Obool), tc_fun(_912196, tc_HOL_Obool), c_Set_Oimage(_912194, _912196, _912198)), hAPP(c_Set_OPow(_912194), _912200)) = hAPP(c_Set_OPow(_912196), _912202))], (7833 ^ _779530) ^ [_912345, _912347, _912349, _912351, _912353] : [c_Orderings_Oorder__class_Omono(tc_fun(_912345, tc_HOL_Obool), tc_fun(_912347, tc_HOL_Obool), _912349), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912347, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912347, tc_HOL_Obool)), hAPP(_912349, _912351)), hAPP(_912349, _912353))), hAPP(_912349, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912345, tc_HOL_Obool)), _912351), _912353)))))], (7839 ^ _779530) ^ [_912542, _912544, _912546] : [hAPP(hAPP(c_COMBC(_912542, tc_fun(_912542, tc_HOL_Obool), tc_HOL_Obool), c_member(_912542)), _912544) = hAPP(hAPP(c_COMBC(_912542, tc_fun(_912542, tc_HOL_Obool), tc_HOL_Obool), c_member(_912542)), _912546), -(_912544 = _912546)], (7845 ^ _779530) ^ [_912677, _912679, _912681] : [_912679 = _912681, -(hAPP(hAPP(c_COMBC(_912677, tc_fun(_912677, tc_HOL_Obool), tc_HOL_Obool), c_member(_912677)), _912679) = hAPP(hAPP(c_COMBC(_912677, tc_fun(_912677, tc_HOL_Obool), tc_HOL_Obool), c_member(_912677)), _912681))], (7851 ^ _779530) ^ [_912818, _912820, _912822] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912818, tc_HOL_Obool)), _912820), _912822) = hAPP(c_Set_OCollect(_912818), hAPP(hAPP(c_COMBS(_912818, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _912818), c_fdisj), hAPP(hAPP(c_COMBC(_912818, tc_fun(_912818, tc_HOL_Obool), tc_HOL_Obool), c_member(_912818)), _912820))), hAPP(hAPP(c_COMBC(_912818, tc_fun(_912818, tc_HOL_Obool), tc_HOL_Obool), c_member(_912818)), _912822))))], (7853 ^ _779530) ^ [_912911, _912913, _912915, _912917] : [class_Orderings_Oorder(_912911), class_Orderings_Oorder(_912913), c_Orderings_Oorder__class_Omono(_912913, _912911, _912915), -(c_Orderings_Oord__class_OLeast(_912911, hAPP(hAPP(c_COMBC(_912911, tc_fun(_912911, tc_HOL_Obool), tc_HOL_Obool), c_member(_912911)), hAPP(c_Set_Oimage(_912913, _912911, _912915), _912917))) = hAPP(_912915, c_Orderings_Oord__class_OLeast(_912913, hAPP(hAPP(c_COMBC(_912913, tc_fun(_912913, tc_HOL_Obool), tc_HOL_Obool), c_member(_912913)), _912917)))), 7866 ^ _779530 : [(7867 ^ _779530) ^ [_913195] : [hBOOL(hAPP(hAPP(c_member(_912913), _913195), _912917)), 7871 ^ _779530 : [(7872 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912913), 7870 ^ [_912911, _912913, _912915, _912917, _913195]), _912917)))], (7874 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912913), _913195), 7870 ^ [_912911, _912913, _912915, _912917, _913195]))]]]]], (7878 ^ _779530) ^ [_913488, _913490, _913492] : [-(hAPP(c_Set_OPow(_913488), hAPP(hAPP(c_Set_Oinsert(_913488), _913490), _913492)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_913488, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_913488), _913492)), hAPP(c_Set_Oimage(tc_fun(_913488, tc_HOL_Obool), tc_fun(_913488, tc_HOL_Obool), hAPP(c_Set_Oinsert(_913488), _913490)), hAPP(c_Set_OPow(_913488), _913492))))], (7880 ^ _779530) ^ [_913591, _913593, _913595, _913597] : [c_Orderings_Obot__class_Obot(tc_fun(_913591, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_913593, _913591, _913595), _913597), -(_913597 = c_Orderings_Obot__class_Obot(tc_fun(_913593, tc_HOL_Obool)))], (7886 ^ _779530) ^ [_913702, _913704, _913706, _913708] : [_913708 = c_Orderings_Obot__class_Obot(tc_fun(_913704, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_913702, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_913704, _913702, _913706), _913708))], (7892 ^ _779530) ^ [_913819, _913821, _913823] : [-(hAPP(c_Set_Oimage(_913819, _913821, _913823), c_Orderings_Obot__class_Obot(tc_fun(_913819, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_913821, tc_HOL_Obool)))], (7894 ^ _779530) ^ [_913884, _913886, _913888, _913890] : [hAPP(c_Set_Oimage(_913884, _913886, _913888), _913890) = c_Orderings_Obot__class_Obot(tc_fun(_913886, tc_HOL_Obool)), -(_913890 = c_Orderings_Obot__class_Obot(tc_fun(_913884, tc_HOL_Obool)))], (7900 ^ _779530) ^ [_913995, _913997, _913999, _914001] : [_914001 = c_Orderings_Obot__class_Obot(tc_fun(_913995, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_913995, _913997, _913999), _914001) = c_Orderings_Obot__class_Obot(tc_fun(_913997, tc_HOL_Obool)))], (7906 ^ _779530) ^ [_914112, _914114, _914116, _914118, _914120] : [-(hAPP(c_Set_Oimage(_914112, _914114, _914116), hAPP(hAPP(c_Set_Oinsert(_914112), _914118), _914120)) = hAPP(hAPP(c_Set_Oinsert(_914114), hAPP(_914116, _914118)), hAPP(c_Set_Oimage(_914112, _914114, _914116), _914120)))], (7908 ^ _779530) ^ [_914200, _914202, _914204, _914206, _914208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914200, tc_HOL_Obool)), _914202), hAPP(c_Set_Oimage(_914204, _914200, _914206), _914208))), 7912 ^ _779530 : [(7913 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914204, tc_HOL_Obool)), 7911 ^ [_914200, _914202, _914204, _914206, _914208]), _914208)))], (7915 ^ _779530) ^ [] : [-(_914202 = hAPP(c_Set_Oimage(_914204, _914200, _914206), 7911 ^ [_914200, _914202, _914204, _914206, _914208]))]]], (7917 ^ _779530) ^ [_914404, _914406, _914408, _914410, _914412] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914404, tc_HOL_Obool)), _914406), hAPP(c_Set_Oimage(_914408, _914404, _914410), _914412)))), 7918 ^ _779530 : [(7919 ^ _779530) ^ [_914484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914408, tc_HOL_Obool)), _914484), _914412)), _914406 = hAPP(c_Set_Oimage(_914408, _914404, _914410), _914484)]]], (7927 ^ _779530) ^ [_914649, _914651, _914653, _914655, _914657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914649, tc_HOL_Obool)), _914651), _914653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914655, tc_HOL_Obool)), hAPP(c_Set_Oimage(_914649, _914655, _914657), _914651)), hAPP(c_Set_Oimage(_914649, _914655, _914657), _914653))))], (7933 ^ _779530) ^ [_914800, _914802, _914804, _914806, _914808, _914810] : [-(hAPP(c_Set_Oimage(_914800, _914802, hAPP(c_Fun_Ocomp(_914804, _914802, _914800, _914806), _914808)), _914810) = hAPP(c_Set_Oimage(_914804, _914802, _914806), hAPP(c_Set_Oimage(_914800, _914804, _914808), _914810)))], (7935 ^ _779530) ^ [_914862, _914864, _914866, _914868, _914870] : [hBOOL(hAPP(hAPP(c_member(_914862), _914864), _914866)), -(hAPP(c_Set_Oimage(_914862, _914868, hAPP(c_COMBK(_914868, _914862), _914870)), _914866) = hAPP(hAPP(c_Set_Oinsert(_914868), _914870), c_Orderings_Obot__class_Obot(tc_fun(_914868, tc_HOL_Obool))))], (7941 ^ _779530) ^ [_915011, _915013] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915011, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_915011, tc_HOL_Obool))), _915013) = _915013)], (7943 ^ _779530) ^ [_915052, _915054] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915052, tc_HOL_Obool)), _915054), c_Orderings_Obot__class_Obot(tc_fun(_915052, tc_HOL_Obool))) = _915054)], (7945 ^ _779530) ^ [_915111, _915113, _915115] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915111, tc_HOL_Obool)), _915113), _915115) = c_Orderings_Obot__class_Obot(tc_fun(_915111, tc_HOL_Obool)), 7948 ^ _779530 : [(7949 ^ _779530) ^ [] : [-(_915113 = c_Orderings_Obot__class_Obot(tc_fun(_915111, tc_HOL_Obool)))], (7951 ^ _779530) ^ [] : [-(_915115 = c_Orderings_Obot__class_Obot(tc_fun(_915111, tc_HOL_Obool)))]]], (7953 ^ _779530) ^ [_915264, _915266, _915268] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915264, tc_HOL_Obool)), _915266), _915268) = c_Orderings_Obot__class_Obot(tc_fun(_915264, tc_HOL_Obool))), _915266 = c_Orderings_Obot__class_Obot(tc_fun(_915264, tc_HOL_Obool)), _915268 = c_Orderings_Obot__class_Obot(tc_fun(_915264, tc_HOL_Obool))], (7963 ^ _779530) ^ [_915451, _915453, _915455, _915457] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915451, tc_HOL_Obool)), _915453), hAPP(hAPP(c_Set_Oinsert(_915451), _915455), _915457)) = hAPP(hAPP(c_Set_Oinsert(_915451), _915455), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915451, tc_HOL_Obool)), _915453), _915457)))], (7965 ^ _779530) ^ [_915518, _915520, _915522, _915524] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915518, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915518), _915520), _915522)), _915524) = hAPP(hAPP(c_Set_Oinsert(_915518), _915520), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915518, tc_HOL_Obool)), _915522), _915524)))], (7967 ^ _779530) ^ [_915585, _915587, _915589] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915585, tc_HOL_Obool)), _915587), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915585, tc_HOL_Obool)), _915587), _915589))))], (7969 ^ _779530) ^ [_915633, _915635, _915637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915633, tc_HOL_Obool)), _915635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915633, tc_HOL_Obool)), _915637), _915635))))], (7971 ^ _779530) ^ [_915699, _915701, _915703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915699, tc_HOL_Obool)), _915701), _915703)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915699, tc_HOL_Obool)), _915701), _915703) = _915703)], (7977 ^ _779530) ^ [_915816, _915818, _915820] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915816, tc_HOL_Obool)), _915818), _915820) = _915820, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915816, tc_HOL_Obool)), _915818), _915820)))], (7983 ^ _779530) ^ [_915939, _915941, _915943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915939, tc_HOL_Obool)), _915941), _915943)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915939, tc_HOL_Obool)), _915941), _915943) = _915943)], (7989 ^ _779530) ^ [_916060, _916062, _916064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916060, tc_HOL_Obool)), _916062), _916064)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916060, tc_HOL_Obool)), _916064), _916062) = _916064)], (7995 ^ _779530) ^ [_916181, _916183, _916185, _916187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916181, tc_HOL_Obool)), _916183), _916185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916181, tc_HOL_Obool)), _916187), _916185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916181, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916181, tc_HOL_Obool)), _916183), _916187)), _916185)))], (8005 ^ _779530) ^ [_916400, _916402, _916404, _916406, _916408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916400, tc_HOL_Obool)), _916402), _916404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916400, tc_HOL_Obool)), _916406), _916408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916400, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916400, tc_HOL_Obool)), _916402), _916406)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916400, tc_HOL_Obool)), _916404), _916408))))], (8015 ^ _779530) ^ [_916654, _916656] : [-(hBOOL(hAPP(hAPP(c_member(_916654), 8016 ^ [_916654, _916656]), _916656))), -(_916656 = c_Orderings_Obot__class_Obot(tc_fun(_916654, tc_HOL_Obool)))], (8022 ^ _779530) ^ [_916705, _916707] : [_916707 = c_Orderings_Obot__class_Obot(tc_fun(_916705, tc_HOL_Obool)), 8025 ^ _779530 : [(8026 ^ _779530) ^ [_916785] : [hBOOL(hAPP(hAPP(c_member(_916705), _916785), _916707))]]], (8028 ^ _779530) ^ [_916836, _916838] : [8029 ^ _779530 : [(8030 ^ _779530) ^ [_916889] : [hBOOL(hAPP(hAPP(c_member(_916836), _916889), _916838))]], _916838 = c_Orderings_Obot__class_Obot(tc_fun(_916836, tc_HOL_Obool))], (8034 ^ _779530) ^ [_916945, _916947] : [-(_916947 = c_Orderings_Obot__class_Obot(tc_fun(_916945, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_916945), 8037 ^ [_916945, _916947]), _916947)))], (8041 ^ _779530) ^ [_917014, _917016] : [hBOOL(hAPP(hAPP(c_member(_917014), _917016), c_Orderings_Obot__class_Obot(tc_fun(_917014, tc_HOL_Obool))))], (8043 ^ _779530) ^ [_917051, _917053, _917055] : [_917051 = c_Orderings_Obot__class_Obot(tc_fun(_917053, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_917053), _917055), _917051))], (8049 ^ _779530) ^ [_917155, _917157, _917159] : [-(hBOOL(hAPP(hAPP(c_member(_917155), _917157), hAPP(hAPP(c_Set_Oinsert(_917155), _917157), _917159))))], (8061 ^ _779530) ^ [_917352, _917354, _917356, _917358] : [8062 ^ _779530 : [(8063 ^ _779530) ^ [] : [_917354 = _917356], (8065 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_917352), _917354), _917358))]], -(hBOOL(hAPP(hAPP(c_member(_917352), _917354), hAPP(hAPP(c_Set_Oinsert(_917352), _917356), _917358))))], (8051 ^ _779530) ^ [_917218, _917220, _917222, _917224] : [hBOOL(hAPP(hAPP(c_member(_917218), _917220), hAPP(hAPP(c_Set_Oinsert(_917218), _917222), _917224))), -(_917220 = _917222), -(hBOOL(hAPP(hAPP(c_member(_917218), _917220), _917224)))], (8069 ^ _779530) ^ [_917516, _917518, _917520, _917522] : [-(hBOOL(hAPP(hAPP(c_member(_917516), _917518), _917520))), -(hBOOL(hAPP(hAPP(c_member(_917516), _917518), _917522))), 8076 ^ _779530 : [(8077 ^ _779530) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_917516), _917518), _917520) = hAPP(hAPP(c_Set_Oinsert(_917516), _917518), _917522), -(_917520 = _917522)], (8083 ^ _779530) ^ [] : [_917520 = _917522, -(hAPP(hAPP(c_Set_Oinsert(_917516), _917518), _917520) = hAPP(hAPP(c_Set_Oinsert(_917516), _917518), _917522))]]], (8089 ^ _779530) ^ [_917861, _917863, _917865, _917867] : [hBOOL(hAPP(hAPP(c_member(_917861), _917863), _917865)), -(hBOOL(hAPP(hAPP(c_member(_917861), _917863), hAPP(hAPP(c_Set_Oinsert(_917861), _917867), _917865))))], (8095 ^ _779530) ^ [_917986, _917988, _917990] : [hBOOL(hAPP(hAPP(c_member(_917986), _917988), _917990)), -(hAPP(hAPP(c_Set_Oinsert(_917986), _917988), _917990) = _917990)], (8101 ^ _779530) ^ [_918095, _918097, _918099, _918101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918095, tc_HOL_Obool)), _918097), _918099)), hBOOL(hAPP(hAPP(c_member(_918095), _918101), _918097)), -(hBOOL(hAPP(hAPP(c_member(_918095), _918101), _918099)))], (8111 ^ _779530) ^ [_918280, _918282, _918284, _918286] : [hBOOL(hAPP(hAPP(c_member(_918280), _918282), _918284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918280, tc_HOL_Obool)), _918284), _918286)), -(hBOOL(hAPP(hAPP(c_member(_918280), _918282), _918286)))], (8121 ^ _779530) ^ [_918465, _918467, _918469, _918471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918465, tc_HOL_Obool)), _918467), _918469)), hBOOL(hAPP(hAPP(c_member(_918465), _918471), _918467)), -(hBOOL(hAPP(hAPP(c_member(_918465), _918471), _918469)))], (8131 ^ _779530) ^ [_918650, _918652, _918654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_918650, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_918650, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_918650), _918652)), hAPP(c_Set_OPow(_918650), _918654))), hAPP(c_Set_OPow(_918650), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_918650, tc_HOL_Obool)), _918652), _918654)))))], (8133 ^ _779530) ^ [_918746, _918748, _918750] : [hAPP(c_Set_Oimage(_918748, tc_fun(_918748, tc_HOL_Obool), _918746), _918750) = hAPP(c_Set_OPow(_918748), _918750)], (8135 ^ _779530) ^ [_918788, _918790] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_918788, tc_HOL_Obool)), _918790), hAPP(c_Set_OPow(_918788), _918790))))], (8137 ^ _779530) ^ [_918828, _918830, _918832] : [-(hAPP(c_Set_OCollect(_918828), hAPP(hAPP(c_COMBS(_918828, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _918828), c_fdisj), _918830)), _918832)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_918828, tc_HOL_Obool)), hAPP(c_Set_OCollect(_918828), _918830)), hAPP(c_Set_OCollect(_918828), _918832)))], (8139 ^ _779530) ^ [_918901, _918903, _918905, _918907, _918909] : [class_Orderings_Oorder(_918901), class_Orderings_Oorder(_918903), c_Orderings_Oorder__class_Omono(_918903, _918901, _918905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918903), _918907), _918909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918901), hAPP(_918905, _918907)), hAPP(_918905, _918909))))], (8157 ^ _779530) ^ [_919213, _919215] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_919213, tc_HOL_Obool)), _919215)), -(hBOOL(hAPP(hAPP(c_member(_919213), _919215), c_Orderings_Obot__class_Obot(tc_fun(_919213, tc_HOL_Obool)))))], (8163 ^ _779530) ^ [_919324, _919326] : [hBOOL(hAPP(hAPP(c_member(_919324), _919326), c_Orderings_Obot__class_Obot(tc_fun(_919324, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_919324, tc_HOL_Obool)), _919326)))], (8169 ^ _779530) ^ [_919441, _919443, _919445, _919447, _919449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919441, tc_HOL_Obool)), hAPP(c_Set_Oimage(_919443, _919441, _919445), _919447)), _919449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_919441, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_919443, tc_HOL_Obool), tc_fun(_919441, tc_HOL_Obool), c_Set_Oimage(_919443, _919441, _919445)), hAPP(c_Set_OPow(_919443), _919447))), hAPP(c_Set_OPow(_919441), _919449))))], (8175 ^ _779530) ^ [_919638, _919640] : [-(hAPP(c_Set_OCollect(_919638), hAPP(hAPP(c_COMBC(_919638, tc_fun(_919638, tc_HOL_Obool), tc_HOL_Obool), c_member(_919638)), _919640)) = _919640)], (8177 ^ _779530) ^ [_919701, _919703, _919705] : [hBOOL(hAPP(hAPP(c_member(_919701), _919703), hAPP(c_Set_OCollect(_919701), _919705))), -(hBOOL(hAPP(_919705, _919703)))], (8183 ^ _779530) ^ [_919804, _919806, _919808] : [hBOOL(hAPP(_919808, _919806)), -(hBOOL(hAPP(hAPP(c_member(_919804), _919806), hAPP(c_Set_OCollect(_919804), _919808))))], (8189 ^ _779530) ^ [_919913, _919915, _919917] : [hBOOL(hAPP(hAPP(c_member(_919913), _919915), hAPP(c_Set_OCollect(_919913), _919917))), -(hBOOL(hAPP(_919917, _919915)))], (8195 ^ _779530) ^ [_920020, _920022, _920024] : [hBOOL(hAPP(hAPP(c_member(_920020), _920022), hAPP(c_Set_OCollect(_920020), _920024))), -(hBOOL(hAPP(_920024, _920022)))], (8201 ^ _779530) ^ [_920145, _920147, _920149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920145, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_920145, tc_fun(_920145, tc_HOL_Obool), tc_HOL_Obool), c_member(_920145)), _920147)), hAPP(hAPP(c_COMBC(_920145, tc_fun(_920145, tc_HOL_Obool), tc_HOL_Obool), c_member(_920145)), _920149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920145, tc_HOL_Obool)), _920147), _920149)))], (8207 ^ _779530) ^ [_920320, _920322, _920324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920320, tc_HOL_Obool)), _920322), _920324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920320, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_920320, tc_fun(_920320, tc_HOL_Obool), tc_HOL_Obool), c_member(_920320)), _920322)), hAPP(hAPP(c_COMBC(_920320, tc_fun(_920320, tc_HOL_Obool), tc_HOL_Obool), c_member(_920320)), _920324))))], (8213 ^ _779530) ^ [_920519, _920521, _920523] : [hBOOL(hAPP(c_Predicate_OPowp(_920519, hAPP(hAPP(c_COMBC(_920519, tc_fun(_920519, tc_HOL_Obool), tc_HOL_Obool), c_member(_920519)), _920521)), _920523)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_920519, tc_HOL_Obool)), _920523), hAPP(c_Set_OPow(_920519), _920521))))], (8219 ^ _779530) ^ [_920664, _920666, _920668] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_920664, tc_HOL_Obool)), _920668), hAPP(c_Set_OPow(_920664), _920666))), -(hBOOL(hAPP(c_Predicate_OPowp(_920664, hAPP(hAPP(c_COMBC(_920664, tc_fun(_920664, tc_HOL_Obool), tc_HOL_Obool), c_member(_920664)), _920666)), _920668)))], (8225 ^ _779530) ^ [_920811, _920813, _920815, _920817, _920819, _920821] : [-(hBOOL(hAPP(hAPP(c_member(_920811), _920813), _920815))), -(hAPP(c_Fun_Ooverride__on(_920811, _920817, _920819, _920821, _920815), _920813) = hAPP(_920819, _920813))], (8231 ^ _779530) ^ [_920874, _920876, _920878, _920880, _920882, _920884] : [hBOOL(hAPP(hAPP(c_member(_920874), _920876), _920878)), -(hAPP(c_Fun_Ooverride__on(_920874, _920880, _920882, _920884, _920878), _920876) = hAPP(_920884, _920876))], (8237 ^ _779530) ^ [_920997, _920999, _921001] : [-(hAPP(hAPP(c_Set_Oinsert(_920997), _920999), _921001) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920997, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_920997), _920999), c_Orderings_Obot__class_Obot(tc_fun(_920997, tc_HOL_Obool)))), _921001))], (8239 ^ _779530) ^ [_921077, _921079, _921081, _921083, _921085, _921087] : [hBOOL(hAPP(hAPP(c_member(_921077), _921079), _921081)), -(hAPP(c_Fun_Ooverride__on(_921077, _921083, _921085, _921087, _921081), _921079) = hAPP(_921087, _921079))], (8245 ^ _779530) ^ [_921194, _921196, _921198, _921200, _921202, _921204] : [-(hBOOL(hAPP(hAPP(c_member(_921194), _921196), _921198))), -(hAPP(c_Fun_Ooverride__on(_921194, _921200, _921202, _921204, _921198), _921196) = hAPP(_921202, _921196))], (8251 ^ _779530) ^ [_921277, _921279, _921281] : [hBOOL(hAPP(hAPP(c_member(_921277), _921279), hAPP(hAPP(c_Set_Oinsert(_921277), _921281), c_Orderings_Obot__class_Obot(tc_fun(_921277, tc_HOL_Obool))))), -(_921279 = _921281)], (8257 ^ _779530) ^ [_921392, _921394, _921396] : [_921394 = _921396, -(hBOOL(hAPP(hAPP(c_member(_921392), _921394), hAPP(hAPP(c_Set_Oinsert(_921392), _921396), c_Orderings_Obot__class_Obot(tc_fun(_921392, tc_HOL_Obool))))))], (8263 ^ _779530) ^ [_921513, _921515, _921517] : [hBOOL(hAPP(hAPP(c_member(_921513), _921515), hAPP(hAPP(c_Set_Oinsert(_921513), _921517), c_Orderings_Obot__class_Obot(tc_fun(_921513, tc_HOL_Obool))))), -(_921515 = _921517)], (8269 ^ _779530) ^ [_921653, _921655, _921657, _921659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921653, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_921653), _921655), _921657)), _921659)), 8272 ^ _779530 : [(8273 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921653), _921655), _921659)))], (8275 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921653, tc_HOL_Obool)), _921657), _921659)))]]], (8277 ^ _779530) ^ [_921826, _921828, _921830, _921832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921826, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_921826), _921828), _921830)), _921832))), hBOOL(hAPP(hAPP(c_member(_921826), _921828), _921832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921826, tc_HOL_Obool)), _921830), _921832))], (8287 ^ _779530) ^ [_922035, _922037, _922039, _922041, _922043] : [class_Lattices_Osemilattice__sup(_922035), class_Lattices_Osemilattice__sup(_922037), c_Orderings_Oorder__class_Omono(_922037, _922035, _922039), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922035), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922035), hAPP(_922039, _922041)), hAPP(_922039, _922043))), hAPP(_922039, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922037), _922041), _922043)))))], (8301 ^ _779530) ^ [_922298, _922300, _922302, _922304, _922306] : [class_Lattices_Olattice(_922298), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922300, _922298)), _922302), _922304), _922306) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922298), hAPP(_922302, _922306)), hAPP(_922304, _922306)))], (8307 ^ _779530) ^ [_922435, _922437, _922439, _922441, _922443] : [class_Lattices_Olattice(_922435), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922437, _922435)), _922439), _922441), _922443) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922435), hAPP(_922439, _922443)), hAPP(_922441, _922443)))], (8313 ^ _779530) ^ [_922572, _922574] : [class_Lattices_Obounded__lattice__bot(_922572), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922572), c_Orderings_Obot__class_Obot(_922572)), _922574) = _922574)], (8319 ^ _779530) ^ [_922667, _922669] : [class_Lattices_Obounded__lattice__bot(_922667), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922667), _922669), c_Orderings_Obot__class_Obot(_922667)) = _922669)], (8325 ^ _779530) ^ [_922762, _922764, _922766] : [class_Lattices_Obounded__lattice__bot(_922762), 8328 ^ _779530 : [(8329 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922762), _922764), _922766) = c_Orderings_Obot__class_Obot(_922762), 8332 ^ _779530 : [(8333 ^ _779530) ^ [] : [-(_922764 = c_Orderings_Obot__class_Obot(_922762))], (8335 ^ _779530) ^ [] : [-(_922766 = c_Orderings_Obot__class_Obot(_922762))]]], (8337 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_922762), _922764), _922766) = c_Orderings_Obot__class_Obot(_922762)), _922764 = c_Orderings_Obot__class_Obot(_922762), _922766 = c_Orderings_Obot__class_Obot(_922762)]]], (8347 ^ _779530) ^ [_923089, _923091, _923093] : [class_Lattices_Olattice(_923089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923089), _923091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923089), _923091), _923093))))], (8353 ^ _779530) ^ [_923196, _923198, _923200] : [class_Lattices_Osemilattice__sup(_923196), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923196), _923198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923196), _923198), _923200))))], (8359 ^ _779530) ^ [_923303, _923305, _923307] : [class_Lattices_Olattice(_923303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923303), _923305), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923303), _923307), _923305))))], (8365 ^ _779530) ^ [_923410, _923412, _923414] : [class_Lattices_Osemilattice__sup(_923410), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923410), _923412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923410), _923414), _923412))))], (8371 ^ _779530) ^ [_923517, _923519, _923521] : [class_Lattices_Osemilattice__sup(_923517), 8374 ^ _779530 : [(8375 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923517), _923519), _923521)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923517), _923519), _923521) = _923521)], (8381 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923517), _923519), _923521) = _923521, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923517), _923519), _923521)))]]], (8387 ^ _779530) ^ [_923773, _923775] : [class_Lattices_Osemilattice__sup(_923773), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923773), _923775), _923775) = _923775)], (8393 ^ _779530) ^ [_923864, _923866] : [class_Lattices_Osemilattice__sup(_923864), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923864), _923866), _923866) = _923866)], (8399 ^ _779530) ^ [_923955, _923957, _923959] : [class_Lattices_Osemilattice__sup(_923955), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923955), _923957), _923959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923955), _923959), _923957))], (8405 ^ _779530) ^ [_924064, _924066, _924068] : [class_Lattices_Olattice(_924064), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924064), _924066), _924068) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924064), _924068), _924066))], (8411 ^ _779530) ^ [_924173, _924175, _924177] : [class_Lattices_Osemilattice__sup(_924173), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924173), _924175), _924177) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924173), _924177), _924175))], (8417 ^ _779530) ^ [_924282, _924284, _924286] : [class_Lattices_Osemilattice__sup(_924282), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924282), _924284), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924282), _924284), _924286)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924282), _924284), _924286))], (8423 ^ _779530) ^ [_924407, _924409, _924411] : [class_Lattices_Olattice(_924407), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924407), _924409), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924407), _924409), _924411)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924407), _924409), _924411))], (8429 ^ _779530) ^ [_924532, _924534, _924536] : [class_Lattices_Osemilattice__sup(_924532), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924532), _924534), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924532), _924534), _924536)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924532), _924534), _924536))], (8435 ^ _779530) ^ [_924657, _924659, _924661, _924663] : [class_Lattices_Osemilattice__sup(_924657), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924657), _924659), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924657), _924661), _924663)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924657), _924661), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924657), _924659), _924663)))], (8441 ^ _779530) ^ [_924800, _924802, _924804, _924806] : [class_Lattices_Olattice(_924800), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924800), _924802), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924800), _924804), _924806)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924800), _924804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924800), _924802), _924806)))], (8447 ^ _779530) ^ [_924943, _924945, _924947, _924949] : [class_Lattices_Osemilattice__sup(_924943), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924943), _924945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924943), _924947), _924949)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924943), _924947), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924943), _924945), _924949)))], (8453 ^ _779530) ^ [_925086, _925088, _925090, _925092] : [class_Lattices_Osemilattice__sup(_925086), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925086), _925088), _925090)), _925092) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925086), _925088), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925086), _925090), _925092)))], (8459 ^ _779530) ^ [_925229, _925231, _925233, _925235] : [class_Lattices_Olattice(_925229), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925229), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925229), _925231), _925233)), _925235) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925229), _925231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925229), _925233), _925235)))], (8465 ^ _779530) ^ [_925372, _925374, _925376, _925378] : [class_Lattices_Osemilattice__sup(_925372), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925372), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925372), _925374), _925376)), _925378) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925372), _925374), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925372), _925376), _925378)))], (8471 ^ _779530) ^ [_925515, _925517, _925519, _925521] : [class_Lattices_Osemilattice__sup(_925515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925515), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925515), _925517), _925519)), _925521)), 8478 ^ _779530 : [(8479 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925515), _925517), _925521)))], (8481 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925515), _925519), _925521)))]]], (8483 ^ _779530) ^ [_925738, _925740, _925742, _925744, _925746] : [class_Lattices_Osemilattice__sup(_925738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925738), _925740), _925742)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925738), _925744), _925746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925738), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925738), _925740), _925744)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_925738), _925742), _925746))))], (8497 ^ _779530) ^ [_926009, _926011, _926013, _926015] : [class_Lattices_Osemilattice__sup(_926009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926009), _926011), _926013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926009), _926015), _926013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926009), _926011), _926015)), _926013)))], (8511 ^ _779530) ^ [_926258, _926260, _926262, _926264] : [class_Lattices_Osemilattice__sup(_926258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926258), _926260), _926262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926258), _926264), _926262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926258), _926260), _926264)), _926262)))], (8525 ^ _779530) ^ [_926507, _926509, _926511] : [class_Lattices_Osemilattice__sup(_926507), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926507), _926509), _926511)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926507), _926511), _926509) = _926511)], (8535 ^ _779530) ^ [_926668, _926670, _926672] : [class_Lattices_Osemilattice__sup(_926668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926668), _926670), _926672)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926668), _926670), _926672) = _926672)], (8545 ^ _779530) ^ [_926829, _926831, _926833, _926835] : [class_Lattices_Osemilattice__sup(_926829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926829), _926831), _926833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926829), _926831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_926829), _926835), _926833))))], (8555 ^ _779530) ^ [_927008, _927010, _927012, _927014] : [class_Lattices_Osemilattice__sup(_927008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927008), _927010), _927012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927008), _927010), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927008), _927012), _927014))))], (8565 ^ _779530) ^ [_927187, _927189, _927191, _927193] : [class_Lattices_Osemilattice__sup(_927187), 8568 ^ _779530 : [(8569 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927187), _927189), _927191)), _927193)), 8572 ^ _779530 : [(8573 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), _927189), _927193)))], (8575 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), _927191), _927193)))]]], (8577 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927187), _927189), _927191)), _927193))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), _927189), _927193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927187), _927191), _927193))]]], (8587 ^ _779530) ^ [_927567, _927569, _927571, _927573, _927575] : [class_Orderings_Oorder(_927567), c_Orderings_Oorder__class_Omono(_927567, tc_fun(_927569, tc_HOL_Obool), _927571), -(c_Orderings_Oorder__class_Omono(_927567, tc_fun(_927569, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_927567, tc_fun(_927569, tc_HOL_Obool), tc_fun(_927569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_927569, tc_HOL_Obool), tc_fun(tc_fun(_927569, tc_HOL_Obool), tc_fun(_927569, tc_HOL_Obool)), _927567), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927569, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_927567, tc_fun(_927569, tc_HOL_Obool), tc_fun(_927569, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_927569, tc_HOL_Obool), tc_fun(tc_fun(_927569, tc_HOL_Obool), tc_fun(_927569, tc_HOL_Obool)), _927567), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927569, tc_HOL_Obool))), _927571)), _927573))), _927575)))], (8597 ^ _779530) ^ [_927894, _927896, _927898, _927900, _927902] : [-(hAPP(c_Fun_Othe__inv__into(_927894, _927896, _927898, _927900), _927902) = c_HOL_OThe(_927894, hAPP(hAPP(c_COMBS(_927894, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _927894), c_fconj), hAPP(hAPP(c_COMBC(_927894, tc_fun(_927894, tc_HOL_Obool), tc_HOL_Obool), c_member(_927894)), _927898))), hAPP(hAPP(c_COMBC(_927894, _927896, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_927896, tc_fun(_927896, tc_HOL_Obool), _927894), c_fequal), _927900)), _927902))))], (8599 ^ _779530) ^ [_927994, _927996, _927998, _928000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927994, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927994, tc_HOL_Obool)), _927996), hAPP(hAPP(c_Set_Oinsert(_927994), _927998), c_Orderings_Obot__class_Obot(tc_fun(_927994, tc_HOL_Obool))))), _928000)), hBOOL(hAPP(hAPP(c_member(_927994), _927998), _927996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927994, tc_HOL_Obool)), _927996), hAPP(hAPP(c_Set_Oinsert(_927994), _927998), _928000))))], (8625 ^ _779530) ^ [_928602, _928604, _928606, _928608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928602, tc_HOL_Obool)), _928604), hAPP(hAPP(c_Set_Oinsert(_928602), _928606), _928608)))), 8628 ^ _779530 : [(8629 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928602), _928606), _928604)))], (8631 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928602, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928602, tc_HOL_Obool)), _928604), hAPP(hAPP(c_Set_Oinsert(_928602), _928606), c_Orderings_Obot__class_Obot(tc_fun(_928602, tc_HOL_Obool))))), _928608))]], 8632 ^ _779530 : [(8633 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928602), _928606), _928604))], (8635 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928602, tc_HOL_Obool)), _928604), _928608))]]], (8609 ^ _779530) ^ [_928270, _928272, _928274, _928276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928270, tc_HOL_Obool)), _928272), hAPP(hAPP(c_Set_Oinsert(_928270), _928274), _928276))), 8612 ^ _779530 : [(8613 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928270), _928274), _928272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928270, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928270, tc_HOL_Obool)), _928272), hAPP(hAPP(c_Set_Oinsert(_928270), _928274), c_Orderings_Obot__class_Obot(tc_fun(_928270, tc_HOL_Obool))))), _928276)))], (8619 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928270), _928274), _928272))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928270, tc_HOL_Obool)), _928272), _928276)))]]], (8639 ^ _779530) ^ [_928966, _928968, _928970, _928972, _928974] : [hBOOL(hAPP(hAPP(c_member(_928966), _928968), hAPP(c_Set_Oimage(_928970, _928966, _928972), _928974))), 8643 ^ _779530 : [(8644 ^ _779530) ^ [] : [-(_928968 = hAPP(_928972, 8642 ^ [_928966, _928968, _928970, _928972, _928974]))], (8646 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928970), 8642 ^ [_928966, _928968, _928970, _928972, _928974]), _928974)))]]], (8648 ^ _779530) ^ [_929158, _929160, _929162, _929164, _929166] : [8650 ^ _779530 : [(8651 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929158), 8649 ^ [_929158, _929160, _929162, _929164, _929166]), _929160)))], (8653 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929162), hAPP(_929164, 8649 ^ [_929158, _929160, _929162, _929164, _929166])), _929166))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929162, tc_HOL_Obool)), hAPP(c_Set_Oimage(_929158, _929162, _929164), _929160)), _929166)))], (8657 ^ _779530) ^ [_929400, _929402, _929404, _929406] : [c_Orderings_Oorder__class_Omono(tc_fun(_929400, tc_HOL_Obool), tc_fun(_929400, tc_HOL_Obool), _929402), hBOOL(hAPP(hAPP(c_member(_929400), _929404), _929406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929400, tc_HOL_Obool)), _929406), hAPP(_929402, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929400, tc_HOL_Obool)), _929406), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929400, tc_HOL_Obool), _929402))))), -(hBOOL(hAPP(hAPP(c_member(_929400), _929404), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929400, tc_HOL_Obool), _929402))))], (8671 ^ _779530) ^ [_929707, _929709, _929711, _929713, _929715] : [_929707 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_929709, tc_HOL_Obool), _929711), c_Orderings_Oorder__class_Omono(tc_fun(_929709, tc_HOL_Obool), tc_fun(_929709, tc_HOL_Obool), _929711), hBOOL(hAPP(hAPP(c_member(_929709), _929713), _929715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929709, tc_HOL_Obool)), _929715), hAPP(_929711, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_929709, tc_HOL_Obool)), _929715), _929707)))), -(hBOOL(hAPP(hAPP(c_member(_929709), _929713), _929707)))], (8689 ^ _779530) ^ [_930066, _930068, _930070, _930072, _930074, _930076] : [-(hAPP(c_Set_Oimage(_930066, _930068, hAPP(hAPP(c_COMBS(_930066, _930068, _930068), hAPP(hAPP(c_COMBS(_930066, _930068, tc_fun(_930068, _930068)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_930068, tc_fun(_930068, _930068)), _930066), c_If(_930068)), _930070)), _930072)), _930074)), _930076) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_930068, tc_HOL_Obool)), hAPP(c_Set_Oimage(_930066, _930068, _930072), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930066, tc_HOL_Obool)), _930076), hAPP(c_Set_OCollect(_930066), _930070)))), hAPP(c_Set_Oimage(_930066, _930068, _930074), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930066, tc_HOL_Obool)), _930076), hAPP(c_Set_OCollect(_930066), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _930066), c_fNot), _930070))))))], (8691 ^ _779530) ^ [_930214, _930216] : [class_Lattices_Olattice(_930214), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930214), _930216), _930216) = _930216)], (8697 ^ _779530) ^ [_930305, _930307, _930309, _930311] : [hBOOL(hAPP(_930305, _930307)), hBOOL(hAPP(_930309, _930307)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930311, tc_HOL_Obool)), _930305), _930309), _930307)))], (8707 ^ _779530) ^ [_930476, _930478, _930480, _930482] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930476, tc_HOL_Obool)), _930478), _930480), _930482)), 8710 ^ _779530 : [(8711 ^ _779530) ^ [] : [-(hBOOL(hAPP(_930478, _930482)))], (8713 ^ _779530) ^ [] : [-(hBOOL(hAPP(_930480, _930482)))]]], (8715 ^ _779530) ^ [_930621, _930623, _930625, _930627] : [hBOOL(hAPP(hAPP(c_member(_930621), _930623), _930625)), hBOOL(hAPP(hAPP(c_member(_930621), _930623), _930627)), -(hBOOL(hAPP(hAPP(c_member(_930621), _930623), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930621, tc_HOL_Obool)), _930625), _930627))))], (8725 ^ _779530) ^ [_930822, _930824, _930826, _930828] : [hBOOL(hAPP(hAPP(c_member(_930822), _930824), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930822, tc_HOL_Obool)), _930826), _930828))), 8728 ^ _779530 : [(8729 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930822), _930824), _930826)))], (8731 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_930822), _930824), _930828)))]]], (8733 ^ _779530) ^ [_930997, _930999, _931001, _931003] : [hBOOL(hAPP(hAPP(c_member(_930997), _930999), _931001)), -(hBOOL(hAPP(hAPP(c_member(_930997), _930999), _931003))), -(hBOOL(hAPP(hAPP(c_member(_930997), _930999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930997, tc_HOL_Obool)), _931001), _931003))))], (8743 ^ _779530) ^ [_931157, _931159, _931161, _931163] : [hBOOL(hAPP(hAPP(c_member(_931157), _931159), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931157, tc_HOL_Obool)), _931161), _931163))), 8746 ^ _779530 : [(8747 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_931157), _931159), _931161)))], (8749 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_931157), _931159), _931163))]]], (8751 ^ _779530) ^ [_931336, _931338] : [class_Lattices_Osemilattice__inf(_931336), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931336), _931338), _931338) = _931338)], (8757 ^ _779530) ^ [_931427, _931429] : [class_Lattices_Osemilattice__inf(_931427), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931427), _931429), _931429) = _931429)], (8763 ^ _779530) ^ [_931518, _931520, _931522, _931524, _931526] : [class_Groups_Ominus(_931518), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931520, _931518)), _931522), _931524), _931526) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_931518), hAPP(_931522, _931526)), hAPP(_931524, _931526)))], (8769 ^ _779530) ^ [_931655, _931657, _931659, _931661, _931663] : [class_Lattices_Olattice(_931655), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931657, _931655)), _931659), _931661), _931663) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931655), hAPP(_931659, _931663)), hAPP(_931661, _931663)))], (8775 ^ _779530) ^ [_931792, _931794, _931796] : [class_Lattices_Osemilattice__inf(_931792), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931792), _931794), _931796) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931792), _931796), _931794))], (8781 ^ _779530) ^ [_931901, _931903, _931905] : [class_Lattices_Olattice(_931901), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931901), _931903), _931905) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931901), _931905), _931903))], (8787 ^ _779530) ^ [_932010, _932012, _932014] : [class_Lattices_Osemilattice__inf(_932010), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932010), _932012), _932014) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932010), _932014), _932012))], (8793 ^ _779530) ^ [_932119, _932121, _932123] : [class_Lattices_Osemilattice__inf(_932119), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932119), _932121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932119), _932121), _932123)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932119), _932121), _932123))], (8799 ^ _779530) ^ [_932244, _932246, _932248] : [class_Lattices_Olattice(_932244), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932244), _932246), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932244), _932246), _932248)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932244), _932246), _932248))], (8805 ^ _779530) ^ [_932369, _932371, _932373] : [class_Lattices_Osemilattice__inf(_932369), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932369), _932371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932369), _932371), _932373)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932369), _932371), _932373))], (8811 ^ _779530) ^ [_932494, _932496, _932498, _932500] : [class_Lattices_Osemilattice__inf(_932494), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932494), _932496), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932494), _932498), _932500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932494), _932498), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932494), _932496), _932500)))], (8817 ^ _779530) ^ [_932637, _932639, _932641, _932643] : [class_Lattices_Olattice(_932637), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932637), _932639), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932637), _932641), _932643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932637), _932641), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932637), _932639), _932643)))], (8823 ^ _779530) ^ [_932780, _932782, _932784, _932786] : [class_Lattices_Osemilattice__inf(_932780), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932780), _932782), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932780), _932784), _932786)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932780), _932784), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932780), _932782), _932786)))], (8829 ^ _779530) ^ [_932923, _932925, _932927, _932929] : [class_Lattices_Osemilattice__inf(_932923), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932923), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932923), _932925), _932927)), _932929) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932923), _932925), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932923), _932927), _932929)))], (8835 ^ _779530) ^ [_933066, _933068, _933070, _933072] : [class_Lattices_Olattice(_933066), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933066), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933066), _933068), _933070)), _933072) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933066), _933068), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933066), _933070), _933072)))], (8841 ^ _779530) ^ [_933209, _933211, _933213, _933215] : [class_Lattices_Osemilattice__inf(_933209), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933209), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933209), _933211), _933213)), _933215) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933209), _933211), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933209), _933213), _933215)))], (8847 ^ _779530) ^ [_933352, _933354, _933356, _933358, _933360] : [class_Groups_Ominus(_933352), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933354, _933352)), _933356), _933358), _933360) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933352), hAPP(_933356, _933360)), hAPP(_933358, _933360)))], (8853 ^ _779530) ^ [_933489, _933491, _933493, _933495, _933497] : [class_Lattices_Olattice(_933489), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933491, _933489)), _933493), _933495), _933497) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_933489), hAPP(_933493, _933497)), hAPP(_933495, _933497)))], (8859 ^ _779530) ^ [_933626, _933628, _933630] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933626, tc_HOL_Obool)), _933628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933626, tc_HOL_Obool)), _933630), _933628)) = c_Orderings_Obot__class_Obot(tc_fun(_933626, tc_HOL_Obool)))], (8861 ^ _779530) ^ [_933680, _933682, _933684] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933680, tc_HOL_Obool)), _933682), _933684) = c_Orderings_Obot__class_Obot(tc_fun(_933680, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933680, tc_HOL_Obool)), _933682), _933684) = _933682)], (8867 ^ _779530) ^ [_933813, _933815] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933813, tc_HOL_Obool)), _933815), _933815) = _933815)], (8869 ^ _779530) ^ [_933849, _933851, _933853] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933849, tc_HOL_Obool)), _933851), _933853) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933849, tc_HOL_Obool)), _933853), _933851))], (8871 ^ _779530) ^ [_933898, _933900, _933902] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933898, tc_HOL_Obool)), _933900), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933898, tc_HOL_Obool)), _933900), _933902)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933898, tc_HOL_Obool)), _933900), _933902))], (8873 ^ _779530) ^ [_933958, _933960, _933962, _933964] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933958, tc_HOL_Obool)), _933960), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933958, tc_HOL_Obool)), _933962), _933964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933958, tc_HOL_Obool)), _933962), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933958, tc_HOL_Obool)), _933960), _933964)))], (8875 ^ _779530) ^ [_934031, _934033, _934035, _934037] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934031, tc_HOL_Obool)), _934033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934031, tc_HOL_Obool)), _934035), _934037)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934031, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934031, tc_HOL_Obool)), _934033), _934035)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934031, tc_HOL_Obool)), _934033), _934037)))], (8877 ^ _779530) ^ [_934115, _934117, _934119] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934115, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934115, tc_HOL_Obool)), _934117), _934119)), _934119) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934115, tc_HOL_Obool)), _934117), _934119))], (8879 ^ _779530) ^ [_934175, _934177, _934179, _934181] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934175, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934175, tc_HOL_Obool)), _934177), _934179)), _934181) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934175, tc_HOL_Obool)), _934177), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934175, tc_HOL_Obool)), _934179), _934181)))], (8881 ^ _779530) ^ [_934248, _934250, _934252, _934254] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934248, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934248, tc_HOL_Obool)), _934250), _934252)), _934254) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934248, tc_HOL_Obool)), _934250), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934248, tc_HOL_Obool)), _934252), _934254)))], (8883 ^ _779530) ^ [_934321, _934323, _934325, _934327] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934321, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934321, tc_HOL_Obool)), _934323), _934325)), _934327) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934321, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934321, tc_HOL_Obool)), _934323), _934327)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934321, tc_HOL_Obool)), _934325), _934327)))], (8885 ^ _779530) ^ [_934405, _934407, _934409, _934411] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934405, tc_HOL_Obool)), _934407), _934409)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934405, tc_HOL_Obool)), _934411), _934409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934405, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934405, tc_HOL_Obool)), _934407), _934409)), _934411))], (8887 ^ _779530) ^ [_934489, _934491] : [class_Lattices_Olattice(_934489), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_934489), _934491), _934491) = _934491)], (8893 ^ _779530) ^ [_934580, _934582, _934584, _934586] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934580, tc_HOL_Obool)), _934582), _934584), _934586)), -(hBOOL(hAPP(_934582, _934586)))], (8899 ^ _779530) ^ [_934691, _934693, _934695, _934697] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934691, tc_HOL_Obool)), _934693), _934695), _934697)), -(hBOOL(hAPP(_934695, _934697)))], (8905 ^ _779530) ^ [_934802, _934804, _934806, _934808] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934802, tc_HOL_Obool)), _934804), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934802, tc_HOL_Obool)), _934806), _934808)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_934802, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934802, tc_HOL_Obool)), _934804), _934806)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934802, tc_HOL_Obool)), _934804), _934808)))], (8907 ^ _779530) ^ [_934886, _934888, _934890, _934892] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934886, tc_HOL_Obool)), _934888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_934886, tc_HOL_Obool)), _934890), _934892)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934886, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934886, tc_HOL_Obool)), _934888), _934890)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934886, tc_HOL_Obool)), _934888), _934892)))], (8909 ^ _779530) ^ [_934970, _934972, _934974] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_934970, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934970, tc_HOL_Obool)), _934972), _934974)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934970, tc_HOL_Obool)), _934972), _934974)) = _934972)], (8911 ^ _779530) ^ [_935030, _935032, _935034] : [-(hAPP(c_Set_OPow(_935030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935030, tc_HOL_Obool)), _935032), _935034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_935030, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_935030), _935032)), hAPP(c_Set_OPow(_935030), _935034)))], (8913 ^ _779530) ^ [_935097, _935099, _935101] : [class_Complete__Lattice_Ocomplete__lattice(_935097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935097), _935099), hAPP(_935101, _935099))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935097), _935099), c_Inductive_Ocomplete__lattice__class_Ogfp(_935097, _935101))))], (8923 ^ _779530) ^ [_935268, _935270, _935272] : [class_Complete__Lattice_Ocomplete__lattice(_935268), _935270 = c_Inductive_Ocomplete__lattice__class_Ogfp(_935268, _935272), c_Orderings_Oorder__class_Omono(_935268, _935268, _935272), -(_935270 = hAPP(_935272, _935270))], (8937 ^ _779530) ^ [_935467, _935469] : [class_Complete__Lattice_Ocomplete__lattice(_935467), c_Orderings_Oorder__class_Omono(_935467, _935467, _935469), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_935467, _935469) = hAPP(_935469, c_Inductive_Ocomplete__lattice__class_Ogfp(_935467, _935469)))], (8947 ^ _779530) ^ [_935614, _935616, _935618] : [class_Lattices_Olattice(_935614), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935614), _935616), _935618)), _935616)))], (8953 ^ _779530) ^ [_935721, _935723, _935725] : [class_Lattices_Osemilattice__inf(_935721), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935721), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935721), _935723), _935725)), _935723)))], (8959 ^ _779530) ^ [_935828, _935830, _935832] : [class_Lattices_Olattice(_935828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935828), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935828), _935830), _935832)), _935832)))], (8965 ^ _779530) ^ [_935935, _935937, _935939] : [class_Lattices_Osemilattice__inf(_935935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935935), _935937), _935939)), _935939)))], (8971 ^ _779530) ^ [_936042, _936044, _936046] : [class_Lattices_Osemilattice__inf(_936042), 8974 ^ _779530 : [(8975 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936042), _936044), _936046)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936042), _936044), _936046) = _936044)], (8981 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936042), _936044), _936046) = _936044, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936042), _936044), _936046)))]]], (8987 ^ _779530) ^ [_936298, _936300, _936302, _936304] : [class_Lattices_Osemilattice__inf(_936298), 8990 ^ _779530 : [(8991 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936298), _936302), _936304))), 8994 ^ _779530 : [(8995 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), _936302)))], (8997 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), _936304)))]]], (8999 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936298), _936302), _936304)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), _936302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936298), _936300), _936304))]]], (9009 ^ _779530) ^ [_936678, _936680, _936682, _936684] : [class_Lattices_Osemilattice__inf(_936678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936678), _936680), _936682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936678), _936680), _936684)), _936682)))], (9019 ^ _779530) ^ [_936857, _936859, _936861, _936863] : [class_Lattices_Osemilattice__inf(_936857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936857), _936859), _936861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936857), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936857), _936863), _936859)), _936861)))], (9029 ^ _779530) ^ [_937036, _937038, _937040] : [class_Lattices_Osemilattice__inf(_937036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937036), _937038), _937040)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937036), _937038), _937040) = _937038)], (9039 ^ _779530) ^ [_937197, _937199, _937201] : [class_Lattices_Osemilattice__inf(_937197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937197), _937199), _937201)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937197), _937201), _937199) = _937199)], (9049 ^ _779530) ^ [_937358, _937360, _937362, _937364] : [class_Lattices_Osemilattice__inf(_937358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937358), _937360), _937362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937358), _937360), _937364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937358), _937360), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937358), _937362), _937364))))], (9063 ^ _779530) ^ [_937607, _937609, _937611, _937613] : [class_Lattices_Osemilattice__inf(_937607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937607), _937609), _937611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937607), _937609), _937613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937607), _937609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937607), _937611), _937613))))], (9077 ^ _779530) ^ [_937856, _937858, _937860, _937862, _937864] : [class_Lattices_Osemilattice__inf(_937856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937856), _937858), _937860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937856), _937862), _937864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937856), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937856), _937858), _937862)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937856), _937860), _937864))))], (9091 ^ _779530) ^ [_938127, _938129, _938131, _938133] : [class_Lattices_Osemilattice__inf(_938127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938127), _938129), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938127), _938131), _938133))), 9098 ^ _779530 : [(9099 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938127), _938129), _938131)))], (9101 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938127), _938129), _938133)))]]], (9103 ^ _779530) ^ [_938350, _938352] : [class_Lattices_Obounded__lattice__bot(_938350), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938350), c_Orderings_Obot__class_Obot(_938350)), _938352) = c_Orderings_Obot__class_Obot(_938350))], (9109 ^ _779530) ^ [_938449, _938451] : [class_Lattices_Obounded__lattice__bot(_938449), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938449), _938451), c_Orderings_Obot__class_Obot(_938449)) = c_Orderings_Obot__class_Obot(_938449))], (9115 ^ _779530) ^ [_938548, _938550, _938552, _938554] : [class_Lattices_Odistrib__lattice(_938548), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938548), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938548), _938550), _938552)), _938554) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938548), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938548), _938550), _938554)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938548), _938552), _938554)))], (9121 ^ _779530) ^ [_938707, _938709, _938711, _938713] : [class_Lattices_Odistrib__lattice(_938707), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938707), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938707), _938709), _938711)), _938713) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938707), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938707), _938709), _938713)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938707), _938711), _938713)))], (9127 ^ _779530) ^ [_938866, _938868, _938870, _938872] : [class_Lattices_Odistrib__lattice(_938866), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938866), _938868), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938866), _938870), _938872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938866), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938866), _938868), _938870)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938866), _938868), _938872)))], (9133 ^ _779530) ^ [_939025, _939027, _939029, _939031] : [class_Lattices_Odistrib__lattice(_939025), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939025), _939027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939025), _939029), _939031)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939025), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939025), _939027), _939029)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939025), _939027), _939031)))], (9139 ^ _779530) ^ [_939184, _939186, _939188] : [class_Lattices_Olattice(_939184), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939184), _939186), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939184), _939186), _939188)) = _939186)], (9145 ^ _779530) ^ [_939293, _939295, _939297] : [class_Lattices_Olattice(_939293), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939293), _939295), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939293), _939295), _939297)) = _939295)], (9151 ^ _779530) ^ [_939423, _939425, _939427, _939429] : [hBOOL(hAPP(hAPP(c_member(_939423), _939425), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939423, tc_HOL_Obool)), _939427), _939429))), 9154 ^ _779530 : [(9155 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939423), _939425), _939427)))], (9157 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_939423), _939425), _939429))]]], (9159 ^ _779530) ^ [_939598, _939600, _939602, _939604] : [-(hBOOL(hAPP(hAPP(c_member(_939598), _939600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939598, tc_HOL_Obool)), _939602), _939604)))), hBOOL(hAPP(hAPP(c_member(_939598), _939600), _939602)), -(hBOOL(hAPP(hAPP(c_member(_939598), _939600), _939604)))], (9169 ^ _779530) ^ [_939804, _939806, _939808, _939810] : [hBOOL(hAPP(hAPP(c_member(_939804), _939806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939804, tc_HOL_Obool)), _939808), _939810))), -(hBOOL(hAPP(hAPP(c_member(_939804), _939806), _939808)))], (9175 ^ _779530) ^ [_939935, _939937, _939939, _939941] : [hBOOL(hAPP(hAPP(c_member(_939935), _939937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939935, tc_HOL_Obool)), _939939), _939941))), hBOOL(hAPP(hAPP(c_member(_939935), _939937), _939941))], (9181 ^ _779530) ^ [_940088, _940090, _940092, _940094] : [hBOOL(hAPP(hAPP(c_member(_940088), _940090), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940088, tc_HOL_Obool)), _940092), _940094))), 9184 ^ _779530 : [(9185 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940088), _940090), _940092)))], (9187 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940088), _940090), _940094)))]]], (9189 ^ _779530) ^ [_940255, _940257, _940259, _940261] : [-(hBOOL(hAPP(hAPP(c_member(_940255), _940257), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940255, tc_HOL_Obool)), _940259), _940261)))), hBOOL(hAPP(hAPP(c_member(_940255), _940257), _940259)), hBOOL(hAPP(hAPP(c_member(_940255), _940257), _940261))], (9199 ^ _779530) ^ [_940458, _940460, _940462, _940464] : [hBOOL(hAPP(hAPP(c_member(_940458), _940460), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940458, tc_HOL_Obool)), _940462), _940464))), -(hBOOL(hAPP(hAPP(c_member(_940458), _940460), _940462)))], (9205 ^ _779530) ^ [_940589, _940591, _940593, _940595] : [hBOOL(hAPP(hAPP(c_member(_940589), _940591), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940589, tc_HOL_Obool)), _940593), _940595))), -(hBOOL(hAPP(hAPP(c_member(_940589), _940591), _940595)))], (9211 ^ _779530) ^ [_940720, _940722] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940720, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_940720, tc_HOL_Obool))), _940722) = c_Orderings_Obot__class_Obot(tc_fun(_940720, tc_HOL_Obool)))], (9213 ^ _779530) ^ [_940766, _940768] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940766, tc_HOL_Obool)), _940768), c_Orderings_Obot__class_Obot(tc_fun(_940766, tc_HOL_Obool))) = _940768)], (9215 ^ _779530) ^ [_940807, _940809] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940807, tc_HOL_Obool)), _940809), _940809) = c_Orderings_Obot__class_Obot(tc_fun(_940807, tc_HOL_Obool)))], (9217 ^ _779530) ^ [_940848, _940850] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940848, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_940848, tc_HOL_Obool))), _940850) = c_Orderings_Obot__class_Obot(tc_fun(_940848, tc_HOL_Obool)))], (9219 ^ _779530) ^ [_940894, _940896] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940894, tc_HOL_Obool)), _940896), c_Orderings_Obot__class_Obot(tc_fun(_940894, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_940894, tc_HOL_Obool)))], (9235 ^ _779530) ^ [_941272, _941274, _941276] : [9237 ^ _779530 : [(9238 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941272), 9236 ^ [_941272, _941274, _941276]), _941274)))], (9241 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941272), 9239 ^ [_941272, _941274, _941276]), _941276)))], (9243 ^ _779530) ^ [] : [-(9236 ^ [_941272, _941274, _941276] = 9239 ^ [_941272, _941274, _941276])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941272, tc_HOL_Obool)), _941274), _941276) = c_Orderings_Obot__class_Obot(tc_fun(_941272, tc_HOL_Obool)))], (9221 ^ _779530) ^ [_940958, _940960, _940962] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940958, tc_HOL_Obool)), _940960), _940962) = c_Orderings_Obot__class_Obot(tc_fun(_940958, tc_HOL_Obool)), 9224 ^ _779530 : [(9225 ^ _779530) ^ [_941082] : [hBOOL(hAPP(hAPP(c_member(_940958), _941082), _940960)), 9228 ^ _779530 : [(9229 ^ _779530) ^ [_941172] : [hBOOL(hAPP(hAPP(c_member(_940958), _941172), _940962)), _941082 = _941172]]]]], (9247 ^ _779530) ^ [_941433, _941435, _941437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941433, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941433, tc_HOL_Obool)), _941435), _941437)), _941435)))], (9249 ^ _779530) ^ [_941481, _941483, _941485, _941487, _941489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941481, tc_HOL_Obool)), _941483), _941485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941481, tc_HOL_Obool)), _941487), _941489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941481, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941481, tc_HOL_Obool)), _941483), _941489)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941481, tc_HOL_Obool)), _941485), _941487))))], (9259 ^ _779530) ^ [_941726, _941728, _941730, _941732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941726, tc_HOL_Obool)), _941728), _941730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941726, tc_HOL_Obool)), _941730), _941732)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941726, tc_HOL_Obool)), _941730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941726, tc_HOL_Obool)), _941732), _941728)) = _941728)], (9269 ^ _779530) ^ [_941947, _941949, _941951, _941953] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941947, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_941947), _941949), _941951)), hAPP(hAPP(c_Set_Oinsert(_941947), _941949), _941953)) = hAPP(hAPP(c_Set_Oinsert(_941947), _941949), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941947, tc_HOL_Obool)), _941951), _941953)))], (9271 ^ _779530) ^ [_942022, _942024, _942026] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942022, tc_HOL_Obool)), _942024), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942022, tc_HOL_Obool)), _942026), _942024)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942022, tc_HOL_Obool)), _942024), _942026))], (9273 ^ _779530) ^ [_942082, _942084, _942086] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942082, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942082, tc_HOL_Obool)), _942084), _942086)), _942086) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942082, tc_HOL_Obool)), _942084), _942086))], (9275 ^ _779530) ^ [_942142, _942144, _942146, _942148] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942142, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942142, tc_HOL_Obool)), _942144), _942146)), _942148) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942142, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942142, tc_HOL_Obool)), _942144), _942148)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942142, tc_HOL_Obool)), _942146), _942148)))], (9277 ^ _779530) ^ [_942226, _942228, _942230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942226, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942226, tc_HOL_Obool)), _942228), _942230)), _942228)))], (9279 ^ _779530) ^ [_942274, _942276, _942278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942274, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942274, tc_HOL_Obool)), _942276), _942278)), _942278)))], (9281 ^ _779530) ^ [_942322, _942324, _942326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942322, tc_HOL_Obool)), _942324), _942326)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942322, tc_HOL_Obool)), _942324), _942326) = _942324)], (9287 ^ _779530) ^ [_942443, _942445, _942447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942443, tc_HOL_Obool)), _942445), _942447)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942443, tc_HOL_Obool)), _942447), _942445) = _942445)], (9293 ^ _779530) ^ [_942564, _942566, _942568, _942570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942564, tc_HOL_Obool)), _942566), _942568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942564, tc_HOL_Obool)), _942566), _942570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942564, tc_HOL_Obool)), _942566), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942564, tc_HOL_Obool)), _942568), _942570))))], (9303 ^ _779530) ^ [_942783, _942785, _942787, _942789, _942791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942783, tc_HOL_Obool)), _942785), _942787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942783, tc_HOL_Obool)), _942789), _942791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942783, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942783, tc_HOL_Obool)), _942785), _942789)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942783, tc_HOL_Obool)), _942787), _942791))))], (9313 ^ _779530) ^ [_943028, _943030, _943032, _943034] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943028, tc_HOL_Obool)), _943030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943028, tc_HOL_Obool)), _943032), _943034)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943028, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943028, tc_HOL_Obool)), _943030), _943032)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943028, tc_HOL_Obool)), _943030), _943034)))], (9315 ^ _779530) ^ [_943112, _943114, _943116, _943118] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943112, tc_HOL_Obool)), _943114), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943112, tc_HOL_Obool)), _943116), _943118)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943112, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943112, tc_HOL_Obool)), _943114), _943116)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943112, tc_HOL_Obool)), _943114), _943118)))], (9317 ^ _779530) ^ [_943196, _943198, _943200, _943202] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943196, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943196, tc_HOL_Obool)), _943198), _943200)), _943202) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943196, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943196, tc_HOL_Obool)), _943198), _943202)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943196, tc_HOL_Obool)), _943200), _943202)))], (9319 ^ _779530) ^ [_943280, _943282, _943284, _943286] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943280, tc_HOL_Obool)), _943282), _943284)), _943286) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943280, tc_HOL_Obool)), _943282), _943286)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943280, tc_HOL_Obool)), _943284), _943286)))], (9321 ^ _779530) ^ [_943364, _943366, _943368, _943370] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943364, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943364, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943364, tc_HOL_Obool)), _943366), _943368)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943364, tc_HOL_Obool)), _943368), _943370))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943364, tc_HOL_Obool)), _943370), _943366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943364, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943364, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943364, tc_HOL_Obool)), _943366), _943368)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943364, tc_HOL_Obool)), _943368), _943370))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943364, tc_HOL_Obool)), _943370), _943366)))], (9323 ^ _779530) ^ [_943524, _943526, _943528, _943530] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943524, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_943524, tc_fun(_943524, tc_HOL_Obool), tc_HOL_Obool), c_member(_943524)), _943526)), hAPP(hAPP(c_COMBC(_943524, tc_fun(_943524, tc_HOL_Obool), tc_HOL_Obool), c_member(_943524)), _943528)), _943530)), -(hBOOL(hAPP(hAPP(c_member(_943524), _943530), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943524, tc_HOL_Obool)), _943526), _943528))))], (9329 ^ _779530) ^ [_943723, _943725, _943727, _943729] : [hBOOL(hAPP(hAPP(c_member(_943723), _943729), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943723, tc_HOL_Obool)), _943725), _943727))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943723, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_943723, tc_fun(_943723, tc_HOL_Obool), tc_HOL_Obool), c_member(_943723)), _943725)), hAPP(hAPP(c_COMBC(_943723, tc_fun(_943723, tc_HOL_Obool), tc_HOL_Obool), c_member(_943723)), _943727)), _943729)))], (9335 ^ _779530) ^ [_943928, _943930, _943932, _943934] : [hBOOL(hAPP(hAPP(c_member(_943928), _943930), _943932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943928, tc_HOL_Obool)), _943932), hAPP(_943934, _943932))), 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hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946438, tc_HOL_Obool)), _946442), _946444))], (9451 ^ _779530) ^ [_946517, _946519, _946521, _946523, _946525] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946517, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946517, tc_HOL_Obool)), hAPP(c_Set_Oimage(_946519, _946517, _946521), _946523)), hAPP(c_Set_Oimage(_946519, _946517, _946521), _946525))), hAPP(c_Set_Oimage(_946519, _946517, _946521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946519, tc_HOL_Obool)), _946523), _946525)))))], (9453 ^ _779530) ^ [_946601, _946603, _946605, _946607, _946609] : [class_Lattices_Osemilattice__inf(_946601), class_Lattices_Osemilattice__inf(_946603), c_Orderings_Oorder__class_Omono(_946603, _946601, _946605), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946601), hAPP(_946605, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946603), _946607), _946609))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946601), hAPP(_946605, _946607)), hAPP(_946605, _946609)))))], (9467 ^ _779530) ^ [_946864, _946866, _946868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_946864, tc_HOL_Obool)), _946866), _946868)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946864, tc_HOL_Obool)), _946866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_946864, tc_HOL_Obool)), _946868), _946866)) = _946868)], (9473 ^ _779530) ^ [_947028, _947030, _947032, _947034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947028, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_947028, tc_HOL_Obool)), _947030), _947032)), _947034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947028, tc_HOL_Obool)), _947030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_947028, tc_HOL_Obool)), _947032), _947034))))], (9479 ^ _779530) ^ [_947189, _947191, _947193, _947195] : 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hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_947646, tc_HOL_Obool)), _947650), _947652)))], (9499 ^ _779530) ^ [_947837, _947839, _947841, _947843, _947845, _947847] : [hBOOL(hAPP(hAPP(c_member(_947837), _947839), _947841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947843, tc_HOL_Obool)), hAPP(c_Set_Oimage(_947837, _947843, _947845), _947841)), hAPP(_947847, hAPP(c_Set_Oimage(_947837, _947843, _947845), _947841)))), -(hBOOL(hAPP(hAPP(c_member(_947843), hAPP(_947845, _947839)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_947843, tc_HOL_Obool), _947847))))], (9509 ^ _779530) ^ [_948082, _948084, _948086] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_948082, tc_HOL_Obool)), _948084), _948086) = hAPP(c_Set_OCollect(_948082), hAPP(hAPP(c_COMBS(_948082, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _948082), c_fconj), hAPP(hAPP(c_COMBC(_948082, tc_fun(_948082, tc_HOL_Obool), tc_HOL_Obool), c_member(_948082)), _948084))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _948082), c_fNot), hAPP(hAPP(c_COMBC(_948082, tc_fun(_948082, tc_HOL_Obool), tc_HOL_Obool), c_member(_948082)), _948086)))))], (9511 ^ _779530) ^ [_948185, _948187, _948189, _948191, _948193] : [c_Orderings_Oorder__class_Omono(tc_fun(_948185, tc_HOL_Obool), tc_fun(_948187, tc_HOL_Obool), _948189), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948187, tc_HOL_Obool)), hAPP(_948189, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948185, tc_HOL_Obool)), _948191), _948193))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948187, tc_HOL_Obool)), hAPP(_948189, _948191)), hAPP(_948189, _948193)))))], (9517 ^ _779530) ^ [_948364, _948366, _948368] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948364, tc_HOL_Obool)), _948366), _948368) = hAPP(c_Set_OCollect(_948364), hAPP(hAPP(c_COMBS(_948364, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _948364), c_fconj), hAPP(hAPP(c_COMBC(_948364, tc_fun(_948364, tc_HOL_Obool), tc_HOL_Obool), c_member(_948364)), _948366))), hAPP(hAPP(c_COMBC(_948364, tc_fun(_948364, tc_HOL_Obool), tc_HOL_Obool), c_member(_948364)), _948368))))], (9519 ^ _779530) ^ [_948478, _948480, _948482, _948484] : [hBOOL(hAPP(hAPP(c_member(_948478), _948480), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948478, tc_HOL_Obool)), _948482), hAPP(c_Set_OCollect(_948478), _948484)))), 9522 ^ _779530 : [(9523 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948478), _948480), _948482)))], (9525 ^ _779530) ^ [] : [-(hBOOL(hAPP(_948484, _948480)))]]], (9527 ^ _779530) ^ [_948645, _948647, _948649, _948651] : [-(hBOOL(hAPP(hAPP(c_member(_948645), _948647), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_948645, tc_HOL_Obool)), _948649), hAPP(c_Set_OCollect(_948645), _948651))))), hBOOL(hAPP(hAPP(c_member(_948645), _948647), _948649)), hBOOL(hAPP(_948651, _948647))], (9537 ^ _779530) ^ [_948848, _948850, _948852, _948854] : [c_Orderings_Oorder__class_Omono(tc_fun(_948848, tc_HOL_Obool), tc_fun(_948848, tc_HOL_Obool), _948850), hBOOL(hAPP(hAPP(c_member(_948848), _948852), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_948848, tc_HOL_Obool), _948850))), -(hBOOL(hAPP(hAPP(c_member(_948848), _948852), hAPP(_948850, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_948848, tc_HOL_Obool)), _948854), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_948848, tc_HOL_Obool), _948850))))))], (9547 ^ _779530) ^ [_949079, _949081, _949083, _949085] : [class_Complete__Lattice_Ocomplete__lattice(_949079), _949081 = c_Inductive_Ocomplete__lattice__class_Ogfp(_949079, _949083), c_Orderings_Oorder__class_Omono(_949079, _949079, _949083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949079), _949085), hAPP(_949083, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_949079), _949085), _949081)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949079), _949085), _949081)))], (9565 ^ _779530) ^ [_949384, _949386, _949388] : [class_Complete__Lattice_Ocomplete__lattice(_949384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949384), _949386), hAPP(_949388, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_949384), _949386), c_Inductive_Ocomplete__lattice__class_Ogfp(_949384, _949388))))), c_Orderings_Oorder__class_Omono(_949384, _949384, _949388), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_949384), _949386), c_Inductive_Ocomplete__lattice__class_Ogfp(_949384, _949388))), hAPP(_949388, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_949384), _949386), c_Inductive_Ocomplete__lattice__class_Ogfp(_949384, _949388))))))], (9579 ^ _779530) ^ [_949677, _949679, _949681] : [class_Complete__Lattice_Ocomplete__lattice(_949677), c_Orderings_Oorder__class_Omono(_949677, _949677, _949679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949677), _949681), hAPP(_949679, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_949677), _949681), c_Inductive_Ocomplete__lattice__class_Ogfp(_949677, _949679))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949677), _949681), c_Inductive_Ocomplete__lattice__class_Ogfp(_949677, _949679))))], (9593 ^ _779530) ^ [_949922, _949924, _949926] : [-(hBOOL(hAPP(hAPP(c_member(_949922), _949924), _949926))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949922, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_949922), _949924), _949926)), hAPP(hAPP(c_Set_Oinsert(_949922), _949924), c_Orderings_Obot__class_Obot(tc_fun(_949922, tc_HOL_Obool)))) = _949926)], (9599 ^ _779530) ^ [_949999, _950001, _950003] : [hBOOL(hAPP(hAPP(c_member(_949999), _950001), _950003)), -(hAPP(hAPP(c_Set_Oinsert(_949999), _950001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_949999, tc_HOL_Obool)), _950003), hAPP(hAPP(c_Set_Oinsert(_949999), _950001), c_Orderings_Obot__class_Obot(tc_fun(_949999, tc_HOL_Obool))))) = _950003)], (9605 ^ _779530) ^ [_950168, _950170, _950172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950168, tc_HOL_Obool)), _950170), hAPP(hAPP(c_Set_Oinsert(_950168), _950172), c_Orderings_Obot__class_Obot(tc_fun(_950168, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_950168, _950172, _950170) = _950172)], (9611 ^ _779530) ^ [_950295, _950297, _950299] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950295, tc_HOL_Obool)), _950297), hAPP(hAPP(c_Set_Oinsert(_950295), _950299), c_Orderings_Obot__class_Obot(tc_fun(_950295, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_950295, _950299, _950297) = c_HOL_OThe(_950295, hAPP(hAPP(c_COMBC(_950295, tc_fun(_950295, tc_HOL_Obool), tc_HOL_Obool), c_member(_950295)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950295, tc_HOL_Obool)), _950297), hAPP(hAPP(c_Set_Oinsert(_950295), _950299), c_Orderings_Obot__class_Obot(tc_fun(_950295, tc_HOL_Obool)))))))], (9617 ^ _779530) ^ [_950404, _950406, _950408, _950410, _950412] : [_950404 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_950406, tc_HOL_Obool), _950408), c_Orderings_Oorder__class_Omono(tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool), _950408), hBOOL(hAPP(hAPP(c_member(_950406), _950410), _950412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950406, tc_HOL_Obool)), _950412), hAPP(_950408, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_950406, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_950406, tc_HOL_Obool), tc_fun(tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool)), tc_fun(_950406, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950406, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_950406, tc_HOL_Obool), tc_fun(tc_fun(_950406, tc_HOL_Obool), tc_fun(_950406, tc_HOL_Obool)), tc_fun(_950406, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950406, tc_HOL_Obool))), _950408)), _950412))), _950404))))), -(hBOOL(hAPP(hAPP(c_member(_950406), _950410), _950404)))], (9635 ^ _779530) ^ [_950949, _950951, _950953, _950955] : [c_Orderings_Oorder__class_Omono(tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool), _950951), hBOOL(hAPP(hAPP(c_member(_950949), _950953), _950955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950949, tc_HOL_Obool)), _950955), hAPP(_950951, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_950949, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_950949, tc_HOL_Obool), tc_fun(tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool)), tc_fun(_950949, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950949, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_950949, tc_HOL_Obool), tc_fun(tc_fun(_950949, tc_HOL_Obool), tc_fun(_950949, tc_HOL_Obool)), tc_fun(_950949, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_950949, tc_HOL_Obool))), _950951)), _950955))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_950949, tc_HOL_Obool), _950951)))))), -(hBOOL(hAPP(hAPP(c_member(_950949), _950953), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_950949, tc_HOL_Obool), _950951))))], (9649 ^ _779530) ^ [_951442, _951444, _951446, _951448, _951450] : [_951442 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_951444, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_951444, tc_HOL_Obool), tc_fun(_951444, tc_HOL_Obool), tc_fun(_951444, tc_HOL_Obool)), c_Set_OCollect(_951444)), _951446)), c_Orderings_Oorder__class_Omono(tc_fun(_951444, tc_HOL_Obool), tc_fun(_951444, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_951444, tc_HOL_Obool), tc_fun(_951444, tc_HOL_Obool), tc_fun(_951444, tc_HOL_Obool)), c_Set_OCollect(_951444)), _951446)), hBOOL(hAPP(hAPP(c_member(_951444), _951448), _951450)), 9663 ^ _779530 : [(9664 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_951444), 9662 ^ [_951442, _951444, _951446, _951448, _951450]), _951450)))], (9666 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_951446, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951444, tc_HOL_Obool)), _951450), _951442)), 9662 ^ [_951442, _951444, _951446, _951448, _951450]))]], -(hBOOL(hAPP(hAPP(c_member(_951444), _951448), _951442)))], (9670 ^ _779530) ^ [_951982, _951984, _951986, _951988, _951990] : [class_Groups_Oordered__ab__group__add(_951982), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_951982), _951984), _951986) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_951982), _951988), _951990), 9677 ^ _779530 : [(9678 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951982), _951984), _951986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951982), _951988), _951990)))], (9684 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951982), _951988), _951990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951982), _951984), _951986)))]]], (9690 ^ _779530) ^ [_952358, _952360, _952362, _952364, _952366, _952368] : [hBOOL(hAPP(hAPP(c_member(_952358), _952360), _952362)), -(hAPP(c_Set_Oimage(_952358, _952364, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952358, _952364), _952366), _952360), _952368)), _952362) = hAPP(hAPP(c_Set_Oinsert(_952364), _952368), hAPP(c_Set_Oimage(_952358, _952364, _952366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952358, tc_HOL_Obool)), _952362), hAPP(hAPP(c_Set_Oinsert(_952358), _952360), c_Orderings_Obot__class_Obot(tc_fun(_952358, tc_HOL_Obool)))))))], (9696 ^ _779530) ^ [_952567, _952569, _952571, _952573, _952575, _952577] : [-(hBOOL(hAPP(hAPP(c_member(_952567), _952569), _952571))), -(hAPP(c_Set_Oimage(_952567, _952573, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_952567, _952573), _952575), _952569), _952577)), _952571) = hAPP(c_Set_Oimage(_952567, _952573, _952575), _952571))], (9702 ^ _779530) ^ [_952646, _952648, _952650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952646, tc_HOL_Obool)), _952648), hAPP(_952650, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_952646, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), _952650)), _952648))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_952646, tc_HOL_Obool), _952650)))))), c_Orderings_Oorder__class_Omono(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), _952650), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952646, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_952646, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), _952650)), _952648))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_952646, tc_HOL_Obool), _952650)))), hAPP(_952650, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_952646, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_952646, tc_HOL_Obool), tc_fun(tc_fun(_952646, tc_HOL_Obool), tc_fun(_952646, tc_HOL_Obool)), tc_fun(_952646, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952646, tc_HOL_Obool))), _952650)), _952648))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_952646, tc_HOL_Obool), _952650)))))))], (9738 ^ _779530) ^ [_954053, _954055, _954057, _954059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954053, tc_HOL_Obool)), _954055), hAPP(hAPP(c_Set_Oinsert(_954053), _954057), _954059)))), 9741 ^ _779530 : [(9742 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954053), _954057), _954059)))], (9744 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954053, tc_HOL_Obool)), _954055), _954059))]], 9745 ^ _779530 : [(9746 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_954053), _954057), _954059))], (9748 ^ _779530) ^ [] : [9749 ^ _779530 : [(9750 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954053), _954057), _954055)))], (9752 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954053, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954053, tc_HOL_Obool)), _954055), hAPP(hAPP(c_Set_Oinsert(_954053), _954057), c_Orderings_Obot__class_Obot(tc_fun(_954053, tc_HOL_Obool))))), _954059))]], 9753 ^ _779530 : [(9754 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_954053), _954057), _954055))], (9756 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954053, tc_HOL_Obool)), _954055), _954059))]]]]], (9712 ^ _779530) ^ [_953526, _953528, _953530, _953532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953526, tc_HOL_Obool)), _953528), hAPP(hAPP(c_Set_Oinsert(_953526), _953530), _953532))), 9715 ^ _779530 : [(9716 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_953526), _953530), _953532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953526, tc_HOL_Obool)), _953528), _953532)))], (9722 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953526), _953530), _953532))), 9725 ^ _779530 : [(9726 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_953526), _953530), _953528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953526, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953526, tc_HOL_Obool)), _953528), hAPP(hAPP(c_Set_Oinsert(_953526), _953530), c_Orderings_Obot__class_Obot(tc_fun(_953526, tc_HOL_Obool))))), _953532)))], (9732 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953526), _953530), _953528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953526, tc_HOL_Obool)), _953528), _953532)))]]]]], (9760 ^ _779530) ^ [_954592, _954594, _954596, _954598, _954600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954592, tc_HOL_Obool)), _954594), _954596)), 9766 ^ _779530 : [(9767 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954592), 9765 ^ [_954592, _954594, _954596, _954598, _954600]), _954594)))], (9769 ^ _779530) ^ [] : [-(hBOOL(hAPP(_954598, 9765 ^ [_954592, _954594, _954596, _954598, _954600])))], (9771 ^ _779530) ^ [] : [hBOOL(hAPP(_954600, 9765 ^ [_954592, _954594, _954596, _954598, _954600]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954592, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954592, tc_HOL_Obool)), _954594), hAPP(c_Set_OCollect(_954592), _954598))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954592, tc_HOL_Obool)), _954596), hAPP(c_Set_OCollect(_954592), _954600)))))], (9775 ^ _779530) ^ [_954992, _954994, _954996, _954998, _955000, _955002, _955004] : [hBOOL(hAPP(hAPP(c_member(_954992), _954994), _954996)), c_Nitpick_Ofold__graph_H(_954992, _954998, _955000, _955002, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954992, tc_HOL_Obool)), _954996), hAPP(hAPP(c_Set_Oinsert(_954992), _954994), c_Orderings_Obot__class_Obot(tc_fun(_954992, tc_HOL_Obool)))), _955004), -(c_Nitpick_Ofold__graph_H(_954992, _954998, _955000, _955002, _954996, hAPP(hAPP(_955000, _954994), _955004)))], (9785 ^ _779530) ^ [_955231, _955233, _955235, _955237] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_955231, _955233), _955235), _955237), hAPP(_955235, _955237)) = _955235)], (9787 ^ _779530) ^ [_955275, _955277, _955279] : [class_Orderings_Olinorder(_955275), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955275), _955277), _955279))), -(_955277 = _955279), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955275), _955279), _955277)))], (9801 ^ _779530) ^ [_955410, _955412, _955414] : [class_Orderings_Opreorder(_955410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955410), _955412), _955414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955410), _955414), _955412))], (9811 ^ _779530) ^ [_955570, _955572, _955574, _955576] : [class_Orderings_Oorder(_955570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955570), _955572), _955574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955570), _955576), _955572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955570), _955576), _955574)))], (9825 ^ _779530) ^ [_955803, _955805, _955807, _955809] : [class_Orderings_Opreorder(_955803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955803), _955805), _955807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955803), _955807), _955809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955803), _955805), _955809)))], (9839 ^ _779530) ^ [_956036, _956038, _956040, _956042] : [class_Orderings_Oorder(_956036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956036), _956038), _956040)), _956038 = _956042, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956036), _956042), _956040)))], (9853 ^ _779530) ^ [_956255, _956257, _956259, _956261] : [class_Orderings_Oord(_956255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956255), _956257), _956259)), _956259 = _956261, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956255), _956257), _956261)))], (9867 ^ _779530) ^ [_956474, _956476, _956478, _956480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956474, tc_HOL_Obool)), _956476), _956478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956474, tc_HOL_Obool)), _956478), _956480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_956474, tc_HOL_Obool)), _956476), _956480)))], (9877 ^ _779530) ^ [_956671, _956673, _956675, _956677] : [class_Orderings_Oorder(_956671), _956673 = _956675, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956671), _956677), _956675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956671), _956677), _956673)))], (9891 ^ _779530) ^ [_956890, _956892, _956894, _956896] : [class_Orderings_Oord(_956890), _956892 = _956894, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956890), _956894), _956896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956890), _956892), _956896)))], (9905 ^ _779530) ^ [_957109, _957111, _957113] : [class_Orderings_Oorder(_957109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957109), _957111), _957113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957109), _957113), _957111))], (9915 ^ _779530) ^ [_957269, _957271, _957273] : [class_Orderings_Opreorder(_957269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957269), _957271), _957273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957269), _957273), _957271))], (9925 ^ _779530) ^ [_957429, _957431, _957433] : [class_Orderings_Oorder(_957429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957429), _957431), _957433)), _957433 = _957431], (9935 ^ _779530) ^ [_957575, _957577, _957579] : [class_Orderings_Oorder(_957575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957575), _957577), _957579)), _957577 = _957579], (9945 ^ _779530) ^ [_957721, _957723, _957725] : [class_Orderings_Opreorder(_957721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957721), _957723), _957725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957721), _957725), _957723))], (9955 ^ _779530) ^ [_957881, _957883, _957885] : [class_Orderings_Opreorder(_957881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957881), _957883), _957885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_957881), _957885), _957883))], (9965 ^ _779530) ^ [_958041, _958043, _958045] : [class_Orderings_Oorder(_958041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958041), _958043), _958045)), _958043 = _958045], (9975 ^ _779530) ^ [_958187, _958189, _958191] : [class_Orderings_Olinorder(_958187), -(_958189 = _958191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958187), _958189), _958191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958187), _958191), _958189)))], (9989 ^ _779530) ^ [_958322, _958324, _958326] : [class_Orderings_Olinorder(_958322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958322), _958324), _958326))), 9996 ^ _779530 : [(9997 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958322), _958326), _958324))), -(_958326 = _958324)], (10003 ^ _779530) ^ [] : [_958326 = _958324, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958322), _958326), _958324))]]], (10009 ^ _779530) ^ [_958581, _958583, _958585] : [class_Orderings_Olinorder(_958581), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958581), _958583), _958585))), -(_958583 = _958585), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958581), _958585), _958583)))], (10023 ^ _779530) ^ [_958712, _958714, _958716] : [class_Orderings_Olinorder(_958712), 10026 ^ _779530 : [(10037 ^ _779530) ^ [] : [10038 ^ _779530 : [(10039 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958712), _958716), _958714))], (10041 ^ _779530) ^ [] : [_958714 = _958716]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958712), _958714), _958716))], (10027 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958712), _958714), _958716))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958712), _958716), _958714))), -(_958714 = _958716)]]], (10045 ^ _779530) ^ [_958966, _958968, _958970] : [class_Orderings_Olinorder(_958966), 10048 ^ _779530 : [(10059 ^ _779530) ^ [] : [10060 ^ _779530 : [(10061 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958966), _958968), _958970))], (10063 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958966), _958970), _958968))]], _958968 = _958970], (10049 ^ _779530) ^ [] : [-(_958968 = _958970), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958966), _958968), _958970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958966), _958970), _958968)))]]], (10067 ^ _779530) ^ [_959220, _959222] : [class_Orderings_Opreorder(_959220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959220), _959222), _959222))], (10073 ^ _779530) ^ [_959310, _959312, _959314, _959316, _959318] : [hAPP(_959310, _959312) = _959314, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959316, _959318), _959310), _959312), _959314) = _959310)], (10079 ^ _779530) ^ [_959419, _959421, _959423, _959425, _959427, _959429] : [-(_959419 = _959421), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959423, _959425), _959427), _959421), _959429), _959419) = hAPP(_959427, _959419))], (10085 ^ _779530) ^ [_959477, _959479, _959481, _959483, _959485, _959487, _959489] : [-(_959477 = _959479), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959481, _959483), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959481, _959483), _959485), _959477), _959487)), _959479), _959489) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959481, _959483), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959481, _959483), _959485), _959479), _959489)), _959477), _959487))], (10091 ^ _779530) ^ [_959592, _959594, _959596, _959598, _959600, _959602] : [_959592 = _959594, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959596, _959598), _959600), _959594), _959602), _959592) = _959602)], (10097 ^ _779530) ^ [_959701, _959703, _959705, _959707, _959709, _959711] : [-(_959701 = _959703), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959705, _959707), _959709), _959703), _959711), _959701) = hAPP(_959709, _959701))], (10103 ^ _779530) ^ [_959765, _959767, _959769, _959771, _959773] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959765, _959767), _959769), _959771), _959773), _959771) = _959773)], (10105 ^ _779530) ^ [_959811, _959813, _959815, _959817, _959819, _959821] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959811, _959813), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959811, _959813), _959815), _959817), _959819)), _959817), _959821) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959811, _959813), _959815), _959817), _959821))], (10107 ^ _779530) ^ [_959904, _959906, _959908, _959910, _959912] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_959904, _959906), _959908), _959910), _959912) = _959908, -(hAPP(_959908, _959910) = _959912)], (10113 ^ _779530) ^ [_960013, _960015, _960017, _960019, _960021] : [hAPP(_960017, _960019) = _960021, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_960013, _960015), _960017), _960019), _960021) = _960017)], (10119 ^ _779530) ^ [_960128, _960130, _960132, _960134, _960136] : [class_Groups_Oordered__ab__group__add(_960128), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960128), _960130), _960132) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_960128), _960134), _960136), 10126 ^ _779530 : [(10127 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960128), _960130), _960132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960128), _960134), _960136)))], (10133 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960128), _960134), _960136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960128), _960130), _960132)))]]], (10139 ^ _779530) ^ [_960504, _960506, _960508, _960510, _960512, _960514] : [_960504 = _960506, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_960508, _960510), _960512), _960506), _960514), _960504) = _960514)], (10145 ^ _779530) ^ [_960613, _960615, _960617, _960619, _960621, _960623] : [-(_960613 = _960615), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_960617, _960619), _960621), _960615), _960623), _960613) = hAPP(_960621, _960613))], (10151 ^ _779530) ^ [_960677, _960679] : [class_Complete__Lattice_Ocomplete__lattice(_960677), -(c_Inductive_Ocomplete__lattice__class_Olfp(_960677, hAPP(c_COMBK(_960677, _960677), _960679)) = _960679)], (10157 ^ _779530) ^ [_960770, _960772, _960774, _960776] : [-(c_Nitpick_Ofold__graph_H(_960770, _960772, _960774, _960776, c_Orderings_Obot__class_Obot(tc_fun(_960770, tc_HOL_Obool)), _960776))], (10159 ^ _779530) ^ [_960808, _960810, _960812, _960814] : [-(c_Nitpick_Ofold__graph_H(_960808, _960810, _960812, _960814, c_Orderings_Obot__class_Obot(tc_fun(_960808, tc_HOL_Obool)), _960814))], (10161 ^ _779530) ^ [_960846, _960848, _960850, _960852] : [class_Orderings_Oord(_960846), 10164 ^ _779530 : [(10165 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960848, _960846)), _960850), _960852)), 10168 ^ _779530 : [(10169 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960848, _960846)), _960850), _960852)))], (10171 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960848, _960846)), _960852), _960850))]]], (10173 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960848, _960846)), _960850), _960852))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960848, _960846)), _960850), _960852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960848, _960846)), _960852), _960850)))]]], (10183 ^ _779530) ^ [_961238, _961240, _961242, _961244] : [class_Orderings_Oorder(_961238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961238), _961240), _961242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961238), _961244), _961240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961238), _961244), _961242)))], (10197 ^ _779530) ^ [_961471, _961473, _961475, _961477] : [class_Orderings_Opreorder(_961471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961471), _961473), _961475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961471), _961475), _961477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961471), _961473), _961477)))], (10211 ^ _779530) ^ [_961704, _961706, _961708, _961710] : [class_Orderings_Oorder(_961704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961704), _961706), _961708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961704), _961710), _961706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961704), _961710), _961708)))], (10225 ^ _779530) ^ [_961937, _961939, _961941, _961943] : [class_Orderings_Opreorder(_961937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961937), _961939), _961941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961937), _961941), _961943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961937), _961939), _961943)))], (10239 ^ _779530) ^ [_962170, _962172, _962174] : [class_Orderings_Oorder(_962170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962170), _962172), _962174)), -(_962174 = _962172), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962170), _962172), _962174)))], (10253 ^ _779530) ^ [_962344, _962346, _962348] : [class_Orderings_Oorder(_962344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962344), _962346), _962348)), -(_962346 = _962348), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962344), _962346), _962348)))], (10267 ^ _779530) ^ [_962518, _962520, _962522] : [class_Orderings_Oorder(_962518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962518), _962520), _962522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962518), _962520), _962522))), -(_962520 = _962522)], (10281 ^ _779530) ^ [_962690, _962692, _962694] : [class_Orderings_Olinorder(_962690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962690), _962692), _962694)), 10288 ^ _779530 : [(10289 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962690), _962692), _962694))), -(_962692 = _962694)], (10295 ^ _779530) ^ [] : [_962692 = _962694, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962690), _962692), _962694))]]], (10301 ^ _779530) ^ [_962946, _962948, _962950] : [class_Orderings_Opreorder(_962946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962946), _962948), _962950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962946), _962948), _962950)))], (10311 ^ _779530) ^ [_963105, _963107, _963109] : [class_Orderings_Olinorder(_963105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963105), _963107), _963109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963105), _963109), _963107))], (10321 ^ _779530) ^ [_963265, _963267, _963269] : [class_Orderings_Oorder(_963265), -(_963267 = _963269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963265), _963269), _963267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963265), _963269), _963267)))], (10335 ^ _779530) ^ [_963481, _963483, _963485] : [class_Orderings_Oorder(_963481), -(_963483 = _963485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963481), _963483), _963485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963481), _963483), _963485)))], (10349 ^ _779530) ^ [_963697, _963699, _963701] : [class_Orderings_Olinorder(_963697), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963697), _963699), _963701))), 10356 ^ _779530 : [(10357 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963697), _963699), _963701)), -(_963699 = _963701)], (10363 ^ _779530) ^ [] : [_963699 = _963701, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963697), _963699), _963701)))]]], (10369 ^ _779530) ^ [_964000, _964002, _964004] : [class_Orderings_Olinorder(_964000), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964000), _964002), _964004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964000), _964004), _964002)))], (10379 ^ _779530) ^ [_964120, _964122, _964124] : [class_Orderings_Olinorder(_964120), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964120), _964122), _964124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964120), _964124), _964122)))], (10389 ^ _779530) ^ [_964240, _964242, _964244] : [class_Orderings_Oorder(_964240), 10392 ^ _779530 : [(10403 ^ _779530) ^ [] : [10404 ^ _779530 : [(10405 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964240), _964242), _964244))], (10407 ^ _779530) ^ [] : [_964242 = _964244]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964240), _964242), _964244)))], (10393 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964240), _964242), _964244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964240), _964242), _964244))), -(_964242 = _964244)]]], (10411 ^ _779530) ^ [_964538, _964540, _964542] : [class_Orderings_Opreorder(_964538), 10414 ^ _779530 : [(10415 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964538), _964540), _964542)), 10418 ^ _779530 : [(10419 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964538), _964540), _964542)))], (10421 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964538), _964542), _964540))]]], (10423 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964538), _964540), _964542))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964538), _964540), _964542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964538), _964542), _964540)))]]], (10433 ^ _779530) ^ [_964895, _964897, _964899] : [class_Orderings_Oorder(_964895), 10436 ^ _779530 : [(10437 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964895), _964897), _964899)), 10440 ^ _779530 : [(10441 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964895), _964897), _964899)))], (10443 ^ _779530) ^ [] : [_964897 = _964899]]], (10445 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964895), _964897), _964899))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964895), _964897), _964899)), -(_964897 = _964899)]]], (10455 ^ _779530) ^ [_965231, _965233, _965235] : [class_Orderings_Olinorder(_965231), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965231), _965233), _965235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965231), _965235), _965233)))], (10465 ^ _779530) ^ [_965349, _965351, _965353] : [class_Orderings_Olinorder(_965349), 10468 ^ _779530 : [(10469 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965349), _965351), _965353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965349), _965353), _965351)))], (10475 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965349), _965353), _965351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965349), _965351), _965353))]]], (10481 ^ _779530) ^ [_965558, _965560, _965562] : [class_Orderings_Olinorder(_965558), 10484 ^ _779530 : [(10485 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965558), _965560), _965562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965558), _965562), _965560)))], (10491 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965558), _965562), _965560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_965558), _965560), _965562))]]], (10497 ^ _779530) ^ [_965767, _965769, _965771, _965773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_965767, tc_HOL_Obool)), _965769), _965771)), hBOOL(hAPP(hAPP(c_member(_965767), _965773), _965769)), -(hBOOL(hAPP(hAPP(c_member(_965767), _965773), _965771)))], (10507 ^ _779530) ^ [_965952, _965954, _965956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965952), _965954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965952), _965956)), 10514 ^ _779530 : [(10515 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965954), _965952)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965956), _965952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965954), _965956)))], (10521 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965954), _965956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965954), _965952)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965956), _965952))))]]], (10527 ^ _779530) ^ [_966305, _966307, _966309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966305), _966307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966305), _966309)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966307), _966305)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966309), _966305)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966307), _966309))], (10537 ^ _779530) ^ [_966506, _966508, _966510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966506), _966508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966506), _966510)), 10544 ^ _779530 : [(10545 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966508), _966506) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966510), _966506), -(_966508 = _966510)], (10551 ^ _779530) ^ [] : [_966508 = _966510, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966508), _966506) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966510), _966506))]]], (10557 ^ _779530) ^ [_966829, _966831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966829), _966831)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966831), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966831), _966829)) = _966829)], (10563 ^ _779530) ^ [_966940, _966942, _966944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966940), _966942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966940), _966944)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966942), _966944))))], (10569 ^ _779530) ^ [_967063, _967065, _967067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967063), _967065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967067), _967065)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967067), _967063))))], (10575 ^ _779530) ^ [_967186, _967188] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967186), _967188)), _967186)))], (10577 ^ _779530) ^ [_967234, _967236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_967234, tc_HOL_Obool)), _967236), c_Orderings_Obot__class_Obot(tc_fun(_967234, tc_HOL_Obool))))], (10579 ^ _779530) ^ [_967274, _967276, _967278, _967280] : [class_Lattices_Osemilattice__sup(_967274), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967274), _967276), _967278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967274), _967276), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967274), _967278), _967280))))], (10589 ^ _779530) ^ [_967453, _967455, _967457, _967459] : [class_Lattices_Osemilattice__sup(_967453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967453), _967455), _967457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967453), _967455), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967453), _967459), _967457))))], (10599 ^ _779530) ^ [_967632, _967634, _967636, _967638] : [class_Lattices_Osemilattice__inf(_967632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967632), _967634), _967636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967632), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_967632), _967638), _967634)), _967636)))], (10609 ^ _779530) ^ [_967811, _967813, _967815, _967817] : [class_Lattices_Osemilattice__inf(_967811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), _967813), _967815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967811), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_967811), _967813), _967817)), _967815)))], (10619 ^ _779530) ^ [_967990, _967992, _967994, _967996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_967990, tc_HOL_Obool)), _967992), _967994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_967990, tc_HOL_Obool)), _967994), _967996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_967990, tc_HOL_Obool)), _967992), _967996)))], (10629 ^ _779530) ^ [_968187, _968189, _968191, _968193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968187, tc_HOL_Obool)), _968189), _968191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968187, tc_HOL_Obool)), _968191), _968193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968187, tc_HOL_Obool)), _968189), _968193)))], (10639 ^ _779530) ^ [_968384, _968386, _968388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968384, tc_HOL_Obool)), _968386), _968388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968384, tc_HOL_Obool)), _968386), _968388)))], (10655 ^ _779530) ^ [_968649, _968651, _968653] : [10656 ^ _779530 : [(10657 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968649, tc_HOL_Obool)), _968651), _968653))], (10659 ^ _779530) ^ [] : [_968651 = _968653]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968649, tc_HOL_Obool)), _968651), _968653)))], (10645 ^ _779530) ^ [_968521, _968523, _968525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968521, tc_HOL_Obool)), _968523), _968525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968521, tc_HOL_Obool)), _968523), _968525))), -(_968523 = _968525)], (10663 ^ _779530) ^ [_968826, _968828, _968830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968826, tc_HOL_Obool)), _968828), _968830)), 10666 ^ _779530 : [(10667 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968826, tc_HOL_Obool)), _968828), _968830)))], (10669 ^ _779530) ^ [] : [_968828 = _968830]]], (10671 ^ _779530) ^ [_968975, _968977, _968979] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_968975, tc_HOL_Obool)), _968977), _968979))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_968975, tc_HOL_Obool)), _968977), _968979)), -(_968977 = _968979)], (10681 ^ _779530) ^ [_969153, _969155, _969157, _969159, _969161, _969163, _969165] : [-(hAPP(c_Fun_Ocomp(_969153, _969155, _969157, _969159), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_969157, _969153), _969161), _969163), _969165)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_969157, _969155), hAPP(c_Fun_Ocomp(_969153, _969155, _969157, _969159), _969161)), _969163), hAPP(_969159, _969165)))], (10683 ^ _779530) ^ [_969231, _969233, _969235, _969237, _969239] : [class_Orderings_Oorder(_969231), class_Orderings_Oorder(_969233), c_Orderings_Oorder__class_Ostrict__mono(_969233, _969231, _969235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969233), _969237), _969239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969231), hAPP(_969235, _969237)), hAPP(_969235, _969239))))], (10701 ^ _779530) ^ [_969528, _969530, _969532, _969534, _969536] : [class_Orderings_Oorder(_969528), class_Orderings_Olinorder(_969530), c_Orderings_Oorder__class_Ostrict__mono(_969530, _969528, _969532), 10712 ^ _779530 : [(10713 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969528), hAPP(_969532, _969534)), hAPP(_969532, _969536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969530), _969534), _969536)))], (10719 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969530), _969534), _969536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969528), hAPP(_969532, _969534)), hAPP(_969532, _969536))))]]], (10725 ^ _779530) ^ [_969929, _969931, _969933] : [class_Complete__Lattice_Ocomplete__lattice(_969929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969929), hAPP(_969931, _969933)), _969933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969929), c_Inductive_Ocomplete__lattice__class_Olfp(_969929, _969931)), _969933)))], (10735 ^ _779530) ^ [_970100, _970102, _970104] : [class_Orderings_Owellorder(_970100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970100), _970102), c_Orderings_Oord__class_OLeast(_970100, _970104))), hBOOL(hAPP(_970104, _970102))], (10745 ^ _779530) ^ [_970256, _970258] : [class_Complete__Lattice_Ocomplete__lattice(_970256), c_Orderings_Oorder__class_Omono(_970256, _970256, _970258), -(c_Inductive_Ocomplete__lattice__class_Olfp(_970256, _970258) = hAPP(_970258, c_Inductive_Ocomplete__lattice__class_Olfp(_970256, _970258)))], (10755 ^ _779530) ^ [_970403, _970405, _970407] : [class_Complete__Lattice_Ocomplete__lattice(_970403), _970405 = c_Inductive_Ocomplete__lattice__class_Olfp(_970403, _970407), c_Orderings_Oorder__class_Omono(_970403, _970403, _970407), -(_970405 = hAPP(_970407, _970405))], (10769 ^ _779530) ^ [_970602, _970604] : [class_Complete__Lattice_Ocomplete__lattice(_970602), c_Orderings_Oorder__class_Omono(_970602, _970602, _970604), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970602), c_Inductive_Ocomplete__lattice__class_Olfp(_970602, _970604)), hAPP(_970604, c_Inductive_Ocomplete__lattice__class_Olfp(_970602, _970604)))))], (10779 ^ _779530) ^ [_970763, _970765] : [class_Complete__Lattice_Ocomplete__lattice(_970763), c_Orderings_Oorder__class_Omono(_970763, _970763, _970765), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970763), hAPP(_970765, c_Inductive_Ocomplete__lattice__class_Olfp(_970763, _970765))), c_Inductive_Ocomplete__lattice__class_Olfp(_970763, _970765))))], (10789 ^ _779530) ^ [_970924, _970926, _970928, _970930, _970932] : [class_Groups_Oab__group__add(_970924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970924), _970926), _970928) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_970924), _970930), _970932), 10796 ^ _779530 : [(10797 ^ _779530) ^ [] : [_970926 = _970928, -(_970930 = _970932)], (10803 ^ _779530) ^ [] : [_970930 = _970932, -(_970926 = _970928)]]], (10809 ^ _779530) ^ [_971237, _971239, _971241] : [class_Complete__Lattice_Ocomplete__lattice(_971237), c_Orderings_Oorder__class_Omono(_971237, _971237, _971239), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971237), hAPP(_971239, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971237), c_Inductive_Ocomplete__lattice__class_Olfp(_971237, _971239)), _971241))), _971241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971237), c_Inductive_Ocomplete__lattice__class_Olfp(_971237, _971239)), _971241)))], (10823 ^ _779530) ^ [_971486, _971488, _971490, _971492] : [class_Complete__Lattice_Ocomplete__lattice(_971486), _971488 = c_Inductive_Ocomplete__lattice__class_Olfp(_971486, _971490), c_Orderings_Oorder__class_Omono(_971486, _971486, _971490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971486), hAPP(_971490, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_971486), _971488), _971492))), _971492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_971486), _971488), _971492)))], (10841 ^ _779530) ^ [_971791, _971793, _971795, _971797, _971799] : [_971791 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_971793, tc_HOL_Obool), _971795), c_Orderings_Oorder__class_Omono(tc_fun(_971793, tc_HOL_Obool), tc_fun(_971793, tc_HOL_Obool), _971795), hBOOL(hAPP(hAPP(c_member(_971793), _971797), _971791)), 10855 ^ _779530 : [(10856 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_971793), 10854 ^ [_971791, _971793, _971795, _971797, _971799]), hAPP(_971795, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971793, tc_HOL_Obool)), _971791), hAPP(c_Set_OCollect(_971793), _971799))))))], (10858 ^ _779530) ^ [] : [hBOOL(hAPP(_971799, 10854 ^ [_971791, _971793, _971795, _971797, _971799]))]], -(hBOOL(hAPP(_971799, _971797)))], (10862 ^ _779530) ^ [_972232, _972234, _972236, _972238] : [hBOOL(hAPP(hAPP(c_member(_972232), _972234), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_972232, tc_HOL_Obool), _972236))), c_Orderings_Oorder__class_Omono(tc_fun(_972232, tc_HOL_Obool), tc_fun(_972232, tc_HOL_Obool), _972236), 10872 ^ _779530 : [(10873 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972232), 10871 ^ [_972232, _972234, _972236, _972238]), hAPP(_972236, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972232, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_972232, tc_HOL_Obool), _972236)), hAPP(c_Set_OCollect(_972232), _972238))))))], (10875 ^ _779530) ^ [] : [hBOOL(hAPP(_972238, 10871 ^ [_972232, _972234, _972236, _972238]))]], -(hBOOL(hAPP(_972238, _972234)))], (10879 ^ _779530) ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657] : [c_Nitpick_Ofold__graph_H(_972645, _972647, _972649, _972651, _972653, hAPP(hAPP(_972649, _972655), _972657)), 10884 ^ _779530 : [(10885 ^ _779530) ^ [] : [-(_972653 = c_Orderings_Obot__class_Obot(tc_fun(_972645, tc_HOL_Obool)))], (10887 ^ _779530) ^ [] : [-(hAPP(hAPP(_972649, _972655), _972657) = _972651)]], 10890 ^ _779530 : [(10891 ^ _779530) ^ [] : [-(hAPP(hAPP(_972649, _972655), _972657) = hAPP(hAPP(_972649, 10888 ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657]), 10889 ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657]))], (10893 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972645), 10888 ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657]), _972653)))], (10895 ^ _779530) ^ [] : [-(c_Nitpick_Ofold__graph_H(_972645, _972647, _972649, _972651, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972645, tc_HOL_Obool)), _972653), hAPP(hAPP(c_Set_Oinsert(_972645), 10888 ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657]), c_Orderings_Obot__class_Obot(tc_fun(_972645, tc_HOL_Obool)))), 10889 ^ [_972645, _972647, _972649, _972651, _972653, _972655, _972657]))]]], (10897 ^ _779530) ^ [_973082, _973084, _973086, _973088, _973090, _973092, _973094] : [-(c_Nitpick_Ofold__graph_H(_973082, _973084, _973086, _973088, _973090, hAPP(hAPP(_973086, _973092), _973094))), 10898 ^ _779530 : [(10899 ^ _779530) ^ [] : [_973090 = c_Orderings_Obot__class_Obot(tc_fun(_973082, tc_HOL_Obool)), hAPP(hAPP(_973086, _973092), _973094) = _973088], (10905 ^ _779530) ^ [_973311, _973313] : [hAPP(hAPP(_973086, _973092), _973094) = hAPP(hAPP(_973086, _973313), _973311), hBOOL(hAPP(hAPP(c_member(_973082), _973313), _973090)), c_Nitpick_Ofold__graph_H(_973082, _973084, _973086, _973088, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973082, tc_HOL_Obool)), _973090), hAPP(hAPP(c_Set_Oinsert(_973082), _973313), c_Orderings_Obot__class_Obot(tc_fun(_973082, tc_HOL_Obool)))), _973311)]]], (10917 ^ _779530) ^ [_973603, _973605, _973607, _973609] : [class_Orderings_Oorder(_973603), class_Enum_Oenum(_973605), 10924 ^ _779530 : [(10925 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973605, _973603)), _973607), _973609)), 10928 ^ _779530 : [(10929 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973605, _973603)), _973607), _973609)))], (10931 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_973605), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _973605), c_fNot), hAPP(hAPP(c_COMBS(_973605, _973603, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_973603, tc_fun(_973603, tc_HOL_Obool), _973605), c_fequal), _973607)), _973609)))))]]], (10933 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_973605, _973603)), _973607), _973609))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973605, _973603)), _973607), _973609)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_973605), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _973605), c_fNot), hAPP(hAPP(c_COMBS(_973605, _973603, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_973603, tc_fun(_973603, tc_HOL_Obool), _973605), c_fequal), _973607)), _973609))))]]], (10943 ^ _779530) ^ [_974147, _974149, _974151, _974153, _974155] : [c_Fun_Oinj__on(_974147, _974149, _974151, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974147, tc_HOL_Obool)), _974153), _974155)), 10946 ^ _779530 : [(10947 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_974147, _974149, _974151, _974153))], (10949 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_974147, _974149, _974151, _974155))], (10951 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974149, tc_HOL_Obool)), hAPP(c_Set_Oimage(_974147, _974149, _974151), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974147, tc_HOL_Obool)), _974153), _974155))), hAPP(c_Set_Oimage(_974147, _974149, _974151), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974147, tc_HOL_Obool)), _974155), _974153))) = c_Orderings_Obot__class_Obot(tc_fun(_974149, tc_HOL_Obool)))]]], (10953 ^ _779530) ^ [_974414, _974416, _974418, _974420, _974422] : [-(c_Fun_Oinj__on(_974414, _974416, _974418, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974414, tc_HOL_Obool)), _974420), _974422))), c_Fun_Oinj__on(_974414, _974416, _974418, _974420), c_Fun_Oinj__on(_974414, _974416, _974418, _974422), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_974416, tc_HOL_Obool)), hAPP(c_Set_Oimage(_974414, _974416, _974418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974414, tc_HOL_Obool)), _974420), _974422))), hAPP(c_Set_Oimage(_974414, _974416, _974418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974414, tc_HOL_Obool)), _974422), _974420))) = c_Orderings_Obot__class_Obot(tc_fun(_974416, tc_HOL_Obool))], (10967 ^ _779530) ^ [_974777, _974779, _974781, _974783, _974785] : [c_Fun_Oinj__on(_974777, _974779, _974781, hAPP(hAPP(c_Set_Oinsert(_974777), _974783), _974785)), 10970 ^ _779530 : [(10971 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_974777, _974779, _974781, _974785))], (10973 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_974779), hAPP(_974781, _974783)), hAPP(c_Set_Oimage(_974777, _974779, _974781), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974777, tc_HOL_Obool)), _974785), hAPP(hAPP(c_Set_Oinsert(_974777), _974783), c_Orderings_Obot__class_Obot(tc_fun(_974777, tc_HOL_Obool)))))))]]], (10975 ^ _779530) ^ [_974996, _974998, _975000, _975002, _975004] : [-(c_Fun_Oinj__on(_974996, _974998, _975000, hAPP(hAPP(c_Set_Oinsert(_974996), _975002), _975004))), c_Fun_Oinj__on(_974996, _974998, _975000, _975004), -(hBOOL(hAPP(hAPP(c_member(_974998), hAPP(_975000, _975002)), hAPP(c_Set_Oimage(_974996, _974998, _975000), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974996, tc_HOL_Obool)), _975004), hAPP(hAPP(c_Set_Oinsert(_974996), _975002), c_Orderings_Obot__class_Obot(tc_fun(_974996, tc_HOL_Obool))))))))], (10985 ^ _779530) ^ [_975269, _975271, _975273, _975275] : [c_Partial__Function_Omk__less(_975269, _975271, _975273, _975275), 10988 ^ _779530 : [(10989 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_975271, _975273), _975275)))], (10991 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_975271, _975275), _975273))]]], (10993 ^ _779530) ^ [_975404, _975406, _975408, _975410] : [-(c_Partial__Function_Omk__less(_975404, _975406, _975408, _975410)), hBOOL(hAPP(hAPP(_975406, _975408), _975410)), -(hBOOL(hAPP(hAPP(_975406, _975410), _975408)))], (11003 ^ _779530) ^ [_975570, _975572, _975574, _975576, _975578] : [-(c_Map_Odom(_975570, _975572, c_Fun_Ooverride__on(_975570, tc_Option_Ooption(_975572), _975574, _975576, _975578)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975570, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975570, tc_HOL_Obool)), c_Map_Odom(_975570, _975572, _975574)), hAPP(c_Set_OCollect(_975570), hAPP(hAPP(c_COMBC(_975570, tc_fun(_975570, tc_HOL_Obool), tc_HOL_Obool), c_member(_975570)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975570, tc_HOL_Obool)), _975578), c_Map_Odom(_975570, _975572, _975576)))))), hAPP(c_Set_OCollect(_975570), hAPP(hAPP(c_COMBC(_975570, tc_fun(_975570, tc_HOL_Obool), tc_HOL_Obool), c_member(_975570)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975570, tc_HOL_Obool)), _975578), c_Map_Odom(_975570, _975572, _975576))))))], (11005 ^ _779530) ^ [_975709, _975711, _975713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_975709, tc_HOL_Obool)), _975711), _975713)), -(hBOOL(hAPP(hAPP(c_member(_975709), 11008 ^ [_975709, _975711, _975713]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975709, tc_HOL_Obool)), _975713), _975711))))], (11012 ^ _779530) ^ [_975858, _975860, _975862] : [-(c_Fun_Oinj__on(_975858, _975860, _975862, c_Orderings_Obot__class_Obot(tc_fun(_975858, tc_HOL_Obool))))], (11014 ^ _779530) ^ [_975892, _975894, _975896] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _975892), _975894)), _975896) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _975892), _975896)), _975894))], (11016 ^ _779530) ^ [_975943, _975945, _975947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _975943), _975945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _975943), _975947)), _975945)))], (11022 ^ _779530) ^ [_976054, _976056, _976058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976054), _976056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _976054), _976058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _976058), _976056)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _976058), _976054))))], (11032 ^ _779530) ^ [_976241, _976243] : [-(c_Fun_Oinj__on(_976241, _976241, c_COMBI(_976241), _976243))], (11052 ^ _779530) ^ [_976676, _976678, _976680, _976682] : [11054 ^ _779530 : [(11055 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976676), 11053 ^ [_976676, _976678, _976680, _976682]), _976682)))], (11058 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976676), 11056 ^ [_976676, _976678, _976680, _976682]), _976682)))], (11060 ^ _779530) ^ [] : [-(hAPP(_976680, 11053 ^ [_976676, _976678, _976680, _976682]) = hAPP(_976680, 11056 ^ [_976676, _976678, _976680, _976682]))], (11062 ^ _779530) ^ [] : [11053 ^ [_976676, _976678, _976680, _976682] = 11056 ^ [_976676, _976678, _976680, _976682]]], -(c_Fun_Oinj__on(_976676, _976678, _976680, _976682))], (11034 ^ _779530) ^ [_976291, _976293, _976295, _976297] : [c_Fun_Oinj__on(_976291, _976293, _976295, _976297), 11037 ^ _779530 : [(11038 ^ _779530) ^ [_976399] : [hBOOL(hAPP(hAPP(c_member(_976291), _976399), _976297)), 11041 ^ _779530 : [(11042 ^ _779530) ^ [_976501] : [hBOOL(hAPP(hAPP(c_member(_976291), _976501), _976297)), hAPP(_976295, _976399) = hAPP(_976295, _976501), -(_976399 = _976501)]]]]], (11066 ^ _779530) ^ [_977068, _977070] : [class_Enum_Oenum(_977068), 11069 ^ _779530 : [(11070 ^ _779530) ^ [] : [11071 ^ _779530 : [(11072 ^ _779530) ^ [_977170] : [hBOOL(hAPP(_977070, _977170))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_977068), _977070)))], (11076 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_977068), _977070)), -(hBOOL(hAPP(_977070, 11079 ^ [_977068, _977070])))]]], (11083 ^ _779530) ^ [_977311, _977313] : [class_Enum_Oenum(_977311), 11086 ^ _779530 : [(11087 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_977311), _977313)), -(hBOOL(hAPP(_977313, 11090 ^ [_977311, _977313])))], (11094 ^ _779530) ^ [] : [11095 ^ _779530 : [(11096 ^ _779530) ^ [_977491] : [hBOOL(hAPP(_977313, _977491))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_977311), _977313)))]]], (11100 ^ _779530) ^ [_977554, _977556, _977558, _977560, _977562, _977564] : [c_Fun_Oinj__on(_977554, _977556, _977558, _977560), -(_977562 = _977564), hBOOL(hAPP(hAPP(c_member(_977554), _977562), _977560)), hBOOL(hAPP(hAPP(c_member(_977554), _977564), _977560)), hAPP(_977558, _977562) = hAPP(_977558, _977564)], (11118 ^ _779530) ^ [_977867, _977869, _977871, _977873, _977875, _977877] : [c_Fun_Oinj__on(_977867, _977869, _977871, _977873), hBOOL(hAPP(hAPP(c_member(_977867), _977875), _977873)), hBOOL(hAPP(hAPP(c_member(_977867), _977877), _977873)), 11129 ^ _779530 : [(11130 ^ _779530) ^ [] : [hAPP(_977871, _977875) = hAPP(_977871, _977877), -(_977875 = _977877)], (11136 ^ _779530) ^ [] : [_977875 = _977877, -(hAPP(_977871, _977875) = hAPP(_977871, _977877))]]], (11142 ^ _779530) ^ [_978268, _978270, _978272, _978274, _978276, _978278] : [c_Fun_Oinj__on(_978268, _978270, _978272, _978274), hAPP(_978272, _978276) = hAPP(_978272, _978278), hBOOL(hAPP(hAPP(c_member(_978268), _978276), _978274)), hBOOL(hAPP(hAPP(c_member(_978268), _978278), _978274)), -(_978276 = _978278)], (11160 ^ _779530) ^ [_978577, _978579, _978581, _978583, _978585] : [c_Fun_Oinj__on(_978577, _978579, _978581, _978583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978577, tc_HOL_Obool)), _978585), _978583)), -(c_Fun_Oinj__on(_978577, _978579, _978581, _978585))], (11170 ^ _779530) ^ [_978746, _978748, _978750, _978752, _978754] : [c_Fun_Oinj__on(_978746, _978748, _978750, _978752), c_Fun_Oinj__on(_978746, _978748, _978750, _978754), -(c_Fun_Oinj__on(_978746, _978748, _978750, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978746, tc_HOL_Obool)), _978752), _978754)))], (11180 ^ _779530) ^ [_978921, _978923, _978925, _978927, _978929, _978931] : [c_Fun_Oinj__on(_978921, _978923, hAPP(c_Fun_Ocomp(_978925, _978923, _978921, _978927), _978929), _978931), -(c_Fun_Oinj__on(_978921, _978925, _978929, _978931))], (11186 ^ _779530) ^ [_979030, _979032, _979034, _979036, _979038] : [c_Fun_Oinj__on(_979030, _979032, _979034, _979036), -(c_Fun_Oinj__on(_979030, _979032, _979034, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979030, tc_HOL_Obool)), _979036), _979038)))], (11192 ^ _779530) ^ [_979143, _979145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979143), _979145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979143), _979145)))], (11198 ^ _779530) ^ [_979255, _979257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979255), _979257)), 11201 ^ _779530 : [(11202 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979255), _979257)))], (11204 ^ _779530) ^ [] : [_979255 = _979257]]], (11206 ^ _779530) ^ [_979382, _979384] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979382), _979384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979382), _979384)), -(_979382 = _979384)], (11226 ^ _779530) ^ [_979657, _979659] : [11227 ^ _779530 : [(11228 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979657), _979659))], (11230 ^ _779530) ^ [] : [_979657 = _979659]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979657), _979659)))], (11216 ^ _779530) ^ [_979551, _979553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979551), _979553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979551), _979553))), -(_979551 = _979553)], (11234 ^ _779530) ^ [_979794, _979796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979794), _979796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979794), _979796)))], (11240 ^ _779530) ^ [_979891, _979893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _979891), _979893)), -(_979891 = _979893), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _979891), _979893)))], (11250 ^ _779530) ^ [_980003, _980005] : [11251 ^ _779530 : [(11252 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980003), _980005))], (11254 ^ _779530) ^ [] : [_980003 = _980005]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980003), _980005)))], (11258 ^ _779530) ^ [_980138, _980140, _980142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980138), _980140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980138), _980142)), 11265 ^ _779530 : [(11266 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980140), _980138)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980142), _980138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980140), _980142)))], (11272 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980140), _980142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980140), _980138)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980142), _980138))))]]], (11278 ^ _779530) ^ [_980491, _980493, _980495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _980491), _980493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _980495), _980491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980491), _980495)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _980493), _980495))))], (11288 ^ _779530) ^ [_980678, _980680, _980682, _980684] : [class_Orderings_Oorder(_980678), class_Orderings_Olinorder(_980680), c_Orderings_Oorder__class_Ostrict__mono(_980680, _980678, _980682), -(c_Fun_Oinj__on(_980680, _980678, _980682, _980684))], (11302 ^ _779530) ^ [_980875, _980877, _980879, _980881, _980883] : [c_Fun_Oinj__on(_980875, _980877, _980879, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980875, tc_HOL_Obool)), _980881), _980883)), 11305 ^ _779530 : [(11306 ^ _779530) ^ [] : [hAPP(c_Set_Oimage(_980875, _980877, _980879), _980881) = hAPP(c_Set_Oimage(_980875, _980877, _980879), _980883), -(_980881 = _980883)], (11312 ^ _779530) ^ [] : [_980881 = _980883, -(hAPP(c_Set_Oimage(_980875, _980877, _980879), _980881) = hAPP(c_Set_Oimage(_980875, _980877, _980879), _980883))]]], (11318 ^ _779530) ^ [_981168, _981170, _981172, _981174, _981176, _981178] : [c_Fun_Oinj__on(_981168, _981170, _981172, _981174), 11321 ^ _779530 : [(11322 ^ _779530) ^ [] : [c_Fun_Oinj__on(_981170, _981176, _981178, hAPP(c_Set_Oimage(_981168, _981170, _981172), _981174)), -(c_Fun_Oinj__on(_981168, _981176, hAPP(c_Fun_Ocomp(_981170, _981176, _981168, _981178), _981172), _981174))], (11328 ^ _779530) ^ [] : [c_Fun_Oinj__on(_981168, _981176, hAPP(c_Fun_Ocomp(_981170, _981176, _981168, _981178), _981172), _981174), -(c_Fun_Oinj__on(_981170, _981176, _981178, hAPP(c_Set_Oimage(_981168, _981170, _981172), _981174)))]]], (11334 ^ _779530) ^ [_981460, _981462, _981464, _981466, _981468, _981470] : [c_Fun_Oinj__on(_981460, _981462, _981464, _981466), c_Fun_Oinj__on(_981462, _981468, _981470, hAPP(c_Set_Oimage(_981460, _981462, _981464), _981466)), -(c_Fun_Oinj__on(_981460, _981468, hAPP(c_Fun_Ocomp(_981462, _981468, _981460, _981470), _981464), _981466))], (11344 ^ _779530) ^ [_981647, _981649, _981651, _981653, _981655, _981657] : [c_Fun_Oinj__on(_981647, _981649, hAPP(c_Fun_Ocomp(_981651, _981649, _981647, _981653), _981655), _981657), -(c_Fun_Oinj__on(_981651, _981649, _981653, hAPP(c_Set_Oimage(_981647, _981651, _981655), _981657)))], (11350 ^ _779530) ^ [_981770, _981772, _981774, _981776, _981778] : [c_Fun_Oinj__on(_981770, _981772, _981774, _981776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981770, tc_HOL_Obool)), _981778), _981776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_981772, tc_HOL_Obool)), hAPP(c_Set_Oimage(_981770, _981772, _981774), _981778)), hAPP(c_Set_Oimage(_981770, _981772, _981774), _981776))))], (11360 ^ _779530) ^ [_981983, _981985, _981987, _981989, _981991] : [c_Fun_Oinj__on(_981983, _981985, _981987, _981989), hBOOL(hAPP(hAPP(c_member(_981983), _981991), _981989)), -(hAPP(c_Fun_Othe__inv__into(_981983, _981985, _981989, _981987), hAPP(_981987, _981991)) = _981991)], (11370 ^ _779530) ^ [_982164, _982166, _982168, _982170, _982172, _982174] : [c_Fun_Oinj__on(_982164, _982166, _982168, _982170), hAPP(_982168, _982172) = _982174, hBOOL(hAPP(hAPP(c_member(_982164), _982172), _982170)), -(hAPP(c_Fun_Othe__inv__into(_982164, _982166, _982170, _982168), _982174) = _982172)], (11384 ^ _779530) ^ [_982409, _982411, _982413, _982415] : [c_Fun_Oinj__on(_982409, _982411, _982413, _982415), -(c_Fun_Oinj__on(_982411, _982409, c_Fun_Othe__inv__into(_982409, _982411, _982415, _982413), hAPP(c_Set_Oimage(_982409, _982411, _982413), _982415)))], (11390 ^ _779530) ^ [_982522, _982524, _982526, _982528] : [c_Fun_Oinj__on(_982522, _982524, _982526, _982528), -(hAPP(c_Set_Oimage(_982524, _982522, c_Fun_Othe__inv__into(_982522, _982524, _982528, _982526)), hAPP(c_Set_Oimage(_982522, _982524, _982526), _982528)) = _982528)], (11396 ^ _779530) ^ [_982645, _982647, _982649, _982651, _982653] : [-(c_Map_Odom(_982645, _982647, hAPP(hAPP(c_COMBS(_982645, tc_Option_Ooption(_982647), tc_Option_Ooption(_982647)), hAPP(hAPP(c_COMBS(_982645, tc_Option_Ooption(_982647), tc_fun(tc_Option_Ooption(_982647), tc_Option_Ooption(_982647))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_982647), tc_fun(tc_Option_Ooption(_982647), tc_Option_Ooption(_982647))), _982645), c_If(tc_Option_Ooption(_982647))), _982649)), _982651)), _982653)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982645, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982645, tc_HOL_Obool)), c_Map_Odom(_982645, _982647, _982651)), hAPP(c_Set_OCollect(_982645), _982649))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982645, tc_HOL_Obool)), c_Map_Odom(_982645, _982647, _982653)), hAPP(c_Set_OCollect(_982645), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _982645), c_fNot), _982649)))))], (11398 ^ _779530) ^ [_982800, _982802, _982804, _982806, _982808, _982810] : [c_Fun_Oinj__on(_982800, _982802, _982804, _982806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982800, tc_HOL_Obool)), _982808), _982806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982800, tc_HOL_Obool)), _982810), _982806)), -(hAPP(c_Set_Oimage(_982800, _982802, _982804), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982800, tc_HOL_Obool)), _982808), _982810)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982802, tc_HOL_Obool)), hAPP(c_Set_Oimage(_982800, _982802, _982804), _982808)), hAPP(c_Set_Oimage(_982800, _982802, _982804), _982810)))], (11412 ^ _779530) ^ [_983135, _983137, _983139, _983141, _983143, _983145] : [c_Fun_Oinj__on(_983135, _983137, _983139, _983141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983135, tc_HOL_Obool)), _983143), _983141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983135, tc_HOL_Obool)), _983145), _983141)), -(hAPP(c_Set_Oimage(_983135, _983137, _983139), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983135, tc_HOL_Obool)), _983143), _983145)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983137, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983135, _983137, _983139), _983143)), hAPP(c_Set_Oimage(_983135, _983137, _983139), _983145)))], (11426 ^ _779530) ^ [_983470, _983472, _983474, _983476, _983478, _983480] : [c_Fun_Oinj__on(_983470, _983472, _983474, _983476), -(hBOOL(hAPP(hAPP(c_member(_983472), _983478), hAPP(c_Set_Oimage(_983470, _983472, _983474), _983476)))), -(c_Fun_Oinj__on(_983470, _983472, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_983470, _983472), _983474), _983480), _983478), _983476))], (11436 ^ _779530) ^ [_983630, _983632, _983634, _983636, _983638] : [c_Fun_Oinj__on(_983630, _983632, _983634, _983636), hBOOL(hAPP(hAPP(c_member(_983632), _983638), hAPP(c_Set_Oimage(_983630, _983632, _983634), _983636))), -(hAPP(_983634, hAPP(c_Fun_Othe__inv__into(_983630, _983632, _983636, _983634), _983638)) = _983638)], (11446 ^ _779530) ^ [_983825, _983827, _983829, _983831, _983833, _983835] : [c_Fun_Oinj__on(_983825, _983827, _983829, _983831), hBOOL(hAPP(hAPP(c_member(_983827), _983833), hAPP(c_Set_Oimage(_983825, _983827, _983829), _983831))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983825, tc_HOL_Obool)), _983831), _983835)), -(hBOOL(hAPP(hAPP(c_member(_983825), hAPP(c_Fun_Othe__inv__into(_983825, _983827, _983831, _983829), _983833)), _983835)))], (11460 ^ _779530) ^ [_984112, _984114, _984116, _984118, _984120, _984122, _984124] : [c_Fun_Oinj__on(_984112, _984114, _984116, hAPP(c_Set_Oimage(_984118, _984112, _984120), _984122)), c_Fun_Oinj__on(_984118, _984112, _984120, _984122), hBOOL(hAPP(hAPP(c_member(_984114), _984124), hAPP(c_Set_Oimage(_984112, _984114, _984116), hAPP(c_Set_Oimage(_984118, _984112, _984120), _984122)))), -(hAPP(c_Fun_Othe__inv__into(_984118, _984114, _984122, hAPP(c_Fun_Ocomp(_984112, _984114, _984118, _984116), _984120)), _984124) = hAPP(hAPP(c_Fun_Ocomp(_984112, _984118, _984114, c_Fun_Othe__inv__into(_984118, _984112, _984122, _984120)), c_Fun_Othe__inv__into(_984112, _984114, hAPP(c_Set_Oimage(_984118, _984112, _984120), _984122), _984116)), _984124))], (11474 ^ _779530) ^ [_984474, _984476, _984478, _984480] : [-(_984474 = c_Orderings_Obot__class_Obot(tc_fun(_984476, tc_HOL_Obool))), 11477 ^ _779530 : [(11489 ^ _779530) ^ [] : [11490 ^ _779530 : [(11491 ^ _779530) ^ [_984807] : [hAPP(c_Set_Oimage(_984478, _984476, _984807), _984480) = _984474]], 11493 ^ _779530 : [(11494 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_984476, _984478, 11492 ^ [_984474, _984476, _984478, _984480], _984474))], (11496 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984478, tc_HOL_Obool)), hAPP(c_Set_Oimage(_984476, _984478, 11492 ^ [_984474, _984476, _984478, _984480]), _984474)), _984480)))]]], (11478 ^ _779530) ^ [] : [-(hAPP(c_Set_Oimage(_984478, _984476, 11485 ^ [_984474, _984476, _984478, _984480]), _984480) = _984474), 11479 ^ _779530 : [(11480 ^ _779530) ^ [_984615] : [c_Fun_Oinj__on(_984476, _984478, _984615, _984474), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984478, tc_HOL_Obool)), hAPP(c_Set_Oimage(_984476, _984478, _984615), _984474)), _984480))]]]]], (11498 ^ _779530) ^ [_984953, _984955, _984957, _984959, _984961, _984963] : [hBOOL(hAPP(hAPP(c_member(_984953), _984955), _984957)), -(c_Map_Orestrict__map(_984953, _984959, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_984953, tc_Option_Ooption(_984959)), _984961), _984955), _984963), _984957) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_984953, tc_Option_Ooption(_984959)), c_Map_Orestrict__map(_984953, _984959, _984961, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984953, tc_HOL_Obool)), _984957), hAPP(hAPP(c_Set_Oinsert(_984953), _984955), c_Orderings_Obot__class_Obot(tc_fun(_984953, tc_HOL_Obool)))))), _984955), _984963))], (11504 ^ _779530) ^ [_985170, _985172, _985174, _985176, _985178, _985180] : [-(hBOOL(hAPP(hAPP(c_member(_985170), _985172), _985174))), -(c_Map_Orestrict__map(_985170, _985176, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_985170, tc_Option_Ooption(_985176)), _985178), _985172), _985180), _985174) = c_Map_Orestrict__map(_985170, _985176, _985178, _985174))], (11510 ^ _779530) ^ [_985247, _985249, _985251, _985253, _985255, _985257] : [hBOOL(hAPP(hAPP(c_member(_985247), _985249), _985251)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_985247, tc_Option_Ooption(_985253)), c_Map_Orestrict__map(_985247, _985253, _985255, _985251)), _985249), _985257) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_985247, tc_Option_Ooption(_985253)), c_Map_Orestrict__map(_985247, _985253, _985255, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985247, tc_HOL_Obool)), _985251), hAPP(hAPP(c_Set_Oinsert(_985247), _985249), c_Orderings_Obot__class_Obot(tc_fun(_985247, tc_HOL_Obool)))))), _985249), _985257))], (11516 ^ _779530) ^ [_985485, _985487, _985489, _985491] : [hBOOL(hAPP(hAPP(c_member(_985485), _985487), _985489)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985485, tc_Nat_Onat), _985491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985485, tc_HOL_Obool)), _985489), hAPP(hAPP(c_Set_Oinsert(_985485), _985487), c_Orderings_Obot__class_Obot(tc_fun(_985485, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985485, tc_Nat_Onat), _985491), _985489)), hAPP(_985491, _985487)))], (11522 ^ _779530) ^ [_985676, _985678, _985680, _985682] : [-(hBOOL(hAPP(hAPP(c_member(_985676), _985678), _985680))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985676, tc_Nat_Onat), _985682), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985676, tc_HOL_Obool)), _985680), hAPP(hAPP(c_Set_Oinsert(_985676), _985678), c_Orderings_Obot__class_Obot(tc_fun(_985676, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_985676, tc_Nat_Onat), _985682), _985680))], (11528 ^ _779530) ^ [_985785, _985787, _985789, _985791, _985793] : [_985785 = c_Option_Ooption_ONone(_985787), -(c_Map_Odom(_985789, _985787, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_985789, tc_Option_Ooption(_985787)), _985791), _985793), _985785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985789, tc_HOL_Obool)), c_Map_Odom(_985789, _985787, _985791)), hAPP(hAPP(c_Set_Oinsert(_985789), _985793), c_Orderings_Obot__class_Obot(tc_fun(_985789, tc_HOL_Obool)))))], (11534 ^ _779530) ^ [_985958, _985960, _985962, _985964, _985966] : [-(_985958 = c_Option_Ooption_ONone(_985960)), -(c_Map_Odom(_985962, _985960, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_985962, tc_Option_Ooption(_985960)), _985964), _985966), _985958)) = hAPP(hAPP(c_Set_Oinsert(_985962), _985966), c_Map_Odom(_985962, _985960, _985964)))], (11540 ^ _779530) ^ [_986034, _986036, _986038, _986040, _986042, _986044] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_986034, tc_Option_Ooption(_986036)), c_Map_Orestrict__map(_986034, _986036, _986038, _986040)), _986042), _986044) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_986034, tc_Option_Ooption(_986036)), c_Map_Orestrict__map(_986034, _986036, _986038, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986034, tc_HOL_Obool)), _986040), hAPP(hAPP(c_Set_Oinsert(_986034), _986042), c_Orderings_Obot__class_Obot(tc_fun(_986034, tc_HOL_Obool)))))), _986042), _986044))], (11542 ^ _779530) ^ [_986129, _986131, _986133, _986135] : [c_Fun_Oinj__on(_986129, tc_fun(tc_fun(_986129, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_986129, tc_fun(tc_prod(_986129, _986129), tc_HOL_Obool), tc_fun(tc_fun(_986129, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_986129, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_986129, _986129), tc_HOL_Obool), tc_fun(tc_fun(_986129, tc_HOL_Obool), tc_HOL_Obool)), _986129), c_Equiv__Relations_Oquotient(_986129)), hAPP(hAPP(c_COMBC(_986129, tc_fun(_986129, tc_HOL_Obool), tc_fun(_986129, tc_HOL_Obool)), c_Set_Oinsert(_986129)), c_Orderings_Obot__class_Obot(tc_fun(_986129, tc_HOL_Obool))))), _986131), _986133), hBOOL(hAPP(hAPP(c_member(_986129), _986135), _986133)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_986129), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_986129, tc_HOL_Obool)), _986133), hAPP(hAPP(c_Set_Oinsert(_986129), _986135), c_Orderings_Obot__class_Obot(tc_fun(_986129, tc_HOL_Obool))))), _986131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_986129, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_986129), _986133), _986131)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_986129), hAPP(hAPP(c_Set_Oinsert(_986129), _986135), c_Orderings_Obot__class_Obot(tc_fun(_986129, tc_HOL_Obool)))), _986131)))], (11552 ^ _779530) ^ [_986596, _986598, _986600, _986602] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_986596, tc_HOL_Obool)), c_Map_Odom(_986596, _986598, _986600)), c_Map_Odom(_986596, _986598, _986602)) = c_Orderings_Obot__class_Obot(tc_fun(_986596, tc_HOL_Obool)), -(c_Map_Omap__add(_986596, _986598, _986600, _986602) = c_Map_Omap__add(_986596, _986598, _986602, _986600))], (11558 ^ _779530) ^ [_986745] : [-(c_Finite__Set_Ofun__left__comm__idem(_986745, tc_fun(_986745, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_986745, tc_HOL_Obool), tc_fun(tc_fun(_986745, tc_HOL_Obool), tc_fun(_986745, tc_HOL_Obool)), _986745), hAPP(c_COMBC(tc_fun(_986745, tc_HOL_Obool), tc_fun(_986745, tc_HOL_Obool), tc_fun(_986745, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_986745, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_986745, tc_fun(_986745, tc_HOL_Obool), tc_fun(_986745, tc_HOL_Obool)), c_Set_Oinsert(_986745)), c_Orderings_Obot__class_Obot(tc_fun(_986745, tc_HOL_Obool))))))], (11560 ^ _779530) ^ [_986838, _986840, _986842, _986844] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_986838, tc_Option_Ooption(_986840)), hAPP(c_COMBK(tc_Option_Ooption(_986840), _986838), c_Option_Ooption_ONone(_986840))), _986842), c_Option_Ooption_ONone(_986840)), _986844) = c_Option_Ooption_ONone(_986840))], (11562 ^ _779530) ^ [_986898, _986900, _986902] : [11563 ^ _779530 : [(11564 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986898), _986900)))], (11566 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_986902, _986900), _986898))]], 11569 ^ _779530 : [(11570 ^ _779530) ^ [] : [-(_986898 = _986900)], (11572 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_986902, _986900), _986898))]], 11575 ^ _779530 : [(11576 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _986900), _986898)))], (11578 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_986902, _986900), _986898))]], -(hBOOL(hAPP(hAPP(_986902, _986900), _986898)))], (11582 ^ _779530) ^ [_987244, _987246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987244), _987246)), _987244 = _987246], (11588 ^ _779530) ^ [_987332, _987334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987332), _987334)), _987334 = _987332], (11594 ^ _779530) ^ [_987429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987429), _987429))], (11596 ^ _779530) ^ [_987453, _987455] : [-(_987453 = _987455), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987453), _987455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987455), _987453)))], (11616 ^ _779530) ^ [_987564, _987566] : [11617 ^ _779530 : [(11618 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987564), _987566))], (11620 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987566), _987564))]], _987564 = _987566], (11606 ^ _779530) ^ [_987515, _987517] : [-(_987515 = _987517), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987515), _987517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987517), _987515)))], (11624 ^ _779530) ^ [_987711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _987711), _987711))], (11626 ^ _779530) ^ [_987763, _987765, _987767, _987769, _987771] : [hAPP(c_Map_Omap__add(_987763, _987765, _987767, _987769), _987771) = c_Option_Ooption_ONone(_987765), 11629 ^ _779530 : [(11630 ^ _779530) ^ [] : [-(hAPP(_987769, _987771) = c_Option_Ooption_ONone(_987765))], (11632 ^ _779530) ^ [] : [-(hAPP(_987767, _987771) = c_Option_Ooption_ONone(_987765))]]], (11634 ^ _779530) ^ [_987908, _987910, _987912, _987914, _987916] : [-(hAPP(c_Map_Omap__add(_987908, _987910, _987912, _987914), _987916) = c_Option_Ooption_ONone(_987910)), hAPP(_987914, _987916) = c_Option_Ooption_ONone(_987910), hAPP(_987912, _987916) = c_Option_Ooption_ONone(_987910)], (11644 ^ _779530) ^ [_988091, _988093, _988095, _988097] : [-(hAPP(c_Map_Orestrict__map(_988091, _988093, hAPP(c_COMBK(tc_Option_Ooption(_988093), _988091), c_Option_Ooption_ONone(_988093)), _988095), _988097) = c_Option_Ooption_ONone(_988093))], (11646 ^ _779530) ^ [_988140, _988142, _988144] : [-(c_Map_Omap__add(_988140, _988142, hAPP(c_COMBK(tc_Option_Ooption(_988142), _988140), c_Option_Ooption_ONone(_988142)), _988144) = _988144)], (11648 ^ _779530) ^ [_988182, _988184, _988186, _988188, _988190] : [-(c_Map_Omap__add(_988182, _988184, _988186, c_Map_Omap__add(_988182, _988184, _988188, _988190)) = c_Map_Omap__add(_988182, _988184, c_Map_Omap__add(_988182, _988184, _988186, _988188), _988190))], (11650 ^ _779530) ^ [_988233, _988235, _988237] : [-(c_Map_Omap__add(_988233, _988235, _988237, hAPP(c_COMBK(tc_Option_Ooption(_988235), _988233), c_Option_Ooption_ONone(_988235))) = _988237)], (11652 ^ _779530) ^ [_988271, _988273, _988275, _988277, _988279] : [-(hBOOL(hAPP(hAPP(c_member(_988271), _988273), _988275))), -(hAPP(c_Map_Orestrict__map(_988271, _988277, _988279, _988275), _988273) = c_Option_Ooption_ONone(_988277))], (11658 ^ _779530) ^ [_988330, _988332, _988334, _988336, _988338, _988340] : [class_Groups_Ocomm__monoid__add(_988330), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988332, _988330), hAPP(hAPP(c_COMBC(_988332, tc_fun(_988334, tc_HOL_Obool), _988330), hAPP(hAPP(c_COMBB(tc_fun(_988334, _988330), tc_fun(tc_fun(_988334, tc_HOL_Obool), _988330), _988332), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988334, _988330)), _988336)), _988338)), _988340) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988334, _988330), hAPP(hAPP(c_COMBC(_988334, tc_fun(_988332, tc_HOL_Obool), _988330), hAPP(hAPP(c_COMBB(tc_fun(_988332, _988330), tc_fun(tc_fun(_988332, tc_HOL_Obool), _988330), _988334), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988332, _988330)), hAPP(c_COMBC(_988332, _988334, _988330), _988336))), _988340)), _988338))], (11664 ^ _779530) ^ [_988603, _988605, _988607, _988609, _988611] : [c_Finite__Set_Ofun__left__comm__idem(_988603, _988605, _988607), -(c_Finite__Set_Ofun__left__comm__idem(_988609, _988605, hAPP(hAPP(c_COMBB(_988603, tc_fun(_988605, _988605), _988609), _988607), _988611)))], (11670 ^ _779530) ^ [_988716, _988718, _988720, _988722, _988724] : [c_Finite__Set_Ofun__left__comm__idem(_988716, _988718, _988720), -(hAPP(hAPP(_988720, _988722), hAPP(hAPP(_988720, _988722), _988724)) = hAPP(hAPP(_988720, _988722), _988724))], (11676 ^ _779530) ^ [_988855, _988857, _988859, _988861, _988863] : [hBOOL(hAPP(hAPP(c_member(_988855), _988857), _988859)), -(hAPP(c_Map_Orestrict__map(_988855, _988861, _988863, _988859), _988857) = hAPP(_988863, _988857))], (11682 ^ _779530) ^ [_988968, _988970, _988972, _988974, _988976] : [-(hBOOL(hAPP(hAPP(c_member(_988968), _988970), _988972))), -(hAPP(c_Map_Orestrict__map(_988968, _988974, _988976, _988972), _988970) = c_Option_Ooption_ONone(_988974))], (11688 ^ _779530) ^ [_989029, _989031, _989033, _989035] : [-(hAPP(c_Map_Orestrict__map(_989029, _989031, _989033, c_Orderings_Obot__class_Obot(tc_fun(_989029, tc_HOL_Obool))), _989035) = c_Option_Ooption_ONone(_989031))], (11690 ^ _779530) ^ [_989073] : [-(c_Finite__Set_Ofun__left__comm__idem(_989073, tc_fun(_989073, tc_HOL_Obool), c_Set_Oinsert(_989073)))], (11692 ^ _779530) ^ [_989102] : [class_Lattices_Osemilattice__sup(_989102), -(c_Finite__Set_Ofun__left__comm__idem(_989102, _989102, c_Lattices_Osemilattice__sup__class_Osup(_989102)))], (11698 ^ _779530) ^ [_989181] : [class_Lattices_Osemilattice__inf(_989181), -(c_Finite__Set_Ofun__left__comm__idem(_989181, _989181, c_Lattices_Osemilattice__inf__class_Oinf(_989181)))], (11704 ^ _779530) ^ [_989260, _989262, _989264, _989266] : [c_Finite__Set_Ofun__left__comm__idem(_989260, _989262, _989264), -(hAPP(c_Fun_Ocomp(_989262, _989262, _989262, hAPP(_989264, _989266)), hAPP(_989264, _989266)) = hAPP(_989264, _989266))], (11710 ^ _779530) ^ [_989377, _989379, _989381, _989383, _989385] : [class_Groups_Oab__group__add(_989377), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_989379, _989377), hAPP(hAPP(c_COMBS(_989379, _989377, _989377), hAPP(hAPP(c_COMBB(_989377, tc_fun(_989377, _989377), _989379), c_Groups_Ominus__class_Ominus(_989377)), _989381)), _989383)), _989385) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_989377), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_989379, _989377), _989381), _989385)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_989379, _989377), _989383), _989385)))], (11716 ^ _779530) ^ [_989578, _989580, _989582, _989584, _989586] : [hBOOL(hAPP(hAPP(c_member(_989578), _989580), _989582)), -(hAPP(c_Map_Orestrict__map(_989578, _989584, _989586, _989582), _989580) = hAPP(_989586, _989580))], (11722 ^ _779530) ^ [_989697, _989699, _989701, _989703, _989705] : [-(c_Map_Orestrict__map(_989697, _989699, _989701, hAPP(hAPP(c_Set_Oinsert(_989697), _989703), _989705)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_989697, tc_Option_Ooption(_989699)), c_Map_Orestrict__map(_989697, _989699, _989701, _989705)), _989703), hAPP(_989701, _989703)))], (11724 ^ _779530) ^ [_989763, _989765, _989767, _989769, _989771] : [-(c_Map_Orestrict__map(_989763, _989765, c_Map_Orestrict__map(_989763, _989765, _989767, _989769), _989771) = c_Map_Orestrict__map(_989763, _989765, _989767, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989763, tc_HOL_Obool)), _989769), _989771)))], (11726 ^ _779530) ^ [_989841, _989843, _989845, _989847] : [c_Fun_Oinj__on(_989841, tc_Option_Ooption(_989843), c_Map_Omap__add(_989841, _989843, _989845, _989847), c_Map_Odom(_989841, _989843, _989847)), -(c_Fun_Oinj__on(_989841, tc_Option_Ooption(_989843), _989847, c_Map_Odom(_989841, _989843, _989847)))], (11732 ^ _779530) ^ [_989960, _989962, _989964, _989966] : [c_Fun_Oinj__on(_989960, tc_Option_Ooption(_989962), _989966, c_Map_Odom(_989960, _989962, _989966)), -(c_Fun_Oinj__on(_989960, tc_Option_Ooption(_989962), c_Map_Omap__add(_989960, _989962, _989964, _989966), c_Map_Odom(_989960, _989962, _989966)))], (11738 ^ _779530) ^ [_990103, _990105, _990107] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_990103), _990105), _990107) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_990103, tc_HOL_Obool), tc_HOL_Obool)), -(_990105 = c_Orderings_Obot__class_Obot(tc_fun(_990103, tc_HOL_Obool)))], (11744 ^ _779530) ^ [_990220, _990222, _990224] : [_990222 = c_Orderings_Obot__class_Obot(tc_fun(_990220, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_990220), _990222), _990224) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_990220, tc_HOL_Obool), tc_HOL_Obool)))], (11750 ^ _779530) ^ [_990361, _990363, _990365] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_990361, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_990361), _990363), _990365), -(_990363 = c_Orderings_Obot__class_Obot(tc_fun(_990361, tc_HOL_Obool)))], (11756 ^ _779530) ^ [_990478, _990480, _990482] : [_990480 = c_Orderings_Obot__class_Obot(tc_fun(_990478, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_990478, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_990478), _990480), _990482))], (11762 ^ _779530) ^ [_990601, _990603] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_990601), c_Orderings_Obot__class_Obot(tc_fun(_990601, tc_HOL_Obool))), _990603) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_990601, tc_HOL_Obool), tc_HOL_Obool)))], (11764 ^ _779530) ^ [_990665, _990667, _990669, _990671, _990673] : [hBOOL(hAPP(hAPP(c_member(_990665), _990667), _990669)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_990665, tc_Option_Ooption(_990671)), c_Map_Orestrict__map(_990665, _990671, _990673, _990669)), _990667), c_Option_Ooption_ONone(_990671)) = c_Map_Orestrict__map(_990665, _990671, _990673, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_990665, tc_HOL_Obool)), _990669), hAPP(hAPP(c_Set_Oinsert(_990665), _990667), c_Orderings_Obot__class_Obot(tc_fun(_990665, tc_HOL_Obool))))))], (11770 ^ _779530) ^ [_990856, _990858, _990860, _990862, _990864] : [-(hBOOL(hAPP(hAPP(c_member(_990856), _990858), _990860))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_990856, tc_Option_Ooption(_990862)), c_Map_Orestrict__map(_990856, _990862, _990864, _990860)), _990858), c_Option_Ooption_ONone(_990862)) = c_Map_Orestrict__map(_990856, _990862, _990864, _990860))], (11776 ^ _779530) ^ [_990954, _990956, _990958, _990960] : [hBOOL(hAPP(hAPP(c_member(_990954), _990956), c_Map_Odom(_990954, _990958, _990960))), hAPP(_990960, _990956) = c_Option_Ooption_ONone(_990958)], (11782 ^ _779530) ^ [_991062, _991064, _991066, _991068] : [-(hAPP(_991068, _991064) = c_Option_Ooption_ONone(_991066)), -(hBOOL(hAPP(hAPP(c_member(_991062), _991064), c_Map_Odom(_991062, _991066, _991068))))], (11788 ^ _779530) ^ [_991120, _991122, _991124, _991126, _991128] : [hBOOL(hAPP(hAPP(c_member(_991120), _991122), c_Map_Odom(_991120, _991124, _991126))), -(hAPP(c_Map_Omap__add(_991120, _991124, _991128, _991126), _991122) = hAPP(_991126, _991122))], (11794 ^ _779530) ^ [_991243, _991245, _991247, _991249, _991251] : [-(hBOOL(hAPP(hAPP(c_member(_991243), _991245), c_Map_Odom(_991243, _991247, _991249)))), -(hAPP(c_Map_Omap__add(_991243, _991247, _991251, _991249), _991245) = hAPP(_991251, _991245))], (11800 ^ _779530) ^ [_991303, _991305, _991307, _991309, _991311] : [-(hBOOL(hAPP(hAPP(c_member(_991303), _991305), c_Map_Odom(_991303, _991307, _991309)))), -(hAPP(c_Map_Omap__add(_991303, _991307, _991309, _991311), _991305) = hAPP(_991311, _991305))], (11806 ^ _779530) ^ [_991385, _991387, _991389] : [c_Map_Odom(_991385, _991387, _991389) = c_Orderings_Obot__class_Obot(tc_fun(_991385, tc_HOL_Obool)), -(_991389 = hAPP(c_COMBK(tc_Option_Ooption(_991387), _991385), c_Option_Ooption_ONone(_991387)))], (11812 ^ _779530) ^ [_991498, _991500, _991502] : [_991502 = hAPP(c_COMBK(tc_Option_Ooption(_991500), _991498), c_Option_Ooption_ONone(_991500)), -(c_Map_Odom(_991498, _991500, _991502) = c_Orderings_Obot__class_Obot(tc_fun(_991498, tc_HOL_Obool)))], (11818 ^ _779530) ^ [_991617, _991619] : [-(c_Map_Odom(_991617, _991619, hAPP(c_COMBK(tc_Option_Ooption(_991619), _991617), c_Option_Ooption_ONone(_991619))) = c_Orderings_Obot__class_Obot(tc_fun(_991617, tc_HOL_Obool)))], (11820 ^ _779530) ^ [_991661, _991663, _991665] : [-(c_Map_Odom(_991661, _991663, _991665) = hAPP(c_Set_OCollect(_991661), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _991661), c_fNot), hAPP(hAPP(c_COMBC(_991661, tc_Option_Ooption(_991663), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_991663), tc_fun(tc_Option_Ooption(_991663), tc_HOL_Obool), _991661), c_fequal), _991665)), c_Option_Ooption_ONone(_991663)))))], (11822 ^ _779530) ^ [_991738, _991740, _991742, _991744] : [-(c_Map_Odom(_991738, _991740, c_Map_Omap__add(_991738, _991740, _991742, _991744)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991738, tc_HOL_Obool)), c_Map_Odom(_991738, _991740, _991744)), c_Map_Odom(_991738, _991740, _991742)))], (11824 ^ _779530) ^ [_991795, _991797, _991799, _991801] : [-(c_Map_Odom(_991795, _991797, c_Map_Orestrict__map(_991795, _991797, _991799, _991801)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_991795, tc_HOL_Obool)), c_Map_Odom(_991795, _991797, _991799)), _991801))], (11826 ^ _779530) ^ [_991848, _991850, _991852, _991854, _991856, _991858] : [class_Groups_Ocomm__monoid__add(_991848), c_Fun_Oinj__on(_991850, _991852, _991854, _991856), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991852, _991848), _991858), hAPP(c_Set_Oimage(_991850, _991852, _991854), _991856)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_991850, _991848), hAPP(c_Fun_Ocomp(_991852, _991848, _991850, _991858), _991854)), _991856))], (11836 ^ _779530) ^ [_992061, _992063, _992065, _992067, _992069] : [hAPP(_992061, _992063) = c_Option_Ooption_ONone(_992065), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992067, tc_HOL_Obool)), c_Map_Odom(_992067, _992065, _992061)), hAPP(hAPP(c_Set_Oinsert(_992067), _992063), _992069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992067, tc_HOL_Obool)), c_Map_Odom(_992067, _992065, _992061)), _992069))], (11842 ^ _779530) ^ [_992230, _992232, _992234, _992236, _992238] : [class_Groups_Oab__group__add(_992230), hBOOL(hAPP(c_Finite__Set_Ofinite(_992232), _992234)), 11849 ^ _779530 : [(11850 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_992232), _992236), _992234)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992232, _992230), _992238), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992232, tc_HOL_Obool)), _992234), hAPP(hAPP(c_Set_Oinsert(_992232), _992236), c_Orderings_Obot__class_Obot(tc_fun(_992232, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_992230), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992232, _992230), _992238), _992234)), hAPP(_992238, _992236)))], (11856 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_992232), _992236), _992234))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992232, _992230), _992238), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992232, tc_HOL_Obool)), _992234), hAPP(hAPP(c_Set_Oinsert(_992232), _992236), c_Orderings_Obot__class_Obot(tc_fun(_992232, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992232, _992230), _992238), _992234))]]], (11862 ^ _779530) ^ [_992700, _992702, _992704, _992706, _992708] : [class_Rings_Oring(_992700), hBOOL(hAPP(c_Finite__Set_Ofinite(_992702), _992704)), hBOOL(hAPP(hAPP(c_member(_992702), _992706), _992704)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992702, _992700), _992708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992702, tc_HOL_Obool)), _992704), hAPP(hAPP(c_Set_Oinsert(_992702), _992706), c_Orderings_Obot__class_Obot(tc_fun(_992702, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_992700), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_992702, _992700), _992708), _992704)), hAPP(_992708, _992706)))], (11876 ^ _779530) ^ [_993025, _993027, _993029] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_993025), hAPP(hAPP(c_Set_Oinsert(_993025), _993027), c_Orderings_Obot__class_Obot(tc_fun(_993025, tc_HOL_Obool)))), _993029) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_993025, tc_HOL_Obool)), hAPP(c_Relation_OImage(_993025, _993025, _993029), hAPP(hAPP(c_Set_Oinsert(_993025), _993027), c_Orderings_Obot__class_Obot(tc_fun(_993025, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_993025, tc_HOL_Obool), tc_HOL_Obool))))], (11878 ^ _779530) ^ [_993112, _993114, _993116, _993118] : [hBOOL(hAPP(hAPP(c_member(_993112), _993114), _993116)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_993112, tc_HOL_Obool)), hAPP(c_Relation_OImage(_993112, _993112, _993118), hAPP(hAPP(c_Set_Oinsert(_993112), _993114), c_Orderings_Obot__class_Obot(tc_fun(_993112, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_993112), _993116), _993118))))], (11884 ^ _779530) ^ [_993304, _993306, _993308, _993310] : [c_Map_Odom(_993304, _993306, _993308) = hAPP(hAPP(c_Set_Oinsert(_993304), _993310), c_Orderings_Obot__class_Obot(tc_fun(_993304, tc_HOL_Obool))), -(_993308 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_993304, tc_Option_Ooption(_993306)), hAPP(c_COMBK(tc_Option_Ooption(_993306), _993304), c_Option_Ooption_ONone(_993306))), _993310), hAPP(c_Option_Ooption_OSome(_993306), 11887 ^ [_993304, _993306, _993308, _993310])))], (11891 ^ _779530) ^ [_993489, _993491, _993493, _993495] : [11892 ^ _779530 : [(11893 ^ _779530) ^ [_993578] : [_993493 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_993489, tc_Option_Ooption(_993491)), hAPP(c_COMBK(tc_Option_Ooption(_993491), _993489), c_Option_Ooption_ONone(_993491))), _993495), hAPP(c_Option_Ooption_OSome(_993491), _993578))]], -(c_Map_Odom(_993489, _993491, _993493) = hAPP(hAPP(c_Set_Oinsert(_993489), _993495), c_Orderings_Obot__class_Obot(tc_fun(_993489, tc_HOL_Obool))))], (11897 ^ _779530) ^ [_993677, _993679, _993681, _993683] : [-(c_Map_Orestrict__map(_993677, _993679, _993681, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_993677, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_993677), _993683), c_Orderings_Obot__class_Obot(tc_fun(_993677, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_993677, tc_Option_Ooption(_993679)), _993681), _993683), c_Option_Ooption_ONone(_993679)))], (11899 ^ _779530) ^ [_993748, _993750] : [-(c_Map_Oran(_993748, _993750, hAPP(c_COMBK(tc_Option_Ooption(_993750), _993748), c_Option_Ooption_ONone(_993750))) = c_Orderings_Obot__class_Obot(tc_fun(_993750, tc_HOL_Obool)))], (11901 ^ _779530) ^ [_993792, _993794, _993796, _993798, _993800] : [c_Equiv__Relations_Oequiv(_993792, _993794, _993796), hBOOL(hAPP(hAPP(c_member(tc_fun(_993792, tc_HOL_Obool)), _993798), hAPP(hAPP(c_Equiv__Relations_Oquotient(_993792), _993794), _993796))), hBOOL(hAPP(hAPP(c_member(tc_fun(_993792, tc_HOL_Obool)), _993800), hAPP(hAPP(c_Equiv__Relations_Oquotient(_993792), _993794), _993796))), -(_993798 = _993800), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_993792, tc_HOL_Obool)), _993798), _993800) = c_Orderings_Obot__class_Obot(tc_fun(_993792, tc_HOL_Obool)))], (11919 ^ _779530) ^ [_994110, _994112, _994114, _994116, _994118, _994120, _994122, _994124] : [class_Groups_Ocomm__monoid__add(_994110), c_Fun_Oinj__on(_994112, _994114, _994116, _994118), _994120 = hAPP(c_Set_Oimage(_994112, _994114, _994116), _994118), 11933 ^ _779530 : [(11934 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_994112), 11932 ^ [_994110, _994112, _994114, _994116, _994118, _994120, _994122, _994124]), _994118)))], (11936 ^ _779530) ^ [] : [hAPP(_994122, 11932 ^ [_994110, _994112, _994114, _994116, _994118, _994120, _994122, _994124]) = hAPP(_994124, hAPP(_994116, 11932 ^ [_994110, _994112, _994114, _994116, _994118, _994120, _994122, _994124]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_994114, _994110), _994124), _994120) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_994112, _994110), _994122), _994118))], (11940 ^ _779530) ^ [_994602] : [-(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)), _994602)))))], (11942 ^ _779530) ^ [_994633] : [-(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)), _994633)))))], (11944 ^ _779530) ^ [_994664] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_994664), c_Orderings_Obot__class_Obot(tc_fun(_994664, tc_HOL_Obool)))))], (11946 ^ _779530) ^ [_994696, _994698, _994700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_994696), _994698)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_994696), hAPP(hAPP(c_Set_Oinsert(_994696), _994700), _994698))))], (11952 ^ _779530) ^ [_994807, _994809, _994811, _994813] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_994807), _994809)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_994811), hAPP(c_Set_Oimage(_994807, _994811, _994813), _994809))))], (11958 ^ _779530) ^ [_994918, _994920, _994922] : [11959 ^ _779530 : [(11960 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_994918), _994920))], (11962 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_994918), _994922))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_994918), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_994918, tc_HOL_Obool)), _994920), _994922))))], (11966 ^ _779530) ^ [_995081, _995083, _995085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995081), _995083)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_995081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_995081, tc_HOL_Obool)), _995083), _995085))))], (11972 ^ _779530) ^ [_995198, _995200] : [class_Groups_Oordered__ab__group__add(_995198), -(c_Fun_Oinj__on(_995198, _995198, c_Groups_Ouminus__class_Ouminus(_995198), _995200))], (11978 ^ _779530) ^ [_995277, _995279, _995281] : [-(hBOOL(hAPP(hAPP(c_member(_995277), _995279), _995281))), -(hBOOL(hAPP(hAPP(c_member(_995277), _995279), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_995277, tc_HOL_Obool)), _995281))))], (11984 ^ _779530) ^ [_995337, _995339, _995341] : [11985 ^ _779530 : [(11986 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995337), hAPP(c_Set_OCollect(_995337), _995339)))], (11988 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995337), hAPP(c_Set_OCollect(_995337), _995341)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_995337), hAPP(c_Set_OCollect(_995337), hAPP(hAPP(c_COMBS(_995337, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _995337), c_fconj), _995339)), _995341)))))], (11992 ^ _779530) ^ [_995548, _995550] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_995548), _995550)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_995548, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_995548, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_995548, tc_HOL_Obool), tc_fun(_995548, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_995548, tc_HOL_Obool))), _995550)))))], (11998 ^ _779530) ^ [_995705, _995707] : [class_Finite__Set_Ofinite(_995705), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_995705), _995707)))], (12004 ^ _779530) ^ [_995788, _995790] : [class_Finite__Set_Ofinite(_995788), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_995788), _995790)))], (12010 ^ _779530) ^ [_995871, _995873] : [class_Groups_Ogroup__add(_995871), -(hAPP(c_Groups_Ouminus__class_Ouminus(_995871), hAPP(c_Groups_Ouminus__class_Ouminus(_995871), _995873)) = _995873)], (12016 ^ _779530) ^ [_995966, _995968, _995970] : [class_Groups_Ogroup__add(_995966), 12019 ^ _779530 : [(12020 ^ _779530) ^ [] : [_995968 = hAPP(c_Groups_Ouminus__class_Ouminus(_995966), _995970), -(_995970 = hAPP(c_Groups_Ouminus__class_Ouminus(_995966), _995968))], (12026 ^ _779530) ^ [] : [_995970 = hAPP(c_Groups_Ouminus__class_Ouminus(_995966), _995968), -(_995968 = hAPP(c_Groups_Ouminus__class_Ouminus(_995966), _995970))]]], (12032 ^ _779530) ^ [_996207, _996209, _996211] : [class_Groups_Ogroup__add(_996207), 12035 ^ _779530 : [(12036 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_996207), _996209) = _996211, -(hAPP(c_Groups_Ouminus__class_Ouminus(_996207), _996211) = _996209)], (12042 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_996207), _996211) = _996209, -(hAPP(c_Groups_Ouminus__class_Ouminus(_996207), _996209) = _996211)]]], (12048 ^ _779530) ^ [_996448, _996450, _996452] : [class_Groups_Ogroup__add(_996448), 12051 ^ _779530 : [(12052 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_996448), _996450) = hAPP(c_Groups_Ouminus__class_Ouminus(_996448), _996452), -(_996450 = _996452)], (12058 ^ _779530) ^ [] : [_996450 = _996452, -(hAPP(c_Groups_Ouminus__class_Ouminus(_996448), _996450) = hAPP(c_Groups_Ouminus__class_Ouminus(_996448), _996452))]]], (12064 ^ _779530) ^ [_996689, _996691, _996693, _996695] : [class_Groups_Ouminus(_996689), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_996691, _996689)), _996693), _996695) = hAPP(c_Groups_Ouminus__class_Ouminus(_996689), hAPP(_996693, _996695)))], (12070 ^ _779530) ^ [_996806, _996808] : [class_Lattices_Oboolean__algebra(_996806), -(hAPP(c_Groups_Ouminus__class_Ouminus(_996806), hAPP(c_Groups_Ouminus__class_Ouminus(_996806), _996808)) = _996808)], (12076 ^ _779530) ^ [_996901, _996903, _996905, _996907] : [class_Groups_Ouminus(_996901), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_996903, _996901)), _996905), _996907) = hAPP(c_Groups_Ouminus__class_Ouminus(_996901), hAPP(_996905, _996907)))], (12082 ^ _779530) ^ [_997018, _997020, _997022] : [class_Lattices_Oboolean__algebra(_997018), 12085 ^ _779530 : [(12086 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_997018), _997020) = hAPP(c_Groups_Ouminus__class_Ouminus(_997018), _997022), -(_997020 = _997022)], (12092 ^ _779530) ^ [] : [_997020 = _997022, -(hAPP(c_Groups_Ouminus__class_Ouminus(_997018), _997020) = hAPP(c_Groups_Ouminus__class_Ouminus(_997018), _997022))]]], (12098 ^ _779530) ^ [_997259, _997261] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997259, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997259, tc_HOL_Obool)), _997261)) = _997261)], (12100 ^ _779530) ^ [_997318, _997320, _997322] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997318, tc_HOL_Obool)), _997320) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997318, tc_HOL_Obool)), _997322), -(_997320 = _997322)], (12106 ^ _779530) ^ [_997425, _997427, _997429] : [_997427 = _997429, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997425, tc_HOL_Obool)), _997427) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_997425, tc_HOL_Obool)), _997429))], (12112 ^ _779530) ^ [_997553, _997555] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_997553, tc_HOL_Obool)), hAPP(c_Set_OPow(_997553), _997555))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_997553), _997555)))], (12118 ^ _779530) ^ [_997658, _997660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997658), _997660)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_997658, tc_HOL_Obool)), hAPP(c_Set_OPow(_997658), _997660))))], (12124 ^ _779530) ^ [_997769, _997771, _997773, _997775, _997777] : [hAPP(_997769, _997771) = hAPP(c_Option_Ooption_OSome(_997773), _997775), -(hBOOL(hAPP(hAPP(c_member(_997773), _997775), c_Map_Oran(_997777, _997773, _997769))))], (12130 ^ _779530) ^ [_997890, _997892, _997894] : [class_Lattices_Oboolean__algebra(_997890), 12133 ^ _779530 : [(12134 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997890), hAPP(c_Groups_Ouminus__class_Ouminus(_997890), _997892)), hAPP(c_Groups_Ouminus__class_Ouminus(_997890), _997894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997890), _997894), _997892)))], (12140 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997890), _997894), _997892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997890), hAPP(c_Groups_Ouminus__class_Ouminus(_997890), _997892)), hAPP(c_Groups_Ouminus__class_Ouminus(_997890), _997894))))]]], (12146 ^ _779530) ^ [_998173, _998175, _998177] : [class_Lattices_Oboolean__algebra(_998173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998173), _998175), _998177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998173), hAPP(c_Groups_Ouminus__class_Ouminus(_998173), _998177)), hAPP(c_Groups_Ouminus__class_Ouminus(_998173), _998175))))], (12156 ^ _779530) ^ [_998352, _998354, _998356] : [class_Groups_Oordered__ab__group__add(_998352), 12159 ^ _779530 : [(12160 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998352), _998354), hAPP(c_Groups_Ouminus__class_Ouminus(_998352), _998356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998352), _998356), hAPP(c_Groups_Ouminus__class_Ouminus(_998352), _998354))))], (12166 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998352), _998356), hAPP(c_Groups_Ouminus__class_Ouminus(_998352), _998354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998352), _998354), hAPP(c_Groups_Ouminus__class_Ouminus(_998352), _998356))))]]], (12172 ^ _779530) ^ [_998635, _998637, _998639] : [class_Groups_Oordered__ab__group__add(_998635), 12175 ^ _779530 : [(12176 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998635), hAPP(c_Groups_Ouminus__class_Ouminus(_998635), _998637)), _998639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998635), hAPP(c_Groups_Ouminus__class_Ouminus(_998635), _998639)), _998637)))], (12182 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998635), hAPP(c_Groups_Ouminus__class_Ouminus(_998635), _998639)), _998637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998635), hAPP(c_Groups_Ouminus__class_Ouminus(_998635), _998637)), _998639)))]]], (12188 ^ _779530) ^ [_998918, _998920, _998922] : [class_Groups_Oordered__ab__group__add(_998918), 12191 ^ _779530 : [(12192 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998918), hAPP(c_Groups_Ouminus__class_Ouminus(_998918), _998920)), hAPP(c_Groups_Ouminus__class_Ouminus(_998918), _998922))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998918), _998922), _998920)))], (12198 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998918), _998922), _998920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998918), hAPP(c_Groups_Ouminus__class_Ouminus(_998918), _998920)), hAPP(c_Groups_Ouminus__class_Ouminus(_998918), _998922))))]]], (12204 ^ _779530) ^ [_999201, _999203, _999205] : [class_Groups_Oordered__ab__group__add(_999201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999201), _999203), _999205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999201), hAPP(c_Groups_Ouminus__class_Ouminus(_999201), _999205)), hAPP(c_Groups_Ouminus__class_Ouminus(_999201), _999203))))], (12214 ^ _779530) ^ [_999380, _999382, _999384] : [class_Groups_Oordered__ab__group__add(_999380), 12217 ^ _779530 : [(12218 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999380), hAPP(c_Groups_Ouminus__class_Ouminus(_999380), _999382)), hAPP(c_Groups_Ouminus__class_Ouminus(_999380), _999384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999380), _999384), _999382)))], (12224 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999380), _999384), _999382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999380), hAPP(c_Groups_Ouminus__class_Ouminus(_999380), _999382)), hAPP(c_Groups_Ouminus__class_Ouminus(_999380), _999384))))]]], (12230 ^ _779530) ^ [_999663, _999665, _999667] : [class_Groups_Oordered__ab__group__add(_999663), 12233 ^ _779530 : [(12234 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999663), hAPP(c_Groups_Ouminus__class_Ouminus(_999663), _999665)), _999667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999663), hAPP(c_Groups_Ouminus__class_Ouminus(_999663), _999667)), _999665)))], (12240 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999663), hAPP(c_Groups_Ouminus__class_Ouminus(_999663), _999667)), _999665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999663), hAPP(c_Groups_Ouminus__class_Ouminus(_999663), _999665)), _999667)))]]], (12246 ^ _779530) ^ [_999946, _999948, _999950] : [class_Groups_Oordered__ab__group__add(_999946), 12249 ^ _779530 : [(12250 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999946), _999948), hAPP(c_Groups_Ouminus__class_Ouminus(_999946), _999950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999946), _999950), hAPP(c_Groups_Ouminus__class_Ouminus(_999946), _999948))))], (12256 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999946), _999950), hAPP(c_Groups_Ouminus__class_Ouminus(_999946), _999948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999946), _999948), hAPP(c_Groups_Ouminus__class_Ouminus(_999946), _999950))))]]], (12262 ^ _779530) ^ [_1000247, _1000249, _1000251] : [hBOOL(hAPP(hAPP(c_member(_1000247), _1000249), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000247, tc_HOL_Obool)), _1000251))), hBOOL(hAPP(hAPP(c_member(_1000247), _1000249), _1000251))], (12268 ^ _779530) ^ [_1000365, _1000367, _1000369] : [-(hBOOL(hAPP(hAPP(c_member(_1000365), _1000367), _1000369))), -(hBOOL(hAPP(hAPP(c_member(_1000365), _1000367), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000365, tc_HOL_Obool)), _1000369))))], (12274 ^ _779530) ^ [_1000427, _1000429, _1000431] : [hBOOL(hAPP(hAPP(c_member(_1000427), _1000429), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000427, tc_HOL_Obool)), _1000431))), hBOOL(hAPP(hAPP(c_member(_1000427), _1000429), _1000431))], (12280 ^ _779530) ^ [_1000551, _1000553, _1000555] : [hBOOL(hAPP(hAPP(c_member(_1000551), _1000553), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000551, tc_HOL_Obool)), _1000555))), hBOOL(hAPP(hAPP(c_member(_1000551), _1000553), _1000555))], (12286 ^ _779530) ^ [_1000675, _1000677, _1000679] : [class_Groups_Oab__group__add(_1000675), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1000675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000675), _1000677), _1000679)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000675), _1000679), _1000677))], (12292 ^ _779530) ^ [_1000812, _1000814, _1000816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000812, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000812, tc_HOL_Obool)), _1000814)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000812, tc_HOL_Obool)), _1000816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000812, tc_HOL_Obool)), _1000816), _1000814)))], (12298 ^ _779530) ^ [_1000959, _1000961, _1000963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000959, tc_HOL_Obool)), _1000963), _1000961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000959, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000959, tc_HOL_Obool)), _1000961)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1000959, tc_HOL_Obool)), _1000963))))], (12304 ^ _779530) ^ [_1001112, _1001114, _1001116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001112, tc_HOL_Obool)), _1001114), _1001116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1001112, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1001112, tc_HOL_Obool)), _1001116)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1001112, tc_HOL_Obool)), _1001114))))], (12310 ^ _779530) ^ [_1001263, _1001265, _1001267, _1001269, _1001271, _1001273, _1001275] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001263, tc_Option_Ooption(_1001265)), _1001267), _1001269), hAPP(c_Option_Ooption_OSome(_1001265), _1001271)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001263, tc_Option_Ooption(_1001265)), _1001273), _1001269), hAPP(c_Option_Ooption_OSome(_1001265), _1001275)), -(_1001271 = _1001275)], (12316 ^ _779530) ^ [_1001426, _1001428, _1001430, _1001432, _1001434] : [hAPP(_1001426, _1001428) = hAPP(c_Option_Ooption_OSome(_1001430), _1001432), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001434, tc_Option_Ooption(_1001430)), _1001426), _1001428), hAPP(c_Option_Ooption_OSome(_1001430), _1001432)) = _1001426)], (12322 ^ _779530) ^ [_1001593, _1001595, _1001597, _1001599, _1001601, _1001603, _1001605] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001593, tc_Option_Ooption(_1001595)), _1001597), _1001599), hAPP(c_Option_Ooption_OSome(_1001595), _1001601)), _1001603) = hAPP(c_Option_Ooption_OSome(_1001595), _1001605), 12327 ^ _779530 : [(12328 ^ _779530) ^ [] : [-(_1001603 = _1001599)], (12330 ^ _779530) ^ [] : [-(_1001601 = _1001605)]], 12331 ^ _779530 : [(12332 ^ _779530) ^ [] : [_1001603 = _1001599], (12334 ^ _779530) ^ [] : [-(hAPP(_1001597, _1001603) = hAPP(c_Option_Ooption_OSome(_1001595), _1001605))]]], (12336 ^ _779530) ^ [_1001871, _1001873, _1001875, _1001877, _1001879, _1001881, _1001883] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1001871, tc_Option_Ooption(_1001873)), _1001875), _1001877), hAPP(c_Option_Ooption_OSome(_1001873), _1001879)), _1001881) = hAPP(c_Option_Ooption_OSome(_1001873), _1001883)), 12337 ^ _779530 : [(12338 ^ _779530) ^ [] : [_1001881 = _1001877, _1001879 = _1001883], (12344 ^ _779530) ^ [] : [-(_1001881 = _1001877), hAPP(_1001875, _1001881) = hAPP(c_Option_Ooption_OSome(_1001873), _1001883)]]], (12352 ^ _779530) ^ [_1002188, _1002190, _1002192, _1002194, _1002196, _1002198] : [hAPP(_1002188, _1002190) = hAPP(c_Option_Ooption_OSome(_1002192), _1002194), -(hAPP(c_Map_Omap__add(_1002196, _1002192, _1002198, _1002188), _1002190) = hAPP(c_Option_Ooption_OSome(_1002192), _1002194))], (12358 ^ _779530) ^ [_1002315] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002315), c_Orderings_Obot__class_Obot(tc_fun(_1002315, tc_HOL_Obool)))))], (12360 ^ _779530) ^ [_1002365, _1002367, _1002369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002365), hAPP(hAPP(c_Set_Oinsert(_1002365), _1002367), _1002369))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002365), _1002369)))], (12366 ^ _779530) ^ [_1002472, _1002474, _1002476] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002472), _1002476)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002472), hAPP(hAPP(c_Set_Oinsert(_1002472), _1002474), _1002476))))], (12372 ^ _779530) ^ [_1002585, _1002587, _1002589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002585), _1002587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002585, tc_HOL_Obool)), _1002589), _1002587)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002585), _1002589)))], (12382 ^ _779530) ^ [_1002754, _1002756, _1002758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002754, tc_HOL_Obool)), _1002756), _1002758)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002754), _1002758)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002754), _1002756)))], (12392 ^ _779530) ^ [_1002923, _1002925, _1002927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002923), _1002925)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002923), _1002927)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002923, tc_HOL_Obool)), _1002925), _1002927))))], (12402 ^ _779530) ^ [_1003120, _1003122, _1003124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1003120), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003120, tc_HOL_Obool)), _1003122), _1003124))), 12405 ^ _779530 : [(12406 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1003120), _1003122)))], (12408 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1003120), _1003124)))]]], (12410 ^ _779530) ^ [_1003267, _1003269, _1003271] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1003267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003267, tc_HOL_Obool)), _1003269), _1003271)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003267), _1003269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003267), _1003271))], (12420 ^ _779530) ^ [_1003448, _1003450, _1003452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1003448), _1003450)), 12423 ^ _779530 : [(12424 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1003448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003448, tc_HOL_Obool)), _1003452), _1003450))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1003448), _1003452)))], (12430 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1003448), _1003452)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1003448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1003448, tc_HOL_Obool)), _1003452), _1003450))))]]], (12436 ^ _779530) ^ [_1003726, _1003728, _1003730, _1003732] : [class_Groups_Oab__group__add(_1003726), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003728, _1003726), hAPP(hAPP(c_COMBB(_1003726, _1003726, _1003728), c_Groups_Ouminus__class_Ouminus(_1003726)), _1003730)), _1003732) = hAPP(c_Groups_Ouminus__class_Ouminus(_1003726), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1003728, _1003726), _1003730), _1003732)))], (12442 ^ _779530) ^ [_1003875, _1003877] : [-(hAPP(c_Set_OCollect(_1003875), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1003875), c_fNot), _1003877)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1003875, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1003875), _1003877)))], (12444 ^ _779530) ^ [_1003928, _1003930, _1003932, _1003934] : [c_Equiv__Relations_Oequiv(_1003928, _1003930, _1003932), hBOOL(hAPP(hAPP(c_member(_1003928), _1003934), _1003930)), -(hBOOL(hAPP(hAPP(c_member(_1003928), _1003934), hAPP(c_Relation_OImage(_1003928, _1003928, _1003932), hAPP(hAPP(c_Set_Oinsert(_1003928), _1003934), c_Orderings_Obot__class_Obot(tc_fun(_1003928, tc_HOL_Obool)))))))], (12454 ^ _779530) ^ [_1004135, _1004137, _1004139, _1004141] : [_1004135 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1004137, _1004139), 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)), _1004141))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1004137), _1004135)))], (12460 ^ _779530) ^ [_1004268, _1004270, _1004272] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1004268), hAPP(c_Set_OCollect(_1004268), hAPP(hAPP(c_COMBS(_1004268, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1004268), c_fdisj), _1004270)), _1004272)))), 12463 ^ _779530 : [(12464 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1004268), hAPP(c_Set_OCollect(_1004268), _1004270))))], (12466 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1004268), hAPP(c_Set_OCollect(_1004268), _1004272))))]]], (12468 ^ _779530) ^ [_1004463, _1004465, _1004467] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1004463), hAPP(c_Set_OCollect(_1004463), hAPP(hAPP(c_COMBS(_1004463, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1004463), c_fdisj), _1004465)), _1004467))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004463), hAPP(c_Set_OCollect(_1004463), _1004465))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004463), hAPP(c_Set_OCollect(_1004463), _1004467)))], (12478 ^ _779530) ^ [_1004692, _1004694, _1004696, _1004698, _1004700] : [-(c_Map_Orestrict__map(_1004692, _1004694, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1004692, tc_Option_Ooption(_1004694)), _1004696), _1004698), hAPP(c_Option_Ooption_OSome(_1004694), _1004700)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1004692, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1004692), _1004698), c_Orderings_Obot__class_Obot(tc_fun(_1004692, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1004692, _1004694, _1004696, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1004692, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1004692), _1004698), c_Orderings_Obot__class_Obot(tc_fun(_1004692, tc_HOL_Obool))))))], (12480 ^ _779530) ^ [_1004794, _1004796, _1004798, _1004800, _1004802] : [hAPP(_1004794, _1004796) = c_Option_Ooption_ONone(_1004798), -(c_Map_Oran(_1004800, _1004798, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1004800, tc_Option_Ooption(_1004798)), _1004794), _1004796), hAPP(c_Option_Ooption_OSome(_1004798), _1004802))) = hAPP(hAPP(c_Set_Oinsert(_1004798), _1004802), c_Map_Oran(_1004800, _1004798, _1004794)))], (12486 ^ _779530) ^ [_1004957, _1004959] : [class_Lattices_Oboolean__algebra(_1004957), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1004957), _1004959), hAPP(c_Groups_Ouminus__class_Ouminus(_1004957), _1004959)) = c_Orderings_Obot__class_Obot(_1004957))], (12492 ^ _779530) ^ [_1005062, _1005064] : [class_Lattices_Oboolean__algebra(_1005062), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005062), hAPP(c_Groups_Ouminus__class_Ouminus(_1005062), _1005064)), _1005064) = c_Orderings_Obot__class_Obot(_1005062))], (12498 ^ _779530) ^ [_1005167, _1005169, _1005171] : [class_Lattices_Oboolean__algebra(_1005167), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1005167), _1005169), _1005171) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005167), _1005169), hAPP(c_Groups_Ouminus__class_Ouminus(_1005167), _1005171)))], (12504 ^ _779530) ^ [_1005286, _1005288, _1005290] : [class_Lattices_Oboolean__algebra(_1005286), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1005286), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005286), _1005288), _1005290)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005286), hAPP(c_Groups_Ouminus__class_Ouminus(_1005286), _1005288)), hAPP(c_Groups_Ouminus__class_Ouminus(_1005286), _1005290)))], (12510 ^ _779530) ^ [_1005425, _1005427, _1005429] : [class_Lattices_Oboolean__algebra(_1005425), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1005425), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1005425), _1005427), _1005429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005425), hAPP(c_Groups_Ouminus__class_Ouminus(_1005425), _1005427)), hAPP(c_Groups_Ouminus__class_Ouminus(_1005425), _1005429)))], (12516 ^ _779530) ^ [_1005564, _1005566, _1005568, _1005570, _1005572] : [hAPP(_1005564, _1005566) = hAPP(c_Option_Ooption_OSome(_1005568), _1005570), -(hBOOL(hAPP(hAPP(c_member(_1005572), _1005566), c_Map_Odom(_1005572, _1005568, _1005564))))], (12522 ^ _779530) ^ [_1005681, _1005683, _1005685, _1005687, _1005689, _1005691] : [-(hBOOL(hAPP(hAPP(c_member(_1005681), _1005683), _1005685))), -(hAPP(c_Set_Oimage(_1005681, tc_Option_Ooption(_1005687), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1005681, tc_Option_Ooption(_1005687)), _1005689), _1005683), hAPP(c_Option_Ooption_OSome(_1005687), _1005691))), _1005685) = hAPP(c_Set_Oimage(_1005681, tc_Option_Ooption(_1005687), _1005689), _1005685))], (12528 ^ _779530) ^ [_1005784, _1005786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1005784, tc_HOL_Obool)), _1005786), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005784, tc_HOL_Obool)), _1005786))), -(_1005786 = c_Orderings_Obot__class_Obot(tc_fun(_1005784, tc_HOL_Obool)))], (12534 ^ _779530) ^ [_1005903, _1005905] : [_1005905 = c_Orderings_Obot__class_Obot(tc_fun(_1005903, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1005903, tc_HOL_Obool)), _1005905), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005903, tc_HOL_Obool)), _1005905))))], (12540 ^ _779530) ^ [_1006028, _1006030] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006028, tc_HOL_Obool)), _1006030), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006028, tc_HOL_Obool)), _1006030)) = c_Orderings_Obot__class_Obot(tc_fun(_1006028, tc_HOL_Obool)))], (12542 ^ _779530) ^ [_1006077, _1006079] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006077, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006077, tc_HOL_Obool)), _1006079)), _1006079) = c_Orderings_Obot__class_Obot(tc_fun(_1006077, tc_HOL_Obool)))], (12544 ^ _779530) ^ [_1006126, _1006128, _1006130, _1006132, _1006134] : [hAPP(_1006126, _1006128) = hAPP(c_Option_Ooption_OSome(_1006130), _1006132), -(hAPP(hAPP(c_Set_Oinsert(_1006134), _1006128), c_Map_Odom(_1006134, _1006130, _1006126)) = c_Map_Odom(_1006134, _1006130, _1006126))], (12550 ^ _779530) ^ [_1006257, _1006259, _1006261] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006257, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006257, tc_HOL_Obool)), _1006259), _1006261)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006257, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006257, tc_HOL_Obool)), _1006259)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006257, tc_HOL_Obool)), _1006261)))], (12552 ^ _779530) ^ [_1006330, _1006332, _1006334] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006330, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006330, tc_HOL_Obool)), _1006332), _1006334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006330, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006330, tc_HOL_Obool)), _1006332)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006330, tc_HOL_Obool)), _1006334)))], (12554 ^ _779530) ^ [_1006403, _1006405, _1006407] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006403, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006403, tc_HOL_Obool)), _1006405), _1006407)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006403, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006403, tc_HOL_Obool)), _1006405)), _1006407))], (12556 ^ _779530) ^ [_1006468, _1006470, _1006472] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006468, tc_HOL_Obool)), _1006470), _1006472) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006468, tc_HOL_Obool)), _1006470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006468, tc_HOL_Obool)), _1006472)))], (12558 ^ _779530) ^ [_1006525, _1006527, _1006529] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006525, tc_HOL_Obool)), _1006527), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006525, tc_HOL_Obool)), _1006529)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1006525, tc_HOL_Obool)), _1006527), _1006529))], (12560 ^ _779530) ^ [_1006609, _1006611, _1006613, _1006615, _1006617, _1006619] : [hAPP(c_Map_Omap__add(_1006609, _1006611, _1006613, _1006615), _1006617) = hAPP(c_Option_Ooption_OSome(_1006611), _1006619), -(hAPP(_1006615, _1006617) = hAPP(c_Option_Ooption_OSome(_1006611), _1006619)), 12567 ^ _779530 : [(12568 ^ _779530) ^ [] : [-(hAPP(_1006615, _1006617) = c_Option_Ooption_ONone(_1006611))], (12570 ^ _779530) ^ [] : [-(hAPP(_1006613, _1006617) = hAPP(c_Option_Ooption_OSome(_1006611), _1006619))]]], (12572 ^ _779530) ^ [_1006814, _1006816, _1006818, _1006820, _1006822, _1006824] : [-(hAPP(c_Map_Omap__add(_1006814, _1006816, _1006818, _1006820), _1006822) = hAPP(c_Option_Ooption_OSome(_1006816), _1006824)), 12573 ^ _779530 : [(12574 ^ _779530) ^ [] : [hAPP(_1006820, _1006822) = hAPP(c_Option_Ooption_OSome(_1006816), _1006824)], (12576 ^ _779530) ^ [] : [hAPP(_1006820, _1006822) = c_Option_Ooption_ONone(_1006816), hAPP(_1006818, _1006822) = hAPP(c_Option_Ooption_OSome(_1006816), _1006824)]]], (12584 ^ _779530) ^ [_1007065, _1007067, _1007069, _1007071, _1007073, _1007075] : [hAPP(c_Map_Omap__add(_1007065, _1007067, _1007069, _1007071), _1007073) = hAPP(c_Option_Ooption_OSome(_1007067), _1007075), -(hAPP(_1007071, _1007073) = hAPP(c_Option_Ooption_OSome(_1007067), _1007075)), 12591 ^ _779530 : [(12592 ^ _779530) ^ [] : [-(hAPP(_1007071, _1007073) = c_Option_Ooption_ONone(_1007067))], (12594 ^ _779530) ^ [] : [-(hAPP(_1007069, _1007073) = hAPP(c_Option_Ooption_OSome(_1007067), _1007075))]]], (12596 ^ _779530) ^ [_1007274, _1007276, _1007278, _1007280, _1007282, _1007284] : [-(c_Map_Omap__add(_1007274, _1007276, _1007278, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1007274, tc_Option_Ooption(_1007276)), _1007280), _1007282), hAPP(c_Option_Ooption_OSome(_1007276), _1007284))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1007274, tc_Option_Ooption(_1007276)), c_Map_Omap__add(_1007274, _1007276, _1007278, _1007280)), _1007282), hAPP(c_Option_Ooption_OSome(_1007276), _1007284)))], (12598 ^ _779530) ^ [_1007355, _1007357, _1007359, _1007361, _1007363] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007355), _1007357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1007359, tc_HOL_Obool)), _1007361), hAPP(c_Set_Oimage(_1007355, _1007359, _1007363), _1007357))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007359), _1007361)))], (12608 ^ _779530) ^ [_1007567, _1007569, _1007571, _1007573] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007567, tc_HOL_Obool)), _1007569), hAPP(hAPP(c_Set_Oinsert(_1007567), _1007571), _1007573)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007567, tc_HOL_Obool)), _1007569), _1007573))))], (12614 ^ _779530) ^ [_1007720, _1007722, _1007724, _1007726] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007720, tc_HOL_Obool)), _1007722), _1007726))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1007720, tc_HOL_Obool)), _1007722), hAPP(hAPP(c_Set_Oinsert(_1007720), _1007724), _1007726)))))], (12620 ^ _779530) ^ [_1007879, _1007881, _1007883, _1007885] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007879), hAPP(c_Set_Oimage(_1007881, _1007879, _1007883), _1007885))), c_Fun_Oinj__on(_1007881, _1007879, _1007883, _1007885), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007881), _1007885)))], (12630 ^ _779530) ^ [_1008050, _1008052] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008050, tc_HOL_Obool)), _1008052) = hAPP(c_Set_OCollect(_1008050), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1008050), c_fNot), hAPP(hAPP(c_COMBC(_1008050, tc_fun(_1008050, tc_HOL_Obool), tc_HOL_Obool), c_member(_1008050)), _1008052))))], (12632 ^ _779530) ^ [_1008113, _1008115, _1008117] : [-(hAPP(c_Set_OCollect(_1008113), hAPP(hAPP(c_COMBS(_1008113, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1008113), c_fimplies), _1008115)), _1008117)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1008113, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008113, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1008113), _1008115))), hAPP(c_Set_OCollect(_1008113), _1008117)))], (12634 ^ _779530) ^ [_1008215, _1008217, _1008219, _1008221, _1008223] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1008215, tc_Option_Ooption(_1008217)), _1008219), _1008221), hAPP(c_Option_Ooption_OSome(_1008217), _1008223)) = hAPP(c_COMBK(tc_Option_Ooption(_1008217), _1008215), c_Option_Ooption_ONone(_1008217))], (12636 ^ _779530) ^ [_1008275, _1008277] : [class_Enum_Oenum(_1008275), 12639 ^ _779530 : [(12650 ^ _779530) ^ [] : [12651 ^ _779530 : [(12652 ^ _779530) ^ [] : [hBOOL(hAPP(_1008277, c_Option_Ooption_ONone(_1008275)))], (12654 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1008275), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1008275), tc_HOL_Obool, _1008275), _1008277), c_Option_Ooption_OSome(_1008275))))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1008275)), _1008277)))], (12640 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1008275)), _1008277)), -(hBOOL(hAPP(_1008277, c_Option_Ooption_ONone(_1008275)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1008275), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1008275), tc_HOL_Obool, _1008275), _1008277), c_Option_Ooption_OSome(_1008275)))))]]], (12658 ^ _779530) ^ [_1008609, _1008611] : [class_Enum_Oenum(_1008609), 12661 ^ _779530 : [(12662 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1008609)), _1008611)), 12665 ^ _779530 : [(12666 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1008611, c_Option_Ooption_ONone(_1008609))))], (12668 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1008609), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1008609), tc_HOL_Obool, _1008609), _1008611), c_Option_Ooption_OSome(_1008609)))))]]], (12670 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1008609)), _1008611))), hBOOL(hAPP(_1008611, c_Option_Ooption_ONone(_1008609))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1008609), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1008609), tc_HOL_Obool, _1008609), _1008611), c_Option_Ooption_OSome(_1008609))))]]], (12680 ^ _779530) ^ [_1008988, _1008990, _1008992] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1008988, tc_HOL_Obool)), _1008990), _1008992) = c_Orderings_Obot__class_Obot(tc_fun(_1008988, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008988, tc_HOL_Obool)), _1008990), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008988, tc_HOL_Obool)), _1008992))))], (12686 ^ _779530) ^ [_1009131, _1009133, _1009135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009131, tc_HOL_Obool)), _1009133), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1009131, tc_HOL_Obool)), _1009135))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1009131, tc_HOL_Obool)), _1009133), _1009135) = c_Orderings_Obot__class_Obot(tc_fun(_1009131, tc_HOL_Obool)))], (12692 ^ _779530) ^ [_1009280, _1009282, _1009284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009280), _1009282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009280, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1009280, _1009280, _1009284), _1009282)), _1009282)), c_Fun_Oinj__on(_1009280, _1009280, _1009284, _1009282), -(hAPP(c_Set_Oimage(_1009280, _1009280, _1009284), _1009282) = _1009282)], (12706 ^ _779530) ^ [_1009527, _1009529, _1009531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1009527), _1009529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009527, tc_HOL_Obool)), _1009529), hAPP(c_Set_Oimage(_1009527, _1009527, _1009531), _1009529))), -(c_Fun_Oinj__on(_1009527, _1009527, _1009531, _1009529))], (12716 ^ _779530) ^ [_1009702, _1009704, _1009706, _1009708, _1009710, _1009712] : [-(hBOOL(hAPP(hAPP(c_member(_1009702), _1009704), c_Map_Odom(_1009702, _1009706, _1009708)))), -(c_Map_Omap__add(_1009702, _1009706, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1009702, tc_Option_Ooption(_1009706)), _1009710), _1009704), hAPP(c_Option_Ooption_OSome(_1009706), _1009712)), _1009708) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1009702, tc_Option_Ooption(_1009706)), c_Map_Omap__add(_1009702, _1009706, _1009710, _1009708)), _1009704), hAPP(c_Option_Ooption_OSome(_1009706), _1009712)))], (12722 ^ _779530) ^ [_1009805, _1009807, _1009809, _1009811, _1009813] : [class_Groups_Oab__group__add(_1009805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009807), _1009809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009807, tc_HOL_Obool)), _1009811), _1009809)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009807, _1009805), _1009813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009807, tc_HOL_Obool)), _1009809), _1009811)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1009805), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009807, _1009805), _1009813), _1009809)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1009807, _1009805), _1009813), _1009811)))], (12736 ^ _779530) ^ [_1010122, _1010124, _1010126, _1010128, _1010130] : [class_Groups_Ocomm__monoid__add(_1010122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010124), _1010126)), c_Fun_Oinj__on(_1010124, _1010124, _1010128, _1010126), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010124, _1010122), _1010130), hAPP(c_Set_Oimage(_1010124, _1010124, _1010128), _1010126)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010124, _1010122), hAPP(c_Fun_Ocomp(_1010124, _1010122, _1010124, _1010130), _1010128)), _1010126))], (12750 ^ _779530) ^ [_1010397, _1010399, _1010401, _1010403] : 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_1010650), hAPP(hAPP(c_COMBB(tc_fun(_1010652, tc_HOL_Obool), _1010650, _1010658), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1010652, _1010650), _1010656)), hAPP(hAPP(c_COMBB(tc_fun(_1010652, tc_HOL_Obool), tc_fun(_1010652, tc_HOL_Obool), _1010658), c_Set_OCollect(_1010652)), hAPP(hAPP(c_COMBB(tc_fun(_1010652, tc_HOL_Obool), tc_fun(_1010652, tc_HOL_Obool), _1010658), hAPP(c_COMBS(_1010652, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1010652), c_fconj), hAPP(hAPP(c_COMBC(_1010652, tc_fun(_1010652, tc_HOL_Obool), tc_HOL_Obool), c_member(_1010652)), _1010654)))), hAPP(c_COMBC(_1010652, _1010658, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1010658, tc_fun(_1010658, tc_HOL_Obool), _1010652), c_fequal), _1010660)))))), hAPP(c_Set_Oimage(_1010652, _1010658, _1010660), _1010654)))], (12770 ^ _779530) ^ [_1011061, _1011063, _1011065, _1011067, _1011069, _1011071, _1011073] : [class_Groups_Ocomm__monoid__add(_1011061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011063), _1011065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011067), _1011069)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011063, _1011061), hAPP(hAPP(c_COMBS(_1011063, tc_fun(_1011067, tc_HOL_Obool), _1011061), hAPP(hAPP(c_COMBB(tc_fun(_1011067, _1011061), tc_fun(tc_fun(_1011067, tc_HOL_Obool), _1011061), _1011063), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011067, _1011061)), _1011071)), hAPP(hAPP(c_COMBB(tc_fun(_1011067, tc_HOL_Obool), tc_fun(_1011067, tc_HOL_Obool), _1011063), c_Set_OCollect(_1011067)), hAPP(hAPP(c_COMBB(tc_fun(_1011067, tc_HOL_Obool), tc_fun(_1011067, tc_HOL_Obool), _1011063), hAPP(c_COMBS(_1011067, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1011067), c_fconj), hAPP(hAPP(c_COMBC(_1011067, tc_fun(_1011067, tc_HOL_Obool), tc_HOL_Obool), c_member(_1011067)), _1011069)))), _1011073)))), _1011065) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011067, _1011061), hAPP(hAPP(c_COMBS(_1011067, tc_fun(_1011063, tc_HOL_Obool), _1011061), hAPP(hAPP(c_COMBB(tc_fun(_1011063, _1011061), tc_fun(tc_fun(_1011063, tc_HOL_Obool), _1011061), _1011067), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011063, _1011061)), hAPP(c_COMBC(_1011063, _1011067, _1011061), _1011071))), hAPP(hAPP(c_COMBB(tc_fun(_1011063, tc_HOL_Obool), tc_fun(_1011063, tc_HOL_Obool), _1011067), c_Set_OCollect(_1011063)), hAPP(hAPP(c_COMBB(tc_fun(_1011063, tc_HOL_Obool), tc_fun(_1011063, tc_HOL_Obool), _1011067), hAPP(c_COMBS(_1011063, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1011063), c_fconj), hAPP(hAPP(c_COMBC(_1011063, tc_fun(_1011063, tc_HOL_Obool), tc_HOL_Obool), c_member(_1011063)), _1011065)))), hAPP(c_COMBC(_1011063, _1011067, tc_HOL_Obool), _1011073))))), _1011069))], (12784 ^ _779530) ^ [_1011754, _1011756, _1011758, _1011760, _1011762] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011754, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1011756, _1011754, _1011758), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011756, tc_HOL_Obool)), _1011760), _1011762))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011754, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1011756, _1011754, _1011758), _1011760)), hAPP(c_Relation_OImage(_1011756, _1011754, _1011758), _1011762)))))], (12786 ^ _779530) ^ [_1011838, _1011840] : [-(c_Fun_Oinj__on(_1011838, tc_Option_Ooption(_1011838), c_Option_Ooption_OSome(_1011838), _1011840))], (12788 ^ _779530) ^ [_1011869, _1011871, _1011873, _1011875, _1011877, _1011879] : [c_Finite__Set_Ofolding(_1011869, _1011871, _1011873, _1011875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011869), _1011877)), hBOOL(hAPP(hAPP(c_member(_1011869), _1011879), _1011877)), -(hAPP(_1011875, _1011877) = hAPP(c_Fun_Ocomp(_1011871, _1011871, _1011871, hAPP(_1011875, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011869, tc_HOL_Obool)), _1011877), hAPP(hAPP(c_Set_Oinsert(_1011869), _1011879), c_Orderings_Obot__class_Obot(tc_fun(_1011869, tc_HOL_Obool)))))), hAPP(_1011873, _1011879)))], (12802 ^ _779530) ^ [_1012182, _1012184, _1012186, _1012188, _1012190] : [c_Finite__Set_Ofolding__one(_1012182, _1012184, _1012186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012182), _1012188)), hBOOL(hAPP(hAPP(c_member(_1012182), _1012190), _1012188)), 12813 ^ _779530 : [(12814 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012182, tc_HOL_Obool)), _1012188), hAPP(hAPP(c_Set_Oinsert(_1012182), _1012190), c_Orderings_Obot__class_Obot(tc_fun(_1012182, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1012182, tc_HOL_Obool)), -(hAPP(_1012186, _1012188) = _1012190)], (12820 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012182, tc_HOL_Obool)), _1012188), hAPP(hAPP(c_Set_Oinsert(_1012182), _1012190), c_Orderings_Obot__class_Obot(tc_fun(_1012182, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1012182, tc_HOL_Obool))), -(hAPP(_1012186, _1012188) = hAPP(hAPP(_1012184, _1012190), hAPP(_1012186, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012182, tc_HOL_Obool)), _1012188), hAPP(hAPP(c_Set_Oinsert(_1012182), _1012190), c_Orderings_Obot__class_Obot(tc_fun(_1012182, tc_HOL_Obool)))))))]]], (12826 ^ _779530) ^ [_1012704, _1012706, _1012708, _1012710, _1012712, _1012714, _1012716, _1012718] : [c_Finite__Set_Ofolding__image__simple(_1012704, _1012706, _1012708, _1012710, _1012712, _1012714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012706), _1012716)), hBOOL(hAPP(hAPP(c_member(_1012706), _1012718), _1012716)), -(hAPP(_1012714, _1012716) = hAPP(hAPP(_1012708, hAPP(_1012712, _1012718)), hAPP(_1012714, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012706, tc_HOL_Obool)), _1012716), hAPP(hAPP(c_Set_Oinsert(_1012706), _1012718), c_Orderings_Obot__class_Obot(tc_fun(_1012706, tc_HOL_Obool)))))))], (12840 ^ _779530) ^ [_1013029, _1013031, _1013033, _1013035, _1013037, _1013039, _1013041, _1013043] : [c_Finite__Set_Ofolding__image(_1013029, _1013031, _1013033, _1013035, _1013037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013031), _1013039)), c_Fun_Oinj__on(_1013031, _1013031, _1013041, _1013039), -(hAPP(hAPP(_1013037, _1013043), hAPP(c_Set_Oimage(_1013031, _1013031, _1013041), _1013039)) = hAPP(hAPP(_1013037, hAPP(c_Fun_Ocomp(_1013031, _1013029, _1013031, _1013043), _1013041)), _1013039))], (12854 ^ _779530) ^ [_1013318, _1013320, _1013322, _1013324] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1013318, tc_HOL_Obool)), _1013320), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1013318), _1013322), _1013324))), 12858 ^ _779530 : [(12859 ^ _779530) ^ [] : [-(_1013320 = hAPP(c_Relation_OImage(_1013318, _1013318, _1013324), hAPP(hAPP(c_Set_Oinsert(_1013318), 12857 ^ [_1013318, _1013320, _1013322, _1013324]), c_Orderings_Obot__class_Obot(tc_fun(_1013318, tc_HOL_Obool)))))], (12861 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013318), 12857 ^ [_1013318, _1013320, _1013322, _1013324]), _1013322)))]]], (12863 ^ _779530) ^ [_1013546, _1013548, _1013550, _1013552, _1013554, _1013556, _1013558, _1013560, _1013562, _1013564, _1013566] : [c_Finite__Set_Ofolding(_1013546, _1013548, _1013550, _1013552), -(hAPP(c_Fun_Ocomp(_1013554, _1013556, _1013558, _1013560), hAPP(c_Fun_Ocomp(_1013562, _1013554, _1013558, _1013564), _1013566)) = hAPP(c_Fun_Ocomp(_1013562, _1013556, _1013558, hAPP(c_Fun_Ocomp(_1013554, _1013556, _1013562, _1013560), _1013564)), _1013566))], (12869 ^ _779530) ^ [_1013709, _1013711, _1013713, _1013715, _1013717, _1013719] : [c_Finite__Set_Ofolding(_1013709, _1013711, _1013713, _1013715), -(hAPP(c_Fun_Ocomp(_1013711, _1013711, _1013711, hAPP(_1013713, _1013717)), hAPP(_1013713, _1013719)) = hAPP(c_Fun_Ocomp(_1013711, _1013711, _1013711, hAPP(_1013713, _1013719)), hAPP(_1013713, _1013717)))], (12875 ^ _779530) ^ [_1013854, _1013856, _1013858, _1013860, _1013862, _1013864, _1013866, _1013868] : [c_Finite__Set_Ofolding(_1013854, _1013856, _1013858, _1013860), -(hAPP(c_Fun_Ocomp(_1013856, _1013856, _1013862, hAPP(_1013858, _1013864)), hAPP(c_Fun_Ocomp(_1013856, _1013856, _1013862, hAPP(_1013858, _1013866)), _1013868)) = hAPP(c_Fun_Ocomp(_1013856, _1013856, _1013862, hAPP(_1013858, _1013866)), hAPP(c_Fun_Ocomp(_1013856, _1013856, _1013862, hAPP(_1013858, _1013864)), _1013868)))], (12881 ^ _779530) ^ [_1014035, _1014037, _1014039, _1014041, _1014043, _1014045] : [c_Finite__Set_Ofolding__image__simple(_1014035, _1014037, _1014039, _1014041, _1014043, _1014045), -(hAPP(_1014045, c_Orderings_Obot__class_Obot(tc_fun(_1014037, tc_HOL_Obool))) = _1014041)], (12887 ^ _779530) ^ [_1014144, _1014146, _1014148, _1014150, _1014152, _1014154, _1014156, _1014158] : [c_Finite__Set_Ofolding__image(_1014144, _1014146, _1014148, _1014150, _1014152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014146), _1014154)), -(hAPP(hAPP(_1014152, hAPP(hAPP(c_COMBS(_1014146, _1014144, _1014144), hAPP(hAPP(c_COMBB(_1014144, tc_fun(_1014144, _1014144), _1014146), _1014148), _1014156)), _1014158)), _1014154) = hAPP(hAPP(_1014148, hAPP(hAPP(_1014152, _1014156), _1014154)), hAPP(hAPP(_1014152, _1014158), _1014154)))], (12897 ^ _779530) ^ [_1014405, _1014407, _1014409, _1014411, _1014413, _1014415] : [c_Finite__Set_Ofolding(_1014405, _1014407, _1014409, _1014411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014405), _1014413)), -(hAPP(c_Fun_Ocomp(_1014407, _1014407, _1014407, hAPP(_1014409, _1014415)), hAPP(_1014411, _1014413)) = hAPP(c_Fun_Ocomp(_1014407, _1014407, _1014407, hAPP(_1014411, _1014413)), hAPP(_1014409, _1014415)))], (12907 ^ _779530) ^ [_1014618, _1014620, _1014622, _1014624, _1014626, _1014628, _1014630, _1014632] : [c_Finite__Set_Ofolding(_1014618, _1014620, _1014622, _1014624), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014618), _1014626)), -(hAPP(c_Fun_Ocomp(_1014620, _1014620, _1014628, hAPP(_1014622, _1014630)), hAPP(c_Fun_Ocomp(_1014620, _1014620, _1014628, hAPP(_1014624, _1014626)), _1014632)) = hAPP(c_Fun_Ocomp(_1014620, _1014620, _1014628, hAPP(_1014624, _1014626)), hAPP(c_Fun_Ocomp(_1014620, _1014620, _1014628, hAPP(_1014622, _1014630)), _1014632)))], (12917 ^ _779530) ^ [_1014871, _1014873, _1014875, _1014877, _1014879, _1014881] : [c_Finite__Set_Ofolding(_1014871, _1014873, _1014875, _1014877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014871), _1014879)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014871), _1014881)), -(hAPP(c_Fun_Ocomp(_1014873, _1014873, _1014873, hAPP(_1014877, _1014881)), hAPP(_1014877, _1014879)) = hAPP(c_Fun_Ocomp(_1014873, _1014873, _1014873, hAPP(_1014877, _1014879)), hAPP(_1014877, _1014881)))], (12931 ^ _779530) ^ [_1015152, _1015154, _1015156, _1015158, _1015160, _1015162, _1015164, _1015166] : [c_Finite__Set_Ofolding(_1015152, _1015154, _1015156, _1015158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015152), _1015160)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1015152), _1015162)), -(hAPP(c_Fun_Ocomp(_1015154, _1015154, _1015164, hAPP(_1015158, _1015162)), hAPP(c_Fun_Ocomp(_1015154, _1015154, _1015164, hAPP(_1015158, _1015160)), _1015166)) = hAPP(c_Fun_Ocomp(_1015154, _1015154, _1015164, hAPP(_1015158, _1015160)), hAPP(c_Fun_Ocomp(_1015154, _1015154, _1015164, hAPP(_1015158, _1015162)), _1015166)))], (12956 ^ _779530) ^ [_1015676] : [12958 ^ _779530 : [(12959 ^ _779530) ^ [_1015752] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 12957 ^ [_1015676, _1015752]), _1015676)))], (12961 ^ _779530) ^ [_1015786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12957 ^ [_1015676, _1015786]), _1015786))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1015676)))], (12945 ^ _779530) ^ [_1015489] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1015489)), 12949 ^ _779530 : [(12950 ^ _779530) ^ [_1015569] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1015569), _1015489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015569), 12948 ^ [_1015489])))]]], (12976 ^ _779530) ^ [_1016054] : [12978 ^ _779530 : [(12979 ^ _779530) ^ [_1016130] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 12977 ^ [_1016054, _1016130]), _1016054)))], (12981 ^ _779530) ^ [_1016164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 12977 ^ [_1016054, _1016164]), _1016164))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1016054)))], (12965 ^ _779530) ^ [_1015867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1015867)), 12969 ^ _779530 : [(12970 ^ _779530) ^ [_1015947] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1015947), _1015867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015947), 12968 ^ [_1015867])))]]], (12985 ^ _779530) ^ [_1016251, _1016253, _1016255] : [hAPP(c_Option_Ooption_OSome(_1016251), _1016253) = hAPP(c_Option_Ooption_OSome(_1016251), _1016255), -(_1016253 = _1016255)], (12991 ^ _779530) ^ [_1016346, _1016348, _1016350] : [_1016348 = _1016350, -(hAPP(c_Option_Ooption_OSome(_1016346), _1016348) = hAPP(c_Option_Ooption_OSome(_1016346), _1016350))], (12997 ^ _779530) ^ [_1016447, _1016449, _1016451, _1016453] : [c_Finite__Set_Ofolding__one(_1016447, _1016449, _1016451), -(hAPP(_1016451, hAPP(hAPP(c_Set_Oinsert(_1016447), _1016453), c_Orderings_Obot__class_Obot(tc_fun(_1016447, tc_HOL_Obool)))) = _1016453)], (13003 ^ _779530) ^ [_1016562, _1016564] : [-(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), _1016562)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1016564))))))], (13005 ^ _779530) ^ [_1016604, _1016606, _1016608, _1016610, _1016612, _1016614, _1016616, _1016618] : [c_Finite__Set_Ofolding__image__simple(_1016604, _1016606, _1016608, _1016610, _1016612, _1016614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016606), _1016616)), -(hBOOL(hAPP(hAPP(c_member(_1016606), _1016618), _1016616))), -(hAPP(_1016614, hAPP(hAPP(c_Set_Oinsert(_1016606), _1016618), _1016616)) = hAPP(hAPP(_1016608, hAPP(_1016612, _1016618)), hAPP(_1016614, _1016616)))], (13019 ^ _779530) ^ [_1016848, _1016850, _1016852, _1016854, _1016856, _1016858, _1016860, _1016862] : [c_Finite__Set_Ofolding__image__simple(_1016848, _1016850, _1016852, _1016854, _1016856, _1016858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016850), _1016860)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1016850), _1016862)), -(hAPP(hAPP(_1016852, hAPP(_1016858, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016850, tc_HOL_Obool)), _1016860), _1016862))), hAPP(_1016858, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016850, tc_HOL_Obool)), _1016860), _1016862))) = hAPP(hAPP(_1016852, hAPP(_1016858, _1016860)), hAPP(_1016858, _1016862)))], (13033 ^ _779530) ^ [_1017181, _1017183, _1017185, _1017187, _1017189, _1017191] : [c_Finite__Set_Ofolding(_1017181, _1017183, _1017185, _1017187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017181), _1017189)), -(hBOOL(hAPP(hAPP(c_member(_1017181), _1017191), _1017189))), -(hAPP(_1017187, hAPP(hAPP(c_Set_Oinsert(_1017181), _1017191), _1017189)) = hAPP(c_Fun_Ocomp(_1017183, _1017183, _1017183, hAPP(_1017187, _1017189)), hAPP(_1017185, _1017191)))], (13047 ^ _779530) ^ [_1017417, _1017419, _1017421, _1017423, _1017425, _1017427] : [c_Finite__Set_Ofolding(_1017417, _1017419, _1017421, _1017423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017417), _1017425)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017417), _1017427)), -(hAPP(c_Fun_Ocomp(_1017419, _1017419, _1017419, hAPP(_1017423, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017417, tc_HOL_Obool)), _1017425), _1017427))), hAPP(_1017423, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017417, tc_HOL_Obool)), _1017425), _1017427))) = hAPP(c_Fun_Ocomp(_1017419, _1017419, _1017419, hAPP(_1017423, _1017425)), hAPP(_1017423, _1017427)))], (13061 ^ _779530) ^ [_1017742, _1017744, _1017746, _1017748, _1017750] : [c_Finite__Set_Ofolding__one(_1017742, _1017744, _1017746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017742), _1017748)), -(hBOOL(hAPP(hAPP(c_member(_1017742), _1017750), _1017748))), -(_1017748 = c_Orderings_Obot__class_Obot(tc_fun(_1017742, tc_HOL_Obool))), -(hAPP(_1017746, hAPP(hAPP(c_Set_Oinsert(_1017742), _1017750), _1017748)) = hAPP(hAPP(_1017744, _1017750), hAPP(_1017746, _1017748)))], (13079 ^ _779530) ^ [_1017987, _1017989, _1017991] : [-(hAPP(c_Relation_OImage(_1017987, _1017989, _1017991), c_Orderings_Obot__class_Obot(tc_fun(_1017987, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1017989, tc_HOL_Obool)))], (13081 ^ _779530) ^ [_1018031, _1018033, _1018035, _1018037, _1018039, _1018041, _1018043, _1018045] : [c_Finite__Set_Ofolding__image__simple(_1018031, _1018033, _1018035, _1018037, _1018039, _1018041), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018033), _1018043)), -(hAPP(_1018041, hAPP(hAPP(c_Set_Oinsert(_1018033), _1018045), _1018043)) = hAPP(hAPP(_1018035, hAPP(_1018039, _1018045)), hAPP(_1018041, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018033, tc_HOL_Obool)), _1018043), hAPP(hAPP(c_Set_Oinsert(_1018033), _1018045), c_Orderings_Obot__class_Obot(tc_fun(_1018033, tc_HOL_Obool)))))))], (13091 ^ _779530) ^ [_1018294, _1018296, _1018298, _1018300, _1018302] : [c_Finite__Set_Ofolding__one(_1018294, _1018296, _1018298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018294), _1018300)), 13098 ^ _779530 : [(13099 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018294, tc_HOL_Obool)), _1018300), hAPP(hAPP(c_Set_Oinsert(_1018294), _1018302), c_Orderings_Obot__class_Obot(tc_fun(_1018294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1018294, tc_HOL_Obool)), -(hAPP(_1018298, hAPP(hAPP(c_Set_Oinsert(_1018294), _1018302), _1018300)) = _1018302)], (13105 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018294, tc_HOL_Obool)), _1018300), hAPP(hAPP(c_Set_Oinsert(_1018294), _1018302), c_Orderings_Obot__class_Obot(tc_fun(_1018294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1018294, tc_HOL_Obool))), -(hAPP(_1018298, hAPP(hAPP(c_Set_Oinsert(_1018294), _1018302), _1018300)) = hAPP(hAPP(_1018296, _1018302), hAPP(_1018298, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018294, tc_HOL_Obool)), _1018300), hAPP(hAPP(c_Set_Oinsert(_1018294), _1018302), c_Orderings_Obot__class_Obot(tc_fun(_1018294, tc_HOL_Obool)))))))]]], (13111 ^ _779530) ^ [_1018776, _1018778, _1018780, _1018782, _1018784, _1018786, _1018788, _1018790] : [c_Finite__Set_Ofolding__image__simple(_1018776, _1018778, _1018780, _1018782, _1018784, _1018786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018778), _1018788)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018778), _1018790)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1018778, tc_HOL_Obool)), _1018788), _1018790) = c_Orderings_Obot__class_Obot(tc_fun(_1018778, tc_HOL_Obool)), -(hAPP(_1018786, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018778, tc_HOL_Obool)), _1018788), _1018790)) = hAPP(hAPP(_1018780, hAPP(_1018786, _1018788)), hAPP(_1018786, _1018790)))], (13129 ^ _779530) ^ [_1019165, _1019167, _1019169, _1019171, _1019173] : [c_Finite__Set_Ofolding__one(_1019165, _1019167, _1019169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019165), _1019171)), -(_1019171 = c_Orderings_Obot__class_Obot(tc_fun(_1019165, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019165), _1019173)), -(_1019173 = c_Orderings_Obot__class_Obot(tc_fun(_1019165, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019165, tc_HOL_Obool)), _1019171), _1019173) = c_Orderings_Obot__class_Obot(tc_fun(_1019165, tc_HOL_Obool)), -(hAPP(_1019169, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019165, tc_HOL_Obool)), _1019171), _1019173)) = hAPP(hAPP(_1019167, hAPP(_1019169, _1019171)), hAPP(_1019169, _1019173)))], (13155 ^ _779530) ^ [_1019666, _1019668, _1019670, _1019672, _1019674] : [c_Finite__Set_Ofolding__one(_1019666, _1019668, _1019670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019666), _1019672)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019666), _1019674)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019666, tc_HOL_Obool)), _1019672), _1019674) = c_Orderings_Obot__class_Obot(tc_fun(_1019666, tc_HOL_Obool))), -(hAPP(hAPP(_1019668, hAPP(_1019670, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019666, tc_HOL_Obool)), _1019672), _1019674))), hAPP(_1019670, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019666, tc_HOL_Obool)), _1019672), _1019674))) = hAPP(hAPP(_1019668, hAPP(_1019670, _1019672)), hAPP(_1019670, _1019674)))], (13173 ^ _779530) ^ [_1020022, _1020024, _1020026, _1020028, _1020030, _1020032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1020022, _1020024), tc_HOL_Obool)), _1020026), _1020028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020022, tc_HOL_Obool)), _1020030), _1020032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020024, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1020022, _1020024, _1020026), _1020030)), hAPP(c_Relation_OImage(_1020022, _1020024, _1020028), _1020032))))], (13183 ^ _779530) ^ [_1020261, _1020263, _1020265, _1020267, _1020269] : [-(hAPP(c_Relation_OImage(_1020261, _1020263, _1020265), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1020261, tc_HOL_Obool)), _1020267), _1020269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1020263, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1020261, _1020263, _1020265), _1020267)), hAPP(c_Relation_OImage(_1020261, _1020263, _1020265), _1020269)))], (13185 ^ _779530) ^ [_1020335, _1020337, _1020339, _1020341, _1020343] : [-(hAPP(c_Relation_OImage(_1020335, _1020337, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1020335, _1020337), tc_HOL_Obool)), _1020339), _1020341)), _1020343) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1020337, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1020335, _1020337, _1020339), _1020343)), hAPP(c_Relation_OImage(_1020335, _1020337, _1020341), _1020343)))], (13187 ^ _779530) ^ [_1020421, _1020423] : [-(_1020421 = c_Option_Ooption_ONone(_1020423)), -(_1020421 = hAPP(c_Option_Ooption_OSome(_1020423), 13190 ^ [_1020421, _1020423]))], (13194 ^ _779530) ^ [_1020467, _1020469] : [13195 ^ _779530 : [(13196 ^ _779530) ^ [_1020515] : [_1020467 = hAPP(c_Option_Ooption_OSome(_1020469), _1020515)]], _1020467 = c_Option_Ooption_ONone(_1020469)], (13200 ^ _779530) ^ [_1020583, _1020585] : [-(_1020583 = hAPP(c_Option_Ooption_OSome(_1020585), 13201 ^ [_1020583, _1020585])), -(_1020583 = c_Option_Ooption_ONone(_1020585))], (13207 ^ _779530) ^ [_1020629, _1020631] : [_1020629 = c_Option_Ooption_ONone(_1020631), 13210 ^ _779530 : [(13211 ^ _779530) ^ [_1020701] : [_1020629 = hAPP(c_Option_Ooption_OSome(_1020631), _1020701)]]], (13213 ^ _779530) ^ [_1020747, _1020749] : [hAPP(c_Option_Ooption_OSome(_1020747), _1020749) = c_Option_Ooption_ONone(_1020747)], (13215 ^ _779530) ^ [_1020791, _1020793] : [c_Option_Ooption_ONone(_1020791) = hAPP(c_Option_Ooption_OSome(_1020791), _1020793)], (13217 ^ _779530) ^ [_1020823, _1020825, _1020827, _1020829, _1020831, _1020833] : [c_Finite__Set_Ofolding(_1020823, _1020825, _1020827, _1020829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020823), _1020831)), -(hAPP(_1020829, hAPP(hAPP(c_Set_Oinsert(_1020823), _1020833), _1020831)) = hAPP(c_Fun_Ocomp(_1020825, _1020825, _1020825, hAPP(_1020829, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020823, tc_HOL_Obool)), _1020831), hAPP(hAPP(c_Set_Oinsert(_1020823), _1020833), c_Orderings_Obot__class_Obot(tc_fun(_1020823, tc_HOL_Obool)))))), hAPP(_1020827, _1020833)))], (13227 ^ _779530) ^ [_1021078, _1021080, _1021082, _1021084, _1021086, _1021088] : [c_Finite__Set_Ofolding(_1021078, _1021080, _1021082, _1021084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021078), _1021086)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1021078), _1021088)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1021078, tc_HOL_Obool)), _1021086), _1021088) = c_Orderings_Obot__class_Obot(tc_fun(_1021078, tc_HOL_Obool)), -(hAPP(_1021084, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1021078, tc_HOL_Obool)), _1021086), _1021088)) = hAPP(c_Fun_Ocomp(_1021080, _1021080, _1021080, hAPP(_1021084, _1021086)), hAPP(_1021084, _1021088)))], (13245 ^ _779530) ^ [_1021451, _1021453] : [-(c_Option_Oset(_1021451, hAPP(c_Option_Ooption_OSome(_1021451), _1021453)) = hAPP(hAPP(c_Set_Oinsert(_1021451), _1021453), c_Orderings_Obot__class_Obot(tc_fun(_1021451, tc_HOL_Obool))))], (13247 ^ _779530) ^ [_1021518, _1021520, _1021522, _1021524] : [hBOOL(hAPP(hAPP(c_member(_1021518), _1021520), c_SetInterval_Oord_OatMost(_1021518, _1021522, _1021524))), -(hBOOL(hAPP(hAPP(_1021522, _1021520), _1021524)))], (13253 ^ _779530) ^ [_1021627, _1021629, _1021631, _1021633] : [hBOOL(hAPP(hAPP(_1021631, _1021629), _1021633)), -(hBOOL(hAPP(hAPP(c_member(_1021627), _1021629), c_SetInterval_Oord_OatMost(_1021627, _1021631, _1021633))))], (13259 ^ _779530) ^ [_1021763, _1021765, _1021767, _1021769] : [hBOOL(hAPP(hAPP(c_member(_1021763), _1021765), c_SetInterval_Oord_OatLeast(_1021763, _1021767, _1021769))), -(hBOOL(hAPP(hAPP(_1021767, _1021769), _1021765)))], (13265 ^ _779530) ^ [_1021872, _1021874, _1021876, _1021878] : [hBOOL(hAPP(hAPP(_1021876, _1021878), _1021874)), -(hBOOL(hAPP(hAPP(c_member(_1021872), _1021874), c_SetInterval_Oord_OatLeast(_1021872, _1021876, _1021878))))], (13271 ^ _779530) ^ [_1022008, _1022010, _1022012, _1022014] : [hBOOL(hAPP(hAPP(c_member(_1022008), _1022010), c_SetInterval_Oord_OlessThan(_1022008, _1022012, _1022014))), -(hBOOL(hAPP(hAPP(_1022012, _1022010), _1022014)))], (13277 ^ _779530) ^ [_1022117, _1022119, _1022121, _1022123] : [hBOOL(hAPP(hAPP(_1022121, _1022119), _1022123)), -(hBOOL(hAPP(hAPP(c_member(_1022117), _1022119), c_SetInterval_Oord_OlessThan(_1022117, _1022121, _1022123))))], (13283 ^ _779530) ^ [_1022253, _1022255, _1022257, _1022259] : [hBOOL(hAPP(hAPP(c_member(_1022253), _1022255), c_SetInterval_Oord_OgreaterThan(_1022253, _1022257, _1022259))), -(hBOOL(hAPP(hAPP(_1022257, _1022259), _1022255)))], (13289 ^ _779530) ^ [_1022362, _1022364, _1022366, _1022368] : [hBOOL(hAPP(hAPP(_1022366, _1022368), _1022364)), -(hBOOL(hAPP(hAPP(c_member(_1022362), _1022364), c_SetInterval_Oord_OgreaterThan(_1022362, _1022366, _1022368))))], (13295 ^ _779530) ^ [_1022501, _1022503, _1022505, _1022507, _1022509] : [hBOOL(hAPP(hAPP(c_member(_1022501), _1022503), c_SetInterval_Oord_OatLeastAtMost(_1022501, _1022505, _1022507, _1022509))), 13298 ^ _779530 : [(13299 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1022505, _1022507), _1022503)))], (13301 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1022505, _1022503), _1022509)))]]], (13303 ^ _779530) ^ [_1022650, _1022652, _1022654, _1022656, _1022658] : [-(hBOOL(hAPP(hAPP(c_member(_1022650), _1022652), c_SetInterval_Oord_OatLeastAtMost(_1022650, _1022654, _1022656, _1022658)))), hBOOL(hAPP(hAPP(_1022654, _1022656), _1022652)), hBOOL(hAPP(hAPP(_1022654, _1022652), _1022658))], (13313 ^ _779530) ^ [_1022861, _1022863, _1022865, _1022867, _1022869] : [hBOOL(hAPP(hAPP(c_member(_1022861), _1022863), c_SetInterval_Oord_OgreaterThanLessThan(_1022861, _1022865, _1022867, _1022869))), 13316 ^ _779530 : [(13317 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1022865, _1022867), _1022863)))], (13319 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1022865, _1022863), _1022869)))]]], (13321 ^ _779530) ^ [_1023010, _1023012, _1023014, _1023016, _1023018] : [-(hBOOL(hAPP(hAPP(c_member(_1023010), _1023012), c_SetInterval_Oord_OgreaterThanLessThan(_1023010, _1023014, _1023016, _1023018)))), hBOOL(hAPP(hAPP(_1023014, _1023016), _1023012)), hBOOL(hAPP(hAPP(_1023014, _1023012), _1023018))], (13331 ^ _779530) ^ [_1023224, _1023226, _1023228, _1023230, _1023232, _1023234] : [hBOOL(hAPP(hAPP(c_member(_1023224), _1023226), c_SetInterval_Oord_OatLeastLessThan(_1023224, _1023228, _1023230, _1023232, _1023234))), 13334 ^ _779530 : [(13335 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1023228, _1023232), _1023226)))], (13337 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1023230, _1023226), _1023234)))]]], (13339 ^ _779530) ^ [_1023377, _1023379, _1023381, _1023383, _1023385, _1023387] : [-(hBOOL(hAPP(hAPP(c_member(_1023377), _1023379), c_SetInterval_Oord_OatLeastLessThan(_1023377, _1023381, _1023383, _1023385, _1023387)))), hBOOL(hAPP(hAPP(_1023381, _1023385), _1023379)), hBOOL(hAPP(hAPP(_1023383, _1023379), _1023387))], (13349 ^ _779530) ^ [_1023570, _1023572, _1023574] : [_1023570 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1023572, _1023572), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1023572, _1023572), tc_HOL_Obool)), _1023570), _1023574)))], (13355 ^ _779530) ^ [_1023709, _1023711, _1023713] : [hBOOL(hAPP(hAPP(c_member(_1023709), _1023711), c_Option_Oset(_1023709, _1023713))), -(_1023713 = hAPP(c_Option_Ooption_OSome(_1023709), _1023711))], (13361 ^ _779530) ^ [_1023814, _1023816, _1023818] : [_1023818 = hAPP(c_Option_Ooption_OSome(_1023814), _1023816), -(hBOOL(hAPP(hAPP(c_member(_1023814), _1023816), c_Option_Oset(_1023814, _1023818))))], (13367 ^ _779530) ^ [_1023925] : [-(c_Option_Oset(_1023925, c_Option_Ooption_ONone(_1023925)) = c_Orderings_Obot__class_Obot(tc_fun(_1023925, tc_HOL_Obool)))], (13369 ^ _779530) ^ [_1023973, _1023975] : [c_Option_Oset(_1023973, _1023975) = c_Orderings_Obot__class_Obot(tc_fun(_1023973, tc_HOL_Obool)), -(_1023975 = c_Option_Ooption_ONone(_1023973))], (13375 ^ _779530) ^ [_1024066, _1024068] : [_1024068 = c_Option_Ooption_ONone(_1024066), -(c_Option_Oset(_1024066, _1024068) = c_Orderings_Obot__class_Obot(tc_fun(_1024066, tc_HOL_Obool)))], (13381 ^ _779530) ^ [_1024192, _1024194, _1024196, _1024198, _1024200, _1024202] : [hBOOL(hAPP(hAPP(c_member(_1024192), _1024194), c_SetInterval_Oord_OgreaterThanAtMost(_1024192, _1024196, _1024198, _1024200, _1024202))), 13384 ^ _779530 : [(13385 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1024198, _1024200), _1024194)))], (13387 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1024196, _1024194), _1024202)))]]], (13389 ^ _779530) ^ [_1024345, _1024347, _1024349, _1024351, _1024353, _1024355] : [-(hBOOL(hAPP(hAPP(c_member(_1024345), _1024347), c_SetInterval_Oord_OgreaterThanAtMost(_1024345, _1024349, _1024351, _1024353, _1024355)))), hBOOL(hAPP(hAPP(_1024351, _1024353), _1024347)), hBOOL(hAPP(hAPP(_1024349, _1024347), _1024355))], (13399 ^ _779530) ^ [_1024538, _1024540, _1024542] : [class_Lattices_Olattice(_1024538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024538), _1024540)), hBOOL(hAPP(hAPP(c_member(_1024538), _1024542), _1024540)), 13410 ^ _779530 : [(13411 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024538, tc_HOL_Obool)), _1024540), hAPP(hAPP(c_Set_Oinsert(_1024538), _1024542), c_Orderings_Obot__class_Obot(tc_fun(_1024538, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1024538, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1024538, _1024540) = _1024542)], (13417 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024538, tc_HOL_Obool)), _1024540), hAPP(hAPP(c_Set_Oinsert(_1024538), _1024542), c_Orderings_Obot__class_Obot(tc_fun(_1024538, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1024538, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1024538, _1024540) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1024538), _1024542), c_Big__Operators_Olattice__class_OInf__fin(_1024538, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024538, tc_HOL_Obool)), _1024540), hAPP(hAPP(c_Set_Oinsert(_1024538), _1024542), c_Orderings_Obot__class_Obot(tc_fun(_1024538, tc_HOL_Obool)))))))]]], (13423 ^ _779530) ^ [_1025044, _1025046, _1025048] : [class_Lattices_Olattice(_1025044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025044), _1025046)), hBOOL(hAPP(hAPP(c_member(_1025044), _1025048), _1025046)), 13434 ^ _779530 : [(13435 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025044, tc_HOL_Obool)), _1025046), hAPP(hAPP(c_Set_Oinsert(_1025044), _1025048), c_Orderings_Obot__class_Obot(tc_fun(_1025044, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1025044, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1025044, _1025046) = _1025048)], (13441 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025044, tc_HOL_Obool)), _1025046), hAPP(hAPP(c_Set_Oinsert(_1025044), _1025048), c_Orderings_Obot__class_Obot(tc_fun(_1025044, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1025044, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1025044, _1025046) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1025044), _1025048), c_Big__Operators_Olattice__class_OSup__fin(_1025044, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025044, tc_HOL_Obool)), _1025046), hAPP(hAPP(c_Set_Oinsert(_1025044), _1025048), c_Orderings_Obot__class_Obot(tc_fun(_1025044, tc_HOL_Obool)))))))]]], (13447 ^ _779530) ^ [_1025550, _1025552, _1025554, _1025556, _1025558, _1025560] : [c_Finite__Set_Ofolding__idem(_1025550, _1025552, _1025554, _1025556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025550), _1025558)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025550), _1025560)), -(hAPP(_1025556, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025550, tc_HOL_Obool)), _1025558), _1025560)) = hAPP(c_Fun_Ocomp(_1025552, _1025552, _1025552, hAPP(_1025556, _1025558)), hAPP(_1025556, _1025560)))], (13461 ^ _779530) ^ [_1025831, _1025833, _1025835, _1025837, _1025839, _1025841] : [c_Finite__Set_Ofolding__idem(_1025831, _1025833, _1025835, _1025837), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025831), _1025839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025831, tc_HOL_Obool)), _1025841), _1025839)), -(hAPP(c_Fun_Ocomp(_1025833, _1025833, _1025833, hAPP(_1025837, _1025839)), hAPP(_1025837, _1025841)) = hAPP(_1025837, _1025839))], (13475 ^ _779530) ^ [_1026102, _1026104, _1026106, _1026108, _1026110, _1026112] : [c_Finite__Set_Ofolding__idem(_1026102, _1026104, _1026106, _1026108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026102), _1026110)), -(hAPP(_1026108, hAPP(hAPP(c_Set_Oinsert(_1026102), _1026112), _1026110)) = hAPP(c_Fun_Ocomp(_1026104, _1026104, _1026104, hAPP(_1026108, _1026110)), hAPP(_1026106, _1026112)))], (13485 ^ _779530) ^ [_1026309, _1026311, _1026313, _1026315] : [c_Finite__Set_Ofolding__one(_1026309, _1026311, _1026313), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026309), _1026315)), -(_1026315 = c_Orderings_Obot__class_Obot(tc_fun(_1026309, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1026309), hAPP(hAPP(_1026311, 13498 ^ [_1026309, _1026311, _1026313, _1026315]), 13499 ^ [_1026309, _1026311, _1026313, _1026315])), hAPP(hAPP(c_Set_Oinsert(_1026309), 13498 ^ [_1026309, _1026311, _1026313, _1026315]), hAPP(hAPP(c_Set_Oinsert(_1026309), 13499 ^ [_1026309, _1026311, _1026313, _1026315]), c_Orderings_Obot__class_Obot(tc_fun(_1026309, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1026309), hAPP(_1026313, _1026315)), _1026315)))], (13505 ^ _779530) ^ [_1026795, _1026797, _1026799, _1026801, _1026803, _1026805] : [c_Finite__Set_Ofolding__idem(_1026795, _1026797, _1026799, _1026801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1026795), _1026803)), hBOOL(hAPP(hAPP(c_member(_1026795), _1026805), _1026803)), -(hAPP(c_Fun_Ocomp(_1026797, _1026797, _1026797, hAPP(_1026801, _1026803)), hAPP(_1026799, _1026805)) = hAPP(_1026801, _1026803))], (13519 ^ _779530) ^ [_1027060, _1027062] : [class_Lattices_Olattice(_1027060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027060), _1027062)), -(_1027062 = c_Orderings_Obot__class_Obot(tc_fun(_1027060, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027060), c_Big__Operators_Olattice__class_OInf__fin(_1027060, _1027062)), c_Big__Operators_Olattice__class_OSup__fin(_1027060, _1027062))))], (13533 ^ _779530) ^ [_1027246, _1027248] : [class_Lattices_Olattice(_1027246), -(c_Big__Operators_Olattice__class_OSup__fin(_1027246, hAPP(hAPP(c_Set_Oinsert(_1027246), _1027248), c_Orderings_Obot__class_Obot(tc_fun(_1027246, tc_HOL_Obool)))) = _1027248)], (13539 ^ _779530) ^ [_1027353, _1027355] : [class_Lattices_Olattice(_1027353), -(c_Big__Operators_Olattice__class_OInf__fin(_1027353, hAPP(hAPP(c_Set_Oinsert(_1027353), _1027355), c_Orderings_Obot__class_Obot(tc_fun(_1027353, tc_HOL_Obool)))) = _1027355)], (13545 ^ _779530) ^ [_1027460, _1027462, _1027464, _1027466, _1027468] : [c_Finite__Set_Ofolding__idem(_1027460, _1027462, _1027464, _1027466), -(hAPP(c_Fun_Ocomp(_1027462, _1027462, _1027462, hAPP(_1027464, _1027468)), hAPP(_1027464, _1027468)) = hAPP(_1027464, _1027468))], (13551 ^ _779530) ^ [_1027581, _1027583, _1027585, _1027587, _1027589, _1027591, _1027593] : [c_Finite__Set_Ofolding__idem(_1027581, _1027583, _1027585, _1027587), -(hAPP(c_Fun_Ocomp(_1027583, _1027583, _1027589, hAPP(_1027585, _1027591)), hAPP(c_Fun_Ocomp(_1027583, _1027583, _1027589, hAPP(_1027585, _1027591)), _1027593)) = hAPP(c_Fun_Ocomp(_1027583, _1027583, _1027589, hAPP(_1027585, _1027591)), _1027593))], (13557 ^ _779530) ^ [_1027738, _1027740, _1027742] : [class_Lattices_Olattice(_1027738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027738), _1027740)), hBOOL(hAPP(hAPP(c_member(_1027738), _1027742), _1027740)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1027738), _1027742), c_Big__Operators_Olattice__class_OInf__fin(_1027738, _1027740)) = _1027742)], (13571 ^ _779530) ^ [_1027967, _1027969, _1027971] : [class_Lattices_Olattice(_1027967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027967), _1027969)), hBOOL(hAPP(hAPP(c_member(_1027967), _1027971), _1027969)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1027967), _1027971), c_Big__Operators_Olattice__class_OSup__fin(_1027967, _1027969)) = c_Big__Operators_Olattice__class_OSup__fin(_1027967, _1027969))], (13585 ^ _779530) ^ [_1028202, _1028204, _1028206] : [class_Lattices_Olattice(_1028202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028202), _1028204)), hBOOL(hAPP(hAPP(c_member(_1028202), _1028206), _1028204)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1028202), _1028206), c_Big__Operators_Olattice__class_OInf__fin(_1028202, _1028204)) = c_Big__Operators_Olattice__class_OInf__fin(_1028202, _1028204))], (13599 ^ _779530) ^ [_1028437, _1028439, _1028441] : [class_Lattices_Olattice(_1028437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028437), _1028439)), hBOOL(hAPP(hAPP(c_member(_1028437), _1028441), _1028439)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1028437), _1028441), c_Big__Operators_Olattice__class_OSup__fin(_1028437, _1028439)) = _1028441)], (13613 ^ _779530) ^ [_1028666, _1028668, _1028670] : [class_Lattices_Olattice(_1028666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028666), _1028668)), -(_1028668 = c_Orderings_Obot__class_Obot(tc_fun(_1028666, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1028666, hAPP(hAPP(c_Set_Oinsert(_1028666), _1028670), _1028668)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1028666), _1028670), c_Big__Operators_Olattice__class_OSup__fin(_1028666, _1028668)))], (13627 ^ _779530) ^ [_1028874, _1028876, _1028878] : [class_Lattices_Olattice(_1028874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028874), _1028876)), -(_1028876 = c_Orderings_Obot__class_Obot(tc_fun(_1028874, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1028874, hAPP(hAPP(c_Set_Oinsert(_1028874), _1028878), _1028876)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1028874), _1028878), c_Big__Operators_Olattice__class_OInf__fin(_1028874, _1028876)))], (13641 ^ _779530) ^ [_1029082, _1029084, _1029086] : [class_Lattices_Olattice(_1029082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029082), _1029084)), -(_1029086 = c_Orderings_Obot__class_Obot(tc_fun(_1029082, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029082, tc_HOL_Obool)), _1029086), _1029084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1029082), c_Big__Operators_Olattice__class_OSup__fin(_1029082, _1029086)), c_Big__Operators_Olattice__class_OSup__fin(_1029082, _1029084)) = c_Big__Operators_Olattice__class_OSup__fin(_1029082, _1029084))], (13659 ^ _779530) ^ [_1029396, _1029398, _1029400] : [class_Lattices_Olattice(_1029396), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029396), _1029398)), -(_1029400 = c_Orderings_Obot__class_Obot(tc_fun(_1029396, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029396, tc_HOL_Obool)), _1029400), _1029398)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1029396), c_Big__Operators_Olattice__class_OInf__fin(_1029396, _1029400)), c_Big__Operators_Olattice__class_OInf__fin(_1029396, _1029398)) = c_Big__Operators_Olattice__class_OInf__fin(_1029396, _1029398))], (13677 ^ _779530) ^ [_1029710, _1029712, _1029714] : [class_Lattices_Olattice(_1029710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029710), _1029712)), -(_1029712 = c_Orderings_Obot__class_Obot(tc_fun(_1029710, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029710), _1029714)), -(_1029714 = c_Orderings_Obot__class_Obot(tc_fun(_1029710, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1029710, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029710, tc_HOL_Obool)), _1029712), _1029714)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1029710), c_Big__Operators_Olattice__class_OSup__fin(_1029710, _1029712)), c_Big__Operators_Olattice__class_OSup__fin(_1029710, _1029714)))], (13699 ^ _779530) ^ [_1030059, _1030061, _1030063] : [class_Lattices_Olattice(_1030059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030059), _1030061)), -(_1030061 = c_Orderings_Obot__class_Obot(tc_fun(_1030059, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030059), _1030063)), -(_1030063 = c_Orderings_Obot__class_Obot(tc_fun(_1030059, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1030059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1030059, tc_HOL_Obool)), _1030061), _1030063)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1030059), c_Big__Operators_Olattice__class_OInf__fin(_1030059, _1030061)), c_Big__Operators_Olattice__class_OInf__fin(_1030059, _1030063)))], (13721 ^ _779530) ^ [_1030408, _1030410, _1030412] : [class_Lattices_Olattice(_1030408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030408), _1030410)), -(hBOOL(hAPP(hAPP(c_member(_1030408), _1030412), _1030410))), -(_1030410 = c_Orderings_Obot__class_Obot(tc_fun(_1030408, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1030408, hAPP(hAPP(c_Set_Oinsert(_1030408), _1030412), _1030410)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1030408), _1030412), c_Big__Operators_Olattice__class_OSup__fin(_1030408, _1030410)))], (13739 ^ _779530) ^ [_1030645, _1030647, _1030649] : [class_Lattices_Olattice(_1030645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030645), _1030647)), -(hBOOL(hAPP(hAPP(c_member(_1030645), _1030649), _1030647))), -(_1030647 = c_Orderings_Obot__class_Obot(tc_fun(_1030645, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1030645, hAPP(hAPP(c_Set_Oinsert(_1030645), _1030649), _1030647)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1030645), _1030649), c_Big__Operators_Olattice__class_OInf__fin(_1030645, _1030647)))], (13757 ^ _779530) ^ [_1030882, _1030884, _1030886] : [class_Lattices_Olattice(_1030882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1030882), _1030884)), 13764 ^ _779530 : [(13765 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1030882, tc_HOL_Obool)), _1030884), hAPP(hAPP(c_Set_Oinsert(_1030882), _1030886), c_Orderings_Obot__class_Obot(tc_fun(_1030882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1030882, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1030882, hAPP(hAPP(c_Set_Oinsert(_1030882), _1030886), _1030884)) = _1030886)], (13771 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1030882, tc_HOL_Obool)), _1030884), hAPP(hAPP(c_Set_Oinsert(_1030882), _1030886), c_Orderings_Obot__class_Obot(tc_fun(_1030882, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1030882, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1030882, hAPP(hAPP(c_Set_Oinsert(_1030882), _1030886), _1030884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1030882), _1030886), c_Big__Operators_Olattice__class_OSup__fin(_1030882, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1030882, tc_HOL_Obool)), _1030884), hAPP(hAPP(c_Set_Oinsert(_1030882), _1030886), c_Orderings_Obot__class_Obot(tc_fun(_1030882, tc_HOL_Obool)))))))]]], (13777 ^ _779530) ^ [_1031352, _1031354, _1031356] : [class_Lattices_Olattice(_1031352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031352), _1031354)), 13784 ^ _779530 : [(13785 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031352, tc_HOL_Obool)), _1031354), hAPP(hAPP(c_Set_Oinsert(_1031352), _1031356), c_Orderings_Obot__class_Obot(tc_fun(_1031352, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1031352, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1031352, hAPP(hAPP(c_Set_Oinsert(_1031352), _1031356), _1031354)) = _1031356)], (13791 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031352, tc_HOL_Obool)), _1031354), hAPP(hAPP(c_Set_Oinsert(_1031352), _1031356), c_Orderings_Obot__class_Obot(tc_fun(_1031352, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1031352, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1031352, hAPP(hAPP(c_Set_Oinsert(_1031352), _1031356), _1031354)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1031352), _1031356), c_Big__Operators_Olattice__class_OInf__fin(_1031352, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031352, tc_HOL_Obool)), _1031354), hAPP(hAPP(c_Set_Oinsert(_1031352), _1031356), c_Orderings_Obot__class_Obot(tc_fun(_1031352, tc_HOL_Obool)))))))]]], (13797 ^ _779530) ^ [_1031822, _1031824, _1031826] : [class_Lattices_Olattice(_1031822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031822), _1031824)), -(_1031824 = c_Orderings_Obot__class_Obot(tc_fun(_1031822, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031822), _1031826)), -(_1031826 = c_Orderings_Obot__class_Obot(tc_fun(_1031822, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1031822, tc_HOL_Obool)), _1031824), _1031826) = c_Orderings_Obot__class_Obot(tc_fun(_1031822, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1031822, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1031822, tc_HOL_Obool)), _1031824), _1031826)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1031822), c_Big__Operators_Olattice__class_OSup__fin(_1031822, _1031824)), c_Big__Operators_Olattice__class_OSup__fin(_1031822, _1031826)))], (13823 ^ _779530) ^ [_1032299, _1032301, _1032303] : [class_Lattices_Olattice(_1032299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032299), _1032301)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032299), _1032303)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1032299, tc_HOL_Obool)), _1032301), _1032303) = c_Orderings_Obot__class_Obot(tc_fun(_1032299, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032299), c_Big__Operators_Olattice__class_OSup__fin(_1032299, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1032299, tc_HOL_Obool)), _1032301), _1032303))), c_Big__Operators_Olattice__class_OSup__fin(_1032299, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1032299, tc_HOL_Obool)), _1032301), _1032303))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032299), c_Big__Operators_Olattice__class_OSup__fin(_1032299, _1032301)), c_Big__Operators_Olattice__class_OSup__fin(_1032299, _1032303)))], (13841 ^ _779530) ^ [_1032647, _1032649, _1032651] : [class_Lattices_Olattice(_1032647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032647), _1032649)), -(_1032649 = c_Orderings_Obot__class_Obot(tc_fun(_1032647, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032647), _1032651)), -(_1032651 = c_Orderings_Obot__class_Obot(tc_fun(_1032647, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1032647, tc_HOL_Obool)), _1032649), _1032651) = c_Orderings_Obot__class_Obot(tc_fun(_1032647, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1032647, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1032647, tc_HOL_Obool)), _1032649), _1032651)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032647), c_Big__Operators_Olattice__class_OInf__fin(_1032647, _1032649)), c_Big__Operators_Olattice__class_OInf__fin(_1032647, _1032651)))], (13867 ^ _779530) ^ [_1033124, _1033126, _1033128] : [class_Lattices_Olattice(_1033124), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033124), _1033126)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033124), _1033128)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033124, tc_HOL_Obool)), _1033126), _1033128) = c_Orderings_Obot__class_Obot(tc_fun(_1033124, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1033124), c_Big__Operators_Olattice__class_OInf__fin(_1033124, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1033124, tc_HOL_Obool)), _1033126), _1033128))), c_Big__Operators_Olattice__class_OInf__fin(_1033124, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1033124, tc_HOL_Obool)), _1033126), _1033128))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1033124), c_Big__Operators_Olattice__class_OInf__fin(_1033124, _1033126)), c_Big__Operators_Olattice__class_OInf__fin(_1033124, _1033128)))], (13885 ^ _779530) ^ [_1033472, _1033474] : [class_Lattices_Olattice(_1033472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033472), _1033474)), -(_1033474 = c_Orderings_Obot__class_Obot(tc_fun(_1033472, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1033472), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1033472), 13898 ^ [_1033472, _1033474]), 13899 ^ [_1033472, _1033474])), hAPP(hAPP(c_Set_Oinsert(_1033472), 13898 ^ [_1033472, _1033474]), hAPP(hAPP(c_Set_Oinsert(_1033472), 13899 ^ [_1033472, _1033474]), c_Orderings_Obot__class_Obot(tc_fun(_1033472, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1033472), c_Big__Operators_Olattice__class_OInf__fin(_1033472, _1033474)), _1033474)))], (13905 ^ _779530) ^ [_1033916, _1033918] : [class_Lattices_Olattice(_1033916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033916), _1033918)), -(_1033918 = c_Orderings_Obot__class_Obot(tc_fun(_1033916, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1033916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1033916), 13918 ^ [_1033916, _1033918]), 13919 ^ [_1033916, _1033918])), hAPP(hAPP(c_Set_Oinsert(_1033916), 13918 ^ [_1033916, _1033918]), hAPP(hAPP(c_Set_Oinsert(_1033916), 13919 ^ [_1033916, _1033918]), c_Orderings_Obot__class_Obot(tc_fun(_1033916, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1033916), c_Big__Operators_Olattice__class_OSup__fin(_1033916, _1033918)), _1033918)))], (13925 ^ _779530) ^ [_1034360, _1034362, _1034364] : [class_Lattices_Odistrib__lattice(_1034360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034360), _1034362)), -(_1034362 = c_Orderings_Obot__class_Obot(tc_fun(_1034360, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1034360), _1034364), c_Big__Operators_Olattice__class_OSup__fin(_1034360, _1034362)) = c_Big__Operators_Olattice__class_OSup__fin(_1034360, hAPP(c_Set_OCollect(_1034360), hAPP(hAPP(c_COMBB(tc_fun(_1034360, tc_HOL_Obool), tc_HOL_Obool, _1034360), c_HOL_OEx(_1034360)), hAPP(hAPP(c_COMBC(_1034360, tc_fun(_1034360, tc_HOL_Obool), tc_fun(_1034360, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1034360, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1034360, tc_HOL_Obool), tc_fun(_1034360, tc_HOL_Obool)), _1034360), c_COMBS(_1034360, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1034360, tc_HOL_Obool), tc_fun(_1034360, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1034360), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1034360), c_fconj)), hAPP(hAPP(c_COMBC(_1034360, tc_fun(_1034360, _1034360), tc_fun(_1034360, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1034360, tc_HOL_Obool), tc_fun(tc_fun(_1034360, _1034360), tc_fun(_1034360, tc_HOL_Obool)), _1034360), c_COMBB(_1034360, tc_HOL_Obool, _1034360)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1034360), _1034364))))), hAPP(hAPP(c_COMBC(_1034360, tc_fun(_1034360, tc_HOL_Obool), tc_HOL_Obool), c_member(_1034360)), _1034362))))))], (13939 ^ _779530) ^ [_1034846, _1034848, _1034850] : [class_Lattices_Odistrib__lattice(_1034846), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034846), _1034848)), -(_1034848 = c_Orderings_Obot__class_Obot(tc_fun(_1034846, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034846), _1034850)), -(_1034850 = c_Orderings_Obot__class_Obot(tc_fun(_1034846, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1034846), c_Big__Operators_Olattice__class_OSup__fin(_1034846, _1034848)), c_Big__Operators_Olattice__class_OSup__fin(_1034846, _1034850)) = c_Big__Operators_Olattice__class_OSup__fin(_1034846, hAPP(c_Set_OCollect(_1034846), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_HOL_Obool), tc_HOL_Obool, _1034846), c_HOL_OEx(_1034846)), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool)), tc_fun(_1034846, tc_HOL_Obool), _1034846), hAPP(c_COMBB(tc_fun(_1034846, tc_HOL_Obool), tc_HOL_Obool, _1034846), c_HOL_OEx(_1034846))), hAPP(hAPP(c_COMBC(_1034846, tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool)), tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_fun(tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool))), tc_fun(tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool)), tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool))), _1034846), c_COMBS(_1034846, tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_fun(_1034846, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1034846, tc_fun(tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool))), _1034846), hAPP(c_COMBB(tc_fun(_1034846, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool)), _1034846), c_COMBS(_1034846, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool)), tc_fun(_1034846, tc_fun(_1034846, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1034846), hAPP(c_COMBB(tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1034846), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1034846), c_fconj))), hAPP(hAPP(c_COMBC(_1034846, tc_fun(_1034846, tc_fun(_1034846, _1034846)), tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1034846, _1034846), tc_fun(_1034846, tc_HOL_Obool)), tc_fun(tc_fun(_1034846, tc_fun(_1034846, _1034846)), tc_fun(_1034846, tc_fun(_1034846, tc_HOL_Obool))), _1034846), c_COMBB(tc_fun(_1034846, _1034846), tc_fun(_1034846, tc_HOL_Obool), _1034846)), hAPP(hAPP(c_COMBB(tc_fun(_1034846, tc_HOL_Obool), tc_fun(tc_fun(_1034846, _1034846), tc_fun(_1034846, tc_HOL_Obool)), _1034846), c_COMBB(_1034846, tc_HOL_Obool, _1034846)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1034846)))))), hAPP(hAPP(c_COMBC(_1034846, tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1034846, tc_HOL_Obool), tc_fun(_1034846, tc_HOL_Obool)), _1034846), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1034846)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1034846), c_fconj), hAPP(hAPP(c_COMBC(_1034846, tc_fun(_1034846, tc_HOL_Obool), tc_HOL_Obool), c_member(_1034846)), _1034848)))), hAPP(hAPP(c_COMBC(_1034846, tc_fun(_1034846, tc_HOL_Obool), tc_HOL_Obool), c_member(_1034846)), _1034850))))))))], (13961 ^ _779530) ^ [_1035945, _1035947, _1035949] : [class_Lattices_Odistrib__lattice(_1035945), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035945), _1035947)), -(_1035947 = c_Orderings_Obot__class_Obot(tc_fun(_1035945, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1035945), _1035949), c_Big__Operators_Olattice__class_OInf__fin(_1035945, _1035947)) = c_Big__Operators_Olattice__class_OInf__fin(_1035945, hAPP(c_Set_OCollect(_1035945), hAPP(hAPP(c_COMBB(tc_fun(_1035945, tc_HOL_Obool), tc_HOL_Obool, _1035945), c_HOL_OEx(_1035945)), hAPP(hAPP(c_COMBC(_1035945, tc_fun(_1035945, tc_HOL_Obool), tc_fun(_1035945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1035945, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1035945, tc_HOL_Obool), tc_fun(_1035945, tc_HOL_Obool)), _1035945), c_COMBS(_1035945, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1035945, tc_HOL_Obool), tc_fun(_1035945, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1035945), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1035945), c_fconj)), hAPP(hAPP(c_COMBC(_1035945, tc_fun(_1035945, _1035945), tc_fun(_1035945, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1035945, tc_HOL_Obool), tc_fun(tc_fun(_1035945, _1035945), tc_fun(_1035945, tc_HOL_Obool)), _1035945), c_COMBB(_1035945, tc_HOL_Obool, _1035945)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1035945), _1035949))))), hAPP(hAPP(c_COMBC(_1035945, tc_fun(_1035945, tc_HOL_Obool), tc_HOL_Obool), c_member(_1035945)), _1035947))))))], (13975 ^ _779530) ^ [_1036431, _1036433, _1036435] : [class_Lattices_Odistrib__lattice(_1036431), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036431), _1036433)), -(_1036433 = c_Orderings_Obot__class_Obot(tc_fun(_1036431, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036431), _1036435)), -(_1036435 = c_Orderings_Obot__class_Obot(tc_fun(_1036431, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1036431), c_Big__Operators_Olattice__class_OInf__fin(_1036431, _1036433)), c_Big__Operators_Olattice__class_OInf__fin(_1036431, _1036435)) = c_Big__Operators_Olattice__class_OInf__fin(_1036431, hAPP(c_Set_OCollect(_1036431), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_HOL_Obool), tc_HOL_Obool, _1036431), c_HOL_OEx(_1036431)), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool)), tc_fun(_1036431, tc_HOL_Obool), _1036431), hAPP(c_COMBB(tc_fun(_1036431, tc_HOL_Obool), tc_HOL_Obool, _1036431), c_HOL_OEx(_1036431))), hAPP(hAPP(c_COMBC(_1036431, tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool)), tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_fun(tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool))), tc_fun(tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool)), tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool))), _1036431), c_COMBS(_1036431, tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_fun(_1036431, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1036431, tc_fun(tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool))), _1036431), hAPP(c_COMBB(tc_fun(_1036431, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool)), _1036431), c_COMBS(_1036431, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool)), tc_fun(_1036431, tc_fun(_1036431, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1036431), hAPP(c_COMBB(tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1036431), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036431), c_fconj))), hAPP(hAPP(c_COMBC(_1036431, tc_fun(_1036431, tc_fun(_1036431, _1036431)), tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1036431, _1036431), tc_fun(_1036431, tc_HOL_Obool)), tc_fun(tc_fun(_1036431, tc_fun(_1036431, _1036431)), tc_fun(_1036431, tc_fun(_1036431, tc_HOL_Obool))), _1036431), c_COMBB(tc_fun(_1036431, _1036431), tc_fun(_1036431, tc_HOL_Obool), _1036431)), hAPP(hAPP(c_COMBB(tc_fun(_1036431, tc_HOL_Obool), tc_fun(tc_fun(_1036431, _1036431), tc_fun(_1036431, tc_HOL_Obool)), _1036431), c_COMBB(_1036431, tc_HOL_Obool, _1036431)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1036431)))))), hAPP(hAPP(c_COMBC(_1036431, tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1036431, tc_HOL_Obool), tc_fun(_1036431, tc_HOL_Obool)), _1036431), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1036431)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036431), c_fconj), hAPP(hAPP(c_COMBC(_1036431, tc_fun(_1036431, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036431)), _1036433)))), hAPP(hAPP(c_COMBC(_1036431, tc_fun(_1036431, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036431)), _1036435))))))))], (13997 ^ _779530) ^ [_1037530, _1037532, _1037534] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1037530), _1037532), _1037534) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1037530, tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool)), _1037532), hAPP(hAPP(c_COMBC(_1037530, tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1037530, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool)), _1037530), c_Set_Oinsert(tc_fun(_1037530, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1037530, tc_HOL_Obool), tc_fun(_1037530, tc_HOL_Obool), _1037530), c_Relation_OImage(_1037530, _1037530, _1037534)), hAPP(hAPP(c_COMBC(_1037530, tc_fun(_1037530, tc_HOL_Obool), tc_fun(_1037530, tc_HOL_Obool)), c_Set_Oinsert(_1037530)), c_Orderings_Obot__class_Obot(tc_fun(_1037530, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1037530, tc_HOL_Obool), tc_HOL_Obool)))))], (13999 ^ _779530) ^ [_1037686, _1037688, _1037690] : [class_Lattices_Olattice(_1037686), hAPP(_1037688, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1037686), 14004 ^ [_1037686, _1037688, _1037690]), 14005 ^ [_1037686, _1037688, _1037690])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1037686), hAPP(_1037688, 14004 ^ [_1037686, _1037688, _1037690])), hAPP(_1037688, 14005 ^ [_1037686, _1037688, _1037690])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037686), _1037690)), -(_1037690 = c_Orderings_Obot__class_Obot(tc_fun(_1037686, tc_HOL_Obool))), -(hAPP(_1037688, c_Big__Operators_Olattice__class_OInf__fin(_1037686, _1037690)) = c_Big__Operators_Olattice__class_OInf__fin(_1037686, hAPP(c_Set_Oimage(_1037686, _1037686, _1037688), _1037690)))], (14019 ^ _779530) ^ [_1038089, _1038091, _1038093, _1038095, _1038097, _1038099] : [hBOOL(hAPP(hAPP(c_member(_1038089), _1038091), _1038093)), hBOOL(hAPP(hAPP(_1038095, _1038091), _1038097)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038089, tc_fun(_1038099, tc_HOL_Obool)), _1038093), _1038095), _1038097)))], (14029 ^ _779530) ^ [_1038310, _1038312, _1038314, _1038316, _1038318] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038310, tc_fun(_1038312, tc_HOL_Obool)), _1038314), _1038316), _1038318)), 14033 ^ _779530 : [(14034 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038310), 14032 ^ [_1038310, _1038312, _1038314, _1038316, _1038318]), _1038314)))], (14036 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1038316, 14032 ^ [_1038310, _1038312, _1038314, _1038316, _1038318]), _1038318)))]]], (14038 ^ _779530) ^ [_1038498, _1038500, _1038502, _1038504, _1038506] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038498, tc_fun(_1038500, tc_HOL_Obool)), _1038502), _1038504), _1038506))), 14039 ^ _779530 : [(14040 ^ _779530) ^ [_1038570] : [hBOOL(hAPP(hAPP(c_member(_1038498), _1038570), _1038502)), hBOOL(hAPP(hAPP(_1038504, _1038570), _1038506))]]], (14048 ^ _779530) ^ [_1038722, _1038724, _1038726, _1038728] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038722), _1038724)), 14051 ^ _779530 : [(14062 ^ _779530) ^ [] : [14064 ^ _779530 : [(14065 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038722), 14063 ^ [_1038722, _1038724, _1038726, _1038728]), _1038724)))], (14067 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038726), hAPP(_1038728, 14063 ^ [_1038722, _1038724, _1038726, _1038728])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038726), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038722, tc_fun(_1038726, tc_HOL_Obool)), _1038724), _1038728))))], (14052 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038726), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038722, tc_fun(_1038726, tc_HOL_Obool)), _1038724), _1038728))), 14055 ^ _779530 : [(14056 ^ _779530) ^ [_1038906] : [hBOOL(hAPP(hAPP(c_member(_1038722), _1038906), _1038724)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038726), hAPP(_1038728, _1038906))))]]]]], (14071 ^ _779530) ^ [_1039197, _1039199, _1039201, _1039203, _1039205, _1039207] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039197, tc_fun(_1039199, tc_HOL_Obool)), _1039201), hAPP(c_Fun_Ocomp(_1039203, tc_fun(_1039199, tc_HOL_Obool), _1039197, _1039205), _1039207)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039203, tc_fun(_1039199, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1039197, _1039203, _1039207), _1039201)), _1039205))], (14073 ^ _779530) ^ [_1039272, _1039274, _1039276, _1039278, _1039280, _1039282] : [-(hAPP(c_Relation_OImage(_1039272, _1039274, _1039276), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039278, tc_fun(_1039272, tc_HOL_Obool)), _1039280), _1039282)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039278, tc_fun(_1039274, tc_HOL_Obool)), _1039280), hAPP(hAPP(c_COMBB(tc_fun(_1039272, tc_HOL_Obool), tc_fun(_1039274, tc_HOL_Obool), _1039278), c_Relation_OImage(_1039272, _1039274, _1039276)), _1039282)))], (14075 ^ _779530) ^ [_1039356, _1039358, _1039360, _1039362] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039356), hAPP(c_Set_OCollect(_1039356), _1039358))), 14078 ^ _779530 : [(14089 ^ _779530) ^ [] : [14091 ^ _779530 : [(14092 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1039358, 14090 ^ [_1039356, _1039358, _1039360, _1039362])))], (14094 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039360), hAPP(c_Set_OCollect(_1039360), hAPP(hAPP(c_COMBC(_1039360, _1039356, tc_HOL_Obool), _1039362), 14090 ^ [_1039356, _1039358, _1039360, _1039362]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039360), hAPP(c_Set_OCollect(_1039360), hAPP(hAPP(c_COMBB(tc_fun(_1039356, tc_HOL_Obool), tc_HOL_Obool, _1039360), c_HOL_OEx(_1039356)), hAPP(hAPP(c_COMBB(tc_fun(_1039356, tc_HOL_Obool), tc_fun(_1039356, tc_HOL_Obool), _1039360), hAPP(c_COMBS(_1039356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1039356), c_fconj), _1039358))), _1039362))))))], (14079 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039360), hAPP(c_Set_OCollect(_1039360), hAPP(hAPP(c_COMBB(tc_fun(_1039356, tc_HOL_Obool), tc_HOL_Obool, _1039360), c_HOL_OEx(_1039356)), hAPP(hAPP(c_COMBB(tc_fun(_1039356, tc_HOL_Obool), tc_fun(_1039356, tc_HOL_Obool), _1039360), hAPP(c_COMBS(_1039356, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1039356), c_fconj), _1039358))), _1039362))))), 14082 ^ _779530 : [(14083 ^ _779530) ^ [_1039639] : [hBOOL(hAPP(_1039358, _1039639)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039360), hAPP(c_Set_OCollect(_1039360), hAPP(hAPP(c_COMBC(_1039360, _1039356, tc_HOL_Obool), _1039362), _1039639)))))]]]]], (14098 ^ _779530) ^ [_1040004, _1040006, _1040008, _1040010] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040004), hAPP(c_Set_OCollect(_1040004), _1040006))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040008), hAPP(c_Set_OCollect(_1040008), hAPP(hAPP(c_COMBB(tc_fun(_1040004, tc_HOL_Obool), tc_HOL_Obool, _1040008), c_HOL_OEx(_1040004)), hAPP(hAPP(c_COMBC(_1040008, tc_fun(_1040004, tc_HOL_Obool), tc_fun(_1040004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1040004, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1040004, tc_HOL_Obool), tc_fun(_1040004, tc_HOL_Obool)), _1040008), c_COMBS(_1040004, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1040004, tc_HOL_Obool), tc_fun(_1040004, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1040008), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1040004), c_fconj)), hAPP(hAPP(c_COMBC(_1040008, tc_fun(_1040004, _1040008), tc_fun(_1040004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1040008, tc_HOL_Obool), tc_fun(tc_fun(_1040004, _1040008), tc_fun(_1040004, tc_HOL_Obool)), _1040008), c_COMBB(_1040008, tc_HOL_Obool, _1040004)), c_fequal)), _1040010)))), _1040006))))))], (14104 ^ _779530) ^ [_1040365, _1040367, _1040369, _1040371] : [-(hAPP(c_Relation_OImage(_1040365, _1040367, _1040369), _1040371) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1040365, tc_fun(_1040367, tc_HOL_Obool)), _1040371), hAPP(hAPP(c_COMBB(tc_fun(_1040365, tc_HOL_Obool), tc_fun(_1040367, tc_HOL_Obool), _1040365), c_Relation_OImage(_1040365, _1040367, _1040369)), hAPP(hAPP(c_COMBC(_1040365, tc_fun(_1040365, tc_HOL_Obool), tc_fun(_1040365, tc_HOL_Obool)), c_Set_Oinsert(_1040365)), c_Orderings_Obot__class_Obot(tc_fun(_1040365, tc_HOL_Obool))))))], (14106 ^ _779530) ^ [_1040456, _1040458, _1040460] : [-(c_Map_Oran(_1040456, _1040458, _1040460) = hAPP(c_Set_OCollect(_1040458), hAPP(hAPP(c_COMBB(tc_fun(_1040456, tc_HOL_Obool), tc_HOL_Obool, _1040458), c_HOL_OEx(_1040456)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1040458), tc_fun(_1040456, tc_HOL_Obool), _1040458), hAPP(c_COMBC(_1040456, tc_Option_Ooption(_1040458), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1040458), tc_fun(tc_Option_Ooption(_1040458), tc_HOL_Obool), _1040456), c_fequal), _1040460))), c_Option_Ooption_OSome(_1040458)))))], (14108 ^ _779530) ^ [_1040550, _1040552] : [-(hAPP(c_Set_OPow(_1040550), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1040550, tc_HOL_Obool)), _1040552)) = hAPP(c_Set_OCollect(tc_fun(_1040550, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1040550, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1040550, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1040550, tc_HOL_Obool), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1040550, tc_HOL_Obool)), c_COMBS(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1040550, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1040550, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1040550, tc_HOL_Obool), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_fun(_1040550, tc_HOL_Obool)), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_fun(_1040550, tc_HOL_Obool)), tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1040550, tc_HOL_Obool)), c_COMBB(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1040550, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1040550, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1040550, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1040550, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1040550, tc_HOL_Obool)), _1040552)), c_Set_OPow(_1040550))))))], (14110 ^ _779530) ^ [_1040830, _1040832, _1040834, _1040836, _1040838, _1040840] : [hBOOL(hAPP(hAPP(c_member(_1040830), _1040832), _1040834)), hBOOL(hAPP(hAPP(c_member(_1040836), _1040838), hAPP(_1040840, _1040832))), -(hBOOL(hAPP(hAPP(c_member(_1040836), _1040838), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1040830, tc_fun(_1040836, tc_HOL_Obool)), _1040834), _1040840))))], (14120 ^ _779530) ^ [_1041047, _1041049, _1041051, _1041053] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1041047, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041049, tc_fun(tc_fun(_1041047, tc_HOL_Obool), tc_HOL_Obool)), _1041051), hAPP(hAPP(c_COMBB(tc_fun(_1041047, tc_HOL_Obool), tc_fun(tc_fun(_1041047, tc_HOL_Obool), tc_HOL_Obool), _1041049), c_Set_OPow(_1041047)), _1041053))), hAPP(c_Set_OPow(_1041047), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041049, tc_fun(_1041047, tc_HOL_Obool)), _1041051), _1041053)))))], (14122 ^ _779530) ^ [_1041142, _1041144, _1041146, _1041148] : [-(hAPP(c_Set_Oimage(_1041142, _1041144, _1041146), _1041148) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041142, tc_fun(_1041144, tc_HOL_Obool)), _1041148), hAPP(hAPP(c_COMBC(_1041142, tc_fun(_1041144, tc_HOL_Obool), tc_fun(_1041144, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1041144, tc_fun(tc_fun(_1041144, tc_HOL_Obool), tc_fun(_1041144, tc_HOL_Obool)), _1041142), c_Set_Oinsert(_1041144)), _1041146)), c_Orderings_Obot__class_Obot(tc_fun(_1041144, tc_HOL_Obool)))))], (14124 ^ _779530) ^ [_1041232, _1041234, _1041236, _1041238, _1041240, _1041242] : [c_Equiv__Relations_Oequiv(_1041232, _1041234, _1041236), c_Equiv__Relations_Ocongruent(_1041232, tc_fun(_1041238, tc_HOL_Obool), _1041236, _1041240), hBOOL(hAPP(hAPP(c_member(_1041232), _1041242), _1041234)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041232, tc_fun(_1041238, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1041232, _1041232, _1041236), hAPP(hAPP(c_Set_Oinsert(_1041232), _1041242), c_Orderings_Obot__class_Obot(tc_fun(_1041232, tc_HOL_Obool))))), _1041240) = hAPP(_1041240, _1041242))], (14138 ^ _779530) ^ [_1041533, _1041535, _1041537, _1041539, _1041541, _1041543, _1041545, _1041547, _1041549, _1041551] : [c_Equiv__Relations_Oequiv(_1041533, _1041535, _1041537), c_Equiv__Relations_Oequiv(_1041539, _1041541, _1041543), c_Equiv__Relations_Ocongruent2(_1041533, _1041539, tc_fun(_1041545, tc_HOL_Obool), _1041537, _1041543, _1041547), hBOOL(hAPP(hAPP(c_member(_1041533), _1041549), _1041535)), hBOOL(hAPP(hAPP(c_member(_1041539), _1041551), _1041541)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041533, tc_fun(_1041545, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1041533, _1041533, _1041537), hAPP(hAPP(c_Set_Oinsert(_1041533), _1041549), c_Orderings_Obot__class_Obot(tc_fun(_1041533, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1041539, tc_fun(_1041545, tc_HOL_Obool)), tc_fun(_1041545, tc_HOL_Obool), _1041533), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1041539, tc_fun(_1041545, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1041539, _1041539, _1041543), hAPP(hAPP(c_Set_Oinsert(_1041539), _1041551), c_Orderings_Obot__class_Obot(tc_fun(_1041539, tc_HOL_Obool)))))), _1041547)) = hAPP(hAPP(_1041547, _1041549), _1041551))], (14160 ^ _779530) ^ [_1042116, _1042118, _1042120, _1042122, _1042124] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042116, tc_fun(_1042118, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1042116), _1042120), _1042122)), _1042124) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042118, tc_HOL_Obool)), hAPP(_1042124, _1042120)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042116, tc_fun(_1042118, tc_HOL_Obool)), _1042122), _1042124)))], (14162 ^ _779530) ^ [_1042211, _1042213, _1042215, _1042217, _1042219] : [_1042211 = c_Orderings_Obot__class_Obot(tc_fun(_1042213, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042215, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042213, tc_fun(_1042215, tc_HOL_Obool)), _1042211), _1042217)), _1042219) = _1042219)], (14168 ^ _779530) ^ [_1042344, _1042346, _1042348, _1042350, _1042352] : [-(_1042344 = c_Orderings_Obot__class_Obot(tc_fun(_1042346, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042348, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042346, tc_fun(_1042348, tc_HOL_Obool)), _1042344), _1042350)), _1042352) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042346, tc_fun(_1042348, tc_HOL_Obool)), _1042344), hAPP(hAPP(c_COMBC(_1042346, tc_fun(_1042348, tc_HOL_Obool), tc_fun(_1042348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1042348, tc_HOL_Obool), tc_fun(tc_fun(_1042348, tc_HOL_Obool), tc_fun(_1042348, tc_HOL_Obool)), _1042346), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042348, tc_HOL_Obool))), _1042350)), _1042352)))], (14174 ^ _779530) ^ [_1042489, _1042491, _1042493, _1042495, _1042497] : [_1042489 = c_Orderings_Obot__class_Obot(tc_fun(_1042491, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042493, tc_HOL_Obool)), _1042495), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042491, tc_fun(_1042493, tc_HOL_Obool)), _1042489), _1042497)) = _1042495)], (14180 ^ _779530) ^ [_1042622, _1042624, _1042626, _1042628, _1042630] : [-(_1042622 = c_Orderings_Obot__class_Obot(tc_fun(_1042624, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042626, tc_HOL_Obool)), _1042628), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042624, tc_fun(_1042626, tc_HOL_Obool)), _1042622), _1042630)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042624, tc_fun(_1042626, tc_HOL_Obool)), _1042622), hAPP(hAPP(c_COMBB(tc_fun(_1042626, tc_HOL_Obool), tc_fun(_1042626, tc_HOL_Obool), _1042624), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042626, tc_HOL_Obool)), _1042628)), _1042630)))], (14186 ^ _779530) ^ [_1042730, _1042732, _1042734, _1042736, _1042738, _1042740, _1042742, _1042744] : [c_Equiv__Relations_Oequiv(_1042730, _1042732, _1042734), c_Equiv__Relations_Ocongruent2(_1042730, _1042736, _1042738, _1042734, _1042740, _1042742), hBOOL(hAPP(hAPP(c_member(_1042730), _1042744), _1042732)), -(c_Equiv__Relations_Ocongruent(_1042736, _1042738, _1042740, hAPP(_1042742, _1042744)))], (14217 ^ _779530) ^ [_1043441, _1043443, _1043445, _1043447, _1043449] : [14219 ^ _779530 : [(14220 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043443), 14218 ^ [_1043441, _1043443, _1043445, _1043447, _1043449]), _1043445)))], (14223 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043441), 14221 ^ [_1043441, _1043443, _1043445, _1043447, _1043449]), hAPP(_1043447, 14218 ^ [_1043441, _1043443, _1043445, _1043447, _1043449]))))], (14225 ^ _779530) ^ [] : [hBOOL(hAPP(_1043449, 14221 ^ [_1043441, _1043443, _1043445, _1043447, _1043449]))]], 14226 ^ _779530 : [(14227 ^ _779530) ^ [_1043751] : [hBOOL(hAPP(hAPP(c_member(_1043441), _1043751), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043443, tc_fun(_1043441, tc_HOL_Obool)), _1043445), _1043447))), -(hBOOL(hAPP(_1043449, _1043751)))]]], (14200 ^ _779530) ^ [_1043005, _1043007, _1043009, _1043011, _1043013] : [14202 ^ _779530 : [(14203 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043005), 14201 ^ [_1043005, _1043007, _1043009, _1043011, _1043013]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043007, tc_fun(_1043005, tc_HOL_Obool)), _1043009), _1043011))))], (14205 ^ _779530) ^ [] : [hBOOL(hAPP(_1043013, 14201 ^ [_1043005, _1043007, _1043009, _1043011, _1043013]))]], 14206 ^ _779530 : [(14207 ^ _779530) ^ [_1043227] : [hBOOL(hAPP(hAPP(c_member(_1043007), _1043227), _1043009)), 14210 ^ _779530 : [(14211 ^ _779530) ^ [_1043324] : [hBOOL(hAPP(hAPP(c_member(_1043005), _1043324), hAPP(_1043011, _1043227))), -(hBOOL(hAPP(_1043013, _1043324)))]]]]], (14233 ^ _779530) ^ [_1043886, _1043888, _1043890, _1043892, _1043894, _1043896] : [class_Complete__Lattice_Ocomplete__lattice(_1043886), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043888, _1043886), _1043890), hAPP(hAPP(c_COMBB(tc_fun(_1043892, _1043886), _1043886, _1043888), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043892, _1043886), _1043894)), _1043896)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043892, _1043886), _1043894), hAPP(hAPP(c_COMBB(tc_fun(_1043888, _1043886), _1043886, _1043892), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1043888, _1043886), _1043890)), hAPP(c_COMBC(_1043888, _1043892, _1043886), _1043896))))], (14239 ^ _779530) ^ [_1044095, _1044097, _1044099, _1044101, _1044103, _1044105] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044095, tc_fun(_1044097, tc_HOL_Obool)), _1044099), hAPP(hAPP(c_COMBC(_1044095, tc_fun(_1044101, tc_fun(_1044097, tc_HOL_Obool)), tc_fun(_1044097, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1044101, tc_HOL_Obool), tc_fun(tc_fun(_1044101, tc_fun(_1044097, tc_HOL_Obool)), tc_fun(_1044097, tc_HOL_Obool)), _1044095), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044101, tc_fun(_1044097, tc_HOL_Obool))), _1044103)), _1044105)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044101, tc_fun(_1044097, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044095, tc_fun(_1044101, tc_HOL_Obool)), _1044099), _1044103)), _1044105))], (14241 ^ _779530) ^ [_1044214, _1044216, _1044218, _1044220, _1044222, _1044224] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044214, tc_fun(_1044216, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044218, tc_fun(_1044214, tc_HOL_Obool)), _1044220), _1044222)), _1044224) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044218, tc_fun(_1044216, tc_HOL_Obool)), _1044220), hAPP(hAPP(c_COMBC(_1044218, tc_fun(_1044214, tc_fun(_1044216, tc_HOL_Obool)), tc_fun(_1044216, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1044214, tc_HOL_Obool), tc_fun(tc_fun(_1044214, tc_fun(_1044216, tc_HOL_Obool)), tc_fun(_1044216, tc_HOL_Obool)), _1044218), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044214, tc_fun(_1044216, tc_HOL_Obool))), _1044222)), _1044224)))], (14243 ^ _779530) ^ [_1044333, _1044335, _1044337, _1044339, _1044341, _1044343] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044333, tc_fun(_1044335, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044337, tc_fun(_1044333, tc_HOL_Obool)), _1044339), _1044341)), _1044343) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044337, tc_fun(_1044335, tc_HOL_Obool)), _1044339), hAPP(hAPP(c_COMBC(_1044337, tc_fun(_1044333, tc_fun(_1044335, tc_HOL_Obool)), tc_fun(_1044335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1044333, tc_HOL_Obool), tc_fun(tc_fun(_1044333, tc_fun(_1044335, tc_HOL_Obool)), tc_fun(_1044335, tc_HOL_Obool)), _1044337), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044333, tc_fun(_1044335, tc_HOL_Obool))), _1044341)), _1044343)))], (14245 ^ _779530) ^ [_1044452, _1044454, _1044456, _1044458, _1044460, _1044462, _1044464, _1044466, _1044468] : [c_Equiv__Relations_Oequiv(_1044452, _1044454, _1044456), c_Equiv__Relations_Oequiv(_1044458, _1044460, _1044462), c_Equiv__Relations_Ocongruent2(_1044452, _1044458, tc_fun(_1044464, tc_HOL_Obool), _1044456, _1044462, _1044466), hBOOL(hAPP(hAPP(c_member(_1044458), _1044468), _1044460)), -(c_Equiv__Relations_Ocongruent(_1044452, tc_fun(_1044464, tc_HOL_Obool), _1044456, hAPP(hAPP(c_COMBB(tc_fun(_1044458, tc_fun(_1044464, tc_HOL_Obool)), tc_fun(_1044464, tc_HOL_Obool), _1044452), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044458, tc_fun(_1044464, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1044458, _1044458, _1044462), hAPP(hAPP(c_Set_Oinsert(_1044458), _1044468), c_Orderings_Obot__class_Obot(tc_fun(_1044458, tc_HOL_Obool)))))), _1044466)))], (14263 ^ _779530) ^ [_1044879, _1044881, _1044883, _1044885, _1044887] : [class_Complete__Lattice_Ocomplete__lattice(_1044879), 14266 ^ _779530 : [(14277 ^ _779530) ^ [] : [14279 ^ _779530 : [(14280 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1044881), 14278 ^ [_1044879, _1044881, _1044883, _1044885, _1044887]), _1044883)))], (14282 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044879), hAPP(_1044885, 14278 ^ [_1044879, _1044881, _1044883, _1044885, _1044887])), _1044887))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044881, _1044879), _1044883), _1044885)), _1044887)))], (14267 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1044881, _1044879), _1044883), _1044885)), _1044887)), 14270 ^ _779530 : [(14271 ^ _779530) ^ [_1045060] : [hBOOL(hAPP(hAPP(c_member(_1044881), _1045060), _1044883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044879), hAPP(_1044885, _1045060)), _1044887)))]]]]], (14286 ^ _779530) ^ [_1045373, _1045375, _1045377, _1045379, _1045381] : [class_Complete__Lattice_Ocomplete__lattice(_1045373), class_Orderings_Olinorder(_1045373), 14293 ^ _779530 : [(14294 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045373), _1045375), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1045377, _1045373), _1045379), _1045381))), 14298 ^ _779530 : [(14299 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045377), 14297 ^ [_1045373, _1045375, _1045377, _1045379, _1045381]), _1045379)))], (14301 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045373), _1045375), hAPP(_1045381, 14297 ^ [_1045373, _1045375, _1045377, _1045379, _1045381]))))]]], (14303 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045373), _1045375), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1045377, _1045373), _1045379), _1045381)))), 14304 ^ _779530 : [(14305 ^ _779530) ^ [_1045721] : [hBOOL(hAPP(hAPP(c_member(_1045377), _1045721), _1045379)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1045373), _1045375), hAPP(_1045381, _1045721)))]]]]], (14313 ^ _779530) ^ [_1045915, _1045917, _1045919, _1045921, _1045923] : [hBOOL(hAPP(hAPP(c_member(_1045915), _1045917), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1045919, tc_fun(_1045915, tc_HOL_Obool)), _1045921), _1045923))), 14317 ^ _779530 : [(14318 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045919), 14316 ^ [_1045915, _1045917, _1045919, _1045921, _1045923]), _1045921)))], (14320 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1045915), _1045917), hAPP(_1045923, 14316 ^ [_1045915, _1045917, _1045919, _1045921, _1045923]))))]]], (14322 ^ _779530) ^ [_1046123, _1046125, _1046127, _1046129, _1046131] : [-(hBOOL(hAPP(hAPP(c_member(_1046123), _1046125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1046127, tc_fun(_1046123, tc_HOL_Obool)), _1046129), _1046131)))), 14323 ^ _779530 : [(14324 ^ _779530) ^ [_1046205] : [hBOOL(hAPP(hAPP(c_member(_1046127), _1046205), _1046129)), hBOOL(hAPP(hAPP(c_member(_1046123), _1046125), hAPP(_1046131, _1046205)))]]], (14332 ^ _779530) ^ [_1046372, _1046374, _1046376, _1046378] : [class_Complete__Lattice_Ocomplete__lattice(_1046372), -(_1046374 = c_Orderings_Obot__class_Obot(tc_fun(_1046376, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1046376, _1046372), _1046374), hAPP(c_COMBK(_1046372, _1046376), _1046378)) = _1046378)], (14352 ^ _779530) ^ [_1046756, _1046758, _1046760, _1046762] : [14354 ^ _779530 : [(14355 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1046756), 14353 ^ [_1046756, _1046758, _1046760, _1046762]), _1046760)))], (14357 ^ _779530) ^ [] : [hAPP(_1046762, 14353 ^ [_1046756, _1046758, _1046760, _1046762]) = c_Orderings_Obot__class_Obot(tc_fun(_1046758, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1046756, tc_fun(_1046758, tc_HOL_Obool)), _1046760), _1046762) = c_Orderings_Obot__class_Obot(tc_fun(_1046758, tc_HOL_Obool)))], (14342 ^ _779530) ^ [_1046527, _1046529, _1046531, _1046533] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1046527, tc_fun(_1046529, tc_HOL_Obool)), _1046531), _1046533) = c_Orderings_Obot__class_Obot(tc_fun(_1046529, tc_HOL_Obool)), 14345 ^ _779530 : [(14346 ^ _779530) ^ [_1046643] : [hBOOL(hAPP(hAPP(c_member(_1046527), _1046643), _1046531)), -(hAPP(_1046533, _1046643) = c_Orderings_Obot__class_Obot(tc_fun(_1046529, tc_HOL_Obool)))]]], (14361 ^ _779530) ^ [_1047001, _1047003, _1047005, _1047007] : [_1047001 = c_Orderings_Obot__class_Obot(tc_fun(_1047003, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047003, tc_fun(_1047005, tc_HOL_Obool)), _1047001), hAPP(c_COMBK(tc_fun(_1047005, tc_HOL_Obool), _1047003), _1047007)) = c_Orderings_Obot__class_Obot(tc_fun(_1047005, tc_HOL_Obool)))], (14367 ^ _779530) ^ [_1047138, _1047140, _1047142, _1047144] : [-(_1047138 = c_Orderings_Obot__class_Obot(tc_fun(_1047140, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047140, tc_fun(_1047142, tc_HOL_Obool)), _1047138), hAPP(c_COMBK(tc_fun(_1047142, tc_HOL_Obool), _1047140), _1047144)) = _1047144)], (14373 ^ _779530) ^ [_1047206, _1047208, _1047210] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047206, tc_fun(_1047208, tc_HOL_Obool)), _1047210), hAPP(c_COMBK(tc_fun(_1047208, tc_HOL_Obool), _1047206), c_Orderings_Obot__class_Obot(tc_fun(_1047208, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1047208, tc_HOL_Obool)))], (14385 ^ _779530) ^ [_1047514, _1047516, _1047518, _1047520] : [14387 ^ _779530 : [(14388 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1047516), 14386 ^ [_1047514, _1047516, _1047518, _1047520]), _1047518)))], (14390 ^ _779530) ^ [] : [hAPP(_1047520, 14386 ^ [_1047514, _1047516, _1047518, _1047520]) = c_Orderings_Obot__class_Obot(tc_fun(_1047514, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1047514, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047516, tc_fun(_1047514, tc_HOL_Obool)), _1047518), _1047520))], (14375 ^ _779530) ^ [_1047285, _1047287, _1047289, _1047291] : [c_Orderings_Obot__class_Obot(tc_fun(_1047285, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047287, tc_fun(_1047285, tc_HOL_Obool)), _1047289), _1047291), 14378 ^ _779530 : [(14379 ^ _779530) ^ [_1047401] : [hBOOL(hAPP(hAPP(c_member(_1047287), _1047401), _1047289)), -(hAPP(_1047291, _1047401) = c_Orderings_Obot__class_Obot(tc_fun(_1047285, tc_HOL_Obool)))]]], (14404 ^ _779530) ^ [_1048026, _1048028, _1048030, _1048032, _1048034] : [14406 ^ _779530 : [(14407 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1048028), 14405 ^ [_1048026, _1048028, _1048030, _1048032, _1048034]), _1048030)))], (14409 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048026, tc_HOL_Obool)), hAPP(_1048032, 14405 ^ [_1048026, _1048028, _1048030, _1048032, _1048034])), _1048034))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048026, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048028, tc_fun(_1048026, tc_HOL_Obool)), _1048030), _1048032)), _1048034)))], (14394 ^ _779530) ^ [_1047768, _1047770, _1047772, _1047774, _1047776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1047768, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1047770, tc_fun(_1047768, tc_HOL_Obool)), _1047772), _1047774)), _1047776)), 14397 ^ _779530 : [(14398 ^ _779530) ^ [_1047901] : [hBOOL(hAPP(hAPP(c_member(_1047770), _1047901), _1047772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1047768, tc_HOL_Obool)), hAPP(_1047774, _1047901)), _1047776)))]]], (14413 ^ _779530) ^ [_1048289, _1048291, _1048293, _1048295, _1048297, _1048299] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048289, tc_fun(_1048291, tc_HOL_Obool)), _1048293), hAPP(hAPP(c_COMBB(_1048295, tc_fun(_1048291, tc_HOL_Obool), _1048289), _1048297), _1048299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048295, tc_fun(_1048291, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1048289, _1048295, _1048299), _1048293)), _1048297))], (14415 ^ _779530) ^ [_1048366, _1048368, _1048370, _1048372, _1048374, _1048376] : [-(hAPP(c_Set_Oimage(_1048366, _1048368, _1048370), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048372, tc_fun(_1048366, tc_HOL_Obool)), _1048374), _1048376)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048372, tc_fun(_1048368, tc_HOL_Obool)), _1048374), hAPP(hAPP(c_COMBB(tc_fun(_1048366, tc_HOL_Obool), tc_fun(_1048368, tc_HOL_Obool), _1048372), c_Set_Oimage(_1048366, _1048368, _1048370)), _1048376)))], (14417 ^ _779530) ^ [_1048450, _1048452, _1048454, _1048456, _1048458, _1048460] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048450, tc_fun(_1048452, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1048454, _1048450, _1048456), _1048458)), _1048460) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048454, tc_fun(_1048452, tc_HOL_Obool)), _1048458), hAPP(hAPP(c_COMBB(_1048450, tc_fun(_1048452, tc_HOL_Obool), _1048454), _1048460), _1048456)))], (14419 ^ _779530) ^ [_1048527, _1048529, _1048531, _1048533, _1048535] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048527, tc_fun(_1048529, tc_HOL_Obool)), _1048531), hAPP(hAPP(c_COMBS(_1048527, tc_fun(_1048529, tc_HOL_Obool), tc_fun(_1048529, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1048529, tc_HOL_Obool), tc_fun(tc_fun(_1048529, tc_HOL_Obool), tc_fun(_1048529, tc_HOL_Obool)), _1048527), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048529, tc_HOL_Obool))), _1048533)), _1048535)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048529, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048527, tc_fun(_1048529, tc_HOL_Obool)), _1048531), _1048533)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048527, tc_fun(_1048529, tc_HOL_Obool)), _1048531), _1048535)))], (14421 ^ _779530) ^ [_1048648, _1048650, _1048652, _1048654, _1048656] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048648, tc_fun(_1048650, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048648, tc_HOL_Obool)), _1048652), _1048654)), _1048656) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048650, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048648, tc_fun(_1048650, tc_HOL_Obool)), _1048652), _1048656)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048648, tc_fun(_1048650, tc_HOL_Obool)), _1048654), _1048656)))], (14423 ^ _779530) ^ [_1048737, _1048739, _1048741, _1048743, _1048745] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048737, tc_fun(_1048739, tc_HOL_Obool)), _1048741), hAPP(hAPP(c_COMBB(tc_fun(_1048739, tc_HOL_Obool), tc_fun(_1048739, tc_HOL_Obool), _1048737), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048739, tc_HOL_Obool)), _1048743)), _1048745)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048739, tc_HOL_Obool)), _1048743), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048737, tc_fun(_1048739, tc_HOL_Obool)), _1048741), _1048745)))], (14425 ^ _779530) ^ [_1048827, _1048829, _1048831, _1048833, _1048835] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048827, tc_fun(_1048829, tc_HOL_Obool)), _1048831), hAPP(hAPP(c_COMBC(_1048827, tc_fun(_1048829, tc_HOL_Obool), tc_fun(_1048829, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1048829, tc_HOL_Obool), tc_fun(tc_fun(_1048829, tc_HOL_Obool), tc_fun(_1048829, tc_HOL_Obool)), _1048827), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048829, tc_HOL_Obool))), _1048833)), _1048835)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048829, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048827, tc_fun(_1048829, tc_HOL_Obool)), _1048831), _1048833)), _1048835))], (14427 ^ _779530) ^ [_1048936, _1048938, _1048940, _1048942, _1048944] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048936, tc_HOL_Obool)), _1048938), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048940, tc_fun(_1048936, tc_HOL_Obool)), _1048942), _1048944)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1048940, tc_fun(_1048936, tc_HOL_Obool)), _1048942), hAPP(hAPP(c_COMBB(tc_fun(_1048936, tc_HOL_Obool), tc_fun(_1048936, tc_HOL_Obool), _1048940), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048936, tc_HOL_Obool)), _1048938)), _1048944)))], (14429 ^ _779530) ^ [_1049026, _1049028, _1049030, _1049032, _1049034] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049026, tc_HOL_Obool)), _1049028), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049030, tc_fun(_1049026, tc_HOL_Obool)), _1049032), _1049034)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049030, tc_fun(_1049026, tc_HOL_Obool)), _1049032), hAPP(hAPP(c_COMBB(tc_fun(_1049026, tc_HOL_Obool), tc_fun(_1049026, tc_HOL_Obool), _1049030), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049026, tc_HOL_Obool)), _1049028)), _1049034)))], (14431 ^ _779530) ^ [_1049116, _1049118, _1049120, _1049122, _1049124] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049116, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049118, tc_fun(_1049116, tc_HOL_Obool)), _1049120), _1049122)), _1049124) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049118, tc_fun(_1049116, tc_HOL_Obool)), _1049120), hAPP(hAPP(c_COMBC(_1049118, tc_fun(_1049116, tc_HOL_Obool), tc_fun(_1049116, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1049116, tc_HOL_Obool), tc_fun(tc_fun(_1049116, tc_HOL_Obool), tc_fun(_1049116, tc_HOL_Obool)), _1049118), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049116, tc_HOL_Obool))), _1049122)), _1049124)))], (14433 ^ _779530) ^ [_1049225, _1049227, _1049229, _1049231, _1049233, _1049235, _1049237] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049225, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049227, tc_fun(_1049225, tc_HOL_Obool)), _1049229), _1049231)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049233, tc_fun(_1049225, tc_HOL_Obool)), _1049235), _1049237)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049227, tc_fun(_1049225, tc_HOL_Obool)), _1049229), hAPP(hAPP(c_COMBB(tc_fun(_1049233, tc_fun(_1049225, tc_HOL_Obool)), tc_fun(_1049225, tc_HOL_Obool), _1049227), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049233, tc_fun(_1049225, tc_HOL_Obool)), _1049235)), hAPP(hAPP(c_COMBC(_1049227, tc_fun(_1049233, tc_fun(_1049225, tc_HOL_Obool)), tc_fun(_1049233, tc_fun(_1049225, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1049225, tc_HOL_Obool), tc_fun(_1049225, tc_HOL_Obool)), tc_fun(tc_fun(_1049233, tc_fun(_1049225, tc_HOL_Obool)), tc_fun(_1049233, tc_fun(_1049225, tc_HOL_Obool))), _1049227), c_COMBB(tc_fun(_1049225, tc_HOL_Obool), tc_fun(_1049225, tc_HOL_Obool), _1049233)), hAPP(hAPP(c_COMBB(tc_fun(_1049225, tc_HOL_Obool), tc_fun(tc_fun(_1049225, tc_HOL_Obool), tc_fun(_1049225, tc_HOL_Obool)), _1049227), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1049225, tc_HOL_Obool))), _1049231))), _1049237))))], (14435 ^ _779530) ^ [_1049428, _1049430, _1049432, _1049434, _1049436, _1049438] : [class_Complete__Lattice_Ocomplete__lattice(_1049428), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049430, tc_fun(_1049432, _1049428)), _1049434), _1049436), _1049438) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049430, _1049428), _1049434), hAPP(hAPP(c_COMBC(_1049430, _1049432, _1049428), _1049436), _1049438)))], (14441 ^ _779530) ^ [_1049579, _1049581, _1049583, _1049585, _1049587] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049579, tc_fun(_1049581, tc_HOL_Obool)), _1049583), hAPP(hAPP(c_COMBC(_1049579, tc_fun(_1049581, tc_HOL_Obool), tc_fun(_1049581, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1049581, tc_HOL_Obool), tc_fun(tc_fun(_1049581, tc_HOL_Obool), tc_fun(_1049581, tc_HOL_Obool)), _1049579), c_Groups_Ominus__class_Ominus(tc_fun(_1049581, tc_HOL_Obool))), _1049585)), _1049587)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049581, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049579, tc_fun(_1049581, tc_HOL_Obool)), _1049583), _1049585)), _1049587))], (14443 ^ _779530) ^ [_1049688, _1049690, _1049692, _1049694, _1049696] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049688, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049690, tc_fun(_1049688, tc_HOL_Obool)), _1049692), _1049694)), _1049696) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049690, tc_fun(_1049688, tc_HOL_Obool)), _1049692), hAPP(hAPP(c_COMBC(_1049690, tc_fun(_1049688, tc_HOL_Obool), tc_fun(_1049688, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1049688, tc_HOL_Obool), tc_fun(tc_fun(_1049688, tc_HOL_Obool), tc_fun(_1049688, tc_HOL_Obool)), _1049690), c_Groups_Ominus__class_Ominus(tc_fun(_1049688, tc_HOL_Obool))), _1049694)), _1049696)))], (14445 ^ _779530) ^ [_1049797, _1049799, _1049801, _1049803, _1049805] : [class_Complete__Lattice_Ocomplete__lattice(_1049797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1049799, tc_HOL_Obool)), _1049801), _1049803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049797), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049799, _1049797), _1049801), _1049805)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049799, _1049797), _1049803), _1049805))))], (14455 ^ _779530) ^ [_1050006, _1050008, _1050010, _1050012, _1050014] : [class_Complete__Lattice_Ocomplete__lattice(_1050006), hBOOL(hAPP(hAPP(c_member(_1050008), _1050010), _1050012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050006), hAPP(_1050014, _1050010)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050008, _1050006), _1050012), _1050014))))], (14465 ^ _779530) ^ [_1050197, _1050199, _1050201, _1050203, _1050205, _1050207] : [hBOOL(hAPP(hAPP(c_member(_1050197), _1050199), _1050201)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050197, tc_fun(_1050203, tc_HOL_Obool)), _1050201), hAPP(hAPP(c_COMBB(tc_fun(_1050203, tc_HOL_Obool), tc_fun(_1050203, tc_HOL_Obool), _1050197), hAPP(c_Set_Oinsert(_1050203), _1050205)), _1050207)) = hAPP(hAPP(c_Set_Oinsert(_1050203), _1050205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050197, tc_fun(_1050203, tc_HOL_Obool)), _1050201), _1050207)))], (14471 ^ _779530) ^ [_1050402, _1050404, _1050406, _1050408, _1050410] : [hBOOL(hAPP(hAPP(c_member(_1050402), _1050404), _1050406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1050408, tc_HOL_Obool)), hAPP(_1050410, _1050404)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050402, tc_fun(_1050408, tc_HOL_Obool)), _1050406), _1050410))))], (14477 ^ _779530) ^ [_1050549, _1050551, _1050553, _1050555, _1050557] : [hBOOL(hAPP(hAPP(c_member(_1050549), _1050551), _1050553)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1050555, tc_HOL_Obool)), hAPP(_1050557, _1050551)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050549, tc_fun(_1050555, tc_HOL_Obool)), _1050553), _1050557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050549, tc_fun(_1050555, tc_HOL_Obool)), _1050553), _1050557))], (14483 ^ _779530) ^ [_1050740, _1050742, _1050744, _1050746, _1050748] : [_1050740 = c_Orderings_Obot__class_Obot(tc_fun(_1050742, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1050744), _1050746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050742, tc_fun(_1050744, tc_HOL_Obool)), _1050740), _1050748)) = hAPP(hAPP(c_Set_Oinsert(_1050744), _1050746), c_Orderings_Obot__class_Obot(tc_fun(_1050744, tc_HOL_Obool))))], (14489 ^ _779530) ^ [_1050893, _1050895, _1050897, _1050899, _1050901] : [-(_1050893 = c_Orderings_Obot__class_Obot(tc_fun(_1050895, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1050897), _1050899), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050895, tc_fun(_1050897, tc_HOL_Obool)), _1050893), _1050901)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050895, tc_fun(_1050897, tc_HOL_Obool)), _1050893), hAPP(hAPP(c_COMBB(tc_fun(_1050897, tc_HOL_Obool), tc_fun(_1050897, tc_HOL_Obool), _1050895), hAPP(c_Set_Oinsert(_1050897), _1050899)), _1050901)))], (14495 ^ _779530) ^ [_1050995, _1050997] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1050995, tc_fun(_1050995, tc_HOL_Obool)), _1050997), hAPP(hAPP(c_COMBC(_1050995, tc_fun(_1050995, tc_HOL_Obool), tc_fun(_1050995, tc_HOL_Obool)), c_Set_Oinsert(_1050995)), c_Orderings_Obot__class_Obot(tc_fun(_1050995, tc_HOL_Obool)))) = _1050997)], (14497 ^ _779530) ^ [_1051073, _1051075, _1051077, _1051079, _1051081] : [_1051073 = c_Orderings_Obot__class_Obot(tc_fun(_1051075, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051075, tc_fun(_1051077, tc_HOL_Obool)), _1051073), hAPP(hAPP(c_COMBB(tc_fun(_1051077, tc_HOL_Obool), tc_fun(_1051077, tc_HOL_Obool), _1051075), hAPP(c_Set_Oinsert(_1051077), _1051079)), _1051081)) = c_Orderings_Obot__class_Obot(tc_fun(_1051077, tc_HOL_Obool)))], (14503 ^ _779530) ^ [_1051236, _1051238, _1051240, _1051242, _1051244] : [-(_1051236 = c_Orderings_Obot__class_Obot(tc_fun(_1051238, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051238, tc_fun(_1051240, tc_HOL_Obool)), _1051236), hAPP(hAPP(c_COMBB(tc_fun(_1051240, tc_HOL_Obool), tc_fun(_1051240, tc_HOL_Obool), _1051238), hAPP(c_Set_Oinsert(_1051240), _1051242)), _1051244)) = hAPP(hAPP(c_Set_Oinsert(_1051240), _1051242), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051238, tc_fun(_1051240, tc_HOL_Obool)), _1051236), _1051244)))], (14509 ^ _779530) ^ [_1051356, _1051358, _1051360, _1051362, _1051364] : [_1051356 = c_Orderings_Obot__class_Obot(tc_fun(_1051358, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051358, tc_fun(_1051360, tc_HOL_Obool)), _1051356), hAPP(hAPP(c_COMBB(tc_fun(_1051360, tc_HOL_Obool), tc_fun(_1051360, tc_HOL_Obool), _1051358), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051360, tc_HOL_Obool)), _1051362)), _1051364)) = c_Orderings_Obot__class_Obot(tc_fun(_1051360, tc_HOL_Obool)))], (14515 ^ _779530) ^ [_1051525, _1051527, _1051529, _1051531, _1051533] : [-(_1051525 = c_Orderings_Obot__class_Obot(tc_fun(_1051527, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051527, tc_fun(_1051529, tc_HOL_Obool)), _1051525), hAPP(hAPP(c_COMBB(tc_fun(_1051529, tc_HOL_Obool), tc_fun(_1051529, tc_HOL_Obool), _1051527), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051529, tc_HOL_Obool)), _1051531)), _1051533)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051529, tc_HOL_Obool)), _1051531), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051527, tc_fun(_1051529, tc_HOL_Obool)), _1051525), _1051533)))], (14521 ^ _779530) ^ [_1051651, _1051653, _1051655, _1051657, _1051659] : [_1051651 = c_Orderings_Obot__class_Obot(tc_fun(_1051653, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051653, tc_fun(_1051655, tc_HOL_Obool)), _1051651), hAPP(hAPP(c_COMBC(_1051653, tc_fun(_1051655, tc_HOL_Obool), tc_fun(_1051655, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1051655, tc_HOL_Obool), tc_fun(tc_fun(_1051655, tc_HOL_Obool), tc_fun(_1051655, tc_HOL_Obool)), _1051653), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051655, tc_HOL_Obool))), _1051657)), _1051659)) = c_Orderings_Obot__class_Obot(tc_fun(_1051655, tc_HOL_Obool)))], (14527 ^ _779530) ^ [_1051858, _1051860, _1051862, _1051864, _1051866] : [-(_1051858 = c_Orderings_Obot__class_Obot(tc_fun(_1051860, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051860, tc_fun(_1051862, tc_HOL_Obool)), _1051858), hAPP(hAPP(c_COMBC(_1051860, tc_fun(_1051862, tc_HOL_Obool), tc_fun(_1051862, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1051862, tc_HOL_Obool), tc_fun(tc_fun(_1051862, tc_HOL_Obool), tc_fun(_1051862, tc_HOL_Obool)), _1051860), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051862, tc_HOL_Obool))), _1051864)), _1051866)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051862, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051860, tc_fun(_1051862, tc_HOL_Obool)), _1051858), _1051864)), _1051866))], (14533 ^ _779530) ^ [_1051985, _1051987, _1051989, _1051991, _1051993, _1051995, _1051997, _1051999, _1052001, _1052003, _1052005] : [c_Equiv__Relations_Oequiv(_1051985, _1051987, _1051989), c_Equiv__Relations_Oequiv(_1051991, _1051993, _1051995), c_Equiv__Relations_Ocongruent2(_1051985, _1051991, tc_fun(_1051997, tc_HOL_Obool), _1051989, _1051995, _1051999), hBOOL(hAPP(hAPP(c_member(tc_fun(_1051985, tc_HOL_Obool)), _1052001), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1051985), _1051987), _1051989))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1051991, tc_HOL_Obool)), _1052003), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1051991), _1051993), _1051995))), 14555 ^ _779530 : [(14556 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1051985), 14554 ^ [_1051985, _1051987, _1051989, _1051991, _1051993, _1051995, _1051997, _1051999, _1052001, _1052003, _1052005]), _1051987)))], (14559 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1051991), 14557 ^ [_1051985, _1051987, _1051989, _1051991, _1051993, _1051995, _1051997, _1051999, _1052001, _1052003, _1052005]), _1051993)))], (14561 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1051997, tc_HOL_Obool)), hAPP(hAPP(_1051999, 14554 ^ [_1051985, _1051987, _1051989, _1051991, _1051993, _1051995, _1051997, _1051999, _1052001, _1052003, _1052005]), 14557 ^ [_1051985, _1051987, _1051989, _1051991, _1051993, _1051995, _1051997, _1051999, _1052001, _1052003, _1052005])), _1052005))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1051997, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051985, tc_fun(_1051997, tc_HOL_Obool)), _1052001), hAPP(hAPP(c_COMBB(tc_fun(_1051991, tc_fun(_1051997, tc_HOL_Obool)), tc_fun(_1051997, tc_HOL_Obool), _1051985), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1051991, tc_fun(_1051997, tc_HOL_Obool)), _1052003)), _1051999))), _1052005)))], (14565 ^ _779530) ^ [_1052987, _1052989, _1052991, _1052993, _1052995, _1052997, _1052999] : [c_Equiv__Relations_Oequiv(_1052987, _1052989, _1052991), c_Equiv__Relations_Ocongruent(_1052987, tc_fun(_1052993, tc_HOL_Obool), _1052991, _1052995), hBOOL(hAPP(hAPP(c_member(tc_fun(_1052987, tc_HOL_Obool)), _1052997), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1052987), _1052989), _1052991))), 14579 ^ _779530 : [(14580 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1052987), 14578 ^ [_1052987, _1052989, _1052991, _1052993, _1052995, _1052997, _1052999]), _1052989)))], (14582 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1052993, tc_HOL_Obool)), hAPP(_1052995, 14578 ^ [_1052987, _1052989, _1052991, _1052993, _1052995, _1052997, _1052999])), _1052999))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1052993, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1052987, tc_fun(_1052993, tc_HOL_Obool)), _1052997), _1052995)), _1052999)))], (14586 ^ _779530) ^ [_1053498, _1053500, _1053502] : [class_Lattices_Olattice(_1053498), hAPP(_1053500, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053498), 14591 ^ [_1053498, _1053500, _1053502]), 14592 ^ [_1053498, _1053500, _1053502])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053498), hAPP(_1053500, 14591 ^ [_1053498, _1053500, _1053502])), hAPP(_1053500, 14592 ^ [_1053498, _1053500, _1053502])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053498), _1053502)), -(_1053502 = c_Orderings_Obot__class_Obot(tc_fun(_1053498, tc_HOL_Obool))), -(hAPP(_1053500, c_Big__Operators_Olattice__class_OSup__fin(_1053498, _1053502)) = c_Big__Operators_Olattice__class_OSup__fin(_1053498, hAPP(c_Set_Oimage(_1053498, _1053498, _1053500), _1053502)))], (14606 ^ _779530) ^ [_1053901, _1053903, _1053905, _1053907, _1053909, _1053911] : [c_Equiv__Relations_Oequiv(_1053901, _1053903, _1053905), hBOOL(hAPP(hAPP(c_member(_1053901), _1053907), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053901, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1053901, _1053901, _1053905), hAPP(hAPP(c_Set_Oinsert(_1053901), _1053909), c_Orderings_Obot__class_Obot(tc_fun(_1053901, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1053901, _1053901, _1053905), hAPP(hAPP(c_Set_Oinsert(_1053901), _1053911), c_Orderings_Obot__class_Obot(tc_fun(_1053901, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1053901, _1053901)), hAPP(hAPP(c_Product__Type_OPair(_1053901, _1053901), _1053909), _1053911)), _1053905)))], (14616 ^ _779530) ^ [_1054202, _1054204, _1054206, _1054208, _1054210] : [c_Equiv__Relations_Oequiv(_1054202, _1054204, _1054206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1054202, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1054202, _1054202, _1054206), hAPP(hAPP(c_Set_Oinsert(_1054202), _1054208), c_Orderings_Obot__class_Obot(tc_fun(_1054202, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1054202, _1054202, _1054206), hAPP(hAPP(c_Set_Oinsert(_1054202), _1054210), c_Orderings_Obot__class_Obot(tc_fun(_1054202, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1054202), _1054208), _1054204)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1054202, _1054202)), hAPP(hAPP(c_Product__Type_OPair(_1054202, _1054202), _1054210), _1054208)), _1054206)))], (14630 ^ _779530) ^ [_1054555, _1054557, _1054559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1054555), _1054557)), hBOOL(hAPP(_1054559, _1054557)), 14641 ^ _779530 : [(14642 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1054555), 14640 ^ [_1054555, _1054557, _1054559])))], (14644 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1054555), 14639 ^ [_1054555, _1054557, _1054559]), 14640 ^ [_1054555, _1054557, _1054559])))], (14646 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1054559, 14640 ^ [_1054555, _1054557, _1054559])))], (14648 ^ _779530) ^ [] : [hBOOL(hAPP(_1054559, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054555, tc_HOL_Obool)), 14640 ^ [_1054555, _1054557, _1054559]), hAPP(hAPP(c_Set_Oinsert(_1054555), 14639 ^ [_1054555, _1054557, _1054559]), c_Orderings_Obot__class_Obot(tc_fun(_1054555, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1054559, c_Orderings_Obot__class_Obot(tc_fun(_1054555, tc_HOL_Obool)))))], (14652 ^ _779530) ^ [_1055080, _1055082, _1055084, _1055086, _1055088] : [c_Finite__Set_Ofolding__one__idem(_1055080, _1055082, _1055084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055080), _1055086)), -(_1055086 = c_Orderings_Obot__class_Obot(tc_fun(_1055080, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055080), _1055088)), -(_1055088 = c_Orderings_Obot__class_Obot(tc_fun(_1055080, tc_HOL_Obool))), -(hAPP(_1055084, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055080, tc_HOL_Obool)), _1055086), _1055088)) = hAPP(hAPP(_1055082, hAPP(_1055084, _1055086)), hAPP(_1055084, _1055088)))], (14674 ^ _779530) ^ [_1055445, _1055447, _1055449, _1055451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1055445), _1055447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1055445, tc_HOL_Obool)), _1055447), _1055449)), hBOOL(hAPP(_1055451, c_Orderings_Obot__class_Obot(tc_fun(_1055445, tc_HOL_Obool)))), 14689 ^ _779530 : [(14690 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1055445), 14688 ^ [_1055445, _1055447, _1055449, _1055451])))], (14692 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1055445), 14687 ^ [_1055445, _1055447, _1055449, _1055451]), _1055449)))], (14694 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1055445), 14687 ^ [_1055445, _1055447, _1055449, _1055451]), 14688 ^ [_1055445, _1055447, _1055449, _1055451]))], (14696 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1055451, 14688 ^ [_1055445, _1055447, _1055449, _1055451])))], (14698 ^ _779530) ^ [] : [hBOOL(hAPP(_1055451, hAPP(hAPP(c_Set_Oinsert(_1055445), 14687 ^ [_1055445, _1055447, _1055449, _1055451]), 14688 ^ [_1055445, _1055447, _1055449, _1055451])))]], -(hBOOL(hAPP(_1055451, _1055447)))], (14702 ^ _779530) ^ [_1056110, _1056112, _1056114, _1056116, _1056118, _1056120, _1056122, _1056124] : [hBOOL(hAPP(hAPP(c_member(_1056110), _1056112), _1056114)), hBOOL(hAPP(hAPP(hAPP(_1056116, _1056112), _1056118), _1056120)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1056110, tc_fun(_1056122, tc_fun(_1056124, tc_HOL_Obool))), _1056114), _1056116), _1056118), _1056120)))], (14712 ^ _779530) ^ [_1056333, _1056335, _1056337, _1056339] : [c_Finite__Set_Ofolding__one__idem(_1056333, _1056335, _1056337), -(hAPP(hAPP(_1056335, _1056339), _1056339) = _1056339)], (14718 ^ _779530) ^ [_1056455, _1056457, _1056459, _1056461, _1056463, _1056465] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056455, tc_fun(_1056457, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1056455, tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_fun(_1056457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056457, tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_fun(_1056457, tc_HOL_Obool)), _1056455), c_COMBC(_1056457, tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056457, tc_prod(_1056455, _1056457)), tc_fun(_1056457, tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), _1056455), hAPP(c_COMBB(tc_prod(_1056455, _1056457), tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool), _1056457), c_member(tc_prod(_1056455, _1056457)))), c_Product__Type_OPair(_1056455, _1056457)))), _1056459)), hAPP(hAPP(c_COMBC(_1056455, tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_fun(_1056457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056457, tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_fun(_1056457, tc_HOL_Obool)), _1056455), c_COMBC(_1056457, tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056457, tc_prod(_1056455, _1056457)), tc_fun(_1056457, tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool)), _1056455), hAPP(c_COMBB(tc_prod(_1056455, _1056457), tc_fun(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool), tc_HOL_Obool), _1056457), c_member(tc_prod(_1056455, _1056457)))), c_Product__Type_OPair(_1056455, _1056457)))), _1056461)), _1056463), _1056465)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1056455, _1056457)), hAPP(hAPP(c_Product__Type_OPair(_1056455, _1056457), _1056463), _1056465)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1056455, _1056457), tc_HOL_Obool)), _1056459), _1056461))))], (14724 ^ _779530) ^ [_1057112, _1057114, _1057116, _1057118, _1057120, _1057122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1057112, _1057114)), hAPP(hAPP(c_Product__Type_OPair(_1057112, _1057114), _1057120), _1057122)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool)), _1057116), _1057118))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1057112, tc_fun(_1057114, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1057112, tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_fun(_1057114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057114, tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_fun(_1057114, tc_HOL_Obool)), _1057112), c_COMBC(_1057114, tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057114, tc_prod(_1057112, _1057114)), tc_fun(_1057114, tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), _1057112), hAPP(c_COMBB(tc_prod(_1057112, _1057114), tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool), _1057114), c_member(tc_prod(_1057112, _1057114)))), c_Product__Type_OPair(_1057112, _1057114)))), _1057116)), hAPP(hAPP(c_COMBC(_1057112, tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_fun(_1057114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057114, tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_fun(_1057114, tc_HOL_Obool)), _1057112), c_COMBC(_1057114, tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057114, tc_prod(_1057112, _1057114)), tc_fun(_1057114, tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool)), _1057112), hAPP(c_COMBB(tc_prod(_1057112, _1057114), tc_fun(tc_fun(tc_prod(_1057112, _1057114), tc_HOL_Obool), tc_HOL_Obool), _1057114), c_member(tc_prod(_1057112, _1057114)))), c_Product__Type_OPair(_1057112, _1057114)))), _1057118)), _1057120), _1057122)))], (14730 ^ _779530) ^ [_1057796, _1057798, _1057800, _1057802] : [hAPP(hAPP(c_COMBC(_1057796, tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_fun(_1057798, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057798, tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_fun(_1057798, tc_HOL_Obool)), _1057796), c_COMBC(_1057798, tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057798, tc_prod(_1057796, _1057798)), tc_fun(_1057798, tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), _1057796), hAPP(c_COMBB(tc_prod(_1057796, _1057798), tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool), _1057798), c_member(tc_prod(_1057796, _1057798)))), c_Product__Type_OPair(_1057796, _1057798)))), _1057800) = hAPP(hAPP(c_COMBC(_1057796, tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_fun(_1057798, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057798, tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_fun(_1057798, tc_HOL_Obool)), _1057796), c_COMBC(_1057798, tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1057798, tc_prod(_1057796, _1057798)), tc_fun(_1057798, tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool)), _1057796), hAPP(c_COMBB(tc_prod(_1057796, _1057798), tc_fun(tc_fun(tc_prod(_1057796, _1057798), tc_HOL_Obool), tc_HOL_Obool), _1057798), c_member(tc_prod(_1057796, _1057798)))), c_Product__Type_OPair(_1057796, _1057798)))), _1057802), -(_1057800 = _1057802)], (14736 ^ _779530) ^ [_1058345, _1058347, _1058349, _1058351] : [_1058349 = _1058351, -(hAPP(hAPP(c_COMBC(_1058345, tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_fun(_1058347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058347, tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_fun(_1058347, tc_HOL_Obool)), _1058345), c_COMBC(_1058347, tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058347, tc_prod(_1058345, _1058347)), tc_fun(_1058347, tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), _1058345), hAPP(c_COMBB(tc_prod(_1058345, _1058347), tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool), _1058347), c_member(tc_prod(_1058345, _1058347)))), c_Product__Type_OPair(_1058345, _1058347)))), _1058349) = hAPP(hAPP(c_COMBC(_1058345, tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_fun(_1058347, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058347, tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_fun(_1058347, tc_HOL_Obool)), _1058345), c_COMBC(_1058347, tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058347, tc_prod(_1058345, _1058347)), tc_fun(_1058347, tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool)), _1058345), hAPP(c_COMBB(tc_prod(_1058345, _1058347), tc_fun(tc_fun(tc_prod(_1058345, _1058347), tc_HOL_Obool), tc_HOL_Obool), _1058347), c_member(tc_prod(_1058345, _1058347)))), c_Product__Type_OPair(_1058345, _1058347)))), _1058351))], (14742 ^ _779530) ^ [_1058900, _1058902, _1058904, _1058906, _1058908, _1058910, _1058912, _1058914, _1058916, _1058918] : [c_Equiv__Relations_Ocongruent2(_1058900, _1058902, _1058904, _1058906, _1058908, _1058910), hBOOL(hAPP(hAPP(c_member(tc_prod(_1058900, _1058900)), hAPP(hAPP(c_Product__Type_OPair(_1058900, _1058900), _1058912), _1058914)), _1058906)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1058902, _1058902)), hAPP(hAPP(c_Product__Type_OPair(_1058902, _1058902), _1058916), _1058918)), _1058908)), -(hAPP(hAPP(_1058910, _1058912), _1058916) = hAPP(hAPP(_1058910, _1058914), _1058918))], (14756 ^ _779530) ^ [_1059237, _1059239, _1059241, _1059243, _1059245, _1059247] : [c_Equiv__Relations_Ocongruent(_1059237, _1059239, _1059241, _1059243), hBOOL(hAPP(hAPP(c_member(tc_prod(_1059237, _1059237)), hAPP(hAPP(c_Product__Type_OPair(_1059237, _1059237), _1059245), _1059247)), _1059241)), -(hAPP(_1059243, _1059245) = hAPP(_1059243, _1059247))], (14766 ^ _779530) ^ [_1059457, _1059459, _1059461, _1059463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059457, tc_fun(_1059459, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1059457, tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_fun(_1059459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059459, tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_fun(_1059459, tc_HOL_Obool)), _1059457), c_COMBC(_1059459, tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059459, tc_prod(_1059457, _1059459)), tc_fun(_1059459, tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), _1059457), hAPP(c_COMBB(tc_prod(_1059457, _1059459), tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool), _1059459), c_member(tc_prod(_1059457, _1059459)))), c_Product__Type_OPair(_1059457, _1059459)))), _1059461)), hAPP(hAPP(c_COMBC(_1059457, tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_fun(_1059459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059459, tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_fun(_1059459, tc_HOL_Obool)), _1059457), c_COMBC(_1059459, tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059459, tc_prod(_1059457, _1059459)), tc_fun(_1059459, tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool)), _1059457), hAPP(c_COMBB(tc_prod(_1059457, _1059459), tc_fun(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool), tc_HOL_Obool), _1059459), c_member(tc_prod(_1059457, _1059459)))), c_Product__Type_OPair(_1059457, _1059459)))), _1059463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1059457, _1059459), tc_HOL_Obool)), _1059461), _1059463)))], (14772 ^ _779530) ^ [_1060058, _1060060, _1060062, _1060064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool)), _1060062), _1060064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060058, tc_fun(_1060060, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1060058, tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_fun(_1060060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1060060, tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_fun(_1060060, tc_HOL_Obool)), _1060058), c_COMBC(_1060060, tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1060060, tc_prod(_1060058, _1060060)), tc_fun(_1060060, tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), _1060058), hAPP(c_COMBB(tc_prod(_1060058, _1060060), tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool), _1060060), c_member(tc_prod(_1060058, _1060060)))), c_Product__Type_OPair(_1060058, _1060060)))), _1060062)), hAPP(hAPP(c_COMBC(_1060058, tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_fun(_1060060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1060060, tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_fun(_1060060, tc_HOL_Obool)), _1060058), c_COMBC(_1060060, tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1060060, tc_prod(_1060058, _1060060)), tc_fun(_1060060, tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool)), _1060058), hAPP(c_COMBB(tc_prod(_1060058, _1060060), tc_fun(tc_fun(tc_prod(_1060058, _1060060), tc_HOL_Obool), tc_HOL_Obool), _1060060), c_member(tc_prod(_1060058, _1060060)))), c_Product__Type_OPair(_1060058, _1060060)))), _1060064))))], (14778 ^ _779530) ^ [_1060686, _1060688, _1060690, _1060692] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1060686, tc_fun(_1060688, tc_HOL_Obool))), _1060690), _1060692)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1060686, _1060688)), hAPP(hAPP(c_Product__Type_OPair(_1060686, _1060688), _1060690), _1060692)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1060686, _1060688), tc_HOL_Obool)))))], (14784 ^ _779530) ^ [_1060843, _1060845, _1060847, _1060849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1060843, _1060845)), hAPP(hAPP(c_Product__Type_OPair(_1060843, _1060845), _1060847), _1060849)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1060843, _1060845), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1060843, tc_fun(_1060845, tc_HOL_Obool))), _1060847), _1060849)))], (14790 ^ _779530) ^ [_1061033, _1061035, _1061037, _1061039, _1061041, _1061043] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061033, tc_fun(_1061035, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1061033, tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_fun(_1061035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061035, tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_fun(_1061035, tc_HOL_Obool)), _1061033), c_COMBC(_1061035, tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061035, tc_prod(_1061033, _1061035)), tc_fun(_1061035, tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), _1061033), hAPP(c_COMBB(tc_prod(_1061033, _1061035), tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool), _1061035), c_member(tc_prod(_1061033, _1061035)))), c_Product__Type_OPair(_1061033, _1061035)))), _1061037)), hAPP(hAPP(c_COMBC(_1061033, tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_fun(_1061035, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061035, tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_fun(_1061035, tc_HOL_Obool)), _1061033), c_COMBC(_1061035, tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061035, tc_prod(_1061033, _1061035)), tc_fun(_1061035, tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool)), _1061033), hAPP(c_COMBB(tc_prod(_1061033, _1061035), tc_fun(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool), tc_HOL_Obool), _1061035), c_member(tc_prod(_1061033, _1061035)))), c_Product__Type_OPair(_1061033, _1061035)))), _1061039)), _1061041), _1061043)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1061033, _1061035)), hAPP(hAPP(c_Product__Type_OPair(_1061033, _1061035), _1061041), _1061043)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1061033, _1061035), tc_HOL_Obool)), _1061037), _1061039))))], (14796 ^ _779530) ^ [_1061690, _1061692, _1061694, _1061696, _1061698, _1061700] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1061690, _1061692)), hAPP(hAPP(c_Product__Type_OPair(_1061690, _1061692), _1061698), _1061700)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool)), _1061694), _1061696))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061690, tc_fun(_1061692, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1061690, tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_fun(_1061692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061692, tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_fun(_1061692, tc_HOL_Obool)), _1061690), c_COMBC(_1061692, tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061692, tc_prod(_1061690, _1061692)), tc_fun(_1061692, tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), _1061690), hAPP(c_COMBB(tc_prod(_1061690, _1061692), tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool), _1061692), c_member(tc_prod(_1061690, _1061692)))), c_Product__Type_OPair(_1061690, _1061692)))), _1061694)), hAPP(hAPP(c_COMBC(_1061690, tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_fun(_1061692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061692, tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_fun(_1061692, tc_HOL_Obool)), _1061690), c_COMBC(_1061692, tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061692, tc_prod(_1061690, _1061692)), tc_fun(_1061692, tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool)), _1061690), hAPP(c_COMBB(tc_prod(_1061690, _1061692), tc_fun(tc_fun(tc_prod(_1061690, _1061692), tc_HOL_Obool), tc_HOL_Obool), _1061692), c_member(tc_prod(_1061690, _1061692)))), c_Product__Type_OPair(_1061690, _1061692)))), _1061696)), _1061698), _1061700)))], (14802 ^ _779530) ^ [_1062353, _1062355, _1062357] : [class_Enum_Oenum(_1062353), class_Enum_Oenum(_1062355), 14809 ^ _779530 : [(14810 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1062355, _1062353)), _1062357)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1062355), hAPP(hAPP(c_COMBB(tc_fun(_1062353, tc_HOL_Obool), tc_HOL_Obool, _1062355), c_Enum_Oenum__class_Oenum__ex(_1062353)), hAPP(hAPP(c_COMBB(tc_fun(_1062353, tc_prod(_1062355, _1062353)), tc_fun(_1062353, tc_HOL_Obool), _1062355), hAPP(c_COMBB(tc_prod(_1062355, _1062353), tc_HOL_Obool, _1062353), _1062357)), c_Product__Type_OPair(_1062355, _1062353))))))], (14816 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1062355), hAPP(hAPP(c_COMBB(tc_fun(_1062353, tc_HOL_Obool), tc_HOL_Obool, _1062355), c_Enum_Oenum__class_Oenum__ex(_1062353)), hAPP(hAPP(c_COMBB(tc_fun(_1062353, tc_prod(_1062355, _1062353)), tc_fun(_1062353, tc_HOL_Obool), _1062355), hAPP(c_COMBB(tc_prod(_1062355, _1062353), tc_HOL_Obool, _1062353), _1062357)), c_Product__Type_OPair(_1062355, _1062353))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1062355, _1062353)), _1062357)))]]], (14822 ^ _779530) ^ [_1062792, _1062794, _1062796] : [class_Enum_Oenum(_1062792), class_Enum_Oenum(_1062794), 14829 ^ _779530 : [(14830 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1062794, _1062792)), _1062796)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1062794), hAPP(hAPP(c_COMBB(tc_fun(_1062792, tc_HOL_Obool), tc_HOL_Obool, _1062794), c_Enum_Oenum__class_Oenum__all(_1062792)), hAPP(hAPP(c_COMBB(tc_fun(_1062792, tc_prod(_1062794, _1062792)), tc_fun(_1062792, tc_HOL_Obool), _1062794), hAPP(c_COMBB(tc_prod(_1062794, _1062792), tc_HOL_Obool, _1062792), _1062796)), c_Product__Type_OPair(_1062794, _1062792))))))], (14836 ^ _779530) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1062794), hAPP(hAPP(c_COMBB(tc_fun(_1062792, tc_HOL_Obool), tc_HOL_Obool, _1062794), c_Enum_Oenum__class_Oenum__all(_1062792)), hAPP(hAPP(c_COMBB(tc_fun(_1062792, tc_prod(_1062794, _1062792)), tc_fun(_1062792, tc_HOL_Obool), _1062794), hAPP(c_COMBB(tc_prod(_1062794, _1062792), tc_HOL_Obool, _1062792), _1062796)), c_Product__Type_OPair(_1062794, _1062792))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1062794, _1062792)), _1062796)))]]], (14842 ^ _779530) ^ [_1063255, _1063257, _1063259, _1063261, _1063263] : [hBOOL(hAPP(hAPP(c_member(_1063255), _1063257), hAPP(c_Relation_OImage(_1063259, _1063255, _1063261), _1063263))), 14846 ^ _779530 : [(14847 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1063259), 14845 ^ [_1063255, _1063257, _1063259, _1063261, _1063263]), _1063263)))], (14849 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1063259, _1063255)), hAPP(hAPP(c_Product__Type_OPair(_1063259, _1063255), 14845 ^ [_1063255, _1063257, _1063259, _1063261, _1063263]), _1063257)), _1063261)))]]], (14851 ^ _779530) ^ [_1063471, _1063473, _1063475, _1063477, _1063479] : [-(hBOOL(hAPP(hAPP(c_member(_1063471), _1063473), hAPP(c_Relation_OImage(_1063475, _1063471, _1063477), _1063479)))), 14852 ^ _779530 : [(14853 ^ _779530) ^ [_1063557] : [hBOOL(hAPP(hAPP(c_member(_1063475), _1063557), _1063479)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1063475, _1063471)), hAPP(hAPP(c_Product__Type_OPair(_1063475, _1063471), _1063557), _1063473)), _1063477))]]], (14861 ^ _779530) ^ [_1063737, _1063739, _1063741, _1063743, _1063745, _1063747] : [hBOOL(hAPP(hAPP(c_member(_1063737), _1063739), _1063741)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1063737, _1063743)), hAPP(hAPP(c_Product__Type_OPair(_1063737, _1063743), _1063739), _1063745)), _1063747)), -(hBOOL(hAPP(hAPP(c_member(_1063743), _1063745), hAPP(c_Relation_OImage(_1063737, _1063743, _1063747), _1063741))))], (14871 ^ _779530) ^ [_1063986, _1063988, _1063990, _1063992, _1063994] : [hBOOL(hAPP(hAPP(c_member(_1063986), _1063988), hAPP(c_Relation_OImage(_1063990, _1063986, _1063992), hAPP(hAPP(c_Set_Oinsert(_1063990), _1063994), c_Orderings_Obot__class_Obot(tc_fun(_1063990, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1063990, _1063986)), hAPP(hAPP(c_Product__Type_OPair(_1063990, _1063986), _1063994), _1063988)), _1063992)))], (14877 ^ _779530) ^ [_1064157, _1064159, _1064161, _1064163, _1064165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1064161, _1064157)), hAPP(hAPP(c_Product__Type_OPair(_1064161, _1064157), _1064165), _1064159)), _1064163)), -(hBOOL(hAPP(hAPP(c_member(_1064157), _1064159), hAPP(c_Relation_OImage(_1064161, _1064157, _1064163), hAPP(hAPP(c_Set_Oinsert(_1064161), _1064165), c_Orderings_Obot__class_Obot(tc_fun(_1064161, tc_HOL_Obool)))))))], (14883 ^ _779530) ^ [_1064334, _1064336, _1064338, _1064340, _1064342] : [c_Finite__Set_Ofolding__one__idem(_1064334, _1064336, _1064338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064334), _1064340)), hBOOL(hAPP(hAPP(c_member(_1064334), _1064342), _1064340)), -(hAPP(hAPP(_1064336, _1064342), hAPP(_1064338, _1064340)) = hAPP(_1064338, _1064340))], (14897 ^ _779530) ^ [_1064581, _1064583, _1064585, _1064587, _1064589] : [c_Equiv__Relations_Oequiv(_1064581, _1064583, _1064585), hBOOL(hAPP(hAPP(c_member(tc_prod(_1064581, _1064581)), hAPP(hAPP(c_Product__Type_OPair(_1064581, _1064581), _1064587), _1064589)), _1064585)), -(hAPP(c_Relation_OImage(_1064581, _1064581, _1064585), hAPP(hAPP(c_Set_Oinsert(_1064581), _1064587), c_Orderings_Obot__class_Obot(tc_fun(_1064581, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1064581, _1064581, _1064585), hAPP(hAPP(c_Set_Oinsert(_1064581), _1064589), c_Orderings_Obot__class_Obot(tc_fun(_1064581, tc_HOL_Obool)))))], (14907 ^ _779530) ^ [_1064842, _1064844, _1064846, _1064848, _1064850, _1064852, _1064854] : [c_Equiv__Relations_Oequiv(_1064842, _1064844, _1064846), hBOOL(hAPP(hAPP(c_member(tc_fun(_1064842, tc_HOL_Obool)), _1064848), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1064842), _1064844), _1064846))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1064842, tc_HOL_Obool)), _1064850), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1064842), _1064844), _1064846))), hBOOL(hAPP(hAPP(c_member(_1064842), _1064852), _1064848)), hBOOL(hAPP(hAPP(c_member(_1064842), _1064854), _1064850)), 14926 ^ _779530 : [(14927 ^ _779530) ^ [] : [_1064848 = _1064850, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1064842, _1064842)), hAPP(hAPP(c_Product__Type_OPair(_1064842, _1064842), _1064852), _1064854)), _1064846)))], (14933 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1064842, _1064842)), hAPP(hAPP(c_Product__Type_OPair(_1064842, _1064842), _1064852), _1064854)), _1064846)), -(_1064848 = _1064850)]]], (14939 ^ _779530) ^ [_1065486, _1065488, _1065490, _1065492, _1065494, _1065496, _1065498] : [c_Equiv__Relations_Oequiv(_1065486, _1065488, _1065490), hBOOL(hAPP(hAPP(c_member(tc_fun(_1065486, tc_HOL_Obool)), _1065492), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1065486), _1065488), _1065490))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1065486, tc_HOL_Obool)), _1065494), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1065486), _1065488), _1065490))), hBOOL(hAPP(hAPP(c_member(_1065486), _1065496), _1065492)), hBOOL(hAPP(hAPP(c_member(_1065486), _1065498), _1065494)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1065486, _1065486)), hAPP(hAPP(c_Product__Type_OPair(_1065486, _1065486), _1065496), _1065498)), _1065490)), -(_1065492 = _1065494)], (14965 ^ _779530) ^ [_1066023, _1066025, _1066027, _1066029] : [-(hAPP(c_Relation_OImage(_1066023, _1066025, _1066027), hAPP(hAPP(c_Set_Oinsert(_1066023), _1066029), c_Orderings_Obot__class_Obot(tc_fun(_1066023, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1066025), hAPP(hAPP(c_COMBC(_1066025, tc_fun(tc_prod(_1066023, _1066025), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1066023, _1066025), tc_fun(tc_fun(tc_prod(_1066023, _1066025), tc_HOL_Obool), tc_HOL_Obool), _1066025), c_member(tc_prod(_1066023, _1066025))), hAPP(c_Product__Type_OPair(_1066023, _1066025), _1066029))), _1066027)))], (14967 ^ _779530) ^ [_1066126, _1066128, _1066130, _1066132, _1066134] : [c_Equiv__Relations_Oequiv(_1066126, _1066128, _1066130), 14970 ^ _779530 : [(14971 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1066126, _1066126)), hAPP(hAPP(c_Product__Type_OPair(_1066126, _1066126), _1066132), _1066134)), _1066130)), 14974 ^ _779530 : [(14975 ^ _779530) ^ [] : [-(hAPP(c_Relation_OImage(_1066126, _1066126, _1066130), hAPP(hAPP(c_Set_Oinsert(_1066126), _1066132), c_Orderings_Obot__class_Obot(tc_fun(_1066126, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1066126, _1066126, _1066130), hAPP(hAPP(c_Set_Oinsert(_1066126), _1066134), c_Orderings_Obot__class_Obot(tc_fun(_1066126, tc_HOL_Obool)))))], (14977 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1066126), _1066132), _1066128)))], (14979 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1066126), _1066134), _1066128)))]]], (14981 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1066126, _1066126)), hAPP(hAPP(c_Product__Type_OPair(_1066126, _1066126), _1066132), _1066134)), _1066130))), hAPP(c_Relation_OImage(_1066126, _1066126, _1066130), hAPP(hAPP(c_Set_Oinsert(_1066126), _1066132), c_Orderings_Obot__class_Obot(tc_fun(_1066126, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1066126, _1066126, _1066130), hAPP(hAPP(c_Set_Oinsert(_1066126), _1066134), c_Orderings_Obot__class_Obot(tc_fun(_1066126, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1066126), _1066132), _1066128)), hBOOL(hAPP(hAPP(c_member(_1066126), _1066134), _1066128))]]], (14995 ^ _779530) ^ [_1066726, _1066728, _1066730, _1066732, _1066734] : [c_Equiv__Relations_Oequiv(_1066726, _1066728, _1066730), hBOOL(hAPP(hAPP(c_member(_1066726), _1066732), _1066728)), hBOOL(hAPP(hAPP(c_member(_1066726), _1066734), _1066728)), 15006 ^ _779530 : [(15007 ^ _779530) ^ [] : [hAPP(c_Relation_OImage(_1066726, _1066726, _1066730), hAPP(hAPP(c_Set_Oinsert(_1066726), _1066732), c_Orderings_Obot__class_Obot(tc_fun(_1066726, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1066726, _1066726, _1066730), hAPP(hAPP(c_Set_Oinsert(_1066726), _1066734), c_Orderings_Obot__class_Obot(tc_fun(_1066726, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1066726, _1066726)), hAPP(hAPP(c_Product__Type_OPair(_1066726, _1066726), _1066732), _1066734)), _1066730)))], (15013 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1066726, _1066726)), hAPP(hAPP(c_Product__Type_OPair(_1066726, _1066726), _1066732), _1066734)), _1066730)), -(hAPP(c_Relation_OImage(_1066726, _1066726, _1066730), hAPP(hAPP(c_Set_Oinsert(_1066726), _1066732), c_Orderings_Obot__class_Obot(tc_fun(_1066726, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1066726, _1066726, _1066730), hAPP(hAPP(c_Set_Oinsert(_1066726), _1066734), c_Orderings_Obot__class_Obot(tc_fun(_1066726, tc_HOL_Obool)))))]]], (15019 ^ _779530) ^ [_1067274, _1067276, _1067278, _1067280, _1067282] : [hAPP(c_Relation_OImage(_1067274, _1067274, _1067276), hAPP(hAPP(c_Set_Oinsert(_1067274), _1067278), c_Orderings_Obot__class_Obot(tc_fun(_1067274, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1067274, _1067274, _1067276), hAPP(hAPP(c_Set_Oinsert(_1067274), _1067280), c_Orderings_Obot__class_Obot(tc_fun(_1067274, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1067274, _1067282, _1067276), hBOOL(hAPP(hAPP(c_member(_1067274), _1067280), _1067282)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1067274, _1067274)), hAPP(hAPP(c_Product__Type_OPair(_1067274, _1067274), _1067278), _1067280)), _1067276)))], (15033 ^ _779530) ^ [_1067607, _1067609, _1067611, _1067613, _1067615] : [c_Equiv__Relations_Oequiv(_1067607, _1067609, _1067611), hBOOL(hAPP(hAPP(c_member(tc_prod(_1067607, _1067607)), hAPP(hAPP(c_Product__Type_OPair(_1067607, _1067607), _1067613), _1067615)), _1067611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1067607, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1067607, _1067607, _1067611), hAPP(hAPP(c_Set_Oinsert(_1067607), _1067613), c_Orderings_Obot__class_Obot(tc_fun(_1067607, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1067607, _1067607, _1067611), hAPP(hAPP(c_Set_Oinsert(_1067607), _1067615), c_Orderings_Obot__class_Obot(tc_fun(_1067607, tc_HOL_Obool)))))))], (15043 ^ _779530) ^ [_1067888, _1067890, _1067892, _1067894, _1067896] : [c_Equiv__Relations_Oequiv(_1067888, _1067890, _1067892), hBOOL(hAPP(hAPP(c_member(_1067888), _1067894), _1067890)), hBOOL(hAPP(hAPP(c_member(_1067888), _1067896), _1067890)), 15054 ^ _779530 : [(15055 ^ _779530) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1067888), hAPP(hAPP(c_Set_Oinsert(_1067888), _1067894), c_Orderings_Obot__class_Obot(tc_fun(_1067888, tc_HOL_Obool)))), _1067892) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1067888), hAPP(hAPP(c_Set_Oinsert(_1067888), _1067896), c_Orderings_Obot__class_Obot(tc_fun(_1067888, tc_HOL_Obool)))), _1067892), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1067888, _1067888)), hAPP(hAPP(c_Product__Type_OPair(_1067888, _1067888), _1067894), _1067896)), _1067892)))], (15061 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1067888, _1067888)), hAPP(hAPP(c_Product__Type_OPair(_1067888, _1067888), _1067894), _1067896)), _1067892)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1067888), hAPP(hAPP(c_Set_Oinsert(_1067888), _1067894), c_Orderings_Obot__class_Obot(tc_fun(_1067888, tc_HOL_Obool)))), _1067892) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1067888), hAPP(hAPP(c_Set_Oinsert(_1067888), _1067896), c_Orderings_Obot__class_Obot(tc_fun(_1067888, tc_HOL_Obool)))), _1067892))]]], (15067 ^ _779530) ^ [_1068442, _1068444, _1068446, _1068448, _1068450] : [c_Finite__Set_Ofolding__one__idem(_1068442, _1068444, _1068446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068442), _1068448)), -(_1068448 = c_Orderings_Obot__class_Obot(tc_fun(_1068442, tc_HOL_Obool))), -(hAPP(_1068446, hAPP(hAPP(c_Set_Oinsert(_1068442), _1068450), _1068448)) = hAPP(hAPP(_1068444, _1068450), hAPP(_1068446, _1068448)))], (15081 ^ _779530) ^ [_1068658, _1068660, _1068662, _1068664, _1068666] : [c_Finite__Set_Ofolding__one__idem(_1068658, _1068660, _1068662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068658), _1068664)), -(_1068666 = c_Orderings_Obot__class_Obot(tc_fun(_1068658, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1068658, tc_HOL_Obool)), _1068666), _1068664)), -(hAPP(hAPP(_1068660, hAPP(_1068662, _1068666)), hAPP(_1068662, _1068664)) = hAPP(_1068662, _1068664))], (15099 ^ _779530) ^ [_1069012, _1069014, _1069016, _1069018, _1069020] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1069012, _1069014, _1069016), _1069018), _1069020)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1069012, _1069014)), hAPP(hAPP(c_Product__Type_OPair(_1069012, _1069014), _1069018), _1069020)), _1069016)))], (15105 ^ _779530) ^ [_1069147, _1069149, _1069151, _1069153, _1069155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1069147, _1069149)), hAPP(hAPP(c_Product__Type_OPair(_1069147, _1069149), _1069153), _1069155)), _1069151)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1069147, _1069149, _1069151), _1069153), _1069155)))], (15111 ^ _779530) ^ [_1069303, _1069305] : [c_Nitpick_Orefl_H(_1069303, _1069305), 15114 ^ _779530 : [(15115 ^ _779530) ^ [_1069381] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1069303, _1069303)), hAPP(hAPP(c_Product__Type_OPair(_1069303, _1069303), _1069381), _1069381)), _1069305)))]]], (15117 ^ _779530) ^ [_1069423, _1069425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1069423, _1069423)), hAPP(hAPP(c_Product__Type_OPair(_1069423, _1069423), 15118 ^ [_1069423, _1069425]), 15118 ^ [_1069423, _1069425])), _1069425)), -(c_Nitpick_Orefl_H(_1069423, _1069425))], (15124 ^ _779530) ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602] : [c_Equiv__Relations_Oequiv(_1069590, _1069592, _1069594), c_Equiv__Relations_Ocongruent(_1069590, tc_fun(_1069596, tc_HOL_Obool), _1069594, _1069598), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1069590, tc_fun(_1069596, tc_HOL_Obool)), _1069600), _1069598) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1069590, tc_fun(_1069596, tc_HOL_Obool)), _1069602), _1069598), hBOOL(hAPP(hAPP(c_member(tc_fun(_1069590, tc_HOL_Obool)), _1069600), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1069590), _1069592), _1069594))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1069590, tc_HOL_Obool)), _1069602), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1069590), _1069592), _1069594))), 15146 ^ _779530 : [(15147 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1069590), 15145 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602]), _1069592)))], (15150 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1069590), 15148 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602]), _1069592)))], (15152 ^ _779530) ^ [] : [-(hAPP(_1069598, 15145 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602]) = hAPP(_1069598, 15148 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602]))], (15154 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1069590, _1069590)), hAPP(hAPP(c_Product__Type_OPair(_1069590, _1069590), 15145 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602]), 15148 ^ [_1069590, _1069592, _1069594, _1069596, _1069598, _1069600, _1069602])), _1069594))]], -(_1069600 = _1069602)], (15158 ^ _779530) ^ [_1070575, _1070577] : [c_Relation_Oirrefl(_1070575, _1070577), 15161 ^ _779530 : [(15162 ^ _779530) ^ [_1070657] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1070575, _1070575)), hAPP(hAPP(c_Product__Type_OPair(_1070575, _1070575), _1070657), _1070657)), _1070577))]]], (15164 ^ _779530) ^ [_1070697, _1070699] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1070697, _1070697)), hAPP(hAPP(c_Product__Type_OPair(_1070697, _1070697), 15165 ^ [_1070697, _1070699]), 15165 ^ [_1070697, _1070699])), _1070699))), -(c_Relation_Oirrefl(_1070697, _1070699))], (15171 ^ _779530) ^ [_1070768, _1070770, _1070772, _1070774, _1070776] : [hBOOL(hAPP(hAPP(c_member(_1070768), _1070770), hAPP(c_Relation_OImage(_1070772, _1070768, _1070774), _1070776))), 15175 ^ _779530 : [(15176 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1070772, _1070768)), hAPP(hAPP(c_Product__Type_OPair(_1070772, _1070768), 15174 ^ [_1070768, _1070770, _1070772, _1070774, _1070776]), _1070770)), _1070774)))], (15178 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1070772), 15174 ^ [_1070768, _1070770, _1070772, _1070774, _1070776]), _1070776)))]]], (15180 ^ _779530) ^ [_1070992, _1070994, _1070996, _1070998] : [-(hAPP(c_Relation_OField(_1070992), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1070992, _1070992)), hAPP(hAPP(c_Product__Type_OPair(_1070992, _1070992), _1070994), _1070996)), _1070998)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1070992, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1070992), _1070994), hAPP(hAPP(c_Set_Oinsert(_1070992), _1070996), c_Orderings_Obot__class_Obot(tc_fun(_1070992, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1070992), _1070998)))], (15182 ^ _779530) ^ [_1071083, _1071085, _1071087, _1071089, _1071091] : [class_Groups_Ocomm__monoid__add(_1071083), class_Groups_Oordered__cancel__ab__semigroup__add(_1071083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071085), _1071087)), -(_1071087 = c_Orderings_Obot__class_Obot(tc_fun(_1071085, tc_HOL_Obool))), 15200 ^ _779530 : [(15201 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071085), 15199 ^ [_1071083, _1071085, _1071087, _1071089, _1071091]), _1071087)))], (15203 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071083), hAPP(_1071089, 15199 ^ [_1071083, _1071085, _1071087, _1071089, _1071091])), hAPP(_1071091, 15199 ^ [_1071083, _1071085, _1071087, _1071089, _1071091])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071083), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071085, _1071083), _1071089), _1071087)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1071085, _1071083), _1071091), _1071087))))], (15207 ^ _779530) ^ [_1071629, _1071631] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071629), _1071631)), -(_1071631 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1071629, 15211 ^ [_1071629, _1071631]), 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)), 15210 ^ [_1071629, _1071631]))))], (15215 ^ _779530) ^ [_1071760, _1071762] : [15216 ^ _779530 : [(15217 ^ _779530) ^ [_1071824, _1071826] : [_1071762 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1071760, _1071824), 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)), _1071826)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071760), _1071762)))], (15221 ^ _779530) ^ [_1071896, _1071898, _1071900, _1071902, _1071904, _1071906] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071896, tc_fun(_1071898, tc_HOL_Obool))), _1071900), _1071902), _1071904), _1071906)), -(hBOOL(hAPP(hAPP(_1071900, _1071904), _1071906))), -(hBOOL(hAPP(hAPP(_1071902, _1071904), _1071906)))], (15231 ^ _779530) ^ [_1072054, _1072056, _1072058, _1072060, _1072062, _1072064] : [15232 ^ _779530 : [(15233 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1072054, _1072056), _1072058))], (15235 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1072060, _1072056), _1072058))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1072062, tc_fun(_1072064, tc_HOL_Obool))), _1072060), _1072054), _1072056), _1072058)))], (15239 ^ _779530) ^ [_1072237, _1072239, _1072241, _1072243, _1072245, _1072247] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072237, tc_fun(_1072239, tc_HOL_Obool))), _1072241), _1072243), _1072245), _1072247)), 15242 ^ _779530 : [(15243 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1072241, _1072245), _1072247)))], (15245 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1072243, _1072245), _1072247)))]]], (15247 ^ _779530) ^ [_1072410, _1072412, _1072414, _1072416, _1072418, _1072420] : [hBOOL(hAPP(hAPP(_1072410, _1072412), _1072414)), hBOOL(hAPP(hAPP(_1072416, _1072412), _1072414)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072418, tc_fun(_1072420, tc_HOL_Obool))), _1072410), _1072416), _1072412), _1072414)))], (15257 ^ _779530) ^ [_1072631, _1072633, _1072635, _1072637] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1072631, tc_fun(_1072633, tc_HOL_Obool))), _1072635), _1072637))], (15259 ^ _779530) ^ [_1072703, _1072705, _1072707, _1072709, _1072711, _1072713, _1072715] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1072703, tc_fun(_1072705, tc_fun(_1072707, tc_HOL_Obool))), _1072709), _1072711), _1072713), _1072715)), 15263 ^ _779530 : [(15264 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072703), 15262 ^ [_1072703, _1072705, _1072707, _1072709, _1072711, _1072713, _1072715]), _1072709)))], (15266 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1072711, 15262 ^ [_1072703, _1072705, _1072707, _1072709, _1072711, _1072713, _1072715]), _1072713), _1072715)))]]], (15268 ^ _779530) ^ [_1072921, _1072923, _1072925, _1072927, _1072929, _1072931, _1072933] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1072921, tc_fun(_1072923, tc_fun(_1072925, tc_HOL_Obool))), _1072927), _1072929), _1072931), _1072933))), 15269 ^ _779530 : [(15270 ^ _779530) ^ [_1073006] : [hBOOL(hAPP(hAPP(c_member(_1072921), _1073006), _1072927)), hBOOL(hAPP(hAPP(hAPP(_1072929, _1073006), _1072931), _1072933))]]], (15278 ^ _779530) ^ [_1073174, _1073176, _1073178, _1073180, _1073182, _1073184] : [hBOOL(hAPP(hAPP(_1073174, _1073176), _1073178)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073180, tc_fun(_1073182, tc_HOL_Obool))), _1073174), _1073184), _1073176), _1073178)))], (15284 ^ _779530) ^ [_1073307, _1073309, _1073311, _1073313, _1073315, _1073317] : [hBOOL(hAPP(hAPP(_1073307, _1073309), _1073311)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073313, tc_fun(_1073315, tc_HOL_Obool))), _1073317), _1073307), _1073309), _1073311)))], (15290 ^ _779530) ^ [_1073440, _1073442, _1073444, _1073446, _1073448, _1073450] : [hBOOL(hAPP(hAPP(_1073440, _1073442), _1073444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073446, tc_fun(_1073448, tc_HOL_Obool))), _1073440), _1073450)), -(hBOOL(hAPP(hAPP(_1073450, _1073442), _1073444)))], (15300 ^ _779530) ^ [_1073631, _1073633, _1073635, _1073637, _1073639, _1073641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073631, tc_fun(_1073633, tc_HOL_Obool))), _1073635), _1073637)), hBOOL(hAPP(hAPP(_1073635, _1073639), _1073641)), -(hBOOL(hAPP(hAPP(_1073637, _1073639), _1073641)))], (15310 ^ _779530) ^ [_1073822, _1073824, _1073826, _1073828, _1073830, _1073832] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073822, tc_fun(_1073824, tc_HOL_Obool))), _1073826), _1073828), _1073830), _1073832)), -(hBOOL(hAPP(hAPP(_1073828, _1073830), _1073832)))], (15316 ^ _779530) ^ [_1073955, _1073957, _1073959, _1073961, _1073963, _1073965] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073955, tc_fun(_1073957, tc_HOL_Obool))), _1073959), _1073961), _1073963), _1073965)), -(hBOOL(hAPP(hAPP(_1073959, _1073963), _1073965)))], (15322 ^ _779530) ^ [_1074088, _1074090] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1074088, _1074088)), _1074090)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1074088), hAPP(c_Relation_OField(_1074088), _1074090))))], (15328 ^ _779530) ^ [_1074197] : [-(hAPP(c_Relation_OField(_1074197), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1074197, _1074197), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1074197, tc_HOL_Obool)))], (15330 ^ _779530) ^ [_1074238, _1074240, _1074242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1074238, _1074238), tc_HOL_Obool)), _1074240), _1074242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1074238, tc_HOL_Obool)), hAPP(c_Relation_OField(_1074238), _1074240)), hAPP(c_Relation_OField(_1074238), _1074242))))], (15336 ^ _779530) ^ [_1074383, _1074385, _1074387] : [-(hAPP(c_Relation_OField(_1074383), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1074383, _1074383), tc_HOL_Obool)), _1074385), _1074387)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074383, tc_HOL_Obool)), hAPP(c_Relation_OField(_1074383), _1074385)), hAPP(c_Relation_OField(_1074383), _1074387)))], (15338 ^ _779530) ^ [_1074450, _1074452, _1074454, _1074456, _1074458] : [class_Groups_Ocomm__monoid__add(_1074450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074452), _1074454)), hBOOL(hAPP(hAPP(c_member(_1074452), _1074456), _1074454)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074452, _1074450), _1074458), _1074454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074450), hAPP(_1074458, _1074456)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074452, _1074450), _1074458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074452, tc_HOL_Obool)), _1074454), hAPP(hAPP(c_Set_Oinsert(_1074452), _1074456), c_Orderings_Obot__class_Obot(tc_fun(_1074452, tc_HOL_Obool)))))))], (15352 ^ _779530) ^ [_1074775, _1074777, _1074779, _1074781, _1074783] : [class_Groups_Ocomm__monoid__add(_1074775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074777), _1074779)), hBOOL(hAPP(hAPP(c_member(_1074777), _1074781), _1074779)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074777, _1074775), _1074783), _1074779) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074775), hAPP(_1074783, _1074781)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074777, _1074775), _1074783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1074777, tc_HOL_Obool)), _1074779), hAPP(hAPP(c_Set_Oinsert(_1074777), _1074781), c_Orderings_Obot__class_Obot(tc_fun(_1074777, tc_HOL_Obool)))))))], (15366 ^ _779530) ^ [_1075100, _1075102, _1075104, _1075106, _1075108] : [hBOOL(hAPP(hAPP(c_member(_1075100), _1075102), c_Map_Oran(_1075104, _1075100, c_Map_Orestrict__map(_1075104, _1075100, _1075106, _1075108)))), 15370 ^ _779530 : [(15371 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1075104), 15369 ^ [_1075100, _1075102, _1075104, _1075106, _1075108]), _1075108)))], (15373 ^ _779530) ^ [] : [-(hAPP(_1075106, 15369 ^ [_1075100, _1075102, _1075104, _1075106, _1075108]) = hAPP(c_Option_Ooption_OSome(_1075100), _1075102))]]], (15375 ^ _779530) ^ [_1075302, _1075304, _1075306, _1075308, _1075310] : [-(hAPP(c_Map_Omap__add(_1075302, _1075304, _1075306, _1075308), _1075310) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1075304), _1075304, hAPP(_1075306, _1075310), c_Option_Ooption_OSome(_1075304)), hAPP(_1075308, _1075310)))], (15377 ^ _779530) ^ [_1075359, _1075361, _1075363, _1075365] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075359), _1075361)), -(hAPP(c_Set_Oimage(_1075359, _1075363, _1075365), _1075361) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1075363, tc_HOL_Obool), _1075359, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1075363, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1075359, tc_fun(_1075363, tc_HOL_Obool), tc_fun(_1075363, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1075363, tc_fun(tc_fun(_1075363, tc_HOL_Obool), tc_fun(_1075363, tc_HOL_Obool)), _1075359), c_Set_Oinsert(_1075363)), _1075365)), c_Orderings_Obot__class_Obot(tc_fun(_1075363, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1075363, tc_HOL_Obool))), _1075361))], (15383 ^ _779530) ^ [_1075598, _1075600, _1075602] : [class_Lattices_Oboolean__algebra(_1075598), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075598), _1075600), _1075602) = c_Orderings_Obot__class_Obot(_1075598), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1075598), _1075600), _1075602) = c_Orderings_Otop__class_Otop(_1075598), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1075598), _1075600) = _1075602)], (15397 ^ _779530) ^ [_1075833, _1075835, _1075837, _1075839] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075833), _1075835)), hBOOL(hAPP(hAPP(c_member(_1075833), _1075837), _1075835)), hBOOL(hAPP(hAPP(c_member(_1075833), _1075839), _1075835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1075833), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075833, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075833, tc_HOL_Obool)), _1075835), hAPP(hAPP(c_Set_Oinsert(_1075833), _1075837), c_Orderings_Obot__class_Obot(tc_fun(_1075833, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1075833), _1075839), c_Orderings_Obot__class_Obot(tc_fun(_1075833, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1075833), _1075835))))], (15411 ^ _779530) ^ [_1076188, _1076190, _1076192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1076188), _1076190)), hBOOL(hAPP(hAPP(c_member(_1076188), _1076192), _1076190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1076188), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1076188, tc_HOL_Obool)), _1076190), hAPP(hAPP(c_Set_Oinsert(_1076188), _1076192), c_Orderings_Obot__class_Obot(tc_fun(_1076188, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1076188), _1076190))))], (15421 ^ _779530) ^ [_1076421, _1076423] : [-(hBOOL(hAPP(hAPP(c_member(_1076421), _1076423), c_Orderings_Otop__class_Otop(tc_fun(_1076421, tc_HOL_Obool)))))], (15423 ^ _779530) ^ [_1076470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1076470)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1076470), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1076470), c_Orderings_Otop__class_Otop(tc_fun(_1076470, tc_HOL_Obool)))))], (15429 ^ _779530) ^ [_1076585] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1076585), c_Orderings_Otop__class_Otop(tc_fun(_1076585, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1076585)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1076585), tc_HOL_Obool)))))], (15435 ^ _779530) ^ [_1076721, _1076723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1076721, _1076723)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1076721, _1076723), tc_HOL_Obool)))), 15438 ^ _779530 : [(15439 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1076721), c_Orderings_Otop__class_Otop(tc_fun(_1076721, tc_HOL_Obool)))))], (15441 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1076723), c_Orderings_Otop__class_Otop(tc_fun(_1076723, tc_HOL_Obool)))))]]], (15443 ^ _779530) ^ [_1076886, _1076888] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1076886, _1076888)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1076886, _1076888), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076886), c_Orderings_Otop__class_Otop(tc_fun(_1076886, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076888), c_Orderings_Otop__class_Otop(tc_fun(_1076888, tc_HOL_Obool))))], (15453 ^ _779530) ^ [_1077083, _1077085] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1077083), c_Orderings_Otop__class_Otop(tc_fun(_1077083, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077085), c_Orderings_Otop__class_Otop(tc_fun(_1077085, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1077083, _1077085)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1077083, _1077085), tc_HOL_Obool)))))], (15463 ^ _779530) ^ [_1077278, _1077280] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1077278), c_Orderings_Otop__class_Otop(tc_fun(_1077278, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1077278), _1077280) = hAPP(c_Finite__Set_Ocard(_1077278), c_Orderings_Otop__class_Otop(tc_fun(_1077278, tc_HOL_Obool))), -(_1077280 = c_Orderings_Otop__class_Otop(tc_fun(_1077278, tc_HOL_Obool)))], (15473 ^ _779530) ^ [_1077465] : [-(hAPP(c_Set_OPow(_1077465), c_Orderings_Otop__class_Otop(tc_fun(_1077465, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1077465, tc_HOL_Obool), tc_HOL_Obool)))], (15475 ^ _779530) ^ [_1077506, _1077508, _1077510, _1077512] : [class_Groups_Oab__semigroup__add(_1077506), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077506), _1077508), _1077510)), _1077512) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077506), _1077508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077506), _1077510), _1077512)))], (15481 ^ _779530) ^ [_1077649, _1077651, _1077653, _1077655] : [class_Groups_Ocancel__semigroup__add(_1077649), 15484 ^ _779530 : [(15485 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077649), _1077651), _1077653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077649), _1077651), _1077655), -(_1077653 = _1077655)], (15491 ^ _779530) ^ [] : [_1077653 = _1077655, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077649), _1077651), _1077653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077649), _1077651), _1077655))]]], (15497 ^ _779530) ^ [_1077914, _1077916, _1077918, _1077920] : [class_Groups_Ocancel__semigroup__add(_1077914), 15500 ^ _779530 : [(15501 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077914), _1077916), _1077918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077914), _1077920), _1077918), -(_1077916 = _1077920)], (15507 ^ _779530) ^ [] : [_1077916 = _1077920, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077914), _1077916), _1077918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1077914), _1077920), _1077918))]]], (15513 ^ _779530) ^ [_1078179, _1078181, _1078183, _1078185] : [class_Groups_Ocancel__semigroup__add(_1078179), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078179), _1078181), _1078183) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078179), _1078181), _1078185), -(_1078183 = _1078185)], (15523 ^ _779530) ^ [_1078346, _1078348, _1078350, _1078352] : [class_Groups_Ocancel__ab__semigroup__add(_1078346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078346), _1078348), _1078350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078346), _1078348), _1078352), -(_1078350 = _1078352)], (15533 ^ _779530) ^ [_1078513, _1078515, _1078517, _1078519] : [class_Groups_Ocancel__semigroup__add(_1078513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078513), _1078515), _1078517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078513), _1078519), _1078517), -(_1078515 = _1078519)], (15543 ^ _779530) ^ [_1078680, _1078682, _1078684] : [class_Orderings_Otop(_1078680), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1078682, _1078680)), _1078684) = c_Orderings_Otop__class_Otop(_1078680))], (15549 ^ _779530) ^ [_1078777, _1078779, _1078781, _1078783] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1078777), 15552 ^ _779530 : [(15553 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078777), _1078779), _1078781)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078777), _1078783), _1078781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078777), _1078779), _1078783)))], (15559 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078777), _1078779), _1078783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1078777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078777), _1078779), _1078781)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1078777), _1078783), _1078781))))]]], (15565 ^ _779530) ^ [_1079084, _1079086, _1079088, _1079090] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1079084), 15568 ^ _779530 : [(15569 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079084), _1079086), _1079088)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079084), _1079086), _1079090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079084), _1079088), _1079090)))], (15575 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079084), _1079088), _1079090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079084), _1079086), _1079088)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079084), _1079086), _1079090))))]]], (15581 ^ _779530) ^ [_1079391, _1079393, _1079395, _1079397] : [class_Groups_Oordered__ab__semigroup__add(_1079391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079391), _1079393), _1079395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079391), _1079393), _1079397)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079391), _1079395), _1079397))))], (15591 ^ _779530) ^ [_1079586, _1079588, _1079590, _1079592] : [class_Groups_Oordered__ab__semigroup__add(_1079586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079586), _1079588), _1079590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079586), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079586), _1079592), _1079588)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079586), _1079592), _1079590))))], (15601 ^ _779530) ^ [_1079781, _1079783, _1079785, _1079787, _1079789] : [class_Groups_Oordered__ab__semigroup__add(_1079781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079781), _1079783), _1079785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079781), _1079787), _1079789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079781), _1079783), _1079787)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079781), _1079785), _1079789))))], (15615 ^ _779530) ^ [_1080052, _1080054, _1080056, _1080058] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1080052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080052), _1080054), _1080056)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080052), _1080058), _1080056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080052), _1080054), _1080058)))], (15625 ^ _779530) ^ [_1080247, _1080249, _1080251, _1080253] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1080247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080247), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080247), _1080249), _1080251)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080247), _1080249), _1080253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080247), _1080251), _1080253)))], (15635 ^ _779530) ^ [_1080442, _1080444, _1080446, _1080448] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1080442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080442), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080442), _1080444), _1080446)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080442), _1080444), _1080448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080442), _1080446), _1080448)))], (15645 ^ _779530) ^ [_1080637, _1080639, _1080641, _1080643] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1080637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080637), _1080639), _1080641)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080637), _1080643), _1080641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080637), _1080639), _1080643)))], (15655 ^ _779530) ^ [_1080832, _1080834, _1080836, _1080838, _1080840] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1080832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080832), _1080834), _1080836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080832), _1080838), _1080840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080832), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080832), _1080834), _1080838)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080832), _1080836), _1080840))))], (15669 ^ _779530) ^ [_1081103, _1081105, _1081107, _1081109] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1081103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081103), _1081105), _1081107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081103), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081103), _1081109), _1081105)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081103), _1081109), _1081107))))], (15679 ^ _779530) ^ [_1081298, _1081300, _1081302, _1081304] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1081298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081298), _1081300), _1081302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081298), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081298), _1081300), _1081304)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081298), _1081302), _1081304))))], (15689 ^ _779530) ^ [_1081493, _1081495, _1081497, _1081499] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1081493), 15692 ^ _779530 : [(15693 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081493), _1081495), _1081497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081493), _1081495), _1081499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081493), _1081497), _1081499)))], (15699 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081493), _1081497), _1081499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081493), _1081495), _1081497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081493), _1081495), _1081499))))]]], (15705 ^ _779530) ^ [_1081800, _1081802, _1081804, _1081806] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1081800), 15708 ^ _779530 : [(15709 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081800), _1081802), _1081804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081800), _1081806), _1081804))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081800), _1081802), _1081806)))], (15715 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081800), _1081802), _1081806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081800), _1081802), _1081804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081800), _1081806), _1081804))))]]], (15721 ^ _779530) ^ [_1082107, _1082109, _1082111] : [class_Groups_Ogroup__add(_1082107), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082107), _1082109), _1082111)), _1082111) = _1082109)], (15727 ^ _779530) ^ [_1082216, _1082218, _1082220] : [class_Groups_Ogroup__add(_1082216), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082216), _1082218), _1082220)), _1082220) = _1082218)], (15733 ^ _779530) ^ [_1082325, _1082327, _1082329] : [class_Groups_Oab__group__add(_1082325), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082325), _1082327), _1082329)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082325), hAPP(c_Groups_Ouminus__class_Ouminus(_1082325), _1082327)), hAPP(c_Groups_Ouminus__class_Ouminus(_1082325), _1082329)))], (15739 ^ _779530) ^ [_1082464, _1082466, _1082468] : [class_Groups_Ogroup__add(_1082464), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082464), _1082466), _1082468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082464), hAPP(c_Groups_Ouminus__class_Ouminus(_1082464), _1082468)), hAPP(c_Groups_Ouminus__class_Ouminus(_1082464), _1082466)))], (15745 ^ _779530) ^ [_1082603, _1082605, _1082607] : [class_Groups_Ogroup__add(_1082603), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082603), _1082605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082603), hAPP(c_Groups_Ouminus__class_Ouminus(_1082603), _1082605)), _1082607)) = _1082607)], (15751 ^ _779530) ^ [_1082722, _1082724, _1082726] : [class_Groups_Ogroup__add(_1082722), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082722), hAPP(c_Groups_Ouminus__class_Ouminus(_1082722), _1082724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082722), _1082724), _1082726)) = _1082726)], (15757 ^ _779530) ^ [_1082841, _1082843] : [-(hBOOL(hAPP(hAPP(c_member(_1082841), _1082843), c_Orderings_Otop__class_Otop(tc_fun(_1082841, tc_HOL_Obool)))))], (15759 ^ _779530) ^ [_1082878, _1082880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1082878, _1082880)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1082878, _1082880), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1082880), c_Orderings_Otop__class_Otop(tc_fun(_1082880, tc_HOL_Obool)))))], (15765 ^ _779530) ^ [_1083015, _1083017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083015), _1083017)), _1083015))], (15767 ^ _779530) ^ [_1083063, _1083065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083063), _1083065)), _1083065))], (15769 ^ _779530) ^ [_1083117, _1083119, _1083121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083117), _1083119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083117), _1083121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083119), _1083121)))], (15775 ^ _779530) ^ [_1083236, _1083238, _1083240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083238), _1083240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083236), _1083238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083236), _1083240))))], (15781 ^ _779530) ^ [_1083361, _1083363, _1083365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083361), _1083363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083361), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083363), _1083365))))], (15787 ^ _779530) ^ [_1083472, _1083474, _1083476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083472), _1083474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083472), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083476), _1083474))))], (15793 ^ _779530) ^ [_1083583, _1083585, _1083587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083583), _1083585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083583), _1083587)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083585), _1083587))))], (15799 ^ _779530) ^ [_1083706, _1083708, _1083710, _1083712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083706), _1083708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083710), _1083712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083706), _1083710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083708), _1083712))))], (15809 ^ _779530) ^ [_1083897, _1083899, _1083901, _1083903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083897), _1083899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083901), _1083899) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083897), _1083903), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1083901), _1083903)))], (15819 ^ _779530) ^ [_1084078, _1084080, _1084082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084078), _1084080)), _1084082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084078), _1084082)))], (15825 ^ _779530) ^ [_1084189, _1084191, _1084193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084189), _1084191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084191), _1084193))))], (15831 ^ _779530) ^ [_1084300, _1084302, _1084304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084300), _1084302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1084300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084304), _1084302))))], (15837 ^ _779530) ^ [_1084420] : [c_Orderings_Otop__class_Otop(tc_fun(_1084420, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1084420, tc_HOL_Obool))], (15839 ^ _779530) ^ [_1084453] : [class_Finite__Set_Ofinite(_1084453), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1084453), c_Orderings_Otop__class_Otop(tc_fun(_1084453, tc_HOL_Obool)))))], (15845 ^ _779530) ^ [_1084544, _1084546, _1084548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084544), _1084546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084544), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084546), _1084548))))], (15851 ^ _779530) ^ [_1084655, _1084657, _1084659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084655), _1084657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084659), _1084657))))], (15857 ^ _779530) ^ [_1084766, _1084768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084768), _1084766))))], (15859 ^ _779530) ^ [_1084802, _1084804] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084802), _1084804))))], (15861 ^ _779530) ^ [_1084853, _1084855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084853), _1084855)), -(_1084855 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084853), 15864 ^ [_1084853, _1084855]))], (15868 ^ _779530) ^ [_1084960, _1084962] : [15869 ^ _779530 : [(15870 ^ _779530) ^ [_1085010] : [_1084962 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1084960), _1085010)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1084960), _1084962)))], (15874 ^ _779530) ^ [_1085092, _1085094, _1085096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085092), _1085094)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085092), _1085096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085094), _1085096)))], (15880 ^ _779530) ^ [_1085211, _1085213, _1085215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085213), _1085215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085211), _1085213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085211), _1085215))))], (15886 ^ _779530) ^ [_1085336, _1085338, _1085340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085336), _1085338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085338), _1085340))))], (15892 ^ _779530) ^ [_1085447, _1085449, _1085451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085447), _1085449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085447), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085451), _1085449))))], (15898 ^ _779530) ^ [_1085558, _1085560, _1085562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085558), _1085560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085558), _1085562)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085560), _1085562))))], (15904 ^ _779530) ^ [_1085681, _1085683, _1085685, _1085687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085681), _1085683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085685), _1085687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085681), _1085685)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085683), _1085687))))], (15914 ^ _779530) ^ [_1085872, _1085874, _1085876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085872), _1085874)), _1085876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085874), _1085876)))], (15920 ^ _779530) ^ [_1085983, _1085985, _1085987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1085983), _1085985)), _1085987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085983), _1085987)))], (15926 ^ _779530) ^ [_1086094, _1086096, _1086098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086094), _1086096)), _1086098)), 15929 ^ _779530 : [(15930 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1086094), _1086098)))], (15932 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1086096), _1086098)))]]], (15934 ^ _779530) ^ [_1086245, _1086247] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1086245, tc_HOL_Obool)), _1086247), c_Orderings_Otop__class_Otop(tc_fun(_1086245, tc_HOL_Obool)))))], (15936 ^ _779530) ^ [_1086285, _1086287] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086285), _1086287)), _1086287) = _1086285)], (15938 ^ _779530) ^ [_1086322, _1086324] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086322), _1086324)), _1086322) = _1086324)], (15940 ^ _779530) ^ [_1086359, _1086361, _1086363] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086359), _1086361)), _1086363) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086361), _1086363)))], (15942 ^ _779530) ^ [_1086410, _1086412, _1086414] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086410), _1086412)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086410), _1086414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086412), _1086414))], (15944 ^ _779530) ^ [_1086461, _1086463, _1086465] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086461), _1086463)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086465), _1086463)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086461), _1086465))], (15946 ^ _779530) ^ [_1086512, _1086514] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086512, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1086512, tc_HOL_Obool))), _1086514) = c_Orderings_Otop__class_Otop(tc_fun(_1086512, tc_HOL_Obool)))], (15948 ^ _779530) ^ [_1086558, _1086560] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086558, tc_HOL_Obool)), _1086560), c_Orderings_Otop__class_Otop(tc_fun(_1086558, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1086558, tc_HOL_Obool)))], (15950 ^ _779530) ^ [_1086604, _1086606] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086604, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1086604, tc_HOL_Obool))), _1086606) = _1086606)], (15952 ^ _779530) ^ [_1086645, _1086647] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086645, tc_HOL_Obool)), _1086647), c_Orderings_Otop__class_Otop(tc_fun(_1086645, tc_HOL_Obool))) = _1086647)], (15954 ^ _779530) ^ [_1086686, _1086688, _1086690, _1086692, _1086694] : [c_Fun_Oinj__on(_1086686, _1086688, _1086690, c_Orderings_Otop__class_Otop(tc_fun(_1086686, tc_HOL_Obool))), 15957 ^ _779530 : [(15958 ^ _779530) ^ [] : [hAPP(_1086690, _1086692) = hAPP(_1086690, _1086694), -(_1086692 = _1086694)], (15964 ^ _779530) ^ [] : [_1086692 = _1086694, -(hAPP(_1086690, _1086692) = hAPP(_1086690, _1086694))]]], (15970 ^ _779530) ^ [_1086943, _1086945, _1086947, _1086949, _1086951] : [c_Fun_Oinj__on(_1086943, _1086945, _1086947, c_Orderings_Otop__class_Otop(tc_fun(_1086943, tc_HOL_Obool))), hAPP(_1086947, _1086949) = hAPP(_1086947, _1086951), -(_1086949 = _1086951)], (15980 ^ _779530) ^ [_1087110, _1087112, _1087114, _1087116, _1087118] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1087110, _1087112, _1087114), _1087116), _1087118), c_Orderings_Obot__class_Obot(tc_fun(_1087112, tc_HOL_Obool))) = _1087118)], (15982 ^ _779530) ^ [_1087159, _1087161, _1087163] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087159), _1087161)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087159), _1087163)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087159), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087159, tc_HOL_Obool)), _1087161), _1087163))), hAPP(c_Finite__Set_Ocard(_1087159), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087159, tc_HOL_Obool)), _1087161), _1087163))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087159), _1087161)), hAPP(c_Finite__Set_Ocard(_1087159), _1087163)))], (15992 ^ _779530) ^ [_1087416, _1087418, _1087420] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087416), _1087418)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087416), _1087420)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087416), _1087418)), hAPP(c_Finite__Set_Ocard(_1087416), _1087420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087416), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087416, tc_HOL_Obool)), _1087418), _1087420))), hAPP(c_Finite__Set_Ocard(_1087416), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087416, tc_HOL_Obool)), _1087418), _1087420))))], (16002 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (16004 ^ _779530) ^ [_1087697, _1087699, _1087701, _1087703, _1087705] : [class_Groups_Ocomm__monoid__add(_1087697), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087699, _1087697), hAPP(hAPP(c_COMBS(_1087699, _1087697, _1087697), hAPP(hAPP(c_COMBB(_1087697, tc_fun(_1087697, _1087697), _1087699), c_Groups_Oplus__class_Oplus(_1087697)), _1087701)), _1087703)), _1087705) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087697), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087699, _1087697), _1087701), _1087705)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087699, _1087697), _1087703), _1087705)))], (16010 ^ _779530) ^ [_1087898] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1087898, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1087898), hAPP(c_COMBK(tc_HOL_Obool, _1087898), c_fTrue)))], (16012 ^ _779530) ^ [_1087937, _1087939, _1087941, _1087943, _1087945] : [-(hAPP(c_Set_Oimage(_1087937, _1087939, hAPP(hAPP(c_COMBB(_1087941, _1087939, _1087937), _1087943), _1087945)), c_Orderings_Otop__class_Otop(tc_fun(_1087937, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1087941, _1087939, _1087943), hAPP(c_Set_Oimage(_1087937, _1087941, _1087945), c_Orderings_Otop__class_Otop(tc_fun(_1087937, tc_HOL_Obool)))))], (16014 ^ _779530) ^ [_1088009, _1088011] : [class_Orderings_Otop(_1088009), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088009), _1088011), c_Orderings_Otop__class_Otop(_1088009))))], (16020 ^ _779530) ^ [_1088102, _1088104] : [class_Lattices_Obounded__lattice__top(_1088102), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1088102), _1088104), c_Orderings_Otop__class_Otop(_1088102)) = c_Orderings_Otop__class_Otop(_1088102))], (16026 ^ _779530) ^ [_1088201, _1088203] : [class_Lattices_Obounded__lattice__top(_1088201), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1088201), c_Orderings_Otop__class_Otop(_1088201)), _1088203) = c_Orderings_Otop__class_Otop(_1088201))], (16032 ^ _779530) ^ [_1088300, _1088302] : [class_Lattices_Obounded__lattice__top(_1088300), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1088300), c_Orderings_Otop__class_Otop(_1088300)), _1088302) = _1088302)], (16038 ^ _779530) ^ [_1088395, _1088397] : [class_Lattices_Obounded__lattice__top(_1088395), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1088395), _1088397), c_Orderings_Otop__class_Otop(_1088395)) = _1088397)], (16044 ^ _779530) ^ [_1088490, _1088492, _1088494] : [class_Lattices_Obounded__lattice__top(_1088490), 16047 ^ _779530 : [(16048 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1088490), _1088492), _1088494) = c_Orderings_Otop__class_Otop(_1088490), 16051 ^ _779530 : [(16052 ^ _779530) ^ [] : [-(_1088492 = c_Orderings_Otop__class_Otop(_1088490))], (16054 ^ _779530) ^ [] : [-(_1088494 = c_Orderings_Otop__class_Otop(_1088490))]]], (16056 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1088490), _1088492), _1088494) = c_Orderings_Otop__class_Otop(_1088490)), _1088492 = c_Orderings_Otop__class_Otop(_1088490), _1088494 = c_Orderings_Otop__class_Otop(_1088490)]]], (16066 ^ _779530) ^ [_1088817] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1088817), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1088817)), c_Option_Ooption_ONone(_1088817)), hAPP(c_Set_Oimage(_1088817, tc_Option_Ooption(_1088817), c_Option_Ooption_OSome(_1088817)), c_Orderings_Otop__class_Otop(tc_fun(_1088817, tc_HOL_Obool)))))], (16068 ^ _779530) ^ [_1088875, _1088877, _1088879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088875), _1088877)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088875), _1088879)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088875, tc_HOL_Obool)), _1088877), _1088879) = c_Orderings_Obot__class_Obot(tc_fun(_1088875, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1088875), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088875, tc_HOL_Obool)), _1088877), _1088879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1088875), _1088877)), hAPP(c_Finite__Set_Ocard(_1088875), _1088879)))], (16082 ^ _779530) ^ [_1089174, _1089176, _1089178, _1089180, _1089182] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1089174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089174), _1089176), _1089178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089174), _1089180), _1089182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089174), _1089176), _1089180)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089174), _1089178), _1089182))))], (16096 ^ _779530) ^ [_1089445, _1089447, _1089449, _1089451, _1089453] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1089445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089445), _1089447), _1089449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089445), _1089451), _1089453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089445), _1089447), _1089451)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089445), _1089449), _1089453))))], (16110 ^ _779530) ^ [_1089716, _1089718, _1089720, _1089722] : [c_Fun_Oinj__on(_1089716, _1089718, _1089720, _1089722), -(hAPP(c_Finite__Set_Ocard(_1089718), hAPP(c_Set_Oimage(_1089716, _1089718, _1089720), _1089722)) = hAPP(c_Finite__Set_Ocard(_1089716), _1089722))], (16116 ^ _779530) ^ [_1089835, _1089837, _1089839] : [class_Groups_Ogroup__add(_1089835), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1089835), _1089837), hAPP(c_Groups_Ouminus__class_Ouminus(_1089835), _1089839)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089835), _1089837), _1089839))], (16122 ^ _779530) ^ [_1089954, _1089956, _1089958] : [class_Groups_Oab__group__add(_1089954), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1089954), _1089956), _1089958) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089954), _1089956), hAPP(c_Groups_Ouminus__class_Ouminus(_1089954), _1089958)))], (16128 ^ _779530) ^ [_1090073, _1090075, _1090077] : [class_Groups_Ogroup__add(_1090073), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1090073), _1090075), _1090077) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090073), _1090075), hAPP(c_Groups_Ouminus__class_Ouminus(_1090073), _1090077)))], (16134 ^ _779530) ^ [_1090192, _1090194, _1090196, _1090198] : [-(hBOOL(hAPP(hAPP(c_member(_1090192), hAPP(_1090194, _1090196)), hAPP(c_Set_Oimage(_1090198, _1090192, _1090194), c_Orderings_Otop__class_Otop(tc_fun(_1090198, tc_HOL_Obool))))))], (16136 ^ _779530) ^ [_1090243, _1090245, _1090247, _1090249, _1090251] : [_1090243 = hAPP(_1090245, _1090247), -(hBOOL(hAPP(hAPP(c_member(_1090249), _1090243), hAPP(c_Set_Oimage(_1090251, _1090249, _1090245), c_Orderings_Otop__class_Otop(tc_fun(_1090251, tc_HOL_Obool))))))], (16142 ^ _779530) ^ [_1090388, _1090390, _1090392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090390), _1090392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090388), _1090392)), _1090390)))], (16148 ^ _779530) ^ [_1090507, _1090509, _1090511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090507), _1090511)), _1090509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090507), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090509), _1090511))))], (16154 ^ _779530) ^ [_1090628, _1090630] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1090628), _1090630))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090630), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090628), _1090630)) = _1090628)], (16160 ^ _779530) ^ [_1090681, _1090683, _1090685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1090681), _1090683)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090683), _1090685)), _1090681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090683), _1090681)), _1090685))], (16166 ^ _779530) ^ [_1090818, _1090820, _1090822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1090818), _1090820)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090820), _1090818)), _1090822) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090820), _1090822)), _1090818))], (16172 ^ _779530) ^ [_1090955, _1090957, _1090959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1090955), _1090957)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090959), _1090957)), _1090955) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1090959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1090957), _1090955)))], (16178 ^ _779530) ^ [_1091092, _1091094, _1091096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091092), _1091094)), 16181 ^ _779530 : [(16182 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091094), _1091092) = _1091096, -(_1091094 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091096), _1091092))], (16188 ^ _779530) ^ [] : [_1091094 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091096), _1091092), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091094), _1091092) = _1091096)]]], (16194 ^ _779530) ^ [_1091351, _1091353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091351), _1091353)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091353), _1091351)), _1091351) = _1091353)], (16200 ^ _779530) ^ [_1091462, _1091464, _1091466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091462), _1091464)), 16203 ^ _779530 : [(16204 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091464), _1091462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091466), _1091462)), _1091464)))], (16210 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091466), _1091462)), _1091464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091464), _1091462))))]]], (16216 ^ _779530) ^ [_1091751, _1091753, _1091755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091751), _1091753)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091755), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091753), _1091751)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091755), _1091753)), _1091751))], (16222 ^ _779530) ^ [_1091888, _1091890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091888), _1091890)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1091890), _1091888)) = _1091890)], (16228 ^ _779530) ^ [_1091999, _1092001, _1092003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091999), _1092001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1092003), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092001), _1092003)), _1091999))))], (16234 ^ _779530) ^ [_1092140, _1092142, _1092144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1092140), _1092142)), _1092144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1092140), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092144), _1092142))))], (16240 ^ _779530) ^ [_1092259, _1092261, _1092263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1092259), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092263), _1092261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1092259), _1092261)), _1092263)))], (16246 ^ _779530) ^ [_1092384, _1092386, _1092388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1092384), _1092386)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1092388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1092386), _1092384)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092388), _1092384)), _1092386))], (16252 ^ _779530) ^ [_1092521, _1092523] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092521, tc_HOL_Obool)), _1092523), c_Orderings_Otop__class_Otop(tc_fun(_1092521, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1092521, tc_HOL_Obool)))], (16254 ^ _779530) ^ [_1092567, _1092569, _1092571, _1092573, _1092575] : [hAPP(c_Set_Oimage(_1092567, _1092569, _1092571), c_Orderings_Otop__class_Otop(tc_fun(_1092567, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1092569, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1092569, _1092573, _1092575), c_Orderings_Otop__class_Otop(tc_fun(_1092569, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1092573, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1092567, _1092573, hAPP(c_Fun_Ocomp(_1092569, _1092573, _1092567, _1092575), _1092571)), c_Orderings_Otop__class_Otop(tc_fun(_1092567, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1092573, tc_HOL_Obool)))], (16264 ^ _779530) ^ [_1092826, _1092828, _1092830, _1092832, _1092834] : [c_Fun_Oinj__on(_1092826, _1092828, _1092830, c_Orderings_Otop__class_Otop(tc_fun(_1092826, tc_HOL_Obool))), 16267 ^ _779530 : [(16268 ^ _779530) ^ [] : [hAPP(c_Set_Oimage(_1092826, _1092828, _1092830), _1092832) = hAPP(c_Set_Oimage(_1092826, _1092828, _1092830), _1092834), -(_1092832 = _1092834)], (16274 ^ _779530) ^ [] : [_1092832 = _1092834, -(hAPP(c_Set_Oimage(_1092826, _1092828, _1092830), _1092832) = hAPP(c_Set_Oimage(_1092826, _1092828, _1092830), _1092834))]]], (16280 ^ _779530) ^ [_1093107, _1093109, _1093111, _1093113, _1093115] : [c_Fun_Oinj__on(_1093107, _1093109, _1093111, c_Orderings_Otop__class_Otop(tc_fun(_1093107, tc_HOL_Obool))), c_Fun_Oinj__on(_1093113, _1093107, _1093115, c_Orderings_Otop__class_Otop(tc_fun(_1093113, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1093113, _1093109, hAPP(c_Fun_Ocomp(_1093107, _1093109, _1093113, _1093111), _1093115), c_Orderings_Otop__class_Otop(tc_fun(_1093113, tc_HOL_Obool))))], (16290 ^ _779530) ^ [_1093306] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093306, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1093306, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1093306, tc_HOL_Obool)))], (16292 ^ _779530) ^ [_1093347] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093347, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1093347, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1093347, tc_HOL_Obool)))], (16294 ^ _779530) ^ [_1093388, _1093390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), _1093390)), 16297 ^ _779530 : [(16298 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093388, tc_HOL_Obool)), _1093390))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), c_Orderings_Otop__class_Otop(tc_fun(_1093388, tc_HOL_Obool)))))], (16304 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), c_Orderings_Otop__class_Otop(tc_fun(_1093388, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093388, tc_HOL_Obool)), _1093390))))]]], (16310 ^ _779530) ^ [_1093666, _1093668] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093666, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093666, tc_HOL_Obool)), _1093668)), _1093668) = c_Orderings_Otop__class_Otop(tc_fun(_1093666, tc_HOL_Obool)))], (16312 ^ _779530) ^ [_1093715, _1093717] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093715, tc_HOL_Obool)), _1093717), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093715, tc_HOL_Obool)), _1093717)) = c_Orderings_Otop__class_Otop(tc_fun(_1093715, tc_HOL_Obool)))], (16314 ^ _779530) ^ [_1093764, _1093766] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1093764, tc_HOL_Obool)), _1093766) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1093764, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1093764, tc_HOL_Obool))), _1093766))], (16316 ^ _779530) ^ [_1093813, _1093815, _1093817, _1093819, _1093821] : [class_Groups_Ocomm__monoid__add(_1093813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093815), _1093817)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1093815, _1093813), hAPP(hAPP(c_COMBS(_1093815, _1093813, _1093813), hAPP(hAPP(c_COMBB(_1093813, tc_fun(_1093813, _1093813), _1093815), c_Groups_Oplus__class_Oplus(_1093813)), _1093819)), _1093821)), _1093817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093813), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1093815, _1093813), _1093819), _1093817)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1093815, _1093813), _1093821), _1093817)))], (16326 ^ _779530) ^ [_1094080, _1094082] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094080), hAPP(c_Set_OCollect(_1094080), _1094082))), 16329 ^ _779530 : [(16330 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094080), hAPP(c_Set_OCollect(_1094080), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1094080), c_fNot), _1094082)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1094080), c_Orderings_Otop__class_Otop(tc_fun(_1094080, tc_HOL_Obool)))))], (16336 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094080), c_Orderings_Otop__class_Otop(tc_fun(_1094080, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1094080), hAPP(c_Set_OCollect(_1094080), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1094080), c_fNot), _1094082)))))]]], (16342 ^ _779530) ^ [_1094410, _1094412, _1094414, _1094416] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1094410, tc_fun(_1094412, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1094410, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1094412, tc_HOL_Obool), tc_fun(_1094412, tc_HOL_Obool), _1094410), hAPP(c_COMBC(_1094412, tc_fun(_1094412, tc_HOL_Obool), tc_HOL_Obool), c_member(_1094412))), _1094414)), _1094416)), -(hBOOL(hAPP(hAPP(c_member(_1094412), _1094416), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1094410, tc_fun(_1094412, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1094410, tc_HOL_Obool))), _1094414))))], (16348 ^ _779530) ^ [_1094629, _1094631, _1094633, _1094635] : [hBOOL(hAPP(hAPP(c_member(_1094631), _1094635), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1094629, tc_fun(_1094631, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1094629, tc_HOL_Obool))), _1094633))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1094629, tc_fun(_1094631, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1094629, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1094631, tc_HOL_Obool), tc_fun(_1094631, tc_HOL_Obool), _1094629), hAPP(c_COMBC(_1094631, tc_fun(_1094631, tc_HOL_Obool), tc_HOL_Obool), c_member(_1094631))), _1094633)), _1094635)))], (16354 ^ _779530) ^ [_1094854, _1094856, _1094858, _1094860, _1094862] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094854), hAPP(c_Set_Oimage(_1094856, _1094854, _1094858), c_Orderings_Otop__class_Otop(tc_fun(_1094856, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1094860), hAPP(c_Set_Oimage(_1094856, _1094860, hAPP(hAPP(c_COMBB(_1094854, _1094860, _1094856), _1094862), _1094858)), c_Orderings_Otop__class_Otop(tc_fun(_1094856, tc_HOL_Obool))))))], (16360 ^ _779530) ^ [_1095021, _1095023, _1095025, _1095027] : [c_Fun_Oinj__on(_1095021, _1095023, _1095025, c_Orderings_Otop__class_Otop(tc_fun(_1095021, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1095021, _1095023, c_Orderings_Otop__class_Otop(tc_fun(_1095021, tc_HOL_Obool)), _1095025), hAPP(_1095025, _1095027)) = _1095027)], (16366 ^ _779530) ^ [_1095148, _1095150, _1095152, _1095154, _1095156, _1095158, _1095160] : [c_Finite__Set_Ofolding__image__simple(_1095148, _1095150, _1095152, _1095154, _1095156, _1095158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095150), _1095160)), -(hAPP(_1095158, _1095160) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1095148, _1095150, _1095152), _1095156), _1095154), _1095160))], (16376 ^ _779530) ^ [_1095345, _1095347, _1095349, _1095351, _1095353, _1095355, _1095357] : [c_Finite__Set_Ofolding__image(_1095345, _1095347, _1095349, _1095351, _1095353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095347), _1095355)), -(hAPP(hAPP(_1095353, _1095357), _1095355) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1095345, _1095347, _1095349), _1095357), _1095351), _1095355))], (16386 ^ _779530) ^ [_1095546, _1095548, _1095550] : [-(c_Map_Odom(_1095546, _1095548, hAPP(hAPP(c_COMBB(_1095548, tc_Option_Ooption(_1095548), _1095546), c_Option_Ooption_OSome(_1095548)), _1095550)) = c_Orderings_Otop__class_Otop(tc_fun(_1095546, tc_HOL_Obool)))], (16388 ^ _779530) ^ [_1095596, _1095598, _1095600] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095596), _1095598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095596), _1095598)), hAPP(c_Finite__Set_Ocard(_1095596), hAPP(hAPP(c_Set_Oinsert(_1095596), _1095600), _1095598)))))], (16394 ^ _779530) ^ [_1095729, _1095731, _1095733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095729), _1095731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095729, tc_HOL_Obool)), _1095733), _1095731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095729), _1095733)), hAPP(c_Finite__Set_Ocard(_1095729), _1095731))))], (16404 ^ _779530) ^ [_1095920, _1095922, _1095924] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095920), _1095922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1095920, tc_HOL_Obool)), _1095924), _1095922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095920), _1095922)), hAPP(c_Finite__Set_Ocard(_1095920), _1095924))), -(_1095924 = _1095922)], (16418 ^ _779530) ^ [_1096165, _1096167, _1096169, _1096171] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096165), _1096167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1096169), hAPP(c_Set_Oimage(_1096165, _1096169, _1096171), _1096167))), hAPP(c_Finite__Set_Ocard(_1096165), _1096167))))], (16424 ^ _779530) ^ [_1096298, _1096300, _1096302, _1096304] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096298), _1096300)), hAPP(c_Finite__Set_Ocard(_1096302), hAPP(c_Set_Oimage(_1096298, _1096302, _1096304), _1096300)) = hAPP(c_Finite__Set_Ocard(_1096298), _1096300), -(c_Fun_Oinj__on(_1096298, _1096302, _1096304, _1096300))], (16434 ^ _779530) ^ [_1096481, _1096483, _1096485, _1096487] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096481), _1096483)), 16437 ^ _779530 : [(16438 ^ _779530) ^ [] : [c_Fun_Oinj__on(_1096481, _1096485, _1096487, _1096483), -(hAPP(c_Finite__Set_Ocard(_1096485), hAPP(c_Set_Oimage(_1096481, _1096485, _1096487), _1096483)) = hAPP(c_Finite__Set_Ocard(_1096481), _1096483))], (16444 ^ _779530) ^ [] : [hAPP(c_Finite__Set_Ocard(_1096485), hAPP(c_Set_Oimage(_1096481, _1096485, _1096487), _1096483)) = hAPP(c_Finite__Set_Ocard(_1096481), _1096483), -(c_Fun_Oinj__on(_1096481, _1096485, _1096487, _1096483))]]], (16450 ^ _779530) ^ [_1096765, _1096767, _1096769, _1096771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1096765), hAPP(c_Set_Oimage(_1096767, _1096765, _1096769), _1096771))), hAPP(c_Finite__Set_Ocard(_1096767), _1096771))), c_Fun_Oinj__on(_1096767, _1096765, _1096769, _1096771)], (16456 ^ _779530) ^ [_1096895, _1096897, _1096899, _1096901] : [c_Fun_Oinj__on(_1096895, _1096897, _1096899, c_Orderings_Otop__class_Otop(tc_fun(_1096895, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1096895, tc_fun(_1096901, _1096897), hAPP(hAPP(c_COMBB(_1096897, tc_fun(_1096901, _1096897), _1096895), c_COMBK(_1096897, _1096901)), _1096899), c_Orderings_Otop__class_Otop(tc_fun(_1096895, tc_HOL_Obool))))], (16462 ^ _779530) ^ [_1097042, _1097044, _1097046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097042), _1097044)), c_Fun_Oinj__on(_1097042, tc_fun(tc_fun(_1097042, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1097042, tc_fun(tc_prod(_1097042, _1097042), tc_HOL_Obool), tc_fun(tc_fun(_1097042, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1097042, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1097042, _1097042), tc_HOL_Obool), tc_fun(tc_fun(_1097042, tc_HOL_Obool), tc_HOL_Obool)), _1097042), c_Equiv__Relations_Oquotient(_1097042)), hAPP(hAPP(c_COMBC(_1097042, tc_fun(_1097042, tc_HOL_Obool), tc_fun(_1097042, tc_HOL_Obool)), c_Set_Oinsert(_1097042)), c_Orderings_Obot__class_Obot(tc_fun(_1097042, tc_HOL_Obool))))), _1097046), _1097044), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1097042, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1097042), _1097044), _1097046)) = hAPP(c_Finite__Set_Ocard(_1097042), _1097044))], (16472 ^ _779530) ^ [_1097391, _1097393, _1097395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1097391), _1097393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1097391, tc_HOL_Obool)), _1097395), _1097393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1097391), _1097395)), hAPP(c_Finite__Set_Ocard(_1097391), _1097393))))], (16482 ^ _779530) ^ [_1097582] : [class_Lattices_Oboolean__algebra(_1097582), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097582), c_Orderings_Obot__class_Obot(_1097582)) = c_Orderings_Otop__class_Otop(_1097582))], (16488 ^ _779530) ^ [_1097673] : [class_Lattices_Oboolean__algebra(_1097673), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097673), c_Orderings_Otop__class_Otop(_1097673)) = c_Orderings_Obot__class_Obot(_1097673))], (16494 ^ _779530) ^ [_1097764, _1097766] : [class_Lattices_Oboolean__algebra(_1097764), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097764), hAPP(c_Groups_Ouminus__class_Ouminus(_1097764), _1097766)), _1097766) = c_Orderings_Otop__class_Otop(_1097764))], (16500 ^ _779530) ^ [_1097869, _1097871] : [class_Lattices_Oboolean__algebra(_1097869), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097869), _1097871), hAPP(c_Groups_Ouminus__class_Ouminus(_1097869), _1097871)) = c_Orderings_Otop__class_Otop(_1097869))], (16506 ^ _779530) ^ [_1097974, _1097976, _1097978, _1097980] : [c_Fun_Oinj__on(_1097974, _1097976, _1097978, c_Orderings_Otop__class_Otop(tc_fun(_1097974, tc_HOL_Obool))), 16509 ^ _779530 : [(16510 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1097976), _1097980), hAPP(c_Set_Oimage(_1097974, _1097976, _1097978), c_Orderings_Otop__class_Otop(tc_fun(_1097974, tc_HOL_Obool))))), 16514 ^ _779530 : [(16515 ^ _779530) ^ [] : [-(_1097980 = hAPP(_1097978, 16513 ^ [_1097974, _1097976, _1097978, _1097980]))], (16517 ^ _779530) ^ [_1098239] : [_1097980 = hAPP(_1097978, _1098239), -(_1098239 = 16513 ^ [_1097974, _1097976, _1097978, _1097980])]]], (16523 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097976), _1097980), hAPP(c_Set_Oimage(_1097974, _1097976, _1097978), c_Orderings_Otop__class_Otop(tc_fun(_1097974, tc_HOL_Obool)))))), 16524 ^ _779530 : [(16525 ^ _779530) ^ [_1098377] : [_1097980 = hAPP(_1097978, _1098377), 16529 ^ _779530 : [(16530 ^ _779530) ^ [] : [-(_1097980 = hAPP(_1097978, 16528 ^ [_1097974, _1097976, _1097978, _1097980, _1098377]))], (16532 ^ _779530) ^ [] : [16528 ^ [_1097974, _1097976, _1097978, _1097980, _1098377] = _1098377]]]]]]], (16536 ^ _779530) ^ [_1098605, _1098607, _1098609, _1098611, _1098613] : [c_Fun_Oinj__on(_1098605, _1098607, _1098609, c_Orderings_Otop__class_Otop(tc_fun(_1098605, tc_HOL_Obool))), 16539 ^ _779530 : [(16540 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1098607), hAPP(_1098609, _1098611)), hAPP(c_Set_Oimage(_1098605, _1098607, _1098609), _1098613))), -(hBOOL(hAPP(hAPP(c_member(_1098605), _1098611), _1098613)))], (16546 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1098605), _1098611), _1098613)), -(hBOOL(hAPP(hAPP(c_member(_1098607), hAPP(_1098609, _1098611)), hAPP(c_Set_Oimage(_1098605, _1098607, _1098609), _1098613))))]]], (16552 ^ _779530) ^ [_1098916, _1098918] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1098916), c_Orderings_Otop__class_Otop(tc_fun(_1098916, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1098916, _1098916, _1098918), c_Orderings_Otop__class_Otop(tc_fun(_1098916, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1098916, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1098916, _1098916, _1098918, c_Orderings_Otop__class_Otop(tc_fun(_1098916, tc_HOL_Obool))))], (16562 ^ _779530) ^ [_1099111, _1099113] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099111), c_Orderings_Otop__class_Otop(tc_fun(_1099111, tc_HOL_Obool)))), c_Fun_Oinj__on(_1099111, _1099111, _1099113, c_Orderings_Otop__class_Otop(tc_fun(_1099111, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1099111, _1099111, _1099113), c_Orderings_Otop__class_Otop(tc_fun(_1099111, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1099111, tc_HOL_Obool)))], (16572 ^ _779530) ^ [_1099306, _1099308, _1099310, _1099312, _1099314] : [c_Fun_Oinj__on(_1099306, _1099308, _1099310, c_Orderings_Otop__class_Otop(tc_fun(_1099306, tc_HOL_Obool))), 16575 ^ _779530 : [(16576 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099308, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099306, _1099308, _1099310), _1099312)), hAPP(c_Set_Oimage(_1099306, _1099308, _1099310), _1099314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099306, tc_HOL_Obool)), _1099312), _1099314)))], (16582 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099306, tc_HOL_Obool)), _1099312), _1099314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099308, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099306, _1099308, _1099310), _1099312)), hAPP(c_Set_Oimage(_1099306, _1099308, _1099310), _1099314))))]]], (16588 ^ _779530) ^ [_1099647, _1099649, _1099651, _1099653, _1099655] : [c_Fun_Oinj__on(_1099647, _1099649, _1099651, c_Orderings_Otop__class_Otop(tc_fun(_1099647, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1099647, _1099649, _1099651), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099647, tc_HOL_Obool)), _1099653), _1099655)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099649, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099647, _1099649, _1099651), _1099653)), hAPP(c_Set_Oimage(_1099647, _1099649, _1099651), _1099655)))], (16594 ^ _779530) ^ [_1099830, _1099832, _1099834, _1099836, _1099838] : [c_Fun_Oinj__on(_1099830, _1099832, _1099834, c_Orderings_Otop__class_Otop(tc_fun(_1099830, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1099830, _1099832, _1099834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099830, tc_HOL_Obool)), _1099836), _1099838)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099832, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1099830, _1099832, _1099834), _1099836)), hAPP(c_Set_Oimage(_1099830, _1099832, _1099834), _1099838)))], (16600 ^ _779530) ^ [_1100013, _1100015, _1100017, _1100019] : [hAPP(c_Set_Oimage(_1100013, _1100015, _1100017), c_Orderings_Otop__class_Otop(tc_fun(_1100013, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1100015, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100015, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100015, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1100013, _1100015, _1100017), _1100019))), hAPP(c_Set_Oimage(_1100013, _1100015, _1100017), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100013, tc_HOL_Obool)), _1100019)))))], (16606 ^ _779530) ^ [_1100208, _1100210, _1100212, _1100214, _1100216, _1100218] : [c_Fun_Oinj__on(_1100208, _1100210, _1100212, _1100214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100210, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1100208, _1100210, _1100212), _1100214)), _1100216)), c_Fun_Oinj__on(_1100210, _1100208, _1100218, _1100216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100208, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1100210, _1100208, _1100218), _1100216)), _1100214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100208), _1100214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100210), _1100216)), -(hAPP(c_Finite__Set_Ocard(_1100208), _1100214) = hAPP(c_Finite__Set_Ocard(_1100210), _1100216))], (16632 ^ _779530) ^ [_1100705, _1100707, _1100709] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1100705), _1100707)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100705, tc_HOL_Obool)), _1100707), _1100709)), -(hAPP(c_Finite__Set_Ocard(_1100705), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100705, tc_HOL_Obool)), _1100709), _1100707)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1100705), _1100709)), hAPP(c_Finite__Set_Ocard(_1100705), 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c_Orderings_Otop__class_Otop(tc_fun(_1101487, tc_HOL_Obool))))], (16662 ^ _779530) ^ [_1101543, _1101545, _1101547, _1101549, _1101551] : [class_Groups_Ocomm__monoid__add(_1101543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1101545), _1101547)), -(hBOOL(hAPP(hAPP(c_member(_1101545), _1101549), _1101547))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101545, _1101543), _1101551), hAPP(hAPP(c_Set_Oinsert(_1101545), _1101549), _1101547)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101543), hAPP(_1101551, _1101549)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101545, _1101543), _1101551), _1101547)))], (16676 ^ _779530) ^ [_1101793, _1101795, _1101797, _1101799, _1101801] : [class_Groups_Ocomm__monoid__add(_1101793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1101795), _1101797)), -(hBOOL(hAPP(hAPP(c_member(_1101795), _1101799), _1101797))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1101795, _1101793), _1101801), 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102310, _1102308), _1102316), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102310, tc_HOL_Obool)), _1102312), _1102314))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102310, _1102308), _1102316), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102310, tc_HOL_Obool)), _1102312), _1102314))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102308), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102310, _1102308), _1102316), _1102312)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102310, _1102308), _1102316), _1102314)))], (16718 ^ _779530) ^ [_1102696, _1102698, _1102700, _1102702, _1102704, _1102706] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102696, tc_fun(_1102698, tc_fun(_1102700, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1102696, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1102698, 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c_Orderings_Otop__class_Otop(tc_fun(_1103668, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1103670, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1103668, _1103670, _1103672), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1103668, tc_HOL_Obool)), _1103674))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1103670, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1103668, _1103670, _1103672), _1103674)))))], (16736 ^ _779530) ^ [_1103843, _1103845, _1103847] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1103843), _1103845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1103843), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1103843, tc_HOL_Obool)), _1103845), hAPP(hAPP(c_Set_Oinsert(_1103843), _1103847), c_Orderings_Obot__class_Obot(tc_fun(_1103843, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1103843), _1103845))))], (16742 ^ _779530) ^ [_1104008, _1104010, _1104012, _1104014, _1104016] : [c_Fun_Oinj__on(_1104008, _1104010, _1104012, _1104014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104010, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1104008, _1104010, _1104012), _1104014)), _1104016)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104010), _1104016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1104008), _1104014)), hAPP(c_Finite__Set_Ocard(_1104010), _1104016))))], (16756 ^ _779530) ^ [_1104283, _1104285, _1104287, _1104289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1104283), _1104285)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104287), _1104289)), 16763 ^ _779530 : [(16774 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1104283), _1104285)), hAPP(c_Finite__Set_Ocard(_1104287), _1104289))), 16778 ^ _779530 : [(16779 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_1104283, _1104287, 16777 ^ [_1104283, _1104285, _1104287, _1104289], _1104285))], (16781 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104287, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1104283, _1104287, 16777 ^ [_1104283, _1104285, _1104287, _1104289]), _1104285)), _1104289)))]]], (16764 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1104283), _1104285)), hAPP(c_Finite__Set_Ocard(_1104287), _1104289)))), 16765 ^ _779530 : [(16766 ^ _779530) ^ [_1104494] : [c_Fun_Oinj__on(_1104283, _1104287, _1104494, _1104285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104287, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1104283, _1104287, _1104494), _1104285)), _1104289))]]]]], (16783 ^ _779530) ^ [_1104810, _1104812, _1104814, _1104816, _1104818] : [class_Groups_Ocomm__monoid__add(_1104810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1104812), _1104814)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104812, _1104810), _1104816), hAPP(hAPP(c_Set_Oinsert(_1104812), _1104818), _1104814)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104810), hAPP(_1104816, _1104818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1104812, _1104810), _1104816), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1104812, tc_HOL_Obool)), _1104814), hAPP(hAPP(c_Set_Oinsert(_1104812), _1104818), c_Orderings_Obot__class_Obot(tc_fun(_1104812, tc_HOL_Obool)))))))], (16793 ^ _779530) ^ [_1105079, _1105081, _1105083, _1105085, _1105087] : [class_Groups_Ocomm__monoid__add(_1105079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105081), _1105083)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105081), _1105085)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105081, tc_HOL_Obool)), _1105083), _1105085) = c_Orderings_Obot__class_Obot(tc_fun(_1105081, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105081, _1105079), _1105087), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1105081, tc_HOL_Obool)), _1105083), _1105085)) = 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105476, _1105474), _1105482), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105476, tc_HOL_Obool)), _1105478), _1105480))))], (16825 ^ _779530) ^ [_1105835, _1105837, _1105839, _1105841] : [-(hAPP(c_Option_Ooption_Ooption__case(_1105835, _1105837, _1105839, _1105841), c_Option_Ooption_ONone(_1105837)) = _1105839)], (16827 ^ _779530) ^ [_1105874, _1105876, _1105878, _1105880, _1105882] : [-(hAPP(c_Option_Ooption_Ooption__case(_1105874, _1105876, _1105878, _1105880), hAPP(c_Option_Ooption_OSome(_1105876), _1105882)) = hAPP(_1105880, _1105882))], (16829 ^ _779530) ^ [_1105921, _1105923, _1105925, _1105927] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1105921), _1105923)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1105921), _1105925)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105921, tc_Nat_Onat), _1105927), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1105921, tc_HOL_Obool)), _1105923), _1105925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105921, tc_Nat_Onat), _1105927), _1105923)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105921, tc_Nat_Onat), _1105927), _1105925))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1105921, tc_Nat_Onat), _1105927), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105921, tc_HOL_Obool)), _1105923), _1105925))))], (16839 ^ _779530) ^ [_1106214, _1106216, _1106218, _1106220, _1106222, _1106224] : [class_Groups_Ocomm__monoid__add(_1106214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1106216), _1106218)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1106216, _1106214), hAPP(hAPP(c_COMBS(_1106216, _1106214, _1106214), hAPP(hAPP(c_COMBS(_1106216, _1106214, tc_fun(_1106214, _1106214)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1106214, tc_fun(_1106214, _1106214)), _1106216), c_If(_1106214)), _1106220)), _1106222)), _1106224)), _1106218) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106214), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1106216, _1106214), _1106222), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106216, tc_HOL_Obool)), _1106218), hAPP(c_Set_OCollect(_1106216), _1106220)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1106216, _1106214), _1106224), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106216, tc_HOL_Obool)), _1106218), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1106216, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1106216), _1106220))))))], (16849 ^ _779530) ^ [_1106597, _1106599, _1106601] : [class_Rings_Ocomm__ring__1(_1106597), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1106597), _1106599), _1106601) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106597), _1106599), hAPP(c_Groups_Ouminus__class_Ouminus(_1106597), _1106601)))], (16855 ^ _779530) ^ [_1106716, _1106718, _1106720, _1106722, _1106724, _1106726, _1106728] : [c_Big__Operators_Ocomm__monoid__big(_1106716, _1106718, _1106720, _1106722, _1106724), 16858 ^ _779530 : [(16859 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1106718), _1106726)), -(hAPP(hAPP(_1106724, _1106728), _1106726) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1106716, _1106718, _1106720), _1106728), _1106722), _1106726))], (16865 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1106718), _1106726))), -(hAPP(hAPP(_1106724, _1106728), _1106726) = _1106722)]]], (16871 ^ _779530) ^ [_1106984, _1106986, _1106988] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1106984), _1106986)), hBOOL(hAPP(hAPP(c_member(_1106984), _1106988), _1106986)), -(hAPP(c_Finite__Set_Ocard(_1106984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1106984, tc_HOL_Obool)), _1106986), hAPP(hAPP(c_Set_Oinsert(_1106984), _1106988), c_Orderings_Obot__class_Obot(tc_fun(_1106984, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1106984), _1106986)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16881 ^ _779530) ^ [_1107219, _1107221, _1107223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1107219), _1107221)), 16884 ^ _779530 : [(16885 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1107219), _1107223), _1107221)), -(hAPP(c_Finite__Set_Ocard(_1107219), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1107219, tc_HOL_Obool)), _1107221), hAPP(hAPP(c_Set_Oinsert(_1107219), _1107223), c_Orderings_Obot__class_Obot(tc_fun(_1107219, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1107219), _1107221)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16891 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107219), _1107223), _1107221))), -(hAPP(c_Finite__Set_Ocard(_1107219), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1107219, tc_HOL_Obool)), _1107221), hAPP(hAPP(c_Set_Oinsert(_1107219), _1107223), c_Orderings_Obot__class_Obot(tc_fun(_1107219, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1107219), _1107221))]]], (16897 ^ _779530) ^ [_1107583, _1107585, _1107587] : [class_Groups_Olinordered__ab__semigroup__add(_1107583), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107583), _1107585)), -(_1107585 = c_Orderings_Obot__class_Obot(tc_fun(_1107583, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107583), _1107587), c_Big__Operators_Olinorder__class_OMin(_1107583, _1107585)) = c_Big__Operators_Olinorder__class_OMin(_1107583, hAPP(c_Set_OCollect(_1107583), hAPP(hAPP(c_COMBB(tc_fun(_1107583, tc_HOL_Obool), tc_HOL_Obool, _1107583), c_HOL_OEx(_1107583)), hAPP(hAPP(c_COMBC(_1107583, tc_fun(_1107583, tc_HOL_Obool), tc_fun(_1107583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1107583, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1107583, tc_HOL_Obool), tc_fun(_1107583, tc_HOL_Obool)), _1107583), c_COMBS(_1107583, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1107583, tc_HOL_Obool), tc_fun(_1107583, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1107583), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1107583), c_fconj)), hAPP(hAPP(c_COMBC(_1107583, tc_fun(_1107583, _1107583), tc_fun(_1107583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1107583, tc_HOL_Obool), tc_fun(tc_fun(_1107583, _1107583), tc_fun(_1107583, tc_HOL_Obool)), _1107583), c_COMBB(_1107583, tc_HOL_Obool, _1107583)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1107583), _1107587))))), hAPP(hAPP(c_COMBC(_1107583, tc_fun(_1107583, tc_HOL_Obool), tc_HOL_Obool), c_member(_1107583)), _1107585))))))], (16911 ^ _779530) ^ [_1108069, _1108071, _1108073] : [class_Groups_Olinordered__ab__semigroup__add(_1108069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108069), _1108071)), -(_1108071 = c_Orderings_Obot__class_Obot(tc_fun(_1108069, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108069), _1108073), c_Big__Operators_Olinorder__class_OMax(_1108069, _1108071)) = c_Big__Operators_Olinorder__class_OMax(_1108069, hAPP(c_Set_OCollect(_1108069), hAPP(hAPP(c_COMBB(tc_fun(_1108069, tc_HOL_Obool), tc_HOL_Obool, _1108069), c_HOL_OEx(_1108069)), hAPP(hAPP(c_COMBC(_1108069, tc_fun(_1108069, tc_HOL_Obool), tc_fun(_1108069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1108069, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1108069, tc_HOL_Obool), tc_fun(_1108069, tc_HOL_Obool)), _1108069), c_COMBS(_1108069, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1108069, tc_HOL_Obool), tc_fun(_1108069, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1108069), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1108069), c_fconj)), hAPP(hAPP(c_COMBC(_1108069, tc_fun(_1108069, _1108069), tc_fun(_1108069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1108069, tc_HOL_Obool), tc_fun(tc_fun(_1108069, _1108069), tc_fun(_1108069, tc_HOL_Obool)), _1108069), c_COMBB(_1108069, tc_HOL_Obool, _1108069)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1108069), _1108073))))), hAPP(hAPP(c_COMBC(_1108069, tc_fun(_1108069, tc_HOL_Obool), tc_HOL_Obool), c_member(_1108069)), _1108071))))))], (16925 ^ _779530) ^ [_1108555, _1108557, _1108559, _1108561, _1108563, _1108565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1108555), _1108557)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108559), _1108561)), 16935 ^ _779530 : [(16936 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1108559), 16934 ^ [_1108555, _1108557, _1108559, _1108561, _1108563, _1108565]), _1108561)))], (16938 ^ _779530) ^ [] : [hAPP(c_Finite__Set_Ocard(_1108555), hAPP(c_Set_OCollect(_1108555), hAPP(hAPP(c_COMBS(_1108555, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1108555), c_fconj), hAPP(hAPP(c_COMBC(_1108555, tc_fun(_1108555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1108555)), _1108557))), hAPP(hAPP(c_COMBC(_1108555, _1108559, tc_HOL_Obool), _1108563), 16934 ^ [_1108555, _1108557, _1108559, _1108561, _1108563, _1108565])))) = hAPP(_1108565, 16934 ^ [_1108555, _1108557, _1108559, _1108561, _1108563, _1108565])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1108555, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1108559, tc_HOL_Obool), tc_Nat_Onat, _1108555), c_Finite__Set_Ocard(_1108559)), hAPP(hAPP(c_COMBB(tc_fun(_1108559, tc_HOL_Obool), tc_fun(_1108559, tc_HOL_Obool), _1108555), c_Set_OCollect(_1108559)), hAPP(hAPP(c_COMBB(tc_fun(_1108559, tc_HOL_Obool), tc_fun(_1108559, tc_HOL_Obool), _1108555), hAPP(c_COMBS(_1108559, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1108559), c_fconj), hAPP(hAPP(c_COMBC(_1108559, tc_fun(_1108559, tc_HOL_Obool), tc_HOL_Obool), c_member(_1108559)), _1108561)))), _1108563)))), _1108557) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1108559, tc_Nat_Onat), _1108565), _1108561))], (16942 ^ _779530) ^ [_1109265, _1109267, _1109269] : [-(c_Smallcheck_Oorelse(_1109265, _1109267, _1109269) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1109265), _1109265, _1109269, c_Option_Ooption_OSome(_1109265)), _1109267))], (16944 ^ _779530) ^ [_1109308, _1109310] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1109308, tc_HOL_Obool)), _1109310)))], (16946 ^ _779530) ^ [] : [-(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))], (16948 ^ _779530) ^ [_1109358, _1109360] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109358), _1109360) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109360), _1109358))], (16950 ^ _779530) ^ [_1109395, _1109397, _1109399] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109397), _1109399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109397), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109395), _1109399)))], (16952 ^ _779530) ^ [_1109446, _1109448, _1109450] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109446), _1109448)), _1109450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109446), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109448), _1109450)))], (16954 ^ _779530) ^ [_1109515, _1109517, _1109519] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109515), _1109517) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109515), _1109519), -(_1109517 = _1109519)], (16960 ^ _779530) ^ [_1109614, _1109616, _1109618] : [_1109616 = _1109618, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109614), _1109616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109614), _1109618))], (16966 ^ _779530) ^ [_1109737, _1109739, _1109741] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109737), _1109739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109741), _1109739), -(_1109737 = _1109741)], (16972 ^ _779530) ^ [_1109836, _1109838, _1109840] : [_1109836 = _1109840, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109836), _1109838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109840), _1109838))], (16978 ^ _779530) ^ [_1109941, _1109943] : [-(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)), _1109941), _1109943))], (16980 ^ _779530) ^ [_1109971, _1109973] : [class_Groups_Oone(_1109971), 16983 ^ _779530 : [(16984 ^ _779530) ^ [] : [c_Groups_Oone__class_Oone(_1109971) = _1109973, -(_1109973 = c_Groups_Oone__class_Oone(_1109971))], (16990 ^ _779530) ^ [] : [_1109973 = c_Groups_Oone__class_Oone(_1109971), -(c_Groups_Oone__class_Oone(_1109971) = _1109973)]]], (16996 ^ _779530) ^ [_1110188, _1110190] : [class_Groups_Olinordered__ab__group__add(_1110188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110188), _1110190)), -(_1110190 = c_Orderings_Obot__class_Obot(tc_fun(_1110188, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1110188), c_Big__Operators_Olinorder__class_OMax(_1110188, _1110190)) = c_Big__Operators_Olinorder__class_OMin(_1110188, hAPP(c_Set_Oimage(_1110188, _1110188, c_Groups_Ouminus__class_Ouminus(_1110188)), _1110190)))], (17010 ^ _779530) ^ [_1110388, _1110390] : [class_Groups_Olinordered__ab__group__add(_1110388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110388), _1110390)), -(_1110390 = c_Orderings_Obot__class_Obot(tc_fun(_1110388, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1110388), c_Big__Operators_Olinorder__class_OMin(_1110388, _1110390)) = c_Big__Operators_Olinorder__class_OMax(_1110388, hAPP(c_Set_Oimage(_1110388, _1110388, c_Groups_Ouminus__class_Ouminus(_1110388)), _1110390)))], (17024 ^ _779530) ^ [_1110588, _1110590] : [class_Orderings_Olinorder(_1110588), -(c_Big__Operators_Olinorder__class_OMin(_1110588, hAPP(hAPP(c_Set_Oinsert(_1110588), _1110590), c_Orderings_Obot__class_Obot(tc_fun(_1110588, tc_HOL_Obool)))) = _1110590)], (17030 ^ _779530) ^ [_1110695, _1110697] : [class_Orderings_Olinorder(_1110695), -(c_Big__Operators_Olinorder__class_OMax(_1110695, hAPP(hAPP(c_Set_Oinsert(_1110695), _1110697), c_Orderings_Obot__class_Obot(tc_fun(_1110695, tc_HOL_Obool)))) = _1110697)], (17036 ^ _779530) ^ [_1110802, _1110804] : [-(hAPP(c_Finite__Set_Ocard(_1110802), _1110804) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1110802, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1110802), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1110804))], (17038 ^ _779530) ^ [_1110847, _1110849, _1110851] : [class_Rings_Ocomm__semiring__1(_1110847), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110847), _1110849), _1110851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110847), _1110851), _1110849))], (17044 ^ _779530) ^ [_1110956, _1110958, _1110960, _1110962] : [class_Rings_Ocomm__semiring__1(_1110956), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110956), _1110958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110956), _1110960), _1110962)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110956), _1110960), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110956), _1110958), _1110962)))], (17050 ^ _779530) ^ [_1111099, _1111101, _1111103, _1111105] : [class_Rings_Ocomm__semiring__1(_1111099), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111099), _1111101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111099), _1111103), _1111105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111099), _1111101), _1111103)), _1111105))], (17056 ^ _779530) ^ [_1111242, _1111244, _1111246, _1111248] : [class_Rings_Ocomm__semiring__1(_1111242), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111242), _1111244), _1111246)), _1111248) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111242), _1111244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111242), _1111246), _1111248)))], (17062 ^ _779530) ^ [_1111385, _1111387, _1111389, _1111391] : [class_Rings_Ocomm__semiring__1(_1111385), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111385), _1111387), _1111389)), _1111391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111385), _1111387), _1111391)), _1111389))], (17068 ^ _779530) ^ [_1111528, _1111530, _1111532, _1111534, _1111536] : [class_Rings_Ocomm__semiring__1(_1111528), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), _1111530), _1111532)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), _1111534), _1111536)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), _1111530), _1111534)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1111528), _1111532), _1111536)))], (17074 ^ _779530) ^ [_1111705, _1111707, _1111709] : [class_Orderings_Olinorder(_1111705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111705), _1111707)), hBOOL(hAPP(hAPP(c_member(_1111705), _1111709), _1111707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111705), _1111709), c_Big__Operators_Olinorder__class_OMax(_1111705, _1111707))))], (17088 ^ _779530) ^ [_1111932, _1111934, _1111936] : [class_Orderings_Olinorder(_1111932), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111932), _1111934)), hBOOL(hAPP(hAPP(c_member(_1111932), _1111936), _1111934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1111932), c_Big__Operators_Olinorder__class_OMin(_1111932, _1111934)), _1111936)))], (17102 ^ _779530) ^ [_1112159, _1112161] : [class_Orderings_Olinorder(_1112159), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112159), _1112161)), -(_1112161 = c_Orderings_Obot__class_Obot(tc_fun(_1112159, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1112159), c_Big__Operators_Olinorder__class_OMin(_1112159, _1112161)), _1112161)))], (17116 ^ _779530) ^ [_1112339, _1112341] : [class_Orderings_Olinorder(_1112339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112339), _1112341)), -(_1112341 = c_Orderings_Obot__class_Obot(tc_fun(_1112339, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1112339), c_Big__Operators_Olinorder__class_OMax(_1112339, _1112341)), _1112341)))], (17130 ^ _779530) ^ [_1112519, _1112521, _1112523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1112519), _1112521)), -(hBOOL(hAPP(hAPP(c_member(_1112519), _1112523), _1112521))), -(hAPP(c_Finite__Set_Ocard(_1112519), hAPP(hAPP(c_Set_Oinsert(_1112519), _1112523), _1112521)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1112519), _1112521)))], (17140 ^ _779530) ^ [_1112677, _1112679, _1112681] : [class_Orderings_Olinorder(_1112677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1112677, tc_HOL_Obool)), _1112679), _1112681)), -(_1112679 = c_Orderings_Obot__class_Obot(tc_fun(_1112677, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112677), _1112681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112677), c_Big__Operators_Olinorder__class_OMin(_1112677, _1112681)), c_Big__Operators_Olinorder__class_OMin(_1112677, _1112679))))], (17158 ^ _779530) ^ [_1112983, _1112985, _1112987] : [class_Orderings_Olinorder(_1112983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1112983, tc_HOL_Obool)), _1112985), _1112987)), -(_1112985 = c_Orderings_Obot__class_Obot(tc_fun(_1112983, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112983), _1112987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1112983), c_Big__Operators_Olinorder__class_OMax(_1112983, _1112985)), c_Big__Operators_Olinorder__class_OMax(_1112983, _1112987))))], (17176 ^ _779530) ^ [_1113289, _1113291, _1113293, _1113295, _1113297, _1113299, _1113301] : [c_Big__Operators_Ocomm__monoid__big(_1113289, _1113291, _1113293, _1113295, _1113297), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1113291), _1113299))), -(hAPP(hAPP(_1113297, _1113301), _1113299) = _1113295)], (17186 ^ _779530) ^ [_1113417, _1113419, _1113421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113417), _1113419)), -(hAPP(c_Finite__Set_Ocard(_1113417), hAPP(hAPP(c_Set_Oinsert(_1113417), _1113421), _1113419)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1113417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113417, tc_HOL_Obool)), _1113419), hAPP(hAPP(c_Set_Oinsert(_1113417), _1113421), c_Orderings_Obot__class_Obot(tc_fun(_1113417, tc_HOL_Obool)))))))], (17192 ^ _779530) ^ [_1113594, _1113596, _1113598] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113594), _1113596)), hBOOL(hAPP(hAPP(c_member(_1113594), _1113598), _1113596)), -(hAPP(c_Finite__Set_Ocard(_1113594), _1113596) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1113594), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113594, tc_HOL_Obool)), _1113596), hAPP(hAPP(c_Set_Oinsert(_1113594), _1113598), c_Orderings_Obot__class_Obot(tc_fun(_1113594, tc_HOL_Obool)))))))], (17202 ^ _779530) ^ [_1113823, _1113825, _1113827, _1113829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1113823), _1113825)), hBOOL(hAPP(hAPP(c_member(_1113823), _1113827), _1113825)), -(hBOOL(hAPP(hAPP(c_member(_1113823), _1113827), _1113829))), -(hAPP(c_Finite__Set_Ocard(_1113823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113823, tc_HOL_Obool)), _1113825), hAPP(hAPP(c_Set_Oinsert(_1113823), _1113827), _1113829))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1113823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113823, tc_HOL_Obool)), _1113825), _1113829))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17216 ^ _779530) ^ [_1114103, _1114105] : [class_Rings_Olinordered__semidom(_1114103), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1114103), _1114105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114103), _1114105), c_Groups_Oone__class_Oone(_1114103)))))], (17222 ^ _779530) ^ [_1114212, _1114214] : [-(c_Relation_OId__on(_1114212, _1114214) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1114212, tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool)), _1114214), hAPP(hAPP(c_COMBC(_1114212, tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool), tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1114212, _1114212), tc_fun(tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool), tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool)), _1114212), c_Set_Oinsert(tc_prod(_1114212, _1114212))), hAPP(hAPP(c_COMBS(_1114212, _1114212, tc_prod(_1114212, _1114212)), c_Product__Type_OPair(_1114212, _1114212)), c_COMBI(_1114212)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1114212, _1114212), tc_HOL_Obool)))))], (17224 ^ _779530) ^ [_1114351, _1114353] : [c_Equiv__Relations_Oequiv(_1114351, c_Orderings_Otop__class_Otop(tc_fun(_1114351, tc_HOL_Obool)), _1114353), -(c_Equiv__Relations_Oequivp(_1114351, hAPP(hAPP(c_COMBC(_1114351, tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_fun(_1114351, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1114351, tc_fun(tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_fun(_1114351, tc_HOL_Obool)), _1114351), c_COMBC(_1114351, tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1114351, tc_prod(_1114351, _1114351)), tc_fun(_1114351, tc_fun(tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_HOL_Obool)), _1114351), hAPP(c_COMBB(tc_prod(_1114351, _1114351), tc_fun(tc_fun(tc_prod(_1114351, _1114351), tc_HOL_Obool), tc_HOL_Obool), _1114351), c_member(tc_prod(_1114351, _1114351)))), c_Product__Type_OPair(_1114351, _1114351)))), _1114353)))], (17230 ^ _779530) ^ [_1114672, _1114674] : [c_Equiv__Relations_Oequivp(_1114672, hAPP(hAPP(c_COMBC(_1114672, tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_fun(_1114672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1114672, tc_fun(tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_fun(_1114672, tc_HOL_Obool)), _1114672), c_COMBC(_1114672, tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1114672, tc_prod(_1114672, _1114672)), tc_fun(_1114672, tc_fun(tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_HOL_Obool)), _1114672), hAPP(c_COMBB(tc_prod(_1114672, _1114672), tc_fun(tc_fun(tc_prod(_1114672, _1114672), tc_HOL_Obool), tc_HOL_Obool), _1114672), c_member(tc_prod(_1114672, _1114672)))), c_Product__Type_OPair(_1114672, _1114672)))), _1114674)), -(c_Equiv__Relations_Oequiv(_1114672, c_Orderings_Otop__class_Otop(tc_fun(_1114672, tc_HOL_Obool)), _1114674))], (17236 ^ _779530) ^ [_1114999, _1115001, _1115003, _1115005] : [c_Fun_Oinj__on(_1114999, _1115001, _1115003, c_Orderings_Otop__class_Otop(tc_fun(_1114999, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1114999, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1114999, _1115001, _1115003), hAPP(hAPP(c_Set_Oinsert(_1115001), _1115005), c_Orderings_Obot__class_Obot(tc_fun(_1115001, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1114999), c_HOL_OThe(_1114999, hAPP(hAPP(c_COMBC(_1114999, _1115001, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1115001, tc_fun(_1115001, tc_HOL_Obool), _1114999), c_fequal), _1115003)), _1115005))), c_Orderings_Obot__class_Obot(tc_fun(_1114999, tc_HOL_Obool))))))], (17242 ^ _779530) ^ [_1115232, _1115234, _1115236, _1115238, _1115240] : [class_Groups_Ocomm__monoid__mult(_1115232), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115234), _1115236)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115234), _1115238)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1115234, tc_HOL_Obool)), _1115236), _1115238) = c_Orderings_Obot__class_Obot(tc_fun(_1115234, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115232, _1115234, c_Groups_Otimes__class_Otimes(_1115232)), _1115240), c_Groups_Oone__class_Oone(_1115232)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1115234, tc_HOL_Obool)), _1115236), _1115238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115232), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115232, _1115234, c_Groups_Otimes__class_Otimes(_1115232)), _1115240), c_Groups_Oone__class_Oone(_1115232)), _1115236)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1115232, _1115234, c_Groups_Otimes__class_Otimes(_1115232)), _1115240), c_Groups_Oone__class_Oone(_1115232)), _1115238)))], (17260 ^ _779530) ^ [_1115675, _1115677, _1115679, _1115681, _1115683, _1115685] : [-(c_Map_Omap__comp(_1115675, _1115677, _1115679, _1115681, _1115683, _1115685) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1115677), _1115675, c_Option_Ooption_ONone(_1115677), _1115681), hAPP(_1115683, _1115685)))], (17262 ^ _779530) ^ [_1115730, _1115732, _1115734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1115730), _1115732)), hBOOL(hAPP(hAPP(c_member(_1115730), _1115734), _1115732)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1115730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115730, tc_HOL_Obool)), _1115732), hAPP(hAPP(c_Set_Oinsert(_1115730), _1115734), c_Orderings_Obot__class_Obot(tc_fun(_1115730, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1115730), _1115732))], (17272 ^ _779530) ^ [_1115959] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115959), hAPP(c_Nat_OSuc, _1115959))))], (17274 ^ _779530) ^ [_1115990, _1115992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1115990), _1115992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115990)), hAPP(c_Nat_OSuc, _1115992))))], (17280 ^ _779530) ^ [_1116099, _1116101, _1116103, _1116105, _1116107, _1116109] : [hAPP(_1116099, _1116101) = _1116103, hBOOL(hAPP(hAPP(c_member(_1116105), _1116103), _1116107)), -(hBOOL(hAPP(hAPP(c_member(_1116109), _1116101), hAPP(c_Set_Ovimage(_1116109, _1116105, _1116099), _1116107))))], (17290 ^ _779530) ^ [_1116292, _1116294] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116292), hAPP(c_Nat_OSuc, _1116294)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116292), _1116294)))], (17292 ^ _779530) ^ [_1116338, _1116340] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116338)), _1116340) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116338), _1116340)))], (17294 ^ _779530) ^ [_1116384, _1116386, _1116388, _1116390, _1116392] : [class_Rings_Osemiring(_1116384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116384), _1116386), _1116388)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116384), _1116390), _1116388)), _1116392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116384), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116384), _1116386), _1116390)), _1116388)), _1116392))], (17300 ^ _779530) ^ [_1116577, _1116579, _1116581, _1116583] : [class_Rings_Ocomm__semiring(_1116577), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116577), _1116579), _1116581)), _1116583) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116577), _1116579), _1116583)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116577), _1116581), _1116583)))], (17306 ^ _779530) ^ [_1116736] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1116736))], (17308 ^ _779530) ^ [_1116761, _1116763, _1116765] : [class_Rings_Ocomm__semiring__1(_1116761), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116761), _1116763), _1116765) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116761), _1116765), _1116763))], (17314 ^ _779530) ^ [_1116870, _1116872, _1116874, _1116876] : [class_Rings_Ocomm__semiring__1(_1116870), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116870), _1116872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116870), _1116874), _1116876)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116870), _1116874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116870), _1116872), _1116876)))], (17320 ^ _779530) ^ [_1117013, _1117015, _1117017, _1117019] : [class_Rings_Ocomm__semiring__1(_1117013), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117013), _1117015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117013), _1117017), _1117019)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117013), _1117015), _1117017)), _1117019))], (17326 ^ _779530) ^ [_1117156, _1117158, _1117160, _1117162] : [class_Rings_Ocomm__semiring__1(_1117156), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117156), _1117158), _1117160)), _1117162) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117156), _1117158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117156), _1117160), _1117162)))], (17332 ^ _779530) ^ [_1117299, _1117301, _1117303, _1117305] : [class_Rings_Ocomm__semiring__1(_1117299), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117299), _1117301), _1117303)), _1117305) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117299), _1117301), _1117305)), _1117303))], (17338 ^ _779530) ^ [_1117442, _1117444, _1117446, _1117448, _1117450] : [class_Rings_Ocomm__semiring__1(_1117442), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), _1117444), _1117446)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), _1117448), _1117450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), _1117444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), _1117446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117442), _1117448), _1117450))))], (17344 ^ _779530) ^ [_1117619, _1117621, _1117623, _1117625, _1117627] : [class_Rings_Ocomm__semiring__1(_1117619), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), _1117621), _1117623)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), _1117625), _1117627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), _1117625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117619), _1117621), _1117623)), _1117627)))], (17350 ^ _779530) ^ [_1117796, _1117798, _1117800, _1117802, _1117804] : [class_Rings_Ocomm__semiring__1(_1117796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), _1117798), _1117800)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), _1117802), _1117804)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), _1117798), _1117802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117796), _1117800), _1117804)))], (17356 ^ _779530) ^ [_1117991, _1117993, _1117995] : [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, _1117991)), _1117993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1117991)), _1117995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117993), _1117995)))], (17362 ^ _779530) ^ [_1118122, _1118124, _1118126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118124), _1118126)), -(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, _1118122)), _1118124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1118122)), _1118126))))], (17368 ^ _779530) ^ [_1118259, _1118261, _1118263] : [class_Rings_Oidom(_1118259), 17371 ^ _779530 : [(17382 ^ _779530) ^ [] : [17383 ^ _779530 : [(17384 ^ _779530) ^ [] : [_1118261 = _1118263], (17386 ^ _779530) ^ [] : [_1118261 = hAPP(c_Groups_Ouminus__class_Ouminus(_1118259), _1118263)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118259), _1118261), _1118261) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118259), _1118263), _1118263))], (17372 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118259), _1118261), _1118261) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118259), _1118263), _1118263), -(_1118261 = _1118263), -(_1118261 = hAPP(c_Groups_Ouminus__class_Ouminus(_1118259), _1118263))]]], (17390 ^ _779530) ^ [_1118578, _1118580, _1118582] : [class_Rings_Oring(_1118578), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118578), hAPP(c_Groups_Ouminus__class_Ouminus(_1118578), _1118580)), hAPP(c_Groups_Ouminus__class_Ouminus(_1118578), _1118582)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118578), _1118580), _1118582))], (17396 ^ _779530) ^ [_1118707, _1118709, _1118711] : [class_Rings_Oring(_1118707), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118707), hAPP(c_Groups_Ouminus__class_Ouminus(_1118707), _1118709)), _1118711) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118707), _1118709), hAPP(c_Groups_Ouminus__class_Ouminus(_1118707), _1118711)))], (17402 ^ _779530) ^ [_1118836, _1118838, _1118840] : [class_Rings_Oring(_1118836), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1118836), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118836), _1118838), _1118840)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118836), hAPP(c_Groups_Ouminus__class_Ouminus(_1118836), _1118838)), _1118840))], (17408 ^ _779530) ^ [_1118965, _1118967, _1118969] : [class_Rings_Oring(_1118965), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1118965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118965), _1118967), _1118969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118965), _1118967), hAPP(c_Groups_Ouminus__class_Ouminus(_1118965), _1118969)))], (17414 ^ _779530) ^ [_1119112, _1119114, _1119116] : [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, _1119112)), _1119114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1119112)), _1119116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119114), _1119116)))], (17420 ^ _779530) ^ [_1119243, _1119245, _1119247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119245), _1119247)), -(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, _1119243)), _1119245)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1119243)), _1119247))))], (17426 ^ _779530) ^ [_1119380] : [-(c_Equiv__Relations_Oequivp(_1119380, c_fequal))], (17444 ^ _779530) ^ [_1119716, _1119718] : [-(c_Equiv__Relations_Oequivp(_1119716, _1119718)), 17449 ^ _779530 : [(17450 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1119718, 17445 ^ [_1119716, _1119718]), 17446 ^ [_1119716, _1119718])))], (17452 ^ _779530) ^ [] : [hAPP(_1119718, 17445 ^ [_1119716, _1119718]) = hAPP(_1119718, 17446 ^ [_1119716, _1119718])]], 17453 ^ _779530 : [(17454 ^ _779530) ^ [] : [-(hAPP(_1119718, 17445 ^ [_1119716, _1119718]) = hAPP(_1119718, 17446 ^ [_1119716, _1119718]))], (17456 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1119718, 17445 ^ [_1119716, _1119718]), 17446 ^ [_1119716, _1119718]))]]], (17428 ^ _779530) ^ [_1119418, _1119420] : [c_Equiv__Relations_Oequivp(_1119418, _1119420), 17431 ^ _779530 : [(17432 ^ _779530) ^ [_1119512, _1119514] : [hBOOL(hAPP(hAPP(_1119420, _1119514), _1119512)), -(hAPP(_1119420, _1119514) = hAPP(_1119420, _1119512))], (17438 ^ _779530) ^ [_1119611, _1119613] : [hAPP(_1119420, _1119613) = hAPP(_1119420, _1119611), -(hBOOL(hAPP(hAPP(_1119420, _1119613), _1119611)))]]], (17460 ^ _779530) ^ [_1120045, _1120047, _1120049] : [c_Equiv__Relations_Oequivp(_1120045, _1120047), -(hBOOL(hAPP(hAPP(_1120047, _1120049), _1120049)))], (17466 ^ _779530) ^ [_1120134, _1120136, _1120138, _1120140] : [c_Equiv__Relations_Oequivp(_1120134, _1120136), hBOOL(hAPP(hAPP(_1120136, _1120138), _1120140)), -(hBOOL(hAPP(hAPP(_1120136, _1120140), _1120138)))], (17476 ^ _779530) ^ [_1120291, _1120293, _1120295, _1120297, _1120299] : [c_Equiv__Relations_Oequivp(_1120291, _1120293), hBOOL(hAPP(hAPP(_1120293, _1120295), _1120297)), hBOOL(hAPP(hAPP(_1120293, _1120297), _1120299)), -(hBOOL(hAPP(hAPP(_1120293, _1120295), _1120299)))], (17490 ^ _779530) ^ [_1120520, _1120522, _1120524, _1120526] : [class_Groups_Oab__semigroup__mult(_1120520), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120520), _1120522), _1120524)), _1120526) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120520), _1120522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120520), _1120524), _1120526)))], (17496 ^ _779530) ^ [_1120663, _1120665] : [-(hAPP(c_Set_Ovimage(_1120663, _1120663, c_COMBI(_1120663)), _1120665) = _1120665)], (17498 ^ _779530) ^ [_1120697, _1120699] : [class_Lattices_Oab__semigroup__idem__mult(_1120697), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120697), _1120699), _1120699) = _1120699)], (17504 ^ _779530) ^ [_1120788, _1120790] : [class_Lattices_Oab__semigroup__idem__mult(_1120788), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120788), _1120790), _1120790) = _1120790)], (17510 ^ _779530) ^ [_1120879, _1120881, _1120883] : [class_Lattices_Oab__semigroup__idem__mult(_1120879), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120879), _1120881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120879), _1120881), _1120883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120879), _1120881), _1120883))], (17516 ^ _779530) ^ [_1121013] : [_1121013 = hAPP(c_Nat_OSuc, _1121013)], (17518 ^ _779530) ^ [_1121048] : [hAPP(c_Nat_OSuc, _1121048) = _1121048], (17520 ^ _779530) ^ [_1121089, _1121091] : [hAPP(c_Nat_OSuc, _1121089) = hAPP(c_Nat_OSuc, _1121091), -(_1121089 = _1121091)], (17526 ^ _779530) ^ [_1121174, _1121176] : [_1121174 = _1121176, -(hAPP(c_Nat_OSuc, _1121174) = hAPP(c_Nat_OSuc, _1121176))], (17532 ^ _779530) ^ [_1121283, _1121285, _1121287] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121283)), _1121285) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121283)), _1121287), -(_1121285 = _1121287)], (17538 ^ _779530) ^ [_1121394, _1121396, _1121398] : [_1121396 = _1121398, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121394)), _1121396) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121394)), _1121398))], (17544 ^ _779530) ^ [_1121511, _1121513] : [hAPP(c_Nat_OSuc, _1121511) = hAPP(c_Nat_OSuc, _1121513), -(_1121511 = _1121513)], (17550 ^ _779530) ^ [_1121624, _1121626, _1121628, _1121630, _1121632] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1121624, _1121626, _1121628), _1121630), _1121632)), -(hBOOL(hAPP(_1121630, hAPP(_1121628, _1121632))))], (17556 ^ _779530) ^ [_1121731, _1121733, _1121735, _1121737, _1121739] : [hBOOL(hAPP(_1121737, hAPP(_1121735, _1121739))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1121731, _1121733, _1121735), _1121737), _1121739)))], (17562 ^ _779530) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (17564 ^ _779530) ^ [_1121886, _1121888, _1121890, _1121892, _1121894] : [hBOOL(hAPP(hAPP(c_member(_1121886), _1121888), hAPP(c_Set_Ovimage(_1121886, _1121890, _1121892), _1121894))), -(hBOOL(hAPP(hAPP(c_member(_1121890), hAPP(_1121892, _1121888)), _1121894)))], (17570 ^ _779530) ^ [_1122013, _1122015, _1122017, _1122019, _1122021] : [hBOOL(hAPP(hAPP(c_member(_1122017), hAPP(_1122019, _1122015)), _1122021)), -(hBOOL(hAPP(hAPP(c_member(_1122013), _1122015), hAPP(c_Set_Ovimage(_1122013, _1122017, _1122019), _1122021))))], (17576 ^ _779530) ^ [_1122146, _1122148, _1122150, _1122152, _1122154] : [hBOOL(hAPP(hAPP(c_member(_1122146), _1122148), hAPP(c_Set_Ovimage(_1122146, _1122150, _1122152), _1122154))), -(hBOOL(hAPP(hAPP(c_member(_1122150), hAPP(_1122152, _1122148)), _1122154)))], (17582 ^ _779530) ^ [_1122277, _1122279, _1122281, _1122283, _1122285] : [hBOOL(hAPP(hAPP(c_member(_1122277), hAPP(_1122279, _1122281)), _1122283)), -(hBOOL(hAPP(hAPP(c_member(_1122285), _1122281), hAPP(c_Set_Ovimage(_1122285, _1122277, _1122279), _1122283))))], (17588 ^ _779530) ^ [_1122408, _1122410] : [class_Orderings_Oorder(_1122408), 17591 ^ _779530 : [(17592 ^ _779530) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1122408, _1122410), 17595 ^ _779530 : [(17596 ^ _779530) ^ [_1122542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122408), hAPP(_1122410, _1122542)), hAPP(_1122410, hAPP(c_Nat_OSuc, _1122542)))))]]], (17598 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122408), hAPP(_1122410, 17599 ^ [_1122408, _1122410])), hAPP(_1122410, hAPP(c_Nat_OSuc, 17599 ^ [_1122408, _1122410])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1122408, _1122410))]]], (17605 ^ _779530) ^ [_1122715, _1122717, _1122719] : [-(hAPP(c_Set_Ovimage(_1122715, _1122717, _1122719), c_Orderings_Obot__class_Obot(tc_fun(_1122717, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1122715, tc_HOL_Obool)))], (17607 ^ _779530) ^ [_1122759, _1122761, _1122763, _1122765] : [class_Rings_Ocomm__semiring__1(_1122759), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122759), _1122761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122759), _1122763), _1122765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122759), _1122761), _1122763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122759), _1122761), _1122765)))], (17613 ^ _779530) ^ [_1122918, _1122920, _1122922, _1122924, _1122926] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1122918), 17616 ^ _779530 : [(17627 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122920), _1122924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122922), _1122926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122920), _1122926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122922), _1122924))), 17630 ^ _779530 : [(17631 ^ _779530) ^ [] : [_1122920 = _1122922], (17633 ^ _779530) ^ [] : [_1122924 = _1122926]]], (17617 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122920), _1122924)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122922), _1122926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1122918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122920), _1122926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122918), _1122922), _1122924)), -(_1122920 = _1122922), -(_1122924 = _1122926)]]], (17635 ^ _779530) ^ [_1123336, _1123338, _1123340, _1123342] : [class_Rings_Ocomm__semiring__1(_1123336), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123336), _1123338), _1123340)), _1123342) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123336), _1123338), _1123342)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123336), _1123340), _1123342)))], (17641 ^ _779530) ^ [_1123495, _1123497, _1123499, _1123501] : [class_Rings_Ocomm__semiring__1(_1123495), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123495), _1123497), _1123499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123495), _1123501), _1123499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123495), _1123497), _1123501)), _1123499))], (17647 ^ _779530) ^ [_1123654, _1123656, _1123658, _1123660, _1123662] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1123654), 17650 ^ _779530 : [(17661 ^ _779530) ^ [] : [17662 ^ _779530 : [(17663 ^ _779530) ^ [] : [_1123656 = _1123660], (17665 ^ _779530) ^ [] : [_1123658 = _1123662]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123656), _1123658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123660), _1123662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123656), _1123662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123660), _1123658)))], (17651 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123656), _1123658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123660), _1123662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123656), _1123662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123654), _1123660), _1123658)), -(_1123656 = _1123660), -(_1123658 = _1123662)]]], (17669 ^ _779530) ^ [_1124066, _1124068, _1124070, _1124072, _1124074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1124066, tc_HOL_Obool)), _1124068), _1124070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1124072, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1124072, _1124066, _1124074), _1124068)), hAPP(c_Set_Ovimage(_1124072, _1124066, _1124074), _1124070))))], (17675 ^ _779530) ^ [_1124217, _1124219, _1124221] : [-(hAPP(c_Set_Ovimage(_1124217, _1124219, _1124221), c_Orderings_Otop__class_Otop(tc_fun(_1124219, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1124217, tc_HOL_Obool)))], (17677 ^ _779530) ^ [_1124261, _1124263, _1124265, _1124267, _1124269] : [-(hAPP(c_Set_Ovimage(_1124261, _1124263, _1124265), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1124263, tc_HOL_Obool)), _1124267), _1124269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1124261, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1124261, _1124263, _1124265), _1124267)), hAPP(c_Set_Ovimage(_1124261, _1124263, _1124265), _1124269)))], (17679 ^ _779530) ^ [_1124335, _1124337, _1124339, _1124341, _1124343] : [-(hAPP(c_Set_Ovimage(_1124335, _1124337, _1124339), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1124337, tc_HOL_Obool)), _1124341), _1124343)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1124335, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1124335, _1124337, _1124339), _1124341)), hAPP(c_Set_Ovimage(_1124335, _1124337, _1124339), _1124343)))], (17681 ^ _779530) ^ [_1124409, _1124411, _1124413, _1124415, _1124417, _1124419] : [-(hAPP(c_Set_Ovimage(_1124409, _1124411, hAPP(c_Fun_Ocomp(_1124413, _1124411, _1124409, _1124415), _1124417)), _1124419) = hAPP(c_Set_Ovimage(_1124409, _1124413, _1124417), hAPP(c_Set_Ovimage(_1124413, _1124411, _1124415), _1124419)))], (17683 ^ _779530) ^ [_1124480, _1124482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124480), _1124482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124482), hAPP(c_Nat_OSuc, _1124480))))], (17689 ^ _779530) ^ [_1124525, _1124527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124527), hAPP(c_Nat_OSuc, _1124525))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124525), _1124527))], (17705 ^ _779530) ^ [_1124758, _1124760] : [17706 ^ _779530 : [(17707 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124758), _1124760))], (17709 ^ _779530) ^ [] : [_1124758 = _1124760]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124758), hAPP(c_Nat_OSuc, _1124760))))], (17695 ^ _779530) ^ [_1124646, _1124648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124646), hAPP(c_Nat_OSuc, _1124648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124646), _1124648))), -(_1124646 = _1124648)], (17713 ^ _779530) ^ [_1124916, _1124918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124916)), hAPP(c_Nat_OSuc, _1124918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124916), _1124918)))], (17719 ^ _779530) ^ [_1125021, _1125023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125021), _1125023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125021)), hAPP(c_Nat_OSuc, _1125023))))], (17725 ^ _779530) ^ [_1125131, _1125133] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125131), _1125133))), 17728 ^ _779530 : [(17729 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125131), hAPP(c_Nat_OSuc, _1125133))), -(_1125131 = _1125133)], (17735 ^ _779530) ^ [] : [_1125131 = _1125133, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125131), hAPP(c_Nat_OSuc, _1125133))))]]], (17741 ^ _779530) ^ [_1125364, _1125366] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125364), _1125366))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125364), hAPP(c_Nat_OSuc, _1125366))), -(_1125366 = _1125364)], (17751 ^ _779530) ^ [_1125512, _1125514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125512), _1125514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125512), hAPP(c_Nat_OSuc, _1125514))))], (17757 ^ _779530) ^ [_1125615, _1125617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125615), _1125617)), -(hAPP(c_Nat_OSuc, _1125615) = _1125617), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125615)), _1125617)))], (17767 ^ _779530) ^ [_1125739, _1125741, _1125743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125739), _1125741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125741), _1125743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125739)), _1125743)))], (17777 ^ _779530) ^ [_1125908, _1125910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125908), hAPP(c_Nat_OSuc, _1125910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125908), _1125910))), -(_1125908 = _1125910)], (17787 ^ _779530) ^ [_1126026, _1126028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126026)), _1126028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126026), _1126028)))], (17793 ^ _779530) ^ [_1126129, _1126131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126129)), hAPP(c_Nat_OSuc, _1126131))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1126129), _1126131)))], (17799 ^ _779530) ^ [_1126238, _1126240] : [class_Groups_Omonoid__mult(_1126238), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126238), c_Groups_Oone__class_Oone(_1126238)), _1126240) = _1126240)], (17805 ^ _779530) ^ [_1126333, _1126335] : [class_Groups_Ocomm__monoid__mult(_1126333), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126333), c_Groups_Oone__class_Oone(_1126333)), _1126335) = _1126335)], (17811 ^ _779530) ^ [_1126428, _1126430] : [class_Groups_Omonoid__mult(_1126428), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126428), _1126430), c_Groups_Oone__class_Oone(_1126428)) = _1126430)], (17817 ^ _779530) ^ [_1126523, _1126525] : [class_Groups_Ocomm__monoid__mult(_1126523), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126523), _1126525), c_Groups_Oone__class_Oone(_1126523)) = _1126525)], (17823 ^ _779530) ^ [_1126618, _1126620] : [class_Rings_Ocomm__semiring__1(_1126618), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126618), _1126620), c_Groups_Oone__class_Oone(_1126618)) = _1126620)], (17829 ^ _779530) ^ [_1126713, _1126715] : [class_Rings_Ocomm__semiring__1(_1126713), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126713), c_Groups_Oone__class_Oone(_1126713)), _1126715) = _1126715)], (17835 ^ _779530) ^ [_1126808, _1126810] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126808)), _1126810) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126808), hAPP(c_Nat_OSuc, _1126810)))], (17837 ^ _779530) ^ [_1126851, _1126853] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126851)), _1126853) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126851), _1126853)))], (17839 ^ _779530) ^ [_1126894, _1126896] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126894), hAPP(c_Nat_OSuc, _1126896)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126894), _1126896)))], (17841 ^ _779530) ^ [_1126937, _1126939, _1126941, _1126943, _1126945] : [-(hAPP(c_Set_Ovimage(_1126937, _1126939, _1126941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126939, tc_HOL_Obool)), _1126943), _1126945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126937, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1126937, _1126939, _1126941), _1126943)), hAPP(c_Set_Ovimage(_1126937, _1126939, _1126941), _1126945)))], (17843 ^ _779530) ^ [_1127020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127020)), _1127020))], (17845 ^ _779530) ^ [_1127060, _1127062] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127060), _1127062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127062)), _1127060)))], (17851 ^ _779530) ^ [_1127105, _1127107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127107)), _1127105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127105), _1127107))], (17867 ^ _779530) ^ [_1127344, _1127346] : [17868 ^ _779530 : [(17869 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127344), _1127346))], (17871 ^ _779530) ^ [] : [_1127344 = hAPP(c_Nat_OSuc, _1127346)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127344), hAPP(c_Nat_OSuc, _1127346))))], (17857 ^ _779530) ^ [_1127226, _1127228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127226), hAPP(c_Nat_OSuc, _1127228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127226), _1127228))), -(_1127226 = hAPP(c_Nat_OSuc, _1127228))], (17875 ^ _779530) ^ [_1127508, _1127510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127508)), hAPP(c_Nat_OSuc, _1127510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127508), _1127510)))], (17881 ^ _779530) ^ [_1127613, _1127615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127613), _1127615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127613)), hAPP(c_Nat_OSuc, _1127615))))], (17887 ^ _779530) ^ [_1127724, _1127726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127724), _1127726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127724), hAPP(c_Nat_OSuc, _1127726))))], (17893 ^ _779530) ^ [_1127827, _1127829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127827), hAPP(c_Nat_OSuc, _1127829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127827), _1127829))), -(_1127827 = hAPP(c_Nat_OSuc, _1127829))], (17903 ^ _779530) ^ [_1127951, _1127953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127951)), _1127953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127951), _1127953)))], (17909 ^ _779530) ^ [_1128054, _1128056] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1128054)), hAPP(c_Nat_OSuc, _1128056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128054), _1128056))], (17911 ^ _779530) ^ [_1128097, _1128099, _1128101] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1128097)), _1128099)), hAPP(c_Nat_OSuc, _1128101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128097), _1128099)), _1128101))], (17913 ^ _779530) ^ [_1128154, _1128156, _1128158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128154), _1128156)), _1128158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128154), _1128158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128156), _1128158)))], (17915 ^ _779530) ^ [_1128211, _1128213, _1128215] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128211), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128213), _1128215)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128211), _1128213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128211), _1128215)))], (17917 ^ _779530) ^ [_1128268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128268), _1128268))))], (17919 ^ _779530) ^ [_1128302] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128302), _1128302)))))], (17921 ^ _779530) ^ [_1128342, _1128344, _1128346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128342), _1128344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128342), _1128346)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128344), _1128346))))], (17927 ^ _779530) ^ [_1128465, _1128467, _1128469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128465), _1128467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128469), _1128465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128469), _1128467))))], (17933 ^ _779530) ^ [_1128588, _1128590, _1128592, _1128594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128588), _1128590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128592), _1128594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128588), _1128592)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128590), _1128594))))], (17943 ^ _779530) ^ [_1128779, _1128781, _1128783] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128781), _1128783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128779), _1128781)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128779), _1128783)))], (17945 ^ _779530) ^ [_1128836, _1128838, _1128840] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128836), _1128838)), _1128840) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128836), _1128840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128838), _1128840)))], (17947 ^ _779530) ^ [_1128893, _1128895, _1128897, _1128899] : [-(hAPP(c_Set_Ovimage(_1128893, _1128895, _1128897), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1128895, tc_HOL_Obool)), _1128899)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1128893, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1128893, _1128895, _1128897), _1128899)))], (17949 ^ _779530) ^ [_1128952] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1128952) = _1128952)], (17951 ^ _779530) ^ [_1128993, _1128995] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128993), _1128995), 17954 ^ _779530 : [(17955 ^ _779530) ^ [] : [-(_1128993 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17957 ^ _779530) ^ [] : [-(_1128995 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17959 ^ _779530) ^ [_1129104, _1129106] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129104), _1129106)), _1129104 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1129106 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17969 ^ _779530) ^ [_1129247] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129247), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1129247)], (17971 ^ _779530) ^ [_1129291, _1129293] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129291), _1129293) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17974 ^ _779530 : [(17975 ^ _779530) ^ [] : [-(_1129291 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17977 ^ _779530) ^ [] : [-(_1129293 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17979 ^ _779530) ^ [_1129402, _1129404] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129402), _1129404) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1129402 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1129404 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17989 ^ _779530) ^ [_1129545, _1129547, _1129549, _1129551] : [c_Natural_Oevaln(_1129545, _1129547, _1129549, _1129551), -(c_Natural_Oevaln(_1129545, _1129547, hAPP(c_Nat_OSuc, _1129549), _1129551))], (17995 ^ _779530) ^ [_1129640, _1129642, _1129644] : [class_Rings_Olinordered__semidom(_1129640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129640), c_Groups_Oone__class_Oone(_1129640)), _1129642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129640), c_Groups_Oone__class_Oone(_1129640)), _1129644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129640), c_Groups_Oone__class_Oone(_1129640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129640), _1129642), _1129644))))], (18009 ^ _779530) ^ [_1129895, _1129897, _1129899, _1129901, _1129903, _1129905] : [class_Rings_Oring(_1129895), 18012 ^ _779530 : [(18013 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), _1129897), _1129899)), _1129901) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), _1129903), _1129899)), _1129905), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1129895), _1129897), _1129903)), _1129899)), _1129901) = _1129905)], (18019 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1129895), _1129897), _1129903)), _1129899)), _1129901) = _1129905, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), _1129897), _1129899)), _1129901) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1129895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1129895), _1129903), _1129899)), _1129905))]]], (18025 ^ _779530) ^ [_1130292, _1130294, _1130296, _1130298, _1130300, _1130302] : [class_Rings_Oring(_1130292), 18028 ^ _779530 : [(18029 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), _1130294), _1130296)), _1130298) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), _1130300), _1130296)), _1130302), -(_1130298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130292), _1130300), _1130294)), _1130296)), _1130302))], (18035 ^ _779530) ^ [] : [_1130298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1130292), _1130300), _1130294)), _1130296)), _1130302), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), _1130294), _1130296)), _1130298) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1130292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130292), _1130300), _1130296)), _1130302))]]], (18041 ^ _779530) ^ [_1130689, _1130691] : [class_Rings_Oring__1__no__zero__divisors(_1130689), 18044 ^ _779530 : [(18055 ^ _779530) ^ [] : [18056 ^ _779530 : [(18057 ^ _779530) ^ [] : [_1130691 = c_Groups_Oone__class_Oone(_1130689)], (18059 ^ _779530) ^ [] : [_1130691 = hAPP(c_Groups_Ouminus__class_Ouminus(_1130689), c_Groups_Oone__class_Oone(_1130689))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130689), _1130691), _1130691) = c_Groups_Oone__class_Oone(_1130689))], (18045 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1130689), _1130691), _1130691) = c_Groups_Oone__class_Oone(_1130689), -(_1130691 = c_Groups_Oone__class_Oone(_1130689)), -(_1130691 = hAPP(c_Groups_Ouminus__class_Ouminus(_1130689), c_Groups_Oone__class_Oone(_1130689)))]]], (18063 ^ _779530) ^ [_1130996] : [class_Lattices_Oab__semigroup__idem__mult(_1130996), -(c_Finite__Set_Ofun__left__comm__idem(_1130996, _1130996, c_Groups_Otimes__class_Otimes(_1130996)))], (18069 ^ _779530) ^ [_1131075, _1131077, _1131079, _1131081] : [-(hAPP(c_Set_Ovimage(_1131075, _1131077, _1131079), hAPP(c_Set_OCollect(_1131077), _1131081)) = hAPP(c_Set_OCollect(_1131075), hAPP(hAPP(c_COMBB(_1131077, tc_HOL_Obool, _1131075), _1131081), _1131079)))], (18071 ^ _779530) ^ [_1131131, _1131133, _1131135] : [c_Hoare__Mirabelle_Otriple__valid(_1131131, hAPP(c_Nat_OSuc, _1131133), _1131135), -(c_Hoare__Mirabelle_Otriple__valid(_1131131, _1131133, _1131135))], (18077 ^ _779530) ^ [_1131220, _1131222, _1131224, _1131226, _1131228, _1131230] : [-(hAPP(c_Set_Ovimage(_1131220, _1131222, _1131224), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1131226, tc_fun(_1131222, tc_HOL_Obool)), _1131228), _1131230)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1131226, tc_fun(_1131220, tc_HOL_Obool)), _1131228), hAPP(hAPP(c_COMBB(tc_fun(_1131222, tc_HOL_Obool), tc_fun(_1131220, tc_HOL_Obool), _1131226), c_Set_Ovimage(_1131220, _1131222, _1131224)), _1131230)))], (18079 ^ _779530) ^ [_1131304, _1131306, _1131308, _1131310, _1131312] : [class_Rings_Osemiring__0(_1131304), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131304), _1131306), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131308, _1131304), _1131310), _1131312)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131308, _1131304), hAPP(hAPP(c_COMBB(_1131304, _1131304, _1131308), hAPP(c_Groups_Otimes__class_Otimes(_1131304), _1131306)), _1131310)), _1131312))], (18085 ^ _779530) ^ [_1131467, _1131469, _1131471, _1131473, _1131475] : [class_Rings_Osemiring__0(_1131467), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131467), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131469, _1131467), _1131471), _1131473)), _1131475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131469, _1131467), hAPP(hAPP(c_COMBC(_1131469, _1131467, _1131467), hAPP(hAPP(c_COMBB(_1131467, tc_fun(_1131467, _1131467), _1131469), c_Groups_Otimes__class_Otimes(_1131467)), _1131471)), _1131475)), _1131473))], (18091 ^ _779530) ^ [_1131650, _1131652, _1131654, _1131656, _1131658, _1131660, _1131662] : [class_Rings_Osemiring__0(_1131650), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131650), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131652, _1131650), _1131654), _1131656)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131658, _1131650), _1131660), _1131662)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131652, _1131650), hAPP(hAPP(c_COMBC(_1131652, tc_fun(_1131658, tc_HOL_Obool), _1131650), hAPP(hAPP(c_COMBB(tc_fun(_1131658, _1131650), tc_fun(tc_fun(_1131658, tc_HOL_Obool), _1131650), _1131652), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1131658, _1131650)), hAPP(hAPP(c_COMBC(_1131652, tc_fun(_1131658, _1131650), tc_fun(_1131658, _1131650)), hAPP(hAPP(c_COMBB(tc_fun(_1131650, _1131650), tc_fun(tc_fun(_1131658, _1131650), tc_fun(_1131658, _1131650)), _1131652), c_COMBB(_1131650, _1131650, _1131658)), hAPP(hAPP(c_COMBB(_1131650, tc_fun(_1131650, _1131650), _1131652), c_Groups_Otimes__class_Otimes(_1131650)), _1131654))), _1131660))), _1131662)), _1131656))], (18097 ^ _779530) ^ [_1131989, _1131991, _1131993, _1131995, _1131997, _1131999] : [class_Rings_Oordered__ring(_1131989), 18100 ^ _779530 : [(18101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), _1131991), _1131993)), _1131995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), _1131997), _1131993)), _1131999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131989), _1131995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1131989), _1131997), _1131991)), _1131993)), _1131999))))], (18107 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131989), _1131995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1131989), _1131997), _1131991)), _1131993)), _1131999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), _1131991), _1131993)), _1131995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131989), _1131997), _1131993)), _1131999))))]]], (18113 ^ _779530) ^ [_1132428, _1132430, _1132432, _1132434, _1132436, _1132438] : [class_Rings_Oordered__ring(_1132428), 18116 ^ _779530 : [(18117 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), _1132430), _1132432)), _1132434)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), _1132436), _1132432)), _1132438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132428), _1132430), _1132436)), _1132432)), _1132434)), _1132438)))], (18123 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132428), _1132430), _1132436)), _1132432)), _1132434)), _1132438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132428), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), _1132430), _1132432)), _1132434)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132428), _1132436), _1132432)), _1132438))))]]], (18129 ^ _779530) ^ [_1132867, _1132869, _1132871, _1132873, _1132875, _1132877] : [class_Rings_Oordered__ring(_1132867), 18132 ^ _779530 : [(18133 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), _1132869), _1132871)), _1132873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), _1132875), _1132871)), _1132877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132867), _1132869), _1132875)), _1132871)), _1132873)), _1132877)))], (18139 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1132867), _1132869), _1132875)), _1132871)), _1132873)), _1132877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1132867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), _1132869), _1132871)), _1132873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132867), _1132875), _1132871)), _1132877))))]]], (18145 ^ _779530) ^ [_1133306, _1133308, _1133310, _1133312, _1133314, _1133316] : [class_Rings_Oordered__ring(_1133306), 18148 ^ _779530 : [(18149 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), _1133308), _1133310)), _1133312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), _1133314), _1133310)), _1133316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133306), _1133312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1133306), _1133314), _1133308)), _1133310)), _1133316))))], (18155 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133306), _1133312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1133306), _1133314), _1133308)), _1133310)), _1133316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), _1133308), _1133310)), _1133312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133306), _1133314), _1133310)), _1133316))))]]], (18161 ^ _779530) ^ [_1133745, _1133747, _1133749, _1133751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133745, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1133747, _1133745, _1133749), hAPP(c_Set_Ovimage(_1133747, _1133745, _1133749), _1133751))), _1133751)))], (18163 ^ _779530) ^ [_1133798, _1133800, _1133802, _1133804] : [hAPP(c_Set_Oimage(_1133798, _1133800, _1133802), c_Orderings_Otop__class_Otop(tc_fun(_1133798, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1133800, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1133798, _1133800, _1133802), hAPP(c_Set_Ovimage(_1133798, _1133800, _1133802), _1133804)) = _1133804)], (18169 ^ _779530) ^ [_1133941, _1133943] : [class_Rings_Ocomm__semiring__1(_1133941), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133941), _1133943), _1133943) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133941), c_Groups_Oone__class_Oone(_1133941)), c_Groups_Oone__class_Oone(_1133941))), _1133943))], (18175 ^ _779530) ^ [_1134072, _1134074, _1134076] : [class_Rings_Ocomm__semiring__1(_1134072), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134072), _1134074), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134072), _1134076), _1134074)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134072), _1134076), c_Groups_Oone__class_Oone(_1134072))), _1134074))], (18181 ^ _779530) ^ [_1134217, _1134219, _1134221] : [class_Rings_Ocomm__semiring__1(_1134217), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134217), _1134219), _1134221)), _1134221) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134217), _1134219), c_Groups_Oone__class_Oone(_1134217))), _1134221))], (18187 ^ _779530) ^ [_1134377, _1134379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134377), _1134379)), -(_1134379 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1134377), 18190 ^ [_1134377, _1134379])))], (18194 ^ _779530) ^ [_1134490, _1134492] : [18195 ^ _779530 : [(18196 ^ _779530) ^ [_1134543] : [_1134492 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1134490), _1134543))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134490), _1134492)))], (18200 ^ _779530) ^ [_1134610, _1134612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134610), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1134612), _1134610)))))], (18202 ^ _779530) ^ [_1134649, _1134651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134649), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1134649), _1134651)))))], (18204 ^ _779530) ^ [_1134688, _1134690] : [class_Rings_Ocomm__ring__1(_1134688), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1134688), _1134690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134688), hAPP(c_Groups_Ouminus__class_Ouminus(_1134688), c_Groups_Oone__class_Oone(_1134688))), _1134690))], (18210 ^ _779530) ^ [_1134818, _1134820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134818), _1134820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1134818)), _1134820)))], (18216 ^ _779530) ^ [_1134917, _1134919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1134917)), _1134919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134917), _1134919)))], (18222 ^ _779530) ^ [_1135037, _1135039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135037), hAPP(c_Nat_OSuc, _1135039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1135037), _1135039)))], (18228 ^ _779530) ^ [_1135136, _1135138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1135136), _1135138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135136), hAPP(c_Nat_OSuc, _1135138))))], (18234 ^ _779530) ^ [_1135256, _1135258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1135256)), _1135258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135256), _1135258)))], (18240 ^ _779530) ^ [_1135355, _1135357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135355), _1135357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1135355)), _1135357)))], (18246 ^ _779530) ^ [_1135460, _1135462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1135460), _1135462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135460), hAPP(c_Nat_OSuc, _1135462))))], (18252 ^ _779530) ^ [_1135563, _1135565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135563), _1135565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1135563)), _1135565)))], (18258 ^ _779530) ^ [_1135666, _1135668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1135666), _1135668)), 18261 ^ _779530 : [(18262 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135668), hAPP(c_Nat_OSuc, _1135666))), -(_1135668 = _1135666)], (18268 ^ _779530) ^ [] : [_1135668 = _1135666, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135668), hAPP(c_Nat_OSuc, _1135666))))]]], (18274 ^ _779530) ^ [_1135907, _1135909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1135907)), _1135909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135907), _1135909)))], (18280 ^ _779530) ^ [_1136010, _1136012] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136010), _1136012)), hAPP(c_Nat_OSuc, _1136010))))], (18282 ^ _779530) ^ [_1136049, _1136051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1136049), _1136051)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1136051)), _1136049) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136051), _1136049)))], (18288 ^ _779530) ^ [_1136172] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1136172)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1136172)], (18290 ^ _779530) ^ [_1136204, _1136206, _1136208, _1136210] : [-(hAPP(c_Set_Ovimage(_1136204, _1136206, _1136208), _1136210) = hAPP(c_Set_OCollect(_1136204), hAPP(hAPP(c_COMBC(_1136204, tc_fun(_1136206, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1136206, tc_fun(tc_fun(_1136206, tc_HOL_Obool), tc_HOL_Obool), _1136204), c_member(_1136206)), _1136208)), _1136210)))], (18292 ^ _779530) ^ [_1136276] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136276) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1136276)))], (18294 ^ _779530) ^ [_1136308, _1136310, _1136312, _1136314, _1136316, _1136318] : [hAPP(_1136308, _1136310) = c_Option_Ooption_ONone(_1136312), -(c_Map_Omap__comp(_1136312, _1136314, _1136316, _1136318, _1136308, _1136310) = c_Option_Ooption_ONone(_1136314))], (18300 ^ _779530) ^ [_1136451, _1136453, _1136455, _1136457, _1136459, _1136461, _1136463] : [c_Map_Omap__comp(_1136451, _1136453, _1136455, _1136457, _1136459, _1136461) = hAPP(c_Option_Ooption_OSome(_1136453), _1136463), 18304 ^ _779530 : [(18305 ^ _779530) ^ [] : [-(hAPP(_1136459, _1136461) = hAPP(c_Option_Ooption_OSome(_1136451), 18303 ^ [_1136451, _1136453, _1136455, _1136457, _1136459, _1136461, _1136463]))], (18307 ^ _779530) ^ [] : [-(hAPP(_1136457, 18303 ^ [_1136451, _1136453, _1136455, _1136457, _1136459, _1136461, _1136463]) = hAPP(c_Option_Ooption_OSome(_1136453), _1136463))]]], (18309 ^ _779530) ^ [_1136655, _1136657, _1136659, _1136661, _1136663, _1136665, _1136667] : [-(c_Map_Omap__comp(_1136655, _1136657, _1136659, _1136661, _1136663, _1136665) = hAPP(c_Option_Ooption_OSome(_1136657), _1136667)), 18310 ^ _779530 : [(18311 ^ _779530) ^ [_1136733] : [hAPP(_1136663, _1136665) = hAPP(c_Option_Ooption_OSome(_1136655), _1136733), hAPP(_1136661, _1136733) = hAPP(c_Option_Ooption_OSome(_1136657), _1136667)]]], (18319 ^ _779530) ^ [_1136895, _1136897, _1136899, _1136901, _1136903, _1136905, _1136907] : [hAPP(_1136895, _1136897) = hAPP(c_Option_Ooption_OSome(_1136899), _1136901), -(c_Map_Omap__comp(_1136899, _1136903, _1136905, _1136907, _1136895, _1136897) = hAPP(_1136907, _1136901))], (18325 ^ _779530) ^ [_1137042, _1137044, _1137046, _1137048, _1137050] : [hBOOL(hAPP(hAPP(c_member(_1137042), _1137044), hAPP(c_Set_Ovimage(_1137042, _1137046, _1137048), hAPP(hAPP(c_Set_Oinsert(_1137046), _1137050), c_Orderings_Obot__class_Obot(tc_fun(_1137046, tc_HOL_Obool)))))), -(hAPP(_1137048, _1137044) = _1137050)], (18331 ^ _779530) ^ [_1137181, _1137183, _1137185, _1137187, _1137189] : [hAPP(_1137187, _1137183) = _1137189, -(hBOOL(hAPP(hAPP(c_member(_1137181), _1137183), hAPP(c_Set_Ovimage(_1137181, _1137185, _1137187), hAPP(hAPP(c_Set_Oinsert(_1137185), _1137189), c_Orderings_Obot__class_Obot(tc_fun(_1137185, tc_HOL_Obool)))))))], (18337 ^ _779530) ^ [_1137326, _1137328, _1137330, _1137332, _1137334] : [-(hAPP(c_Set_Ovimage(_1137326, _1137328, _1137330), hAPP(hAPP(c_Set_Oinsert(_1137328), _1137332), _1137334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1137326, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1137326, _1137328, _1137330), hAPP(hAPP(c_Set_Oinsert(_1137328), _1137332), c_Orderings_Obot__class_Obot(tc_fun(_1137328, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1137326, _1137328, _1137330), _1137334)))], (18339 ^ _779530) ^ [_1137410, _1137412, _1137414, _1137416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1137410), hAPP(c_Set_Ovimage(_1137410, _1137412, _1137414), _1137416))), hAPP(c_Set_Oimage(_1137410, _1137412, _1137414), c_Orderings_Otop__class_Otop(tc_fun(_1137410, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1137412, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1137412), _1137416)))], (18349 ^ _779530) ^ [_1137611, _1137613, _1137615, _1137617, _1137619] : [hAPP(c_Set_Oimage(_1137611, _1137613, _1137615), c_Orderings_Otop__class_Otop(tc_fun(_1137611, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1137613, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1137611, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1137611, _1137613, _1137615), _1137617)), _1137619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1137613, tc_HOL_Obool)), _1137617), hAPP(c_Set_Oimage(_1137611, _1137613, _1137615), _1137619))))], (18359 ^ _779530) ^ [_1137854, _1137856, _1137858, _1137860] : [-(hAPP(c_Set_Oimage(_1137854, _1137856, _1137858), hAPP(c_Set_Ovimage(_1137854, _1137856, _1137858), _1137860)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1137856, tc_HOL_Obool)), _1137860), hAPP(c_Set_Oimage(_1137854, _1137856, _1137858), c_Orderings_Otop__class_Otop(tc_fun(_1137854, tc_HOL_Obool)))))], (18361 ^ _779530) ^ [_1137920, _1137922, _1137924, _1137926] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1137920), _1137922)), c_Fun_Oinj__on(_1137924, _1137920, _1137926, c_Orderings_Otop__class_Otop(tc_fun(_1137924, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1137924), hAPP(c_Set_Ovimage(_1137924, _1137920, _1137926), _1137922))))], (18371 ^ _779530) ^ [_1138101, _1138103, _1138105, _1138107] : [c_Fun_Oinj__on(_1138101, _1138103, _1138105, c_Orderings_Otop__class_Otop(tc_fun(_1138101, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1138101, _1138103, _1138105), hAPP(c_Set_Oimage(_1138101, _1138103, _1138105), _1138107)) = _1138107)], (18377 ^ _779530) ^ [_1138224, _1138226, _1138228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138224), _1138226)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1138228), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1138226), _1138224))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1138228), _1138224)), hAPP(c_Nat_OSuc, _1138226)))], (18383 ^ _779530) ^ [_1138373, _1138375, _1138377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1138373), _1138375)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1138375), _1138373))), _1138377) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1138375)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1138373), _1138377)))], (18389 ^ _779530) ^ [_1138522, _1138524, _1138526] : [class_Rings_Olinordered__idom(_1138522), -(_1138524 = _1138526), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138522), _1138524), _1138526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138522), _1138526), _1138524)))], (18403 ^ _779530) ^ [_1138657, _1138659, _1138661, _1138663, _1138665] : [-(c_Map_Omap__comp(_1138657, _1138659, _1138661, _1138663, hAPP(c_COMBK(tc_Option_Ooption(_1138657), _1138661), c_Option_Ooption_ONone(_1138657)), _1138665) = c_Option_Ooption_ONone(_1138659))], (18405 ^ _779530) ^ [_1138707, _1138709, _1138711, _1138713, _1138715] : [-(c_Map_Omap__comp(_1138707, _1138709, _1138711, hAPP(c_COMBK(tc_Option_Ooption(_1138709), _1138707), c_Option_Ooption_ONone(_1138709)), _1138713, _1138715) = c_Option_Ooption_ONone(_1138709))], (18407 ^ _779530) ^ [_1138757] : [-(c_Relation_OId__on(_1138757, c_Orderings_Obot__class_Obot(tc_fun(_1138757, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1138757, _1138757), tc_HOL_Obool)))], (18409 ^ _779530) ^ [_1138811, _1138813, _1138815, _1138817] : [hBOOL(hAPP(hAPP(c_member(_1138811), _1138813), _1138815)), -(hAPP(c_Set_Ovimage(_1138817, _1138811, hAPP(c_COMBK(_1138811, _1138817), _1138813)), _1138815) = c_Orderings_Otop__class_Otop(tc_fun(_1138817, tc_HOL_Obool)))], (18415 ^ _779530) ^ [_1138936, _1138938, _1138940, _1138942] : [-(hBOOL(hAPP(hAPP(c_member(_1138936), _1138938), _1138940))), -(hAPP(c_Set_Ovimage(_1138942, _1138936, hAPP(c_COMBK(_1138936, _1138942), _1138938)), _1138940) = c_Orderings_Obot__class_Obot(tc_fun(_1138942, tc_HOL_Obool)))], (18421 ^ _779530) ^ [_1139003, _1139005, _1139007] : [-(hAPP(c_Relation_OImage(_1139003, _1139003, c_Relation_OId__on(_1139003, _1139005)), _1139007) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1139003, tc_HOL_Obool)), _1139005), _1139007))], (18423 ^ _779530) ^ [_1139051, _1139053, _1139055, _1139057] : [-(hAPP(c_Set_Ovimage(_1139051, _1139053, _1139055), _1139057) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1139053, tc_fun(_1139051, tc_HOL_Obool)), _1139057), hAPP(hAPP(c_COMBB(tc_fun(_1139053, tc_HOL_Obool), tc_fun(_1139051, tc_HOL_Obool), _1139053), c_Set_Ovimage(_1139051, _1139053, _1139055)), hAPP(hAPP(c_COMBC(_1139053, tc_fun(_1139053, tc_HOL_Obool), tc_fun(_1139053, tc_HOL_Obool)), c_Set_Oinsert(_1139053)), c_Orderings_Obot__class_Obot(tc_fun(_1139053, tc_HOL_Obool))))))], (18425 ^ _779530) ^ [_1139142, _1139144, _1139146, _1139148, _1139150] : [class_Groups_Ocomm__monoid__mult(_1139142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139144), _1139146)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1139142, _1139144, c_Groups_Otimes__class_Otimes(_1139142)), hAPP(hAPP(c_COMBS(_1139144, _1139142, _1139142), hAPP(hAPP(c_COMBB(_1139142, tc_fun(_1139142, _1139142), _1139144), c_Groups_Otimes__class_Otimes(_1139142)), _1139148)), _1139150)), c_Groups_Oone__class_Oone(_1139142)), _1139146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139142), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1139142, _1139144, c_Groups_Otimes__class_Otimes(_1139142)), _1139148), c_Groups_Oone__class_Oone(_1139142)), _1139146)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1139142, _1139144, c_Groups_Otimes__class_Otimes(_1139142)), _1139150), c_Groups_Oone__class_Oone(_1139142)), _1139146)))], (18435 ^ _779530) ^ [_1139457, _1139459, _1139461] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1139457), _1139459)), 18438 ^ _779530 : [(18439 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1139457), _1139461), _1139459)), -(hAPP(c_Finite__Set_Ocard(_1139457), hAPP(hAPP(c_Set_Oinsert(_1139457), _1139461), _1139459)) = hAPP(c_Finite__Set_Ocard(_1139457), _1139459))], (18445 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1139457), _1139461), _1139459))), -(hAPP(c_Finite__Set_Ocard(_1139457), hAPP(hAPP(c_Set_Oinsert(_1139457), _1139461), _1139459)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1139457), _1139459)))]]], (18451 ^ _779530) ^ [_1139751, _1139753, _1139755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1139751), _1139753)), -(hBOOL(hAPP(hAPP(c_member(_1139751), _1139755), _1139753))), -(hAPP(c_Finite__Set_Ocard(_1139751), hAPP(hAPP(c_Set_Oinsert(_1139751), _1139755), _1139753)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1139751), _1139753)))], (18461 ^ _779530) ^ [_1139909, _1139911, _1139913, _1139915, _1139917] : [c_Fun_Oinj__on(_1139909, _1139911, _1139913, c_Orderings_Otop__class_Otop(tc_fun(_1139909, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139911, tc_HOL_Obool)), _1139915), hAPP(c_Set_Oimage(_1139909, _1139911, _1139913), _1139917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139909, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1139909, _1139911, _1139913), _1139915)), _1139917)))], (18471 ^ _779530) ^ [_1140132, _1140134, _1140136, _1140138, _1140140, _1140142] : [class_Groups_Oab__semigroup__mult(_1140132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140134), _1140136)), -(hBOOL(hAPP(hAPP(c_member(_1140134), _1140138), _1140136))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1140132, _1140134, c_Groups_Otimes__class_Otimes(_1140132)), _1140140), _1140142), hAPP(hAPP(c_Set_Oinsert(_1140134), _1140138), _1140136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140132), hAPP(_1140140, _1140138)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1140132, _1140134, c_Groups_Otimes__class_Otimes(_1140132)), _1140140), _1140142), _1140136)))], (18485 ^ _779530) ^ [_1140431, _1140433, _1140435, _1140437, _1140439, _1140441] : [hBOOL(hAPP(hAPP(c_member(_1140431), _1140433), _1140435)), 18488 ^ _779530 : [(18489 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1140431), _1140437), _1140435)), -(hAPP(c_Set_Ovimage(_1140439, _1140431, hAPP(hAPP(c_COMBC(_1140439, _1140431, _1140431), hAPP(hAPP(c_COMBC(_1140439, _1140431, tc_fun(_1140431, _1140431)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1140431, tc_fun(_1140431, _1140431)), _1140439), c_If(_1140431)), hAPP(hAPP(c_COMBC(_1140439, tc_fun(_1140439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140439)), _1140441))), _1140433)), _1140437)), _1140435) = c_Orderings_Otop__class_Otop(tc_fun(_1140439, tc_HOL_Obool)))], (18495 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1140431), _1140437), _1140435))), -(hAPP(c_Set_Ovimage(_1140439, _1140431, hAPP(hAPP(c_COMBC(_1140439, _1140431, _1140431), hAPP(hAPP(c_COMBC(_1140439, _1140431, tc_fun(_1140431, _1140431)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1140431, tc_fun(_1140431, _1140431)), _1140439), c_If(_1140431)), hAPP(hAPP(c_COMBC(_1140439, tc_fun(_1140439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140439)), _1140441))), _1140433)), _1140437)), _1140435) = _1140441)]]], (18501 ^ _779530) ^ [_1140922, _1140924, _1140926, _1140928, _1140930, _1140932] : [-(hBOOL(hAPP(hAPP(c_member(_1140922), _1140924), _1140926))), 18504 ^ _779530 : [(18505 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1140922), _1140928), _1140926)), -(hAPP(c_Set_Ovimage(_1140930, _1140922, hAPP(hAPP(c_COMBC(_1140930, _1140922, _1140922), hAPP(hAPP(c_COMBC(_1140930, _1140922, tc_fun(_1140922, _1140922)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1140922, tc_fun(_1140922, _1140922)), _1140930), c_If(_1140922)), hAPP(hAPP(c_COMBC(_1140930, tc_fun(_1140930, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140930)), _1140932))), _1140924)), _1140928)), _1140926) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1140930, tc_HOL_Obool)), _1140932))], (18511 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1140922), _1140928), _1140926))), -(hAPP(c_Set_Ovimage(_1140930, _1140922, hAPP(hAPP(c_COMBC(_1140930, _1140922, _1140922), hAPP(hAPP(c_COMBC(_1140930, _1140922, tc_fun(_1140922, _1140922)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1140922, tc_fun(_1140922, _1140922)), _1140930), c_If(_1140922)), hAPP(hAPP(c_COMBC(_1140930, tc_fun(_1140930, tc_HOL_Obool), tc_HOL_Obool), c_member(_1140930)), _1140932))), _1140924)), _1140928)), _1140926) = c_Orderings_Obot__class_Obot(tc_fun(_1140930, tc_HOL_Obool)))]]], (18517 ^ _779530) ^ [_1141427, _1141429, _1141431, _1141433] : [_1141427 = _1141429, hBOOL(hAPP(hAPP(c_member(_1141431), _1141427), _1141433)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1141431, _1141431)), hAPP(hAPP(c_Product__Type_OPair(_1141431, _1141431), _1141427), _1141429)), c_Relation_OId__on(_1141431, _1141433))))], (18527 ^ _779530) ^ [_1141643, _1141645, _1141647, _1141649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1141643, _1141643)), hAPP(hAPP(c_Product__Type_OPair(_1141643, _1141643), _1141645), _1141647)), c_Relation_OId__on(_1141643, _1141649))), 18530 ^ _779530 : [(18531 ^ _779530) ^ [] : [-(_1141645 = _1141647)], (18533 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1141643), _1141645), _1141649)))]]], (18535 ^ _779530) ^ [_1141804, _1141806, _1141808, _1141810] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1141804, _1141804)), hAPP(hAPP(c_Product__Type_OPair(_1141804, _1141804), _1141806), _1141808)), c_Relation_OId__on(_1141804, _1141810)))), _1141806 = _1141808, hBOOL(hAPP(hAPP(c_member(_1141804), _1141806), _1141810))], (18545 ^ _779530) ^ [_1142028, _1142030, _1142032, _1142034, _1142036, _1142038] : [c_Map_Omap__comp(_1142028, _1142030, _1142032, _1142034, _1142036, _1142038) = c_Option_Ooption_ONone(_1142030), -(hAPP(_1142036, _1142038) = c_Option_Ooption_ONone(_1142028)), 18553 ^ _779530 : [(18554 ^ _779530) ^ [] : [-(hAPP(_1142036, _1142038) = hAPP(c_Option_Ooption_OSome(_1142028), 18552 ^ [_1142028, _1142030, _1142032, _1142034, _1142036, _1142038]))], (18556 ^ _779530) ^ [] : [-(hAPP(_1142034, 18552 ^ [_1142028, _1142030, _1142032, _1142034, _1142036, _1142038]) = c_Option_Ooption_ONone(_1142030))]]], (18558 ^ _779530) ^ [_1142254, _1142256, _1142258, _1142260, _1142262, _1142264] : [-(c_Map_Omap__comp(_1142254, _1142256, _1142258, _1142260, _1142262, _1142264) = c_Option_Ooption_ONone(_1142256)), 18559 ^ _779530 : [(18560 ^ _779530) ^ [] : [hAPP(_1142262, _1142264) = c_Option_Ooption_ONone(_1142254)], (18562 ^ _779530) ^ [_1142366] : [hAPP(_1142262, _1142264) = hAPP(c_Option_Ooption_OSome(_1142254), _1142366), hAPP(_1142260, _1142366) = c_Option_Ooption_ONone(_1142256)]]], (18570 ^ _779530) ^ [_1142519, _1142521, _1142523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1142519), _1142521)), -(hAPP(c_Finite__Set_Ocard(_1142519), hAPP(hAPP(c_Set_Oinsert(_1142519), _1142523), _1142521)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1142519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1142519, tc_HOL_Obool)), _1142521), hAPP(hAPP(c_Set_Oinsert(_1142519), _1142523), c_Orderings_Obot__class_Obot(tc_fun(_1142519, tc_HOL_Obool)))))))], (18576 ^ _779530) ^ [_1142696, _1142698, _1142700, _1142702, _1142704] : [class_Groups_Ocomm__monoid__mult(_1142696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142698), _1142700)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1142698), _1142702)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142696), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1142696, _1142698, c_Groups_Otimes__class_Otimes(_1142696)), _1142704), c_Groups_Oone__class_Oone(_1142696)), _1142700)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1142696, _1142698, c_Groups_Otimes__class_Otimes(_1142696)), _1142704), c_Groups_Oone__class_Oone(_1142696)), _1142702)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142696), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1142696, _1142698, c_Groups_Otimes__class_Otimes(_1142696)), _1142704), c_Groups_Oone__class_Oone(_1142696)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1142698, tc_HOL_Obool)), _1142700), _1142702))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1142696, _1142698, c_Groups_Otimes__class_Otimes(_1142696)), _1142704), c_Groups_Oone__class_Oone(_1142696)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1142698, tc_HOL_Obool)), _1142700), _1142702))))], (18590 ^ _779530) ^ [_1143121, _1143123, _1143125, _1143127, _1143129, _1143131, _1143133] : [class_Groups_Oab__semigroup__mult(_1143121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1143123), _1143125)), c_Fun_Oinj__on(_1143123, _1143127, _1143129, _1143125), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1143121, _1143127, c_Groups_Otimes__class_Otimes(_1143121)), _1143131), _1143133), hAPP(c_Set_Oimage(_1143123, _1143127, _1143129), _1143125)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1143121, _1143123, c_Groups_Otimes__class_Otimes(_1143121)), hAPP(c_Fun_Ocomp(_1143127, _1143121, _1143123, _1143131), _1143129)), _1143133), _1143125))], (18604 ^ _779530) ^ [_1143432, _1143434, _1143436, _1143438, _1143440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1143432), _1143434)), 18607 ^ _779530 : [(18608 ^ _779530) ^ [] : [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), _1143434), _1143436)), _1143438)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143432), _1143436)), _1143440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1143434), _1143432)), _1143436)), _1143438)), _1143440)))], (18614 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1143434), _1143432)), _1143436)), _1143438)), _1143440)), -(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), _1143434), _1143436)), _1143438)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143432), _1143436)), _1143440))))]]], (18620 ^ _779530) ^ [_1143823, _1143825, _1143827, _1143829, _1143831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1143823), _1143825)), 18623 ^ _779530 : [(18624 ^ _779530) ^ [] : [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), _1143823), _1143827)), _1143829)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143825), _1143827)), _1143831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143829), 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), _1143825), _1143823)), _1143827)), _1143831))))], (18630 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143829), 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), _1143825), _1143823)), _1143827)), _1143831))), -(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), _1143823), _1143827)), _1143829)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143825), _1143827)), _1143831))))]]], (18636 ^ _779530) ^ [_1144214, _1144216] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144214), hAPP(c_Nat_OSuc, _1144216)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144214), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1144216))], (18638 ^ _779530) ^ [_1144260] : [-(hAPP(c_Nat_OSuc, _1144260) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1144260))], (18640 ^ _779530) ^ [_1144289] : [-(hAPP(c_Nat_OSuc, _1144289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1144289), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18642 ^ _779530) ^ [_1144321, _1144323, _1144325, _1144327, _1144329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144321), _1144323)), 18645 ^ _779530 : [(18646 ^ _779530) ^ [] : [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), _1144323), _1144325)), _1144327)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144321), _1144325)), _1144329))), -(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), _1144323), _1144321)), _1144325)), _1144327)), _1144329)))], (18652 ^ _779530) ^ [] : [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), _1144323), _1144321)), _1144325)), _1144327)), _1144329)), -(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), _1144323), _1144325)), _1144327)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144321), _1144325)), _1144329))))]]], (18658 ^ _779530) ^ [_1144712, _1144714, _1144716, _1144718, _1144720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144712), _1144714)), -(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), _1144714), _1144716)), _1144718)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144712), _1144716)), _1144720)) = 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), _1144714), _1144712)), _1144716)), _1144718)), _1144720))], (18664 ^ _779530) ^ [_1144913, _1144915] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144913), _1144915) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144915), _1144913))], (18666 ^ _779530) ^ [_1144950, _1144952, _1144954] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144950), _1144952)), _1144954) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144952), _1144954)))], (18668 ^ _779530) ^ [_1145001, _1145003, _1145005, _1145007] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145001), _1145003)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145005), _1145003)), _1145007)) = 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), _1145001), _1145005)), _1145003)), _1145007))], (18670 ^ _779530) ^ [_1145072, _1145074, _1145076, _1145078, _1145080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145072), _1145074)), 18673 ^ _779530 : [(18674 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145072), _1145076)), _1145078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145074), _1145076)), _1145080), -(_1145078 = 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), _1145074), _1145072)), _1145076)), _1145080))], (18680 ^ _779530) ^ [] : [_1145078 = 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), _1145074), _1145072)), _1145076)), _1145080), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145072), _1145076)), _1145078) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145074), _1145076)), _1145080))]]], (18686 ^ _779530) ^ [_1145433, _1145435, _1145437, _1145439, _1145441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145433), _1145435)), -(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), _1145433), _1145437)), _1145439)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145435), _1145437)), _1145441)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145439), 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), _1145435), _1145433)), _1145437)), _1145441)))], (18692 ^ _779530) ^ [_1145634, _1145636, _1145638, _1145640, _1145642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145634), _1145636)), 18695 ^ _779530 : [(18696 ^ _779530) ^ [] : [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), _1145634), _1145638)), _1145640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145636), _1145638)), _1145642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145640), 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), _1145636), _1145634)), _1145638)), _1145642))))], (18702 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145640), 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), _1145636), _1145634)), _1145638)), _1145642))), -(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), _1145634), _1145638)), _1145640)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145636), _1145638)), _1145642))))]]], (18708 ^ _779530) ^ [_1146025, _1146027, _1146029, _1146031, _1146033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1146025), _1146027)), 18711 ^ _779530 : [(18712 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146027), _1146029)), _1146031) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146025), _1146029)), _1146033), -(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), _1146027), _1146025)), _1146029)), _1146031) = _1146033)], (18718 ^ _779530) ^ [] : [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), _1146027), _1146025)), _1146029)), _1146031) = _1146033, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146027), _1146029)), _1146031) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146025), _1146029)), _1146033))]]], (18724 ^ _779530) ^ [_1146386, _1146388, _1146390, _1146392, _1146394, _1146396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1146386), _1146388)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1146390), _1146392)), 18734 ^ _779530 : [(18735 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1146390), 18733 ^ [_1146386, _1146388, _1146390, _1146392, _1146394, _1146396]), _1146392)))], (18737 ^ _779530) ^ [] : [hAPP(c_Finite__Set_Ocard(_1146386), hAPP(c_Set_OCollect(_1146386), hAPP(hAPP(c_COMBS(_1146386, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1146386), c_fconj), hAPP(hAPP(c_COMBC(_1146386, tc_fun(_1146386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1146386)), _1146388))), hAPP(hAPP(c_COMBC(_1146386, _1146390, tc_HOL_Obool), _1146394), 18733 ^ [_1146386, _1146388, _1146390, _1146392, _1146394, _1146396])))) = _1146396]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1146386, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1146390, tc_HOL_Obool), tc_Nat_Onat, _1146386), c_Finite__Set_Ocard(_1146390)), hAPP(hAPP(c_COMBB(tc_fun(_1146390, tc_HOL_Obool), tc_fun(_1146390, tc_HOL_Obool), _1146386), c_Set_OCollect(_1146390)), hAPP(hAPP(c_COMBB(tc_fun(_1146390, tc_HOL_Obool), tc_fun(_1146390, tc_HOL_Obool), _1146386), hAPP(c_COMBS(_1146390, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1146390), c_fconj), hAPP(hAPP(c_COMBC(_1146390, tc_fun(_1146390, tc_HOL_Obool), tc_HOL_Obool), c_member(_1146390)), _1146392)))), _1146394)))), _1146388) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146396), hAPP(c_Finite__Set_Ocard(_1146390), _1146392)))], (18741 ^ _779530) ^ [_1147076, _1147078, _1147080, _1147082, _1147084] : [class_Groups_Ocomm__monoid__mult(_1147076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1147078), _1147080)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1147078), _1147082)), 18755 ^ _779530 : [(18756 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1147078), 18754 ^ [_1147076, _1147078, _1147080, _1147082, _1147084]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1147078, tc_HOL_Obool)), _1147080), _1147082))))], (18758 ^ _779530) ^ [] : [hAPP(_1147084, 18754 ^ [_1147076, _1147078, _1147080, _1147082, _1147084]) = c_Groups_Oone__class_Oone(_1147076)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1147076, _1147078, c_Groups_Otimes__class_Otimes(_1147076)), _1147084), c_Groups_Oone__class_Oone(_1147076)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1147078, tc_HOL_Obool)), _1147080), _1147082)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147076), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1147076, _1147078, c_Groups_Otimes__class_Otimes(_1147076)), _1147084), c_Groups_Oone__class_Oone(_1147076)), _1147080)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1147076, _1147078, c_Groups_Otimes__class_Otimes(_1147076)), _1147084), c_Groups_Oone__class_Oone(_1147076)), _1147082)))], (18762 ^ _779530) ^ [_1147619, _1147621] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1147619, _1147621)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1147619, _1147621), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1147621), c_Orderings_Otop__class_Otop(tc_fun(_1147621, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1147619), c_Orderings_Otop__class_Otop(tc_fun(_1147619, tc_HOL_Obool)))))], (18772 ^ _779530) ^ [_1147779, _1147781, _1147783] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1147779, _1147779)), _1147781), c_Relation_OId__on(_1147779, _1147783))), 18776 ^ _779530 : [(18777 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1147779), 18775 ^ [_1147779, _1147781, _1147783]), _1147783)))], (18779 ^ _779530) ^ [] : [-(_1147781 = hAPP(hAPP(c_Product__Type_OPair(_1147779, _1147779), 18775 ^ [_1147779, _1147781, _1147783]), 18775 ^ [_1147779, _1147781, _1147783]))]]], (18781 ^ _779530) ^ [_1147978, _1147980, _1147982, _1147984, _1147986] : [class_Groups_Oab__semigroup__mult(_1147978), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1147978, _1147978, c_Groups_Otimes__class_Otimes(_1147978), _1147980, _1147982), _1147984)), hBOOL(hAPP(hAPP(c_member(_1147978), _1147986), _1147982)), -(hBOOL(hAPP(hAPP(c_member(_1147978), _1147980), _1147982))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1147978, _1147978, c_Groups_Otimes__class_Otimes(_1147978), _1147986, hAPP(hAPP(c_Set_Oinsert(_1147978), _1147980), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1147978, tc_HOL_Obool)), _1147982), hAPP(hAPP(c_Set_Oinsert(_1147978), _1147986), c_Orderings_Obot__class_Obot(tc_fun(_1147978, tc_HOL_Obool)))))), _1147984)))], (18799 ^ _779530) ^ [_1148322, _1148324, _1148326] : [class_Orderings_Olinorder(_1148322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1148322), _1148324)), hBOOL(hAPP(hAPP(c_member(_1148322), _1148326), _1148324)), 18810 ^ _779530 : [(18811 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148322, tc_HOL_Obool)), _1148324), hAPP(hAPP(c_Set_Oinsert(_1148322), _1148326), c_Orderings_Obot__class_Obot(tc_fun(_1148322, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1148322, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1148322, _1148324) = _1148326)], (18817 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148322, tc_HOL_Obool)), _1148324), hAPP(hAPP(c_Set_Oinsert(_1148322), _1148326), c_Orderings_Obot__class_Obot(tc_fun(_1148322, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1148322, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1148322, _1148324) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148322), _1148326), c_Big__Operators_Olinorder__class_OMin(_1148322, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1148322, tc_HOL_Obool)), _1148324), hAPP(hAPP(c_Set_Oinsert(_1148322), _1148326), c_Orderings_Obot__class_Obot(tc_fun(_1148322, tc_HOL_Obool)))))))]]], (18823 ^ _779530) ^ [_1148837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148837), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18825 ^ _779530) ^ [_1148865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148865)))], (18827 ^ _779530) ^ [_1148890] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1148890))))], (18829 ^ _779530) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18831 ^ _779530) ^ [_1148936, _1148938] : [class_Groups_Ozero(_1148936), 18834 ^ _779530 : [(18835 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1148936) = _1148938, -(_1148938 = c_Groups_Ozero__class_Ozero(_1148936))], (18841 ^ _779530) ^ [] : [_1148938 = c_Groups_Ozero__class_Ozero(_1148936), -(c_Groups_Ozero__class_Ozero(_1148936) = _1148938)]]], (18847 ^ _779530) ^ [_1149153, _1149155] : [class_Orderings_Olinorder(_1149153), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149153), _1149155), _1149155) = _1149155)], (18853 ^ _779530) ^ [_1149244, _1149246, _1149248] : [class_Orderings_Olinorder(_1149244), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149244), _1149246), _1149248) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149244), _1149248), _1149246))], (18859 ^ _779530) ^ [_1149353, _1149355, _1149357] : [class_Orderings_Olinorder(_1149353), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149353), _1149355), _1149357) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149353), _1149357), _1149355))], (18865 ^ _779530) ^ [_1149462, _1149464, _1149466] : [class_Orderings_Olinorder(_1149462), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149462), _1149464), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149462), _1149464), _1149466)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149462), _1149464), _1149466))], (18871 ^ _779530) ^ [_1149587, _1149589, _1149591] : [class_Orderings_Olinorder(_1149587), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149587), _1149589), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149587), _1149589), _1149591)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149587), _1149589), _1149591))], (18877 ^ _779530) ^ [_1149712, _1149714, _1149716, _1149718] : [class_Orderings_Olinorder(_1149712), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149712), _1149714), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149712), _1149716), _1149718)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149712), _1149716), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149712), _1149714), _1149718)))], (18883 ^ _779530) ^ [_1149855, _1149857, _1149859, _1149861] : [class_Orderings_Olinorder(_1149855), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149855), _1149857), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149855), _1149859), _1149861)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149855), _1149859), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149855), _1149857), _1149861)))], (18889 ^ _779530) ^ [_1149998, _1150000, _1150002, _1150004] : [class_Orderings_Olinorder(_1149998), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149998), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149998), _1150000), _1150002)), _1150004) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149998), _1150000), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1149998), _1150002), _1150004)))], (18895 ^ _779530) ^ [_1150141, _1150143, _1150145, _1150147] : [class_Orderings_Olinorder(_1150141), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150141), _1150143), _1150145)), _1150147) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150141), _1150143), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150141), _1150145), _1150147)))], (18901 ^ _779530) ^ [_1150284] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150284) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18903 ^ _779530) ^ [_1150310] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1150310), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18905 ^ _779530) ^ [_1150339, _1150341] : [class_Orderings_Olinorder(_1150339), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150339), _1150341), _1150341) = _1150341)], (18911 ^ _779530) ^ [_1150430, _1150432, _1150434, _1150436] : [class_Orderings_Olinorder(_1150430), 18914 ^ _779530 : [(18925 ^ _779530) ^ [] : [18926 ^ _779530 : [(18927 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), _1150432), _1150436))], (18929 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), _1150434), _1150436))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150430), _1150432), _1150434)), _1150436)))], (18915 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150430), _1150432), _1150434)), _1150436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), _1150432), _1150436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150430), _1150434), _1150436)))]]], (18933 ^ _779530) ^ [_1150779, _1150781, _1150783] : [class_Orderings_Olinorder(_1150779), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150779), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150779), _1150781), _1150783)), _1150781)))], (18939 ^ _779530) ^ [_1150886, _1150888, _1150890] : [class_Orderings_Olinorder(_1150886), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150886), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150886), _1150888), _1150890)), _1150890)))], (18945 ^ _779530) ^ [_1150993, _1150995, _1150997] : [class_Orderings_Olinorder(_1150993), 18948 ^ _779530 : [(18949 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150993), _1150995), _1150997)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150993), _1150995), _1150997) = _1150995)], (18955 ^ _779530) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1150993), _1150995), _1150997) = _1150995, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150993), _1150995), _1150997)))]]], (18961 ^ _779530) ^ [_1151249, _1151251, _1151253, _1151255] : [class_Orderings_Olinorder(_1151249), 18964 ^ _779530 : [(18965 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1151249), _1151253), _1151255))), 18968 ^ _779530 : [(18969 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), _1151253)))], (18971 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), _1151255)))]]], (18973 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1151249), _1151253), _1151255)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), _1151253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151249), _1151251), _1151255))]]], (18983 ^ _779530) ^ [_1151629, _1151631, _1151633, _1151635] : [class_Orderings_Olinorder(_1151629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151629), _1151631), _1151633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151629), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1151629), _1151631), _1151635)), _1151633)))], (18993 ^ _779530) ^ [_1151808, _1151810, _1151812, _1151814] : [class_Orderings_Olinorder(_1151808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151808), _1151810), _1151812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151808), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1151808), _1151814), _1151810)), _1151812)))], (19003 ^ _779530) ^ [_1151987, _1151989, _1151991] : [class_Orderings_Olinorder(_1151987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151987), _1151989), _1151991)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1151987), _1151989), _1151991) = _1151989)], (19013 ^ _779530) ^ [_1152148, _1152150, _1152152] : [class_Orderings_Olinorder(_1152148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152148), _1152150), _1152152)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1152148), _1152152), _1152150) = _1152150)], (19023 ^ _779530) ^ [_1152309, _1152311, _1152313, _1152315] : [class_Orderings_Olinorder(_1152309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152309), _1152311), _1152313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152309), _1152311), _1152315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152309), _1152311), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1152309), _1152313), _1152315))))], (19037 ^ _779530) ^ [_1152558, _1152560, _1152562, _1152564] : [class_Orderings_Olinorder(_1152558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152558), _1152560), _1152562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152558), _1152560), _1152564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152558), _1152560), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1152558), _1152562), _1152564))))], (19051 ^ _779530) ^ [_1152807, _1152809, _1152811, _1152813, _1152815] : [class_Orderings_Olinorder(_1152807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152807), _1152809), _1152811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152807), _1152813), _1152815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152807), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1152807), _1152809), _1152813)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1152807), _1152811), _1152815))))], (19065 ^ _779530) ^ [_1153078, _1153080, _1153082, _1153084] : [class_Orderings_Olinorder(_1153078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153078), _1153080), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153078), _1153082), _1153084))), 19072 ^ _779530 : [(19073 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153078), _1153080), _1153082)))], (19075 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153078), _1153080), _1153084)))]]], (19077 ^ _779530) ^ [_1153301, _1153303, _1153305, _1153307] : [class_Orderings_Olinorder(_1153301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153301), _1153303), _1153305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153301), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153301), _1153303), _1153307)), _1153305)))], (19087 ^ _779530) ^ [_1153480, _1153482, _1153484, _1153486] : [class_Orderings_Olinorder(_1153480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153480), _1153482), _1153484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153480), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153480), _1153486), _1153482)), _1153484)))], (19097 ^ _779530) ^ [_1153659, _1153661, _1153663, _1153665] : [class_Orderings_Olinorder(_1153659), 19100 ^ _779530 : [(19101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153659), _1153663), _1153665))), 19104 ^ _779530 : [(19105 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), _1153663)))], (19107 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), _1153665)))]]], (19109 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153659), _1153663), _1153665)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), _1153663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153659), _1153661), _1153665))]]], (19119 ^ _779530) ^ [_1154039, _1154041, _1154043, _1154045] : [class_Orderings_Olinorder(_1154039), 19122 ^ _779530 : [(19133 ^ _779530) ^ [] : [19134 ^ _779530 : [(19135 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), _1154041), _1154045))], (19137 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), _1154043), _1154045))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154039), _1154041), _1154043)), _1154045)))], (19123 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154039), _1154041), _1154043)), _1154045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), _1154041), _1154045))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154039), _1154043), _1154045)))]]], (19141 ^ _779530) ^ [_1154388, _1154390, _1154392, _1154394] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1154388), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154388), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154388), _1154390), _1154392)), _1154394) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154388), _1154390), _1154394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154388), _1154392), _1154394)))], (19147 ^ _779530) ^ [_1154547, _1154549, _1154551, _1154553] : [class_Groups_Oordered__ab__group__add(_1154547), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154547), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154547), _1154549), _1154551)), _1154553) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154547), _1154549), _1154553)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154547), _1154551), _1154553)))], (19153 ^ _779530) ^ [_1154706] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1154706) = c_Orderings_Oord__class_Omin(_1154706)), class_Lattices_Osemilattice__inf(_1154706), class_Orderings_Olinorder(_1154706)], (19163 ^ _779530) ^ [_1154835, _1154837] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1154835)), hAPP(c_Nat_OSuc, _1154837)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1154835), _1154837)))], (19165 ^ _779530) ^ [_1154881, _1154883, _1154885] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1154881), _1154883)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1154885), _1154883)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1154881), _1154885)), _1154883))], (19167 ^ _779530) ^ [_1154938, _1154940] : [class_Groups_Omonoid__add(_1154938), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154938), c_Groups_Ozero__class_Ozero(_1154938)), _1154940) = _1154940)], (19173 ^ _779530) ^ [_1155033, _1155035] : [class_Groups_Ocomm__monoid__add(_1155033), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155033), c_Groups_Ozero__class_Ozero(_1155033)), _1155035) = _1155035)], (19179 ^ _779530) ^ [_1155128, _1155130] : [class_Groups_Olinordered__ab__group__add(_1155128), 19182 ^ _779530 : [(19183 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1155128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155128), _1155130), _1155130), -(_1155130 = c_Groups_Ozero__class_Ozero(_1155128))], (19189 ^ _779530) ^ [] : [_1155130 = c_Groups_Ozero__class_Ozero(_1155128), -(c_Groups_Ozero__class_Ozero(_1155128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155128), _1155130), _1155130))]]], (19195 ^ _779530) ^ [_1155369, _1155371] : [class_Groups_Omonoid__add(_1155369), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155369), _1155371), c_Groups_Ozero__class_Ozero(_1155369)) = _1155371)], (19201 ^ _779530) ^ [_1155464, _1155466] : [class_Groups_Ocomm__monoid__add(_1155464), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155464), _1155466), c_Groups_Ozero__class_Ozero(_1155464)) = _1155466)], (19207 ^ _779530) ^ [_1155559, _1155561] : [class_Rings_Ocomm__semiring__1(_1155559), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155559), c_Groups_Ozero__class_Ozero(_1155559)), _1155561) = _1155561)], (19213 ^ _779530) ^ [_1155654, _1155656] : [class_Rings_Ocomm__semiring__1(_1155654), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155654), _1155656), c_Groups_Ozero__class_Ozero(_1155654)) = _1155656)], (19219 ^ _779530) ^ [_1155749, _1155751, _1155753] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1155749), 19222 ^ _779530 : [(19223 ^ _779530) ^ [] : [_1155751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155749), _1155751), _1155753), -(_1155753 = c_Groups_Ozero__class_Ozero(_1155749))], (19229 ^ _779530) ^ [] : [_1155753 = c_Groups_Ozero__class_Ozero(_1155749), -(_1155751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155749), _1155751), _1155753))]]], (19235 ^ _779530) ^ [_1155990, _1155992] : [class_Rings_Ocomm__semiring__1(_1155990), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155990), c_Groups_Ozero__class_Ozero(_1155990)), _1155992) = c_Groups_Ozero__class_Ozero(_1155990))], (19241 ^ _779530) ^ [_1156089, _1156091] : [class_Rings_Ocomm__semiring__1(_1156089), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156089), _1156091), c_Groups_Ozero__class_Ozero(_1156089)) = c_Groups_Ozero__class_Ozero(_1156089))], (19247 ^ _779530) ^ [_1156188, _1156190, _1156192] : [class_Rings_Ono__zero__divisors(_1156188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156188), _1156190), _1156192) = c_Groups_Ozero__class_Ozero(_1156188), -(_1156190 = c_Groups_Ozero__class_Ozero(_1156188)), -(_1156192 = c_Groups_Ozero__class_Ozero(_1156188))], (19261 ^ _779530) ^ [_1156360, _1156362, _1156364] : [class_Rings_Ono__zero__divisors(_1156360), -(_1156362 = c_Groups_Ozero__class_Ozero(_1156360)), -(_1156364 = c_Groups_Ozero__class_Ozero(_1156360)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156360), _1156362), _1156364) = c_Groups_Ozero__class_Ozero(_1156360)], (19275 ^ _779530) ^ [_1156580, _1156582, _1156584] : [class_Rings_Oring__no__zero__divisors(_1156580), 19278 ^ _779530 : [(19289 ^ _779530) ^ [] : [19290 ^ _779530 : [(19291 ^ _779530) ^ [] : [_1156582 = c_Groups_Ozero__class_Ozero(_1156580)], (19293 ^ _779530) ^ [] : [_1156584 = c_Groups_Ozero__class_Ozero(_1156580)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156580), _1156582), _1156584) = c_Groups_Ozero__class_Ozero(_1156580))], (19279 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156580), _1156582), _1156584) = c_Groups_Ozero__class_Ozero(_1156580), -(_1156582 = c_Groups_Ozero__class_Ozero(_1156580)), -(_1156584 = c_Groups_Ozero__class_Ozero(_1156580))]]], (19297 ^ _779530) ^ [_1156878, _1156880] : [class_Rings_Omult__zero(_1156878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156878), _1156880), c_Groups_Ozero__class_Ozero(_1156878)) = c_Groups_Ozero__class_Ozero(_1156878))], (19303 ^ _779530) ^ [_1156977, _1156979] : [class_Rings_Omult__zero(_1156977), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156977), c_Groups_Ozero__class_Ozero(_1156977)), _1156979) = c_Groups_Ozero__class_Ozero(_1156977))], (19309 ^ _779530) ^ [_1157076, _1157078, _1157080] : [class_Groups_Ogroup__add(_1157076), 19312 ^ _779530 : [(19313 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157076), _1157078), _1157080) = c_Groups_Ozero__class_Ozero(_1157076), -(_1157078 = _1157080)], (19319 ^ _779530) ^ [] : [_1157078 = _1157080, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157076), _1157078), _1157080) = c_Groups_Ozero__class_Ozero(_1157076))]]], (19325 ^ _779530) ^ [_1157317, _1157319, _1157321] : [class_Groups_Oab__group__add(_1157317), 19328 ^ _779530 : [(19329 ^ _779530) ^ [] : [_1157319 = _1157321, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157317), _1157319), _1157321) = c_Groups_Ozero__class_Ozero(_1157317))], (19335 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157317), _1157319), _1157321) = c_Groups_Ozero__class_Ozero(_1157317), -(_1157319 = _1157321)]]], (19341 ^ _779530) ^ [_1157558, _1157560] : [class_Groups_Ogroup__add(_1157558), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157558), _1157560), _1157560) = c_Groups_Ozero__class_Ozero(_1157558))], (19347 ^ _779530) ^ [_1157653, _1157655] : [class_Groups_Ogroup__add(_1157653), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157653), _1157655), c_Groups_Ozero__class_Ozero(_1157653)) = _1157655)], (19353 ^ _779530) ^ [_1157748] : [class_Rings_Ozero__neq__one(_1157748), c_Groups_Oone__class_Oone(_1157748) = c_Groups_Ozero__class_Ozero(_1157748)], (19359 ^ _779530) ^ [_1157830] : [class_Rings_Ozero__neq__one(_1157830), c_Groups_Ozero__class_Ozero(_1157830) = c_Groups_Oone__class_Oone(_1157830)], (19365 ^ _779530) ^ [_1157912, _1157914, _1157916, _1157918, _1157920] : [class_Orderings_Olinorder(_1157912), class_Orderings_Olinorder(_1157914), c_Orderings_Oorder__class_Omono(_1157914, _1157912, _1157916), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157912), hAPP(_1157916, _1157918)), hAPP(_1157916, _1157920)) = hAPP(_1157916, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157914), _1157918), _1157920)))], (19379 ^ _779530) ^ [_1158161] : [class_Groups_Ogroup__add(_1158161), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1158161), c_Groups_Ozero__class_Ozero(_1158161)) = c_Groups_Ozero__class_Ozero(_1158161))], (19385 ^ _779530) ^ [_1158252, _1158254] : [class_Groups_Ogroup__add(_1158252), 19388 ^ _779530 : [(19389 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1158252) = hAPP(c_Groups_Ouminus__class_Ouminus(_1158252), _1158254), -(c_Groups_Ozero__class_Ozero(_1158252) = _1158254)], (19395 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1158252) = _1158254, -(c_Groups_Ozero__class_Ozero(_1158252) = hAPP(c_Groups_Ouminus__class_Ouminus(_1158252), _1158254))]]], (19401 ^ _779530) ^ [_1158484, _1158486] : [class_Groups_Olinordered__ab__group__add(_1158484), 19404 ^ _779530 : [(19405 ^ _779530) ^ [] : [_1158486 = hAPP(c_Groups_Ouminus__class_Ouminus(_1158484), _1158486), -(_1158486 = c_Groups_Ozero__class_Ozero(_1158484))], (19411 ^ _779530) ^ [] : [_1158486 = c_Groups_Ozero__class_Ozero(_1158484), -(_1158486 = hAPP(c_Groups_Ouminus__class_Ouminus(_1158484), _1158486))]]], (19417 ^ _779530) ^ [_1158710, _1158712] : [class_Groups_Ogroup__add(_1158710), 19420 ^ _779530 : [(19421 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1158710), _1158712) = c_Groups_Ozero__class_Ozero(_1158710), -(_1158712 = c_Groups_Ozero__class_Ozero(_1158710))], (19427 ^ _779530) ^ [] : [_1158712 = c_Groups_Ozero__class_Ozero(_1158710), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1158710), _1158712) = c_Groups_Ozero__class_Ozero(_1158710))]]], (19433 ^ _779530) ^ [_1158942, _1158944] : [class_Groups_Olinordered__ab__group__add(_1158942), 19436 ^ _779530 : [(19437 ^ _779530) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1158942), _1158944) = _1158944, -(_1158944 = c_Groups_Ozero__class_Ozero(_1158942))], (19443 ^ _779530) ^ [] : [_1158944 = c_Groups_Ozero__class_Ozero(_1158942), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1158942), _1158944) = _1158944)]]], (19449 ^ _779530) ^ [_1159177] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1159177)], (19451 ^ _779530) ^ [_1159212] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1159212)], (19453 ^ _779530) ^ [_1159247] : [hAPP(c_Nat_OSuc, _1159247) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19455 ^ _779530) ^ [_1159282] : [hAPP(c_Nat_OSuc, _1159282) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19457 ^ _779530) ^ [_1159317] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1159317)], (19459 ^ _779530) ^ [_1159352] : [hAPP(c_Nat_OSuc, _1159352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19461 ^ _779530) ^ [_1159387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159387), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19463 ^ _779530) ^ [_1159421] : [-(_1159421 = 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)), _1159421)))], (19469 ^ _779530) ^ [_1159453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159453)), _1159453 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19475 ^ _779530) ^ [_1159544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159544), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19477 ^ _779530) ^ [_1159572, _1159574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159572), _1159574)), _1159574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19483 ^ _779530) ^ [_1159656] : [-(_1159656 = 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)), _1159656)))], (19489 ^ _779530) ^ [_1159692, _1159694] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1159692), _1159694) = _1159692, -(_1159694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19495 ^ _779530) ^ [_1159796, _1159798] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1159796), _1159798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19498 ^ _779530 : [(19499 ^ _779530) ^ [] : [-(_1159796 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19501 ^ _779530) ^ [] : [-(_1159798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19503 ^ _779530) ^ [_1159907, _1159909] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1159907), _1159909) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159907 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1159909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19513 ^ _779530) ^ [_1160050] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160050), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1160050)], (19515 ^ _779530) ^ [_1160079] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160079) = _1160079)], (19517 ^ _779530) ^ [_1160105] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160105)))], (19519 ^ _779530) ^ [_1160142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160142), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1160142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19525 ^ _779530) ^ [_1160223] : [_1160223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160223), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19531 ^ _779530) ^ [_1160310] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160310) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19533 ^ _779530) ^ [_1160336] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160336), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1160336)], (19535 ^ _779530) ^ [_1160365] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160365), _1160365) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19537 ^ _779530) ^ [_1160394, _1160396] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160394), _1160396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160396), _1160394) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1160394 = _1160396)], (19557 ^ _779530) ^ [_1160677, _1160679, _1160681] : [19558 ^ _779530 : [(19559 ^ _779530) ^ [] : [_1160677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19561 ^ _779530) ^ [] : [_1160679 = _1160681]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160677), _1160679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160677), _1160681))], (19547 ^ _779530) ^ [_1160565, _1160567, _1160569] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160565), _1160567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160565), _1160569), -(_1160565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1160567 = _1160569)], (19575 ^ _779530) ^ [_1160950, _1160952, _1160954] : [19576 ^ _779530 : [(19577 ^ _779530) ^ [] : [_1160950 = _1160954], (19579 ^ _779530) ^ [] : [_1160952 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160950), _1160952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160954), _1160952))], (19565 ^ _779530) ^ [_1160838, _1160840, _1160842] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160838), _1160840) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1160842), _1160840), -(_1160838 = _1160842), -(_1160840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19593 ^ _779530) ^ [_1161223, _1161225, _1161227] : [19594 ^ _779530 : [(19595 ^ _779530) ^ [] : [_1161225 = _1161227], (19597 ^ _779530) ^ [] : [_1161223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161223), _1161225) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161223), _1161227))], (19583 ^ _779530) ^ [_1161111, _1161113, _1161115] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161111), _1161113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161111), _1161115), -(_1161113 = _1161115), -(_1161111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19611 ^ _779530) ^ [_1161479, _1161481] : [19612 ^ _779530 : [(19613 ^ _779530) ^ [] : [_1161479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19615 ^ _779530) ^ [] : [_1161481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161479), _1161481) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19601 ^ _779530) ^ [_1161381, _1161383] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161381), _1161383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1161381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1161383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19619 ^ _779530) ^ [_1161608] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161608), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19621 ^ _779530) ^ [_1161637] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161637) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19623 ^ _779530) ^ [_1161663, _1161665, _1161667, _1161669] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1161663, _1161665, _1161667, _1161669, c_Orderings_Obot__class_Obot(tc_fun(_1161663, tc_HOL_Obool))), _1161669)))], (19625 ^ _779530) ^ [_1161705, _1161707, _1161709, _1161711] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1161705, _1161707, _1161709, _1161711, c_Orderings_Obot__class_Obot(tc_fun(_1161705, tc_HOL_Obool))), _1161711)))], (19627 ^ _779530) ^ [_1161747, _1161749, _1161751, _1161753, _1161755] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1161747, _1161749, _1161751, _1161753, c_Orderings_Obot__class_Obot(tc_fun(_1161747, tc_HOL_Obool))), _1161755)), -(_1161755 = _1161753)], (19633 ^ _779530) ^ [_1161856, _1161858, _1161860, _1161862, _1161864, _1161866] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1161856, _1161858, _1161860, _1161862, _1161864), _1161866)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1161856), _1161864)))], (19639 ^ _779530) ^ [_1161965] : [class_Orderings_Olinorder(_1161965), -(c_Finite__Set_Ofun__left__comm__idem(_1161965, _1161965, c_Orderings_Oord__class_Omin(_1161965)))], (19645 ^ _779530) ^ [_1162044, _1162046, _1162048] : [class_Groups_Ocomm__monoid__add(_1162044), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162046, _1162044), hAPP(c_COMBK(_1162044, _1162046), c_Groups_Ozero__class_Ozero(_1162044))), _1162048) = c_Groups_Ozero__class_Ozero(_1162044))], (19651 ^ _779530) ^ [_1162159, _1162161] : [hBOOL(hAPP(_1162159, _1162161)), -(hBOOL(hAPP(_1162159, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1162159) = 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), _1162159), c_Nat_OSuc))))], (19661 ^ _779530) ^ [_1162289, _1162291] : [class_Groups_Olinordered__ab__group__add(_1162289), 19664 ^ _779530 : [(19665 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162289), c_Groups_Ozero__class_Ozero(_1162289)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162289), _1162291), _1162291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162289), c_Groups_Ozero__class_Ozero(_1162289)), _1162291)))], (19671 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162289), c_Groups_Ozero__class_Ozero(_1162289)), _1162291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162289), c_Groups_Ozero__class_Ozero(_1162289)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162289), _1162291), _1162291))))]]], (19677 ^ _779530) ^ [_1162572, _1162574] : [class_Groups_Olinordered__ab__group__add(_1162572), 19680 ^ _779530 : [(19681 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162572), _1162574), _1162574)), c_Groups_Ozero__class_Ozero(_1162572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162572), _1162574), c_Groups_Ozero__class_Ozero(_1162572))))], (19687 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162572), _1162574), c_Groups_Ozero__class_Ozero(_1162572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162572), _1162574), _1162574)), c_Groups_Ozero__class_Ozero(_1162572))))]]], (19693 ^ _779530) ^ [_1162855, _1162857, _1162859] : [class_Groups_Oordered__comm__monoid__add(_1162855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162855), c_Groups_Ozero__class_Ozero(_1162855)), _1162857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162855), c_Groups_Ozero__class_Ozero(_1162855)), _1162859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162855), c_Groups_Ozero__class_Ozero(_1162855)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162855), _1162857), _1162859))))], (19707 ^ _779530) ^ [_1163110, _1163112, _1163114] : [class_Groups_Oordered__comm__monoid__add(_1163110), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163110), c_Groups_Ozero__class_Ozero(_1163110)), _1163112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163110), c_Groups_Ozero__class_Ozero(_1163110)), _1163114)), 19718 ^ _779530 : [(19719 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163110), _1163112), _1163114) = c_Groups_Ozero__class_Ozero(_1163110), 19722 ^ _779530 : [(19723 ^ _779530) ^ [] : [-(_1163112 = c_Groups_Ozero__class_Ozero(_1163110))], (19725 ^ _779530) ^ [] : [-(_1163114 = c_Groups_Ozero__class_Ozero(_1163110))]]], (19727 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163110), _1163112), _1163114) = c_Groups_Ozero__class_Ozero(_1163110)), _1163112 = c_Groups_Ozero__class_Ozero(_1163110), _1163114 = c_Groups_Ozero__class_Ozero(_1163110)]]], (19737 ^ _779530) ^ [_1163581, _1163583, _1163585, _1163587] : [class_Groups_Oordered__comm__monoid__add(_1163581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163581), c_Groups_Ozero__class_Ozero(_1163581)), _1163583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163581), _1163585), _1163587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163581), _1163585), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163581), _1163583), _1163587))))], (19751 ^ _779530) ^ [_1163834, _1163836, _1163838, _1163840] : [class_Groups_Oordered__comm__monoid__add(_1163834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163834), c_Groups_Ozero__class_Ozero(_1163834)), _1163836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163834), _1163838), _1163840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163834), _1163838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163834), _1163840), _1163836))))], (19765 ^ _779530) ^ [_1164087, _1164089, _1164091] : [class_Groups_Oordered__comm__monoid__add(_1164087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164087), _1164089), c_Groups_Ozero__class_Ozero(_1164087))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164087), _1164091), c_Groups_Ozero__class_Ozero(_1164087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164087), _1164089), _1164091)), c_Groups_Ozero__class_Ozero(_1164087))))], (19779 ^ _779530) ^ [_1164342, _1164344, _1164346] : [class_Rings_Oordered__cancel__semiring(_1164342), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164342), _1164344), _1164346)), c_Groups_Ozero__class_Ozero(_1164342)))), 19784 ^ _779530 : [(19785 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164342), c_Groups_Ozero__class_Ozero(_1164342)), _1164344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164342), _1164346), c_Groups_Ozero__class_Ozero(_1164342)))], (19791 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164342), _1164344), c_Groups_Ozero__class_Ozero(_1164342))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164342), c_Groups_Ozero__class_Ozero(_1164342)), _1164346))]]], (19799 ^ _779530) ^ [_1164718, _1164720, _1164722] : [class_Rings_Oordered__ring(_1164718), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164718), c_Groups_Ozero__class_Ozero(_1164718)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164718), _1164720), _1164722)))), 19804 ^ _779530 : [(19805 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164718), c_Groups_Ozero__class_Ozero(_1164718)), _1164720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164718), c_Groups_Ozero__class_Ozero(_1164718)), _1164722))], (19811 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164718), _1164720), c_Groups_Ozero__class_Ozero(_1164718))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164718), _1164722), c_Groups_Ozero__class_Ozero(_1164718)))]]], (19819 ^ _779530) ^ [_1165094, _1165096, _1165098, _1165100, _1165102] : [class_Rings_Oordered__semiring(_1165094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165094), _1165096), _1165098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165094), _1165100), _1165102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165094), c_Groups_Ozero__class_Ozero(_1165094)), _1165098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165094), c_Groups_Ozero__class_Ozero(_1165094)), _1165100)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165094), _1165096), _1165100)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165094), _1165098), _1165102))))], (19841 ^ _779530) ^ [_1165517, _1165519, _1165521, _1165523, _1165525] : [class_Rings_Oordered__semiring(_1165517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165517), _1165519), _1165521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165517), _1165523), _1165525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165517), c_Groups_Ozero__class_Ozero(_1165517)), _1165519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165517), c_Groups_Ozero__class_Ozero(_1165517)), _1165523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165517), _1165519), _1165523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165517), _1165521), _1165525))))], (19863 ^ _779530) ^ [_1165940, _1165942, _1165944, _1165946] : [class_Rings_Oordered__ring(_1165940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165940), _1165942), _1165944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165940), _1165946), c_Groups_Ozero__class_Ozero(_1165940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165940), _1165946), _1165944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165940), _1165946), _1165942))))], (19877 ^ _779530) ^ [_1166209, _1166211, _1166213, _1166215] : [class_Rings_Oordered__ring(_1166209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166209), _1166211), _1166213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166209), _1166215), c_Groups_Ozero__class_Ozero(_1166209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166209), _1166213), _1166215)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166209), _1166211), _1166215))))], (19891 ^ _779530) ^ [_1166478, _1166480, _1166482, _1166484] : [class_Rings_Oordered__comm__semiring(_1166478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166478), _1166480), _1166482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166478), c_Groups_Ozero__class_Ozero(_1166478)), _1166484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166478), _1166484), _1166480)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166478), _1166484), _1166482))))], (19905 ^ _779530) ^ [_1166747, _1166749, _1166751, _1166753] : [class_Rings_Oordered__semiring(_1166747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166747), _1166749), _1166751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166747), c_Groups_Ozero__class_Ozero(_1166747)), _1166753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166747), _1166753), _1166749)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166747), _1166753), _1166751))))], (19919 ^ _779530) ^ [_1167016, _1167018, _1167020, _1167022] : [class_Rings_Oordered__semiring(_1167016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167016), _1167018), _1167020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167016), c_Groups_Ozero__class_Ozero(_1167016)), _1167022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167016), _1167018), _1167022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167016), _1167020), _1167022))))], (19933 ^ _779530) ^ [_1167285, _1167287, _1167289] : [class_Rings_Oordered__ring(_1167285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167285), _1167287), c_Groups_Ozero__class_Ozero(_1167285))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167285), _1167289), c_Groups_Ozero__class_Ozero(_1167285))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167285), c_Groups_Ozero__class_Ozero(_1167285)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167285), _1167287), _1167289))))], (19947 ^ _779530) ^ [_1167540, _1167542, _1167544] : [class_Rings_Oordered__cancel__semiring(_1167540), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167540), _1167542), c_Groups_Ozero__class_Ozero(_1167540))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167540), c_Groups_Ozero__class_Ozero(_1167540)), _1167544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167540), _1167542), _1167544)), c_Groups_Ozero__class_Ozero(_1167540))))], (19961 ^ _779530) ^ [_1167795, _1167797, _1167799] : [class_Rings_Oordered__cancel__semiring(_1167795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167795), c_Groups_Ozero__class_Ozero(_1167795)), _1167797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167795), _1167799), c_Groups_Ozero__class_Ozero(_1167795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167795), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167795), _1167799), _1167797)), c_Groups_Ozero__class_Ozero(_1167795))))], (19975 ^ _779530) ^ [_1168050, _1168052, _1168054] : [class_Rings_Oordered__cancel__semiring(_1168050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168050), c_Groups_Ozero__class_Ozero(_1168050)), _1168052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168050), _1168054), c_Groups_Ozero__class_Ozero(_1168050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168050), _1168052), _1168054)), c_Groups_Ozero__class_Ozero(_1168050))))], (19989 ^ _779530) ^ [_1168305, _1168307, _1168309] : [class_Rings_Oordered__cancel__semiring(_1168305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168305), c_Groups_Ozero__class_Ozero(_1168305)), _1168307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168305), c_Groups_Ozero__class_Ozero(_1168305)), _1168309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168305), c_Groups_Ozero__class_Ozero(_1168305)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168305), _1168307), _1168309))))], (20003 ^ _779530) ^ [_1168560, _1168562, _1168564] : [class_Rings_Olinordered__ring__strict(_1168560), 20006 ^ _779530 : [(20007 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168560), _1168562), _1168564)), c_Groups_Ozero__class_Ozero(_1168560))), 20012 ^ _779530 : [(20013 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), c_Groups_Ozero__class_Ozero(_1168560)), _1168562)))], (20015 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), _1168564), c_Groups_Ozero__class_Ozero(_1168560))))]], 20016 ^ _779530 : [(20017 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), _1168562), c_Groups_Ozero__class_Ozero(_1168560))))], (20019 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), c_Groups_Ozero__class_Ozero(_1168560)), _1168564)))]]], (20021 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168560), _1168562), _1168564)), c_Groups_Ozero__class_Ozero(_1168560)))), 20022 ^ _779530 : [(20023 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), c_Groups_Ozero__class_Ozero(_1168560)), _1168562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), _1168564), c_Groups_Ozero__class_Ozero(_1168560)))], (20029 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), _1168562), c_Groups_Ozero__class_Ozero(_1168560))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168560), c_Groups_Ozero__class_Ozero(_1168560)), _1168564))]]]]], (20037 ^ _779530) ^ [_1169150, _1169152, _1169154] : [class_Rings_Olinordered__ring__strict(_1169150), 20040 ^ _779530 : [(20041 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169150), _1169152), _1169154))), 20046 ^ _779530 : [(20047 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), _1169152)))], (20049 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), _1169154)))]], 20050 ^ _779530 : [(20051 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), _1169152), c_Groups_Ozero__class_Ozero(_1169150))))], (20053 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), _1169154), c_Groups_Ozero__class_Ozero(_1169150))))]]], (20055 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169150), _1169152), _1169154)))), 20056 ^ _779530 : [(20057 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), _1169152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), c_Groups_Ozero__class_Ozero(_1169150)), _1169154))], (20063 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), _1169152), c_Groups_Ozero__class_Ozero(_1169150))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169150), _1169154), c_Groups_Ozero__class_Ozero(_1169150)))]]]]], (20071 ^ _779530) ^ [_1169740, _1169742] : [class_Rings_Olinordered__ring(_1169740), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169740), c_Groups_Ozero__class_Ozero(_1169740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169740), _1169742), _1169742))))], (20077 ^ _779530) ^ [_1169849, _1169851, _1169853, _1169855] : [class_Rings_Olinordered__semidom(_1169849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169849), c_Groups_Ozero__class_Ozero(_1169849)), _1169851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169849), _1169853), _1169855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169849), _1169853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169849), _1169851), _1169855))))], (20091 ^ _779530) ^ [_1170102, _1170104] : [class_Groups_Olinordered__ab__group__add(_1170102), 20094 ^ _779530 : [(20095 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170102), c_Groups_Ozero__class_Ozero(_1170102)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170102), _1170104), _1170104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170102), c_Groups_Ozero__class_Ozero(_1170102)), _1170104)))], (20101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170102), c_Groups_Ozero__class_Ozero(_1170102)), _1170104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170102), c_Groups_Ozero__class_Ozero(_1170102)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170102), _1170104), _1170104))))]]], (20107 ^ _779530) ^ [_1170385, _1170387] : [class_Groups_Olinordered__ab__group__add(_1170385), 20110 ^ _779530 : [(20111 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170385), _1170387), _1170387)), c_Groups_Ozero__class_Ozero(_1170385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170385), _1170387), c_Groups_Ozero__class_Ozero(_1170385))))], (20117 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170385), _1170387), c_Groups_Ozero__class_Ozero(_1170385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170385), _1170387), _1170387)), c_Groups_Ozero__class_Ozero(_1170385))))]]], (20123 ^ _779530) ^ [_1170668, _1170670, _1170672] : [class_Groups_Oordered__comm__monoid__add(_1170668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170668), c_Groups_Ozero__class_Ozero(_1170668)), _1170670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170668), c_Groups_Ozero__class_Ozero(_1170668)), _1170672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170668), c_Groups_Ozero__class_Ozero(_1170668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170668), _1170670), _1170672))))], (20137 ^ _779530) ^ [_1170923, _1170925, _1170927] : [class_Groups_Oordered__comm__monoid__add(_1170923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170923), _1170925), c_Groups_Ozero__class_Ozero(_1170923))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170923), _1170927), c_Groups_Ozero__class_Ozero(_1170923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170923), _1170925), _1170927)), c_Groups_Ozero__class_Ozero(_1170923))))], (20151 ^ _779530) ^ [_1171178, _1171180] : [class_Rings_Olinordered__ring(_1171178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171178), _1171180), _1171180)), c_Groups_Ozero__class_Ozero(_1171178)))], (20157 ^ _779530) ^ [_1171288, _1171290, _1171292, _1171294] : [class_Rings_Olinordered__ring__strict(_1171288), 20160 ^ _779530 : [(20161 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171288), _1171290), _1171292)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171288), _1171294), _1171292))), 20166 ^ _779530 : [(20167 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), c_Groups_Ozero__class_Ozero(_1171288)), _1171292)))], (20169 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171290), _1171294)))]], 20170 ^ _779530 : [(20171 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171292), c_Groups_Ozero__class_Ozero(_1171288))))], (20173 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171294), _1171290)))]]], (20175 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171288), _1171290), _1171292)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171288), _1171294), _1171292)))), 20176 ^ _779530 : [(20177 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), c_Groups_Ozero__class_Ozero(_1171288)), _1171292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171290), _1171294))], (20183 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171292), c_Groups_Ozero__class_Ozero(_1171288))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171288), _1171294), _1171290))]]]]], (20191 ^ _779530) ^ [_1171894, _1171896, _1171898, _1171900] : [class_Rings_Olinordered__ring__strict(_1171894), 20194 ^ _779530 : [(20195 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171894), _1171896), _1171898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171894), _1171896), _1171900))), 20200 ^ _779530 : [(20201 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), c_Groups_Ozero__class_Ozero(_1171894)), _1171896)))], (20203 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171898), _1171900)))]], 20204 ^ _779530 : [(20205 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171896), c_Groups_Ozero__class_Ozero(_1171894))))], (20207 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171900), _1171898)))]]], (20209 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171894), _1171896), _1171898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171894), _1171896), _1171900)))), 20210 ^ _779530 : [(20211 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), c_Groups_Ozero__class_Ozero(_1171894)), _1171896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171898), _1171900))], (20217 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171896), c_Groups_Ozero__class_Ozero(_1171894))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171894), _1171900), _1171898))]]]]], (20225 ^ _779530) ^ [_1172500, _1172502, _1172504, _1172506] : [class_Rings_Olinordered__ring__strict(_1172500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172500), c_Groups_Ozero__class_Ozero(_1172500)), _1172502)), 20232 ^ _779530 : [(20233 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172500), _1172502), _1172504)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172500), _1172502), _1172506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172500), _1172504), _1172506)))], (20239 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172500), _1172504), _1172506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172500), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172500), _1172502), _1172504)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172500), _1172502), _1172506))))]]], (20245 ^ _779530) ^ [_1172881, _1172883, _1172885] : [class_Rings_Olinordered__semiring__strict(_1172881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172881), c_Groups_Ozero__class_Ozero(_1172881)), _1172883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172881), c_Groups_Ozero__class_Ozero(_1172881)), _1172885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172881), c_Groups_Ozero__class_Ozero(_1172881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172881), _1172883), _1172885))))], (20259 ^ _779530) ^ [_1173136, _1173138, _1173140] : [class_Rings_Olinordered__semiring__strict(_1173136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173136), c_Groups_Ozero__class_Ozero(_1173136)), _1173138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173136), _1173140), c_Groups_Ozero__class_Ozero(_1173136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173136), _1173138), _1173140)), c_Groups_Ozero__class_Ozero(_1173136))))], (20273 ^ _779530) ^ [_1173391, _1173393, _1173395] : [class_Rings_Olinordered__semiring__strict(_1173391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173391), c_Groups_Ozero__class_Ozero(_1173391)), _1173393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173391), _1173395), c_Groups_Ozero__class_Ozero(_1173391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173391), _1173395), _1173393)), c_Groups_Ozero__class_Ozero(_1173391))))], (20287 ^ _779530) ^ [_1173646, _1173648, _1173650] : [class_Rings_Olinordered__semiring__strict(_1173646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173646), c_Groups_Ozero__class_Ozero(_1173646)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173646), _1173648), _1173650))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173646), c_Groups_Ozero__class_Ozero(_1173646)), _1173648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173646), c_Groups_Ozero__class_Ozero(_1173646)), _1173650)))], (20301 ^ _779530) ^ [_1173901, _1173903, _1173905] : [class_Rings_Olinordered__semiring__strict(_1173901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173901), c_Groups_Ozero__class_Ozero(_1173901)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173901), _1173903), _1173905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173901), c_Groups_Ozero__class_Ozero(_1173901)), _1173905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1173901), c_Groups_Ozero__class_Ozero(_1173901)), _1173903)))], (20315 ^ _779530) ^ [_1174156, _1174158, _1174160, _1174162] : [class_Rings_Olinordered__ring__strict(_1174156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174156), _1174158), c_Groups_Ozero__class_Ozero(_1174156))), 20322 ^ _779530 : [(20323 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174156), _1174158), _1174160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174156), _1174158), _1174162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174156), _1174162), _1174160)))], (20329 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174156), _1174162), _1174160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174156), _1174158), _1174160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174156), _1174158), _1174162))))]]], (20335 ^ _779530) ^ [_1174537, _1174539, _1174541] : [class_Rings_Olinordered__semiring__strict(_1174537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174537), _1174539), c_Groups_Ozero__class_Ozero(_1174537))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174537), c_Groups_Ozero__class_Ozero(_1174537)), _1174541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174537), _1174539), _1174541)), c_Groups_Ozero__class_Ozero(_1174537))))], (20349 ^ _779530) ^ [_1174792, _1174794, _1174796] : [class_Rings_Olinordered__ring__strict(_1174792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174792), _1174794), c_Groups_Ozero__class_Ozero(_1174792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174792), _1174796), c_Groups_Ozero__class_Ozero(_1174792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1174792), c_Groups_Ozero__class_Ozero(_1174792)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1174792), _1174794), _1174796))))], (20363 ^ _779530) ^ [_1175047, _1175049, _1175051, _1175053] : [class_Rings_Olinordered__semiring__strict(_1175047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175047), _1175049), _1175051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175047), c_Groups_Ozero__class_Ozero(_1175047)), _1175053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175047), _1175049), _1175053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175047), _1175051), _1175053))))], (20377 ^ _779530) ^ [_1175316, _1175318, _1175320, _1175322] : [class_Rings_Olinordered__semiring__strict(_1175316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175316), _1175318), _1175320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175316), c_Groups_Ozero__class_Ozero(_1175316)), _1175322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175316), _1175322), _1175318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175316), _1175322), _1175320))))], (20391 ^ _779530) ^ [_1175585, _1175587, _1175589, _1175591] : [class_Rings_Olinordered__comm__semiring__strict(_1175585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175585), _1175587), _1175589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175585), c_Groups_Ozero__class_Ozero(_1175585)), _1175591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175585), _1175591), _1175587)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175585), _1175591), _1175589))))], (20405 ^ _779530) ^ [_1175854, _1175856, _1175858, _1175860] : [class_Rings_Olinordered__ring__strict(_1175854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175854), _1175856), _1175858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175854), _1175860), c_Groups_Ozero__class_Ozero(_1175854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1175854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175854), _1175858), _1175860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175854), _1175856), _1175860))))], (20419 ^ _779530) ^ [_1176123, _1176125, _1176127, _1176129] : [class_Rings_Olinordered__ring__strict(_1176123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176123), _1176125), _1176127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176123), _1176129), c_Groups_Ozero__class_Ozero(_1176123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176123), _1176129), _1176127)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176123), _1176129), _1176125))))], (20433 ^ _779530) ^ [_1176392, _1176394, _1176396] : [class_Groups_Oordered__ab__group__add(_1176392), 20436 ^ _779530 : [(20437 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176392), _1176394), _1176396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176392), _1176394), _1176396)), c_Groups_Ozero__class_Ozero(_1176392))))], (20443 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176392), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176392), _1176394), _1176396)), c_Groups_Ozero__class_Ozero(_1176392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176392), _1176394), _1176396)))]]], (20449 ^ _779530) ^ [_1176675, _1176677, _1176679] : [class_Groups_Oordered__ab__group__add(_1176675), 20452 ^ _779530 : [(20453 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176675), _1176677), _1176679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176675), _1176677), _1176679)), c_Groups_Ozero__class_Ozero(_1176675))))], (20459 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176675), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1176675), _1176677), _1176679)), c_Groups_Ozero__class_Ozero(_1176675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176675), _1176677), _1176679)))]]], (20465 ^ _779530) ^ [_1176958, _1176960, _1176962, _1176964, _1176966, _1176968] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1176958), -(_1176960 = c_Groups_Ozero__class_Ozero(_1176958)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176958), _1176962), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176958), _1176960), _1176966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176958), _1176964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176958), _1176960), _1176968)), _1176962 = _1176964, -(_1176966 = _1176968)], (20483 ^ _779530) ^ [_1177296, _1177298, _1177300] : [class_Rings_Olinordered__ring__strict(_1177296), 20486 ^ _779530 : [(20487 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177296), _1177298), _1177298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177296), _1177300), _1177300)) = c_Groups_Ozero__class_Ozero(_1177296), 20490 ^ _779530 : [(20491 ^ _779530) ^ [] : [-(_1177298 = c_Groups_Ozero__class_Ozero(_1177296))], (20493 ^ _779530) ^ [] : [-(_1177300 = c_Groups_Ozero__class_Ozero(_1177296))]]], (20495 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177296), _1177298), _1177298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177296), _1177300), _1177300)) = c_Groups_Ozero__class_Ozero(_1177296)), _1177298 = c_Groups_Ozero__class_Ozero(_1177296), _1177300 = c_Groups_Ozero__class_Ozero(_1177296)]]], (20505 ^ _779530) ^ [_1177671] : [class_Rings_Olinordered__semidom(_1177671), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177671), c_Groups_Ozero__class_Ozero(_1177671)), c_Groups_Oone__class_Oone(_1177671))))], (20511 ^ _779530) ^ [_1177766] : [class_Rings_Olinordered__semidom(_1177766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177766), c_Groups_Oone__class_Oone(_1177766)), c_Groups_Ozero__class_Ozero(_1177766)))], (20517 ^ _779530) ^ [_1177862] : [class_Rings_Olinordered__semidom(_1177862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177862), c_Groups_Oone__class_Oone(_1177862)), c_Groups_Ozero__class_Ozero(_1177862)))], (20523 ^ _779530) ^ [_1177958] : [class_Rings_Olinordered__semidom(_1177958), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177958), c_Groups_Ozero__class_Ozero(_1177958)), c_Groups_Oone__class_Oone(_1177958))))], (20529 ^ _779530) ^ [_1178053, _1178055] : [class_Groups_Oordered__ab__group__add(_1178053), 20532 ^ _779530 : [(20533 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178053), c_Groups_Ozero__class_Ozero(_1178053)), hAPP(c_Groups_Ouminus__class_Ouminus(_1178053), _1178055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178053), _1178055), c_Groups_Ozero__class_Ozero(_1178053))))], (20539 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178053), _1178055), c_Groups_Ozero__class_Ozero(_1178053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178053), c_Groups_Ozero__class_Ozero(_1178053)), hAPP(c_Groups_Ouminus__class_Ouminus(_1178053), _1178055))))]]], (20545 ^ _779530) ^ [_1178327, _1178329] : [class_Groups_Olinordered__ab__group__add(_1178327), 20548 ^ _779530 : [(20549 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178327), _1178329), hAPP(c_Groups_Ouminus__class_Ouminus(_1178327), _1178329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178327), _1178329), c_Groups_Ozero__class_Ozero(_1178327))))], (20555 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178327), _1178329), c_Groups_Ozero__class_Ozero(_1178327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178327), _1178329), hAPP(c_Groups_Ouminus__class_Ouminus(_1178327), _1178329))))]]], (20561 ^ _779530) ^ [_1178595, _1178597] : [class_Groups_Oordered__ab__group__add(_1178595), 20564 ^ _779530 : [(20565 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178595), hAPP(c_Groups_Ouminus__class_Ouminus(_1178595), _1178597)), c_Groups_Ozero__class_Ozero(_1178595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178595), c_Groups_Ozero__class_Ozero(_1178595)), _1178597)))], (20571 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178595), c_Groups_Ozero__class_Ozero(_1178595)), _1178597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178595), hAPP(c_Groups_Ouminus__class_Ouminus(_1178595), _1178597)), c_Groups_Ozero__class_Ozero(_1178595))))]]], (20577 ^ _779530) ^ [_1178869, _1178871] : [class_Groups_Olinordered__ab__group__add(_1178869), 20580 ^ _779530 : [(20581 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178869), hAPP(c_Groups_Ouminus__class_Ouminus(_1178869), _1178871)), _1178871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178869), c_Groups_Ozero__class_Ozero(_1178869)), _1178871)))], (20587 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178869), c_Groups_Ozero__class_Ozero(_1178869)), _1178871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178869), hAPP(c_Groups_Ouminus__class_Ouminus(_1178869), _1178871)), _1178871)))]]], (20593 ^ _779530) ^ [_1179137, _1179139] : [class_Rings_Olinordered__idom(_1179137), 20596 ^ _779530 : [(20597 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179137), _1179139), hAPP(c_Groups_Ouminus__class_Ouminus(_1179137), _1179139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179137), _1179139), c_Groups_Ozero__class_Ozero(_1179137))))], (20603 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179137), _1179139), c_Groups_Ozero__class_Ozero(_1179137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179137), _1179139), hAPP(c_Groups_Ouminus__class_Ouminus(_1179137), _1179139))))]]], (20609 ^ _779530) ^ [_1179405, _1179407] : [class_Groups_Oordered__ab__group__add(_1179405), 20612 ^ _779530 : [(20613 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179405), c_Groups_Ozero__class_Ozero(_1179405)), hAPP(c_Groups_Ouminus__class_Ouminus(_1179405), _1179407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179405), _1179407), c_Groups_Ozero__class_Ozero(_1179405))))], (20619 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179405), _1179407), c_Groups_Ozero__class_Ozero(_1179405))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179405), c_Groups_Ozero__class_Ozero(_1179405)), hAPP(c_Groups_Ouminus__class_Ouminus(_1179405), _1179407))))]]], (20625 ^ _779530) ^ [_1179679, _1179681] : [class_Groups_Oordered__ab__group__add(_1179679), 20628 ^ _779530 : [(20629 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179679), hAPP(c_Groups_Ouminus__class_Ouminus(_1179679), _1179681)), c_Groups_Ozero__class_Ozero(_1179679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179679), c_Groups_Ozero__class_Ozero(_1179679)), _1179681)))], (20635 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179679), c_Groups_Ozero__class_Ozero(_1179679)), _1179681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179679), hAPP(c_Groups_Ouminus__class_Ouminus(_1179679), _1179681)), c_Groups_Ozero__class_Ozero(_1179679))))]]], (20641 ^ _779530) ^ [_1179953, _1179955] : [class_Groups_Olinordered__ab__group__add(_1179953), 20644 ^ _779530 : [(20645 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179953), hAPP(c_Groups_Ouminus__class_Ouminus(_1179953), _1179955)), _1179955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179953), c_Groups_Ozero__class_Ozero(_1179953)), _1179955)))], (20651 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179953), c_Groups_Ozero__class_Ozero(_1179953)), _1179955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179953), hAPP(c_Groups_Ouminus__class_Ouminus(_1179953), _1179955)), _1179955)))]]], (20657 ^ _779530) ^ [_1180221, _1180223] : [class_Groups_Ogroup__add(_1180221), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180221), _1180223), hAPP(c_Groups_Ouminus__class_Ouminus(_1180221), _1180223)) = c_Groups_Ozero__class_Ozero(_1180221))], (20663 ^ _779530) ^ [_1180326, _1180328, _1180330] : [class_Groups_Ogroup__add(_1180326), 20666 ^ _779530 : [(20667 ^ _779530) ^ [] : [_1180328 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180326), _1180330), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180326), _1180328), _1180330) = c_Groups_Ozero__class_Ozero(_1180326))], (20673 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180326), _1180328), _1180330) = c_Groups_Ozero__class_Ozero(_1180326), -(_1180328 = hAPP(c_Groups_Ouminus__class_Ouminus(_1180326), _1180330))]]], (20679 ^ _779530) ^ [_1180582, _1180584] : [class_Groups_Ogroup__add(_1180582), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180582), hAPP(c_Groups_Ouminus__class_Ouminus(_1180582), _1180584)), _1180584) = c_Groups_Ozero__class_Ozero(_1180582))], (20685 ^ _779530) ^ [_1180687, _1180689] : [class_Groups_Oab__group__add(_1180687), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180687), hAPP(c_Groups_Ouminus__class_Ouminus(_1180687), _1180689)), _1180689) = c_Groups_Ozero__class_Ozero(_1180687))], (20691 ^ _779530) ^ [_1180792, _1180794, _1180796] : [class_Groups_Ogroup__add(_1180792), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180792), _1180794), _1180796) = c_Groups_Ozero__class_Ozero(_1180792), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1180792), _1180794) = _1180796)], (20701 ^ _779530) ^ [_1180953, _1180955] : [class_Groups_Ogroup__add(_1180953), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1180953), c_Groups_Ozero__class_Ozero(_1180953)), _1180955) = hAPP(c_Groups_Ouminus__class_Ouminus(_1180953), _1180955))], (20707 ^ _779530) ^ [_1181058, _1181060, _1181062] : [class_Groups_Ocomm__monoid__add(_1181058), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181060, _1181058), _1181062), c_Orderings_Obot__class_Obot(tc_fun(_1181060, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1181058))], (20713 ^ _779530) ^ [_1181167, _1181169, _1181171] : [class_Groups_Ocomm__monoid__add(_1181167), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181169, _1181167), _1181171), c_Orderings_Obot__class_Obot(tc_fun(_1181169, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1181167))], (20719 ^ _779530) ^ [_1181276, _1181278, _1181280, _1181282] : [class_Groups_Ocomm__monoid__add(_1181276), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1181278), _1181280))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181278, _1181276), _1181282), _1181280) = c_Groups_Ozero__class_Ozero(_1181276))], (20729 ^ _779530) ^ [_1181400, _1181402, _1181404, _1181406] : [class_Groups_Ocomm__monoid__add(_1181400), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1181402), _1181404))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1181402, _1181400), _1181406), _1181404) = c_Groups_Ozero__class_Ozero(_1181400))], (20739 ^ _779530) ^ [_1181539, _1181541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1181539), hAPP(c_Nat_OSuc, _1181541))), -(_1181539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20747 ^ _779530 : [(20748 ^ _779530) ^ [] : [-(_1181539 = hAPP(c_Nat_OSuc, 20746 ^ [_1181539, _1181541]))], (20750 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20746 ^ [_1181539, _1181541]), _1181541)))]]], (20752 ^ _779530) ^ [_1181719, _1181721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1181719), hAPP(c_Nat_OSuc, _1181721)))), 20753 ^ _779530 : [(20754 ^ _779530) ^ [] : [_1181719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20756 ^ _779530) ^ [_1181807] : [_1181719 = hAPP(c_Nat_OSuc, _1181807), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1181807), _1181721))]]], (20764 ^ _779530) ^ [_1181953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1181953), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1181953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20770 ^ _779530) ^ [_1182034] : [_1182034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1182034), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20776 ^ _779530) ^ [_1182133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182133)), -(_1182133 = hAPP(c_Nat_OSuc, 20779 ^ [_1182133]))], (20783 ^ _779530) ^ [_1182224] : [20784 ^ _779530 : [(20785 ^ _779530) ^ [_1182266] : [_1182224 = hAPP(c_Nat_OSuc, _1182266)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182224)))], (20789 ^ _779530) ^ [_1182339, _1182341] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1182339), _1182341), 20794 ^ _779530 : [(20795 ^ _779530) ^ [] : [-(_1182339 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20797 ^ _779530) ^ [] : [-(_1182341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20798 ^ _779530 : [(20799 ^ _779530) ^ [] : [-(_1182339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20801 ^ _779530) ^ [] : [-(_1182341 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (20803 ^ _779530) ^ [_1182523, _1182525] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1182523), _1182525)), 20804 ^ _779530 : [(20805 ^ _779530) ^ [] : [_1182523 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182525 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20811 ^ _779530) ^ [] : [_1182523 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1182525 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20819 ^ _779530) ^ [_1182764, _1182766] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1182764), _1182766) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20824 ^ _779530 : [(20825 ^ _779530) ^ [] : [-(_1182764 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20827 ^ _779530) ^ [] : [-(_1182766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 20828 ^ _779530 : [(20829 ^ _779530) ^ [] : [-(_1182764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20831 ^ _779530) ^ [] : [-(_1182766 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (20833 ^ _779530) ^ [_1182948, _1182950] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1182948), _1182950) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20834 ^ _779530 : [(20835 ^ _779530) ^ [] : [_1182948 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182950 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20841 ^ _779530) ^ [] : [_1182948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1182950 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20859 ^ _779530) ^ [_1183299, _1183301] : [20860 ^ _779530 : [(20861 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183299))], (20863 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183301))]], -(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), _1183299), _1183301))))], (20849 ^ _779530) ^ [_1183189, _1183191] : [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), _1183189), _1183191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183191)))], (20867 ^ _779530) ^ [_1183440] : [-(hAPP(c_Finite__Set_Ocard(_1183440), c_Orderings_Obot__class_Obot(tc_fun(_1183440, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20869 ^ _779530) ^ [_1183469, _1183471] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1183469), _1183471))), -(hAPP(c_Finite__Set_Ocard(_1183469), _1183471) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20875 ^ _779530) ^ [_1183529, _1183531] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183529), _1183531) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20878 ^ _779530 : [(20879 ^ _779530) ^ [] : [-(_1183529 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20881 ^ _779530) ^ [] : [-(_1183531 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (20883 ^ _779530) ^ [_1183640, _1183642] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183640), _1183642) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1183640 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183642 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20893 ^ _779530) ^ [_1183798, _1183800] : [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), _1183798), _1183800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1183800), _1183798)))], (20899 ^ _779530) ^ [_1183897, _1183899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1183899), _1183897)), -(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), _1183897), _1183899))))], (20905 ^ _779530) ^ [_1184002, _1184004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184004), _1184002)), _1184004)))], (20915 ^ _779530) ^ [_1184161, _1184163, _1184165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184161), _1184163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184165), _1184161)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184165), _1184163))))], (20925 ^ _779530) ^ [_1184342, _1184344, _1184346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184342), _1184344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184342), _1184346)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184344), _1184346))))], (20935 ^ _779530) ^ [_1184541, _1184543, _1184545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184541), _1184543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184545), _1184543))), 20938 ^ _779530 : [(20939 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184543)))], (20941 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184541), _1184545)))]]], (20943 ^ _779530) ^ [_1184690, _1184692, _1184694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184690), _1184692)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184694), _1184692)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184690), _1184694))], (20953 ^ _779530) ^ [_1184891, _1184893, _1184895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184891), _1184893)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184891), _1184895))), 20956 ^ _779530 : [(20957 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184891)))], (20959 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184893), _1184895)))]]], (20961 ^ _779530) ^ [_1185040, _1185042, _1185044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185040), _1185042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185040), _1185044)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185042), _1185044))], (20971 ^ _779530) ^ [_1185238, _1185240] : [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), _1185238), _1185240))), 20974 ^ _779530 : [(20975 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185238)))], (20977 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185240)))]]], (20979 ^ _779530) ^ [_1185361, _1185363] : [-(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), _1185361), _1185363)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185363))], (20989 ^ _779530) ^ [_1185516, _1185518, _1185520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185516)), 20992 ^ _779530 : [(20993 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185516), _1185518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185516), _1185520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185518), _1185520)))], (20999 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185518), _1185520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185516), _1185518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185516), _1185520))))]]], (21005 ^ _779530) ^ [_1185799, _1185801, _1185803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1185799)), 21008 ^ _779530 : [(21009 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185799), _1185801) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185799), _1185803), -(_1185801 = _1185803)], (21015 ^ _779530) ^ [] : [_1185801 = _1185803, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185799), _1185801) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185799), _1185803))]]], (21021 ^ _779530) ^ [_1186052, _1186054] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1186052), _1186054)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21023 ^ _779530) ^ [_1186089, _1186091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186089), _1186091)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186089), _1186091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21029 ^ _779530) ^ [_1186203, _1186205] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186203), _1186205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186203), _1186205)))], (21035 ^ _779530) ^ [_1186298, _1186300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186298), _1186300)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1186298), _1186300) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21041 ^ _779530) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21043 ^ _779530) ^ [_1186417, _1186419] : [_1186417 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186417), _1186419), -(_1186419 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1186417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21053 ^ _779530) ^ [_1186518, _1186520, _1186522, _1186524, _1186526, _1186528, _1186530] : [-(hBOOL(hAPP(hAPP(c_member(_1186518), _1186520), _1186522))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1186518, _1186524, _1186526, _1186528, _1186522), _1186530)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1186518, _1186524, _1186526, _1186528, hAPP(hAPP(c_Set_Oinsert(_1186518), _1186520), _1186522)), hAPP(hAPP(_1186526, _1186520), _1186530))))], (21063 ^ _779530) ^ [_1186732, _1186734, _1186736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1186732), _1186734)), 21066 ^ _779530 : [(21077 ^ _779530) ^ [] : [21079 ^ _779530 : [(21080 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1186732), 21078 ^ [_1186732, _1186734, _1186736]), _1186734)))], (21082 ^ _779530) ^ [] : [hAPP(_1186736, 21078 ^ [_1186732, _1186734, _1186736]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1186732, tc_Nat_Onat), _1186736), _1186734) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21067 ^ _779530) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1186732, tc_Nat_Onat), _1186736), _1186734) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 21070 ^ _779530 : [(21071 ^ _779530) ^ [_1186894] : [hBOOL(hAPP(hAPP(c_member(_1186732), _1186894), _1186734)), -(hAPP(_1186736, _1186894) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (21086 ^ _779530) ^ [_1187152, _1187154, _1187156] : [class_Orderings_Olinorder(_1187152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187152), _1187154)), hBOOL(hAPP(hAPP(c_member(_1187152), _1187156), _1187154)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187152), _1187156), c_Big__Operators_Olinorder__class_OMin(_1187152, _1187154)) = c_Big__Operators_Olinorder__class_OMin(_1187152, _1187154))], (21100 ^ _779530) ^ [_1187387, _1187389, _1187391, _1187393, _1187395] : [class_Lattices_Osemilattice__inf(_1187387), class_Orderings_Olinorder(_1187389), c_Orderings_Oorder__class_Omono(_1187389, _1187387, _1187391), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187387), hAPP(_1187391, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1187389), _1187393), _1187395))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1187387), hAPP(_1187391, _1187393)), hAPP(_1187391, _1187395)))))], (21114 ^ _779530) ^ [_1187650, _1187652, _1187654] : [class_Groups_Oordered__comm__monoid__add(_1187650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187650), _1187652), c_Groups_Ozero__class_Ozero(_1187650))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187650), _1187654), c_Groups_Ozero__class_Ozero(_1187650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187650), _1187652), _1187654)), c_Groups_Ozero__class_Ozero(_1187650))))], (21128 ^ _779530) ^ [_1187905, _1187907, _1187909] : [class_Groups_Oordered__comm__monoid__add(_1187905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187905), _1187907), c_Groups_Ozero__class_Ozero(_1187905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187905), _1187909), c_Groups_Ozero__class_Ozero(_1187905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187905), _1187907), _1187909)), c_Groups_Ozero__class_Ozero(_1187905))))], (21142 ^ _779530) ^ [_1188160, _1188162, _1188164, _1188166] : [class_Groups_Oordered__comm__monoid__add(_1188160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188160), c_Groups_Ozero__class_Ozero(_1188160)), _1188162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188160), _1188164), _1188166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188160), _1188164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188160), _1188162), _1188166))))], (21156 ^ _779530) ^ [_1188413, _1188415, _1188417, _1188419] : [class_Groups_Oordered__comm__monoid__add(_1188413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188413), c_Groups_Ozero__class_Ozero(_1188413)), _1188415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188413), _1188417), _1188419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188413), _1188417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188413), _1188415), _1188419))))], (21170 ^ _779530) ^ [_1188666, _1188668, _1188670] : [class_Groups_Oordered__comm__monoid__add(_1188666), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188666), c_Groups_Ozero__class_Ozero(_1188666)), _1188668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188666), c_Groups_Ozero__class_Ozero(_1188666)), _1188670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188666), c_Groups_Ozero__class_Ozero(_1188666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188666), _1188668), _1188670))))], (21184 ^ _779530) ^ [_1188921, _1188923, _1188925] : [class_Groups_Oordered__comm__monoid__add(_1188921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188921), c_Groups_Ozero__class_Ozero(_1188921)), _1188923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188921), c_Groups_Ozero__class_Ozero(_1188921)), _1188925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188921), c_Groups_Ozero__class_Ozero(_1188921)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188921), _1188923), _1188925))))], (21198 ^ _779530) ^ [_1189176, _1189178, _1189180, _1189182] : [class_Rings_Olinordered__semiring__strict(_1189176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189176), _1189178), _1189180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189176), _1189178), _1189182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189176), c_Groups_Ozero__class_Ozero(_1189176)), _1189178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189176), _1189180), _1189182)))], (21212 ^ _779530) ^ [_1189445, _1189447, _1189449, _1189451] : [class_Rings_Olinordered__semiring__strict(_1189445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189445), _1189447), _1189449)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189445), _1189451), _1189449))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189445), c_Groups_Ozero__class_Ozero(_1189445)), _1189449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189445), _1189447), _1189451)))], (21226 ^ _779530) ^ [_1189714, _1189716, _1189718, _1189720] : [class_Rings_Olinordered__semiring__strict(_1189714), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189714), _1189716), _1189718)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189714), _1189716), _1189720))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189714), c_Groups_Ozero__class_Ozero(_1189714)), _1189716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189714), _1189718), _1189720)))], (21240 ^ _779530) ^ [_1189983, _1189985, _1189987, _1189989] : [class_Rings_Olinordered__semiring(_1189983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189983), _1189985), _1189987)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189983), _1189985), _1189989))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189983), c_Groups_Ozero__class_Ozero(_1189983)), _1189985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189983), _1189987), _1189989)))], (21254 ^ _779530) ^ [_1190252, _1190254, _1190256, _1190258] : [class_Rings_Olinordered__semiring__strict(_1190252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190252), _1190254), _1190256)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190252), _1190258), _1190256))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190252), c_Groups_Ozero__class_Ozero(_1190252)), _1190256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190252), _1190254), _1190258)))], (21268 ^ _779530) ^ [_1190521, _1190523, _1190525, _1190527] : [class_Rings_Olinordered__semiring(_1190521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190521), _1190523), _1190525)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190521), _1190527), _1190525))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190521), c_Groups_Ozero__class_Ozero(_1190521)), _1190525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190521), _1190523), _1190527)))], (21282 ^ _779530) ^ [_1190790, _1190792, _1190794, _1190796, _1190798] : [class_Rings_Olinordered__semiring__strict(_1190790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190790), _1190792), _1190794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190790), _1190796), _1190798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190790), c_Groups_Ozero__class_Ozero(_1190790)), _1190792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190790), c_Groups_Ozero__class_Ozero(_1190790)), _1190796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190790), _1190792), _1190796)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190790), _1190794), _1190798))))], (21304 ^ _779530) ^ [_1191213, _1191215, _1191217, _1191219, _1191221] : [class_Rings_Olinordered__semiring__strict(_1191213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191213), _1191215), _1191217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191213), _1191219), _1191221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191213), c_Groups_Ozero__class_Ozero(_1191213)), _1191215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191213), c_Groups_Ozero__class_Ozero(_1191213)), _1191219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191213), _1191215), _1191219)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191213), _1191217), _1191221))))], (21326 ^ _779530) ^ [_1191636, _1191638, _1191640, _1191642, _1191644] : [class_Rings_Olinordered__semiring__strict(_1191636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191636), _1191638), _1191640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191636), _1191642), _1191644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191636), c_Groups_Ozero__class_Ozero(_1191636)), _1191638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191636), 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_1197358)))], (21642 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1197360)))]]], (21644 ^ _779530) ^ [_1197481, _1197483] : [-(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), _1197481), _1197483)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1197481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1197483))], (21664 ^ _779530) ^ [_1197831, _1197833, _1197835] : [21665 ^ _779530 : [(21666 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1197831)))], (21668 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197833), _1197835))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197831), _1197833)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197831), _1197835))))], (21654 ^ _779530) ^ [_1197654, _1197656, _1197658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197654), _1197656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197654), _1197658))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1197654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197656), _1197658)))], (21682 ^ _779530) ^ [_1198188, _1198190, _1198192] : [21683 ^ _779530 : [(21684 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198190)))], (21686 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198188), _1198192))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198188), _1198190)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198192), _1198190))))], (21672 ^ _779530) ^ [_1198011, _1198013, _1198015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198011), _1198013)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198015), _1198013))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198011), _1198015)))], (21690 ^ _779530) ^ [_1198350, _1198352, _1198354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198350)), 21693 ^ _779530 : [(21694 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198350), _1198352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198350), _1198354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198352), _1198354)))], (21700 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198352), _1198354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198350), _1198352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198350), _1198354))))]]], (21706 ^ _779530) ^ [_1198633, _1198635, _1198637] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1198633), _1198635)), 21709 ^ _779530 : [(21710 ^ _779530) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198633, tc_Nat_Onat), _1198637), _1198635) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21714 ^ _779530 : [(21715 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1198633), 21713 ^ [_1198633, _1198635, _1198637]), _1198635)))], (21717 ^ _779530) ^ [] : [-(hAPP(_1198637, 21713 ^ [_1198633, _1198635, _1198637]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21719 ^ _779530) ^ [_1198953] : [hBOOL(hAPP(hAPP(c_member(_1198633), _1198953), _1198635)), -(21713 ^ [_1198633, _1198635, _1198637] = _1198953), -(hAPP(_1198637, _1198953) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21729 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198633, tc_Nat_Onat), _1198637), _1198635) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21730 ^ _779530 : [(21731 ^ _779530) ^ [_1199114] : [hBOOL(hAPP(hAPP(c_member(_1198633), _1199114), _1198635)), hAPP(_1198637, _1199114) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21739 ^ _779530 : [(21740 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1198633), 21738 ^ [_1198633, _1198635, _1198637, _1199114]), _1198635)))], (21742 ^ _779530) ^ [] : [_1199114 = 21738 ^ [_1198633, _1198635, _1198637, _1199114]], (21744 ^ _779530) ^ [] : [hAPP(_1198637, 21738 ^ [_1198633, _1198635, _1198637, _1199114]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (21748 ^ _779530) ^ [_1199467, _1199469, _1199471, _1199473, _1199475] : [class_Groups_Oab__semigroup__mult(_1199467), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1199467, _1199467, c_Groups_Otimes__class_Otimes(_1199467), _1199469, _1199471), _1199473)), -(hBOOL(hAPP(hAPP(c_member(_1199467), _1199469), _1199471))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1199467, _1199467, c_Groups_Otimes__class_Otimes(_1199467), _1199475, hAPP(hAPP(c_Set_Oinsert(_1199467), _1199469), _1199471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1199467), _1199475), _1199473))))], (21762 ^ _779530) ^ [_1199707, _1199709, _1199711] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1199707), _1199709)), 21765 ^ _779530 : [(21766 ^ _779530) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199707, tc_Nat_Onat), _1199711), _1199709) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21770 ^ _779530 : [(21771 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1199707), 21769 ^ [_1199707, _1199709, _1199711]), _1199709)))], (21773 ^ _779530) ^ [] : [-(hAPP(_1199711, 21769 ^ [_1199707, _1199709, _1199711]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21775 ^ _779530) ^ [_1200027] : [hBOOL(hAPP(hAPP(c_member(_1199707), _1200027), _1199709)), -(21769 ^ [_1199707, _1199709, _1199711] = _1200027), -(hAPP(_1199711, _1200027) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21785 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199707, tc_Nat_Onat), _1199711), _1199709) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 21786 ^ _779530 : [(21787 ^ _779530) ^ [_1200188] : [hBOOL(hAPP(hAPP(c_member(_1199707), _1200188), _1199709)), hAPP(_1199711, _1200188) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21795 ^ _779530 : [(21796 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1199707), 21794 ^ [_1199707, _1199709, _1199711, _1200188]), _1199709)))], (21798 ^ _779530) ^ [] : [_1200188 = 21794 ^ [_1199707, _1199709, _1199711, _1200188]], (21800 ^ _779530) ^ [] : [hAPP(_1199711, 21794 ^ [_1199707, _1199709, _1199711, _1200188]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (21804 ^ _779530) ^ [_1200541, _1200543, _1200545, _1200547, _1200549] : [class_Groups_Ocomm__monoid__add(_1200541), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200543), _1200545)), 21811 ^ _779530 : [(21812 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1200543), _1200547), _1200545)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1200543, _1200541), hAPP(hAPP(c_COMBC(_1200543, _1200541, _1200541), hAPP(hAPP(c_COMBS(_1200543, _1200541, tc_fun(_1200541, _1200541)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1200541, tc_fun(_1200541, _1200541)), _1200543), c_If(_1200541)), hAPP(hAPP(c_COMBC(_1200543, _1200543, tc_HOL_Obool), c_fequal), _1200547))), _1200549)), c_Groups_Ozero__class_Ozero(_1200541))), _1200545) = hAPP(_1200549, _1200547))], (21818 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200543), _1200547), _1200545))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1200543, _1200541), hAPP(hAPP(c_COMBC(_1200543, _1200541, _1200541), hAPP(hAPP(c_COMBS(_1200543, _1200541, tc_fun(_1200541, _1200541)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1200541, tc_fun(_1200541, _1200541)), _1200543), c_If(_1200541)), hAPP(hAPP(c_COMBC(_1200543, _1200543, tc_HOL_Obool), c_fequal), _1200547))), _1200549)), c_Groups_Ozero__class_Ozero(_1200541))), _1200545) = c_Groups_Ozero__class_Ozero(_1200541))]]], (21824 ^ _779530) ^ [_1201079, _1201081, _1201083, _1201085, _1201087] : [class_Groups_Ocomm__monoid__add(_1201079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201081), _1201083)), 21831 ^ _779530 : [(21832 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1201081), _1201085), _1201083)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201081, _1201079), hAPP(hAPP(c_COMBC(_1201081, _1201079, _1201079), hAPP(hAPP(c_COMBS(_1201081, _1201079, tc_fun(_1201079, _1201079)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1201079, tc_fun(_1201079, _1201079)), _1201081), c_If(_1201079)), hAPP(c_fequal, _1201085))), _1201087)), c_Groups_Ozero__class_Ozero(_1201079))), _1201083) = hAPP(_1201087, _1201085))], (21838 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201081), _1201085), _1201083))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201081, _1201079), hAPP(hAPP(c_COMBC(_1201081, _1201079, _1201079), hAPP(hAPP(c_COMBS(_1201081, _1201079, tc_fun(_1201079, _1201079)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1201079, tc_fun(_1201079, _1201079)), _1201081), c_If(_1201079)), hAPP(c_fequal, _1201085))), _1201087)), c_Groups_Ozero__class_Ozero(_1201079))), _1201083) = c_Groups_Ozero__class_Ozero(_1201079))]]], (21844 ^ _779530) ^ [_1201589, _1201591, _1201593] : [class_Orderings_Olinorder(_1201589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201589), _1201591)), -(_1201591 = c_Orderings_Obot__class_Obot(tc_fun(_1201589, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1201589, hAPP(hAPP(c_Set_Oinsert(_1201589), _1201593), _1201591)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201589), _1201593), c_Big__Operators_Olinorder__class_OMin(_1201589, _1201591)))], (21858 ^ _779530) ^ [_1201797, _1201799, _1201801] : [class_Orderings_Olinorder(_1201797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201797), _1201799)), -(_1201801 = c_Orderings_Obot__class_Obot(tc_fun(_1201797, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201797, tc_HOL_Obool)), _1201801), _1201799)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1201797), c_Big__Operators_Olinorder__class_OMin(_1201797, _1201801)), c_Big__Operators_Olinorder__class_OMin(_1201797, _1201799)) = c_Big__Operators_Olinorder__class_OMin(_1201797, _1201799))], (21876 ^ _779530) ^ [_1202111, _1202113, _1202115] : [class_Orderings_Olinorder(_1202111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202111), _1202113)), -(_1202113 = c_Orderings_Obot__class_Obot(tc_fun(_1202111, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202111), _1202115)), -(_1202115 = c_Orderings_Obot__class_Obot(tc_fun(_1202111, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1202111, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1202111, tc_HOL_Obool)), _1202113), _1202115)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1202111), c_Big__Operators_Olinorder__class_OMin(_1202111, _1202113)), c_Big__Operators_Olinorder__class_OMin(_1202111, _1202115)))], (21898 ^ _779530) ^ [_1202456, _1202458] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202456))), -(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)), _1202456))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1202458)))) = 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)), _1202456))), 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, _1202458))))))], (21904 ^ _779530) ^ [_1202539, _1202541] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202539)), 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)), _1202539))), 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, _1202541))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21910 ^ _779530) ^ [_1202669, _1202671] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202669)), -(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)), _1202669))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1202671))))) = 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)), _1202669))), 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, _1202671))))))], (21916 ^ _779530) ^ [_1202846, _1202848, _1202850, _1202852, _1202854, _1202856] : [class_Rings_Olinordered__semiring__1(_1202846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202846), _1202848), _1202850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202846), _1202852), _1202850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202846), c_Groups_Ozero__class_Ozero(_1202846)), _1202854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202846), c_Groups_Ozero__class_Ozero(_1202846)), _1202856)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1202846), _1202854), _1202856) = c_Groups_Oone__class_Oone(_1202846), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1202846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202846), _1202854), _1202848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202846), _1202856), _1202852))), _1202850)))], (21942 ^ _779530) ^ [_1203390, _1203392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1203390), _1203392))), 21945 ^ _779530 : [(21946 ^ _779530) ^ [] : [_1203392 = c_Orderings_Obot__class_Obot(tc_fun(_1203390, tc_HOL_Obool))], (21948 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1203390), _1203392)))]]], (21950 ^ _779530) ^ [_1203531, _1203533] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1203531), _1203533)))), -(_1203533 = c_Orderings_Obot__class_Obot(tc_fun(_1203531, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1203531), _1203533))], (21960 ^ _779530) ^ [_1203697] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1203697), c_Orderings_Otop__class_Otop(tc_fun(_1203697, 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(_1203697), c_Orderings_Otop__class_Otop(tc_fun(_1203697, tc_HOL_Obool))))))], (21966 ^ _779530) ^ [_1203814, _1203816, _1203818, _1203820] : [class_Groups_Ocomm__monoid__add(_1203814), 21969 ^ _779530 : [(21970 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1203816), _1203818)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203816, _1203814), _1203820), _1203818) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1203814, _1203816, c_Groups_Oplus__class_Oplus(_1203814)), _1203820), c_Groups_Ozero__class_Ozero(_1203814)), _1203818))], (21976 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1203816), _1203818))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203816, _1203814), _1203820), _1203818) = c_Groups_Ozero__class_Ozero(_1203814))]]], (21982 ^ _779530) ^ [_1204086, _1204088, _1204090, _1204092] : [class_Groups_Ocomm__monoid__add(_1204086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1204088), _1204090)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204088, _1204086), _1204092), _1204090) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1204086, _1204088, c_Groups_Oplus__class_Oplus(_1204086)), _1204092), c_Groups_Ozero__class_Ozero(_1204086)), _1204090))], (21992 ^ _779530) ^ [_1204281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204281)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204281), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1204281)], (21998 ^ _779530) ^ [_1204378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204378)), -(_1204378 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204378), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (22004 ^ _779530) ^ [_1204484, _1204486] : [_1204484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204484), _1204486) = _1204486)], (22010 ^ _779530) ^ [_1204567, _1204569] : [-(_1204567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204567), _1204569) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204567), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1204569)))], (22016 ^ _779530) ^ [_1204635, _1204637] : [_1204635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204635), _1204637) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22022 ^ _779530) ^ [_1204718, _1204720] : [-(_1204718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204718), _1204720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1204718), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1204720)))], (22028 ^ _779530) ^ [_1204780, _1204782, _1204784, _1204786, _1204788] : [class_Groups_Ocomm__monoid__add(_1204780), hBOOL(hAPP(c_Finite__Set_Ofinite(_1204782), _1204784)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204782, _1204780), _1204786), hAPP(c_Set_OCollect(_1204782), hAPP(hAPP(c_COMBS(_1204782, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1204782), c_fconj), hAPP(hAPP(c_COMBC(_1204782, tc_fun(_1204782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204782)), _1204784))), hAPP(hAPP(c_COMBC(_1204782, tc_fun(_1204782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204782)), _1204788)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204782, _1204780), hAPP(hAPP(c_COMBC(_1204782, _1204780, _1204780), hAPP(hAPP(c_COMBS(_1204782, _1204780, tc_fun(_1204780, _1204780)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1204780, tc_fun(_1204780, _1204780)), _1204782), c_If(_1204780)), hAPP(hAPP(c_COMBC(_1204782, tc_fun(_1204782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1204782)), _1204788))), _1204786)), c_Groups_Ozero__class_Ozero(_1204780))), _1204784))], (22038 ^ _779530) ^ [_1205189, _1205191, _1205193, _1205195, _1205197] : [class_Groups_Ocomm__monoid__add(_1205189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1205191), _1205193)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1205191, _1205189), _1205195), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1205191, tc_HOL_Obool)), _1205193), _1205197)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1205191, _1205189), hAPP(hAPP(c_COMBC(_1205191, _1205189, _1205189), hAPP(hAPP(c_COMBS(_1205191, _1205189, tc_fun(_1205189, _1205189)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1205189, tc_fun(_1205189, _1205189)), _1205191), c_If(_1205189)), hAPP(hAPP(c_COMBC(_1205191, tc_fun(_1205191, tc_HOL_Obool), tc_HOL_Obool), c_member(_1205191)), _1205197))), _1205195)), c_Groups_Ozero__class_Ozero(_1205189))), _1205193))], (22048 ^ _779530) ^ [_1205510, _1205512, _1205514, _1205516, _1205518, _1205520, _1205522] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1205510, _1205512, _1205514, _1205516, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1205510, tc_HOL_Obool)), _1205518), hAPP(hAPP(c_Set_Oinsert(_1205510), _1205520), c_Orderings_Obot__class_Obot(tc_fun(_1205510, tc_HOL_Obool))))), _1205522)), hBOOL(hAPP(hAPP(c_member(_1205510), _1205520), _1205518)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1205510, _1205512, _1205514, _1205516, _1205518), hAPP(hAPP(_1205514, _1205520), _1205522))))], (22058 ^ _779530) ^ [_1205765, _1205767, _1205769] : [class_Orderings_Olinorder(_1205765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1205765), _1205767)), -(hBOOL(hAPP(hAPP(c_member(_1205765), _1205769), _1205767))), -(_1205767 = c_Orderings_Obot__class_Obot(tc_fun(_1205765, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1205765, hAPP(hAPP(c_Set_Oinsert(_1205765), _1205769), _1205767)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1205765), _1205769), c_Big__Operators_Olinorder__class_OMin(_1205765, _1205767)))], (22076 ^ _779530) ^ [_1206011, _1206013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206011), _1206013)), -(hAPP(c_Finite__Set_Ocard(_1206011), _1206013) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1206011, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1206011), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206013))], (22082 ^ _779530) ^ [_1206138, _1206140] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1206138), _1206140))), -(hAPP(c_Finite__Set_Ocard(_1206138), _1206140) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22088 ^ _779530) ^ [_1206185, _1206187] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206185), _1206187)), -(hAPP(c_Finite__Set_Ocard(_1206185), _1206187) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1206185, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1206185), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206187))], (22094 ^ _779530) ^ [_1206318, _1206320, _1206322] : [class_Orderings_Olinorder(_1206318), hBOOL(hAPP(c_Finite__Set_Ofinite(_1206318), _1206320)), 22101 ^ _779530 : [(22102 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206318, tc_HOL_Obool)), _1206320), hAPP(hAPP(c_Set_Oinsert(_1206318), _1206322), c_Orderings_Obot__class_Obot(tc_fun(_1206318, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1206318, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1206318, hAPP(hAPP(c_Set_Oinsert(_1206318), _1206322), _1206320)) = _1206322)], (22108 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206318, tc_HOL_Obool)), _1206320), hAPP(hAPP(c_Set_Oinsert(_1206318), _1206322), c_Orderings_Obot__class_Obot(tc_fun(_1206318, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1206318, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1206318, hAPP(hAPP(c_Set_Oinsert(_1206318), _1206322), _1206320)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206318), _1206322), c_Big__Operators_Olinorder__class_OMin(_1206318, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206318, tc_HOL_Obool)), _1206320), hAPP(hAPP(c_Set_Oinsert(_1206318), _1206322), c_Orderings_Obot__class_Obot(tc_fun(_1206318, tc_HOL_Obool)))))))]]], (22114 ^ _779530) ^ [_1206788, _1206790, _1206792] : [class_Orderings_Olinorder(_1206788), hBOOL(hAPP(c_Finite__Set_Ofinite(_1206788), _1206790)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1206788), _1206792)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1206788, tc_HOL_Obool)), _1206790), _1206792) = c_Orderings_Obot__class_Obot(tc_fun(_1206788, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206788), c_Big__Operators_Olinorder__class_OMin(_1206788, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1206788, tc_HOL_Obool)), _1206790), _1206792))), c_Big__Operators_Olinorder__class_OMin(_1206788, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1206788, tc_HOL_Obool)), _1206790), _1206792))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1206788), c_Big__Operators_Olinorder__class_OMin(_1206788, _1206790)), c_Big__Operators_Olinorder__class_OMin(_1206788, _1206792)))], (22132 ^ _779530) ^ [_1207136, _1207138, _1207140] : [class_Orderings_Olinorder(_1207136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207136), _1207138)), -(_1207138 = c_Orderings_Obot__class_Obot(tc_fun(_1207136, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207136), _1207140)), -(_1207140 = c_Orderings_Obot__class_Obot(tc_fun(_1207136, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1207136, tc_HOL_Obool)), _1207138), _1207140) = c_Orderings_Obot__class_Obot(tc_fun(_1207136, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1207136, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207136, tc_HOL_Obool)), _1207138), _1207140)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1207136), c_Big__Operators_Olinorder__class_OMin(_1207136, _1207138)), c_Big__Operators_Olinorder__class_OMin(_1207136, _1207140)))], (22158 ^ _779530) ^ [_1207613, _1207615, _1207617, _1207619, _1207621, _1207623] : [class_Rings_Olinordered__semiring__1__strict(_1207613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207613), _1207615), _1207617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207613), _1207619), _1207617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207613), c_Groups_Ozero__class_Ozero(_1207613)), _1207621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207613), c_Groups_Ozero__class_Ozero(_1207613)), _1207623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207613), _1207621), _1207623) = c_Groups_Oone__class_Oone(_1207613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207613), _1207621), _1207615)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207613), _1207623), _1207619))), _1207617)))], (22184 ^ _779530) ^ [_1208142, _1208144, _1208146, _1208148, _1208150] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1208142, _1208144, c_Hoare__Mirabelle_Otriple_Otriple(_1208142, _1208146, _1208148, _1208150)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22186 ^ _779530) ^ [_1208182] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(_1208182)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22188 ^ _779530) ^ [_1208209, _1208211] : [class_Rings_Olinordered__idom(_1208209), 22191 ^ _779530 : [(22192 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208209), _1208211), _1208211)), c_Groups_Ozero__class_Ozero(_1208209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208209), _1208211), c_Groups_Ozero__class_Ozero(_1208209))))], (22198 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208209), _1208211), c_Groups_Ozero__class_Ozero(_1208209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208209), _1208211), _1208211)), c_Groups_Ozero__class_Ozero(_1208209))))]]], (22204 ^ _779530) ^ [_1208492] : [class_Orderings_Olinorder(_1208492), -(c_Orderings_Oord_Omax(_1208492, hAPP(c_COMBC(_1208492, _1208492, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1208492))) = c_Orderings_Oord__class_Omin(_1208492))], (22210 ^ _779530) ^ [_1208593] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(_1208593)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22212 ^ _779530) ^ [_1208620, _1208622, _1208624, _1208626] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1208620)), c_Hoare__Mirabelle_Otriple_Otriple(_1208620, _1208622, _1208624, _1208626)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22214 ^ _779530) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (22216 ^ _779530) ^ [_1208679, _1208681] : [class_Groups_Olinordered__ab__group__add(_1208679), 22219 ^ _779530 : [(22220 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208679), _1208681), _1208681) = c_Groups_Ozero__class_Ozero(_1208679), -(_1208681 = c_Groups_Ozero__class_Ozero(_1208679))], (22226 ^ _779530) ^ [] : [_1208681 = c_Groups_Ozero__class_Ozero(_1208679), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208679), _1208681), _1208681) = c_Groups_Ozero__class_Ozero(_1208679))]]], (22232 ^ _779530) ^ [_1208920, _1208922, _1208924] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208920), _1208922)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1208920), _1208924)), 22242 ^ _779530 : [(22243 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1208920), 22241 ^ [_1208920, _1208922, _1208924]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1208920, tc_HOL_Obool)), _1208922), _1208924))))], (22245 ^ _779530) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1208920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1208920, tc_HOL_Obool)), _1208922), _1208924)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208920), _1208922)), hAPP(c_Finite__Set_Ocard(_1208920), _1208924)))], (22249 ^ _779530) ^ [_1209264, _1209266, _1209268, _1209270, _1209272] : [class_Groups_Oordered__comm__monoid__add(_1209264), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209266), _1209268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1209266, tc_HOL_Obool)), _1209270), _1209268)), 22263 ^ _779530 : [(22264 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209266), 22262 ^ [_1209264, _1209266, _1209268, _1209270, _1209272]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1209266, tc_HOL_Obool)), _1209268), _1209270))))], (22266 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209264), c_Groups_Ozero__class_Ozero(_1209264)), hAPP(_1209272, 22262 ^ [_1209264, _1209266, _1209268, _1209270, _1209272])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209264), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1209266, _1209264), _1209272), _1209270)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1209266, _1209264), _1209272), _1209268))))], (22270 ^ _779530) ^ [_1209750] : [class_Orderings_Oord(_1209750), -(c_Orderings_Oord__class_Omin(_1209750) = c_Orderings_Oord_Omin(_1209750, c_Orderings_Oord__class_Oless__eq(_1209750)))], (22276 ^ _779530) ^ [_1209837, _1209839, _1209841, _1209843, _1209845] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1209837, _1209837, _1209839, _1209841, _1209843), _1209845)), -(hBOOL(hAPP(hAPP(c_member(_1209837), _1209841), _1209843))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1209837, _1209839, hAPP(hAPP(c_Set_Oinsert(_1209837), _1209841), _1209843)), _1209845)))], (22286 ^ _779530) ^ [_1209993] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OGlb(_1209993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22288 ^ _779530) ^ [_1210021, _1210023] : [class_Orderings_Olinorder(_1210021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1210021), _1210023)), -(_1210023 = c_Orderings_Obot__class_Obot(tc_fun(_1210021, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1210021), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1210021), 22301 ^ [_1210021, _1210023]), 22302 ^ [_1210021, _1210023])), hAPP(hAPP(c_Set_Oinsert(_1210021), 22301 ^ [_1210021, _1210023]), hAPP(hAPP(c_Set_Oinsert(_1210021), 22302 ^ [_1210021, _1210023]), c_Orderings_Obot__class_Obot(tc_fun(_1210021, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1210021), c_Big__Operators_Olinorder__class_OMin(_1210021, _1210023)), _1210023)))], (22308 ^ _779530) ^ [_1210480, _1210482, _1210484] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1210480, _1210482, c_Orderings_Obot__class_Obot(tc_fun(_1210480, tc_HOL_Obool))), _1210484))], (22310 ^ _779530) ^ [_1210518, _1210520, _1210522, _1210524] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1210518, _1210520, _1210522), _1210524)), _1210522 = c_Orderings_Obot__class_Obot(tc_fun(_1210518, tc_HOL_Obool))], (22316 ^ _779530) ^ [_1210643, _1210645, _1210647, _1210649] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1210643, _1210645, hAPP(hAPP(c_Set_Oinsert(_1210643), _1210647), c_Orderings_Obot__class_Obot(tc_fun(_1210643, tc_HOL_Obool)))), _1210649)), -(_1210647 = _1210649)], (22322 ^ _779530) ^ [_1210758, _1210760, _1210762, _1210764] : [_1210762 = _1210764, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1210758, _1210760, hAPP(hAPP(c_Set_Oinsert(_1210758), _1210762), c_Orderings_Obot__class_Obot(tc_fun(_1210758, tc_HOL_Obool)))), _1210764)))], (22328 ^ _779530) ^ [_1210879] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OLoc(_1210879)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22330 ^ _779530) ^ [_1210907, _1210909, _1210911] : [-(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), _1210907)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1210909))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1210911))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1210907), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210911), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1210909)))))], (22332 ^ _779530) ^ [_1210988, _1210990, _1210992, _1210994, _1210996] : [class_Groups_Ocomm__monoid__add(_1210988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1210990), _1210992)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1210990), _1210994)), 22346 ^ _779530 : [(22347 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210990), 22345 ^ [_1210988, _1210990, _1210992, _1210994, _1210996]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1210990, tc_HOL_Obool)), _1210992), _1210994))))], (22349 ^ _779530) ^ [] : [hAPP(_1210996, 22345 ^ [_1210988, _1210990, _1210992, _1210994, _1210996]) = c_Groups_Ozero__class_Ozero(_1210988)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1210990, _1210988), _1210996), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1210990, tc_HOL_Obool)), _1210992), _1210994)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1210988), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1210990, _1210988), _1210996), _1210992)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1210990, _1210988), _1210996), _1210994)))], (22353 ^ _779530) ^ [_1211483, _1211485, _1211487, _1211489, _1211491] : [class_Groups_Ocomm__monoid__add(_1211483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1211485), _1211487)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1211485), _1211489)), 22367 ^ _779530 : [(22368 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1211485), 22366 ^ [_1211483, _1211485, _1211487, _1211489, _1211491]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1211485, tc_HOL_Obool)), _1211487), _1211489))))], (22370 ^ _779530) ^ [] : [hAPP(_1211491, 22366 ^ [_1211483, _1211485, _1211487, _1211489, _1211491]) = c_Groups_Ozero__class_Ozero(_1211483)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1211485, _1211483), _1211491), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1211485, tc_HOL_Obool)), _1211487), _1211489)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211483), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1211485, _1211483), _1211491), _1211487)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1211485, _1211483), _1211491), _1211489)))], (22374 ^ _779530) ^ [_1211996, _1211998, _1212000] : [hAPP(c_Finite__Set_Ocard(_1211996), _1211998) = hAPP(c_Nat_OSuc, _1212000), 22379 ^ _779530 : [(22380 ^ _779530) ^ [] : [-(_1211998 = hAPP(hAPP(c_Set_Oinsert(_1211996), 22377 ^ [_1211996, _1211998, _1212000]), 22378 ^ [_1211996, _1211998, _1212000]))], (22382 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1211996), 22377 ^ [_1211996, _1211998, _1212000]), 22378 ^ [_1211996, _1211998, _1212000]))], (22384 ^ _779530) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1211996), 22378 ^ [_1211996, _1211998, _1212000]) = _1212000)], (22386 ^ _779530) ^ [] : [_1212000 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(22378 ^ [_1211996, _1211998, _1212000] = c_Orderings_Obot__class_Obot(tc_fun(_1211996, tc_HOL_Obool)))]]], (22392 ^ _779530) ^ [_1212414, _1212416, _1212418] : [-(hAPP(c_Finite__Set_Ocard(_1212414), _1212416) = hAPP(c_Nat_OSuc, _1212418)), 22393 ^ _779530 : [(22394 ^ _779530) ^ [_1212514, _1212516] : [_1212416 = hAPP(hAPP(c_Set_Oinsert(_1212414), _1212516), _1212514), -(hBOOL(hAPP(hAPP(c_member(_1212414), _1212516), _1212514))), hAPP(c_Finite__Set_Ocard(_1212414), _1212514) = _1212418, 22405 ^ _779530 : [(22406 ^ _779530) ^ [] : [-(_1212418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22408 ^ _779530) ^ [] : [_1212514 = c_Orderings_Obot__class_Obot(tc_fun(_1212414, tc_HOL_Obool))]]]]], (22412 ^ _779530) ^ [_1212836, _1212838, _1212840, _1212842, _1212844] : [class_Groups_Ocomm__monoid__add(_1212836), class_Groups_Oordered__ab__semigroup__add(_1212836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1212838), _1212840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1212838, tc_HOL_Obool)), _1212842), _1212840)), 22430 ^ _779530 : [(22431 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212838), 22429 ^ [_1212836, _1212838, _1212840, _1212842, _1212844]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1212838, tc_HOL_Obool)), _1212840), _1212842))))], (22433 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212836), c_Groups_Ozero__class_Ozero(_1212836)), hAPP(_1212844, 22429 ^ [_1212836, _1212838, _1212840, _1212842, _1212844])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1212836), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212838, _1212836), _1212844), _1212842)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212838, _1212836), _1212844), _1212840))))], (22437 ^ _779530) ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390] : [class_Groups_Ocomm__monoid__add(_1213380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1213382), _1213384)), 22447 ^ _779530 : [(22448 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1213382), 22446 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390]), _1213384)))], (22451 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1213382), 22449 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390]), _1213384)))], (22453 ^ _779530) ^ [] : [22446 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390] = 22449 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390]], (22455 ^ _779530) ^ [] : [-(hAPP(_1213386, 22446 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390]) = hAPP(_1213386, 22449 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390]))], (22457 ^ _779530) ^ [] : [hAPP(_1213388, hAPP(_1213386, 22446 ^ [_1213380, _1213382, _1213384, _1213386, _1213388, _1213390])) = c_Groups_Ozero__class_Ozero(_1213380)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213390, _1213380), _1213388), hAPP(c_Set_Oimage(_1213382, _1213390, _1213386), _1213384)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213382, _1213380), hAPP(c_Fun_Ocomp(_1213390, _1213380, _1213382, _1213388), _1213386)), _1213384))], (22461 ^ _779530) ^ [_1214117] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214117))))], (22463 ^ _779530) ^ [_1214145, _1214147, _1214149] : [class_Orderings_Olinorder(_1214145), 22466 ^ _779530 : [(22467 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1214145), _1214147) = hAPP(c_SetInterval_Oord__class_OlessThan(_1214145), _1214149), -(_1214147 = _1214149)], (22473 ^ _779530) ^ [] : [_1214147 = _1214149, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1214145), _1214147) = hAPP(c_SetInterval_Oord__class_OlessThan(_1214145), _1214149))]]], (22479 ^ _779530) ^ [] : [-(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)))], (22481 ^ _779530) ^ [_1214404] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214404)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1214404), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214404)))], (22483 ^ _779530) ^ [_1214442] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214442)) = _1214442)], (22485 ^ _779530) ^ [] : [-(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)))], (22487 ^ _779530) ^ [_1214489] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214489)) = 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), _1214489))))], (22489 ^ _779530) ^ [_1214527, _1214529, _1214531] : [class_Groups_Ocomm__monoid__add(_1214527), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214527), _1214529), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214531))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214527), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214527), _1214529), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214531))), hAPP(_1214529, _1214531)))], (22495 ^ _779530) ^ [_1214680, _1214682, _1214684] : [class_Orderings_Oord(_1214680), 22498 ^ _779530 : [(22499 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1214680), _1214682), hAPP(c_SetInterval_Oord__class_OlessThan(_1214680), _1214684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214680), _1214682), _1214684)))], (22505 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214680), _1214682), _1214684)), -(hBOOL(hAPP(hAPP(c_member(_1214680), _1214682), hAPP(c_SetInterval_Oord__class_OlessThan(_1214680), _1214684))))]]], (22511 ^ _779530) ^ [_1214948, _1214950, _1214952] : [class_Orderings_Olinorder(_1214948), 22514 ^ _779530 : [(22515 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1214948, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1214948), _1214950)), hAPP(c_SetInterval_Oord__class_OlessThan(_1214948), _1214952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214948), _1214950), _1214952)))], (22521 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214948), _1214950), _1214952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1214948, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1214948), _1214950)), hAPP(c_SetInterval_Oord__class_OlessThan(_1214948), _1214952))))]]], (22527 ^ _779530) ^ [_1215240, _1215242, _1215244] : [class_Orderings_Olinorder(_1215240), 22530 ^ _779530 : [(22531 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1215240, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1215240), _1215242)), hAPP(c_SetInterval_Oord__class_OlessThan(_1215240), _1215244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215240), _1215242), _1215244)))], (22537 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215240), _1215242), _1215244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1215240, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1215240), _1215242)), hAPP(c_SetInterval_Oord__class_OlessThan(_1215240), _1215244))))]]], (22543 ^ _779530) ^ [_1215532, _1215534] : [class_Orderings_Oorder(_1215532), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1215532, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1215532), _1215534), c_Orderings_Obot__class_Obot(tc_fun(_1215532, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1215532), _1215534)) = hAPP(hAPP(c_Set_Oinsert(_1215532), _1215534), c_Orderings_Obot__class_Obot(tc_fun(_1215532, tc_HOL_Obool))))], (22549 ^ _779530) ^ [_1215691, _1215693, _1215695, _1215697] : [class_Rings_Ocomm__semiring__1(_1215691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215691), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215691), c_Groups_Oone__class_Oone(_1215691)), c_Groups_Oone__class_Oone(_1215691))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215691), hAPP(hAPP(c_COMBB(_1215691, _1215691, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1215691), _1215693)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1215691, _1215691), hAPP(hAPP(c_COMBB(_1215691, tc_fun(_1215691, _1215691), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1215691)), c_Nat_Osemiring__1__class_Oof__nat(_1215691))), _1215695))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1215697))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215691), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215691), _1215697)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215691), _1215693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215691), _1215693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215691), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215691), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215697), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1215695)))))], (22555 ^ _779530) ^ [_1216014, _1216016, _1216018] : [-(c_Option_Ooption_Ooption__size(_1216014, _1216016, hAPP(c_Option_Ooption_OSome(_1216014), _1216018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1216016, _1216018)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22557 ^ _779530) ^ [_1216059, _1216061] : [class_Rings_Olinordered__idom(_1216059), hBOOL(hAPP(hAPP(c_member(_1216059), _1216061), c_Int_Oring__1__class_OInts(_1216059))), 22564 ^ _779530 : [(22565 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216059), c_Groups_Oone__class_Oone(_1216059)), _1216061)), _1216061)), c_Groups_Ozero__class_Ozero(_1216059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216059), _1216061), c_Groups_Ozero__class_Ozero(_1216059))))], (22571 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216059), _1216061), c_Groups_Ozero__class_Ozero(_1216059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216059), c_Groups_Oone__class_Oone(_1216059)), _1216061)), _1216061)), c_Groups_Ozero__class_Ozero(_1216059))))]]], (22577 ^ _779530) ^ [_1216442, _1216444, _1216446] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1216442, _1216444, _1216446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1216446)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22579 ^ _779530) ^ [_1216483, _1216485] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1216483, _1216485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1216483)), c_Com_Ocom_Ocom__size(_1216485))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22581 ^ _779530) ^ [_1216529, _1216531] : [-(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, _1216529)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216531))))], (22583 ^ _779530) ^ [_1216571, _1216573] : [class_Rings_Oring__1(_1216571), -(hBOOL(hAPP(hAPP(c_member(_1216571), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216571), _1216573)), c_Int_Oring__1__class_OInts(_1216571))))], (22589 ^ _779530) ^ [_1216674, _1216676, _1216678] : [class_Nat_Osemiring__char__0(_1216674), 22592 ^ _779530 : [(22593 ^ _779530) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216674), _1216676) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216674), _1216678), -(_1216676 = _1216678)], (22599 ^ _779530) ^ [] : [_1216676 = _1216678, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216674), _1216676) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216674), _1216678))]]], (22605 ^ _779530) ^ [] : [-(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))], (22607 ^ _779530) ^ [_1216945] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1216945) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1216945 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22613 ^ _779530) ^ [_1217022] : [_1217022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217022) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22619 ^ _779530) ^ [_1217120, _1217122] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217120)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217122), 22622 ^ _779530 : [(22623 ^ _779530) ^ [] : [-(_1217120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22625 ^ _779530) ^ [] : [-(_1217122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22627 ^ _779530) ^ [_1217237, _1217239] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217237)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217239)), _1217237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1217239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22637 ^ _779530) ^ [_1217398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217398)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1217398 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22643 ^ _779530) ^ [_1217485] : [_1217485 = 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), _1217485)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22649 ^ _779530) ^ [_1217593, _1217595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217593)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217595)))), 22652 ^ _779530 : [(22653 ^ _779530) ^ [] : [-(_1217593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22655 ^ _779530) ^ [] : [-(_1217595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22657 ^ _779530) ^ [_1217720, _1217722] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217720)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1217722))))), _1217720 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1217722 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22667 ^ _779530) ^ [_1217879] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1217879)) = 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), _1217879)))], (22669 ^ _779530) ^ [_1217929, _1217931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217929), _1217931)), -(_1217931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1217929), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22672 ^ [_1217929, _1217931]))))], (22676 ^ _779530) ^ [_1218048, _1218050] : [22677 ^ _779530 : [(22678 ^ _779530) ^ [_1218104] : [_1218050 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1218048), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1218104)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218048), _1218050)))], (22682 ^ _779530) ^ [_1218183] : [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, _1218183)))))], (22684 ^ _779530) ^ [_1218217] : [-(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, _1218217)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22686 ^ _779530) ^ [_1218269, _1218271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218269)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218269), _1218271)))], (22692 ^ _779530) ^ [_1218374, _1218376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218374), _1218376)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218374)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218376))))], (22698 ^ _779530) ^ [_1218485, _1218487, _1218489] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218485)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218487)), _1218489)) = 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), _1218485), _1218487))), _1218489))], (22700 ^ _779530) ^ [_1218545, _1218547] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218545)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218547)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218545), _1218547)))], (22702 ^ _779530) ^ [_1218606, _1218608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218606)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218606), _1218608)))], (22708 ^ _779530) ^ [_1218711, _1218713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218711), _1218713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218711)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218713))))], (22714 ^ _779530) ^ [_1218822, _1218824] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218822)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218824)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218822), _1218824)))], (22716 ^ _779530) ^ [_1218868, _1218870] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218868), _1218870)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218868)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1218870)))], (22718 ^ _779530) ^ [] : [-(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))], (22720 ^ _779530) ^ [] : [-(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))))], (22722 ^ _779530) ^ [_1218950, _1218952, _1218954] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1218950, tc_Nat_Onat), _1218952), _1218954)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1218950, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1218950), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1218952)), _1218954))], (22724 ^ _779530) ^ [] : [-(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))], (22726 ^ _779530) ^ [_1219026, _1219028, _1219030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219026), _1219028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1219030)), -(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), _1219030)), _1219026)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219030)), _1219028))))], (22736 ^ _779530) ^ [_1219231] : [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), _1219231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1219231)))], (22742 ^ _779530) ^ [_1219316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1219316)), -(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), _1219316))))], (22748 ^ _779530) ^ [_1219407, _1219409] : [class_Rings_Olinordered__semidom(_1219407), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219407), c_Groups_Ozero__class_Ozero(_1219407)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219407), _1219409))))], (22754 ^ _779530) ^ [_1219510, _1219512] : [class_Rings_Olinordered__semidom(_1219510), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219510), c_Groups_Ozero__class_Ozero(_1219510)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219510), _1219512))))], (22760 ^ _779530) ^ [_1219613, _1219615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1219613), _1219615)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219615)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1219613)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1219615), _1219613)))], (22766 ^ _779530) ^ [_1219742, _1219744] : [class_Rings_Olinordered__semidom(_1219742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219742), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219742), _1219744)), c_Groups_Ozero__class_Ozero(_1219742)))], (22772 ^ _779530) ^ [_1219846] : [class_Rings_Osemiring__1(_1219846), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219846), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1219846))], (22778 ^ _779530) ^ [_1219933, _1219935, _1219937] : [class_Rings_Olinordered__semidom(_1219933), 22781 ^ _779530 : [(22782 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219933), _1219935)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219933), _1219937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1219935), _1219937)))], (22788 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1219935), _1219937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219933), _1219935)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1219933), _1219937))))]]], (22794 ^ _779530) ^ [_1220210, _1220212, _1220214] : [class_Rings_Olinordered__semidom(_1220210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220212), _1220214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220210), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220210), _1220212)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220210), _1220214))))], (22804 ^ _779530) ^ [_1220385, _1220387, _1220389] : [class_Rings_Olinordered__semidom(_1220385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220385), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220385), _1220387)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220385), _1220389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220387), _1220389)))], (22814 ^ _779530) ^ [_1220560, _1220562, _1220564] : [class_Rings_Olinordered__semidom(_1220560), 22817 ^ _779530 : [(22818 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220560), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220560), _1220562)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220560), _1220564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220562), _1220564)))], (22824 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220562), _1220564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220560), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220560), _1220562)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220560), _1220564))))]]], (22830 ^ _779530) ^ [_1220837, _1220839, _1220841] : [class_Rings_Osemiring__1(_1220837), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220837), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220839), _1220841)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220837), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220837), _1220839)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220837), _1220841)))], (22836 ^ _779530) ^ [_1220972, _1220974, _1220976] : [class_Rings_Osemiring__1(_1220972), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1220974), _1220976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220972), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220972), _1220974)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1220972), _1220976)))], (22842 ^ _779530) ^ [_1221107] : [class_Rings_Osemiring__1(_1221107), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1221107), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1221107))], (22848 ^ _779530) ^ [_1221194, _1221196, _1221198, _1221200] : [class_Rings_Osemiring__1(_1221194), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1221194), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221196, tc_Nat_Onat), _1221198), _1221200)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1221196, _1221194), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1221194, _1221196), c_Nat_Osemiring__1__class_Oof__nat(_1221194)), _1221198)), _1221200))], (22854 ^ _779530) ^ [_1221343] : [class_Nat_Osemiring__char__0(_1221343), -(c_Fun_Oinj__on(tc_Nat_Onat, _1221343, c_Nat_Osemiring__1__class_Oof__nat(_1221343), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (22860 ^ _779530) ^ [_1221424] : [class_Rings_Oring__1(_1221424), -(hBOOL(hAPP(hAPP(c_member(_1221424), c_Groups_Ozero__class_Ozero(_1221424)), c_Int_Oring__1__class_OInts(_1221424))))], (22866 ^ _779530) ^ [_1221519, _1221521, _1221523] : [class_Rings_Oring__1(_1221519), hBOOL(hAPP(hAPP(c_member(_1221519), _1221521), c_Int_Oring__1__class_OInts(_1221519))), hBOOL(hAPP(hAPP(c_member(_1221519), _1221523), c_Int_Oring__1__class_OInts(_1221519))), -(hBOOL(hAPP(hAPP(c_member(_1221519), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221519), _1221521), _1221523)), c_Int_Oring__1__class_OInts(_1221519))))], (22880 ^ _779530) ^ [_1221774, _1221776, _1221778] : [class_Rings_Oring__1(_1221774), hBOOL(hAPP(hAPP(c_member(_1221774), _1221776), c_Int_Oring__1__class_OInts(_1221774))), hBOOL(hAPP(hAPP(c_member(_1221774), _1221778), c_Int_Oring__1__class_OInts(_1221774))), -(hBOOL(hAPP(hAPP(c_member(_1221774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221774), _1221776), _1221778)), c_Int_Oring__1__class_OInts(_1221774))))], (22894 ^ _779530) ^ [_1222029, _1222031, _1222033] : [class_Rings_Oring__1(_1222029), hBOOL(hAPP(hAPP(c_member(_1222029), _1222031), c_Int_Oring__1__class_OInts(_1222029))), hBOOL(hAPP(hAPP(c_member(_1222029), _1222033), c_Int_Oring__1__class_OInts(_1222029))), -(hBOOL(hAPP(hAPP(c_member(_1222029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1222029), _1222031), _1222033)), c_Int_Oring__1__class_OInts(_1222029))))], (22908 ^ _779530) ^ [_1222284] : [class_Rings_Oring__1(_1222284), -(hBOOL(hAPP(hAPP(c_member(_1222284), c_Groups_Oone__class_Oone(_1222284)), c_Int_Oring__1__class_OInts(_1222284))))], (22914 ^ _779530) ^ [_1222379, _1222381] : [class_Rings_Oring__1(_1222379), hBOOL(hAPP(hAPP(c_member(_1222379), _1222381), c_Int_Oring__1__class_OInts(_1222379))), -(hBOOL(hAPP(hAPP(c_member(_1222379), hAPP(c_Groups_Ouminus__class_Ouminus(_1222379), _1222381)), c_Int_Oring__1__class_OInts(_1222379))))], (22924 ^ _779530) ^ [_1222552, _1222554] : [class_Rings_Osemiring__1(_1222552), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222552), hAPP(c_Nat_OSuc, _1222554)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1222552), c_Groups_Oone__class_Oone(_1222552)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222552), _1222554)))], (22930 ^ _779530) ^ [_1222673, _1222675, _1222677] : [class_Rings_Oring__1(_1222673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222675), _1222677)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1222677), _1222675)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1222673), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222673), _1222677)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222673), _1222675)))], (22940 ^ _779530) ^ [_1222872, _1222874] : [-(c_Option_Ooption_Ooption__size(_1222872, _1222874, c_Option_Ooption_ONone(_1222872)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22942 ^ _779530) ^ [_1222903, _1222905, _1222907, _1222909] : [class_Rings_Osemiring__1(_1222903), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1222905, _1222903), hAPP(c_COMBK(_1222903, _1222905), _1222907)), _1222909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222903), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1222903), hAPP(c_Finite__Set_Ocard(_1222905), _1222909))), _1222907))], (22948 ^ _779530) ^ [_1223048, _1223050] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_1223048, _1223050)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22950 ^ _779530) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22952 ^ _779530) ^ [_1223096, _1223098] : [class_Rings_Olinordered__semidom(_1223096), 22955 ^ _779530 : [(22956 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223096), c_Groups_Ozero__class_Ozero(_1223096)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223096), _1223098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223098)))], (22962 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223096), c_Groups_Ozero__class_Ozero(_1223096)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223096), _1223098))))]]], (22968 ^ _779530) ^ [_1223349, _1223351] : [class_Int_Oring__char__0(_1223349), hBOOL(hAPP(hAPP(c_member(_1223349), _1223351), c_Int_Oring__1__class_OInts(_1223349))), 22975 ^ _779530 : [(22976 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223349), _1223351), _1223351) = c_Groups_Ozero__class_Ozero(_1223349), -(_1223351 = c_Groups_Ozero__class_Ozero(_1223349))], (22982 ^ _779530) ^ [] : [_1223351 = c_Groups_Ozero__class_Ozero(_1223349), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223349), _1223351), _1223351) = c_Groups_Ozero__class_Ozero(_1223349))]]], (22988 ^ _779530) ^ [_1223660, _1223662] : [class_Int_Oring__char__0(_1223660), hBOOL(hAPP(hAPP(c_member(_1223660), _1223662), c_Int_Oring__1__class_OInts(_1223660))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223660), c_Groups_Oone__class_Oone(_1223660)), _1223662)), _1223662) = c_Groups_Ozero__class_Ozero(_1223660)], (22998 ^ _779530) ^ [_1223846, _1223848] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1223846, _1223848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1223848)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23000 ^ _779530) ^ [_1223884, _1223886, _1223888] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1223884, _1223886, _1223888)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1223886)), c_Com_Ocom_Ocom__size(_1223888))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23002 ^ _779530) ^ [_1223933, _1223935] : [class_Rings_Osemiring__1(_1223933), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223933), _1223935) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1223933, hAPP(hAPP(c_COMBC(_1223933, _1223933, _1223933), c_Groups_Oplus__class_Oplus(_1223933)), c_Groups_Oone__class_Oone(_1223933)), _1223935, c_Groups_Ozero__class_Ozero(_1223933)))], (23024 ^ _779530) ^ [_1224367, _1224369, _1224371] : [-(hBOOL(hAPP(_1224367, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224369), _1224371))))), 23027 ^ _779530 : [(23028 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224371), _1224369)))], (23030 ^ _779530) ^ [] : [hBOOL(hAPP(_1224367, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224369)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224371))))]], 23031 ^ _779530 : [(23032 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224369), _1224371)))], (23034 ^ _779530) ^ [] : [hBOOL(hAPP(_1224367, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23008 ^ _779530) ^ [_1224078, _1224080, _1224082] : [hBOOL(hAPP(_1224078, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224080), _1224082)))), 23011 ^ _779530 : [(23012 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224082), _1224080)), -(hBOOL(hAPP(_1224078, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224080)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224082)))))], (23018 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224080), _1224082)), -(hBOOL(hAPP(_1224078, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23038 ^ _779530) ^ [_1224642] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1224642)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1224642)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23040 ^ _779530) ^ [_1224699, _1224701, _1224703, _1224705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1224699, _1224699)), hAPP(hAPP(c_Product__Type_OPair(_1224699, _1224699), _1224701), _1224703)), hAPP(c_Wellfounded_Omeasure(_1224699), _1224705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1224705, _1224701)), hAPP(_1224705, _1224703))))], (23046 ^ _779530) ^ [_1224846, _1224848, _1224850, _1224852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1224852, _1224848)), hAPP(_1224852, _1224850))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1224846, _1224846)), hAPP(hAPP(c_Product__Type_OPair(_1224846, _1224846), _1224848), _1224850)), hAPP(c_Wellfounded_Omeasure(_1224846), _1224852))))], (23052 ^ _779530) ^ [_1224999, _1225001, _1225003, _1225005, _1225007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1224999, _1225001)), hAPP(_1224999, _1225003))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1225005, _1225005)), hAPP(hAPP(c_Product__Type_OPair(_1225005, _1225005), _1225001), _1225003)), _1225007)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1225005, _1225005)), hAPP(hAPP(c_Product__Type_OPair(_1225005, _1225005), _1225001), _1225003)), c_Wellfounded_Omlex__prod(_1225005, _1224999, _1225007))))], (23062 ^ _779530) ^ [_1225246, _1225248] : [-(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), _1225246))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225248))))], (23064 ^ _779530) ^ [_1225285] : [-(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), _1225285))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23066 ^ _779530) ^ [_1225319] : [-(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), _1225319))))], (23068 ^ _779530) ^ [_1225356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225356)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23070 ^ _779530) ^ [_1225402, _1225404] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225404), -(_1225402 = _1225404)], (23076 ^ _779530) ^ [_1225487, _1225489] : [_1225487 = _1225489, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225487) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225489))], (23082 ^ _779530) ^ [_1225590, _1225592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225590)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225592))))], (23084 ^ _779530) ^ [_1225644, _1225646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225644), _1225646)), -(_1225646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225644), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23087 ^ [_1225644, _1225646])))], (23091 ^ _779530) ^ [_1225757, _1225759] : [23092 ^ _779530 : [(23093 ^ _779530) ^ [_1225810] : [_1225759 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225757), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225810))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225757), _1225759)))], (23097 ^ _779530) ^ [_1225877, _1225879, _1225881] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225877), _1225879)), _1225881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225877), _1225881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225879), _1225881)))], (23099 ^ _779530) ^ [_1225934, _1225936, _1225938] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225936), _1225938)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225934), _1225936)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225934), _1225938)))], (23101 ^ _779530) ^ [_1225991] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1225991) = _1225991)], (23103 ^ _779530) ^ [_1226017] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226017), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1226017)], (23105 ^ _779530) ^ [_1226046, _1226048] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226046)), _1226048) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226046), _1226048)))], (23107 ^ _779530) ^ [_1226089, _1226091, _1226093] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226089), _1226091)), _1226093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226089), _1226093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226091), _1226093)))], (23109 ^ _779530) ^ [_1226146, _1226148, _1226150] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226148), _1226150)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226146), _1226148)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226146), _1226150)))], (23111 ^ _779530) ^ [_1226203, _1226205, _1226207] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226203), _1226205)), _1226207) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226205), _1226207)))], (23113 ^ _779530) ^ [_1226254, _1226256] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226254), _1226256) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226256), _1226254))], (23115 ^ _779530) ^ [_1226291, _1226293, _1226295, _1226297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226291), _1226293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226295), _1226297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226291), _1226295)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226293), _1226297))))], (23125 ^ _779530) ^ [_1226482, _1226484, _1226486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226482), _1226484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226486), _1226482)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226486), _1226484))))], (23131 ^ _779530) ^ [_1226605, _1226607] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226605), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226607)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226605), _1226607))], (23133 ^ _779530) ^ [_1226645, _1226647] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226645), _1226647) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226645), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226647)))], (23135 ^ _779530) ^ [_1226685, _1226687] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226685), _1226687)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226685)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226687)))], (23137 ^ _779530) ^ [_1226731, _1226733, _1226735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226731), _1226733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226731), _1226735)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226733), _1226735))))], (23143 ^ _779530) ^ [_1226854, _1226856, _1226858] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226854), _1226856)), _1226858) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226856), _1226858)))], (23145 ^ _779530) ^ [_1226905, _1226907, _1226909] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226907), _1226909)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226907), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226905), _1226909)))], (23147 ^ _779530) ^ [_1226956, _1226958] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226956), _1226958) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226958), _1226956))], (23149 ^ _779530) ^ [_1227008, _1227010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227008), _1227010)), 23152 ^ _779530 : [(23153 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227008), _1227010)))], (23155 ^ _779530) ^ [] : [_1227008 = _1227010]]], (23157 ^ _779530) ^ [_1227135, _1227137] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227135), _1227137))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227135), _1227137)), -(_1227135 = _1227137)], (23167 ^ _779530) ^ [_1227289, _1227291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227289), _1227291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227291), _1227289)), -(_1227289 = _1227291)], (23177 ^ _779530) ^ [_1227438, _1227440, _1227442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227438), _1227440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227440), _1227442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227438), _1227442)))], (23187 ^ _779530) ^ [_1227597, _1227599] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227597), _1227599))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227599), _1227597)))], (23193 ^ _779530) ^ [_1227643] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227643), _1227643)))], (23195 ^ _779530) ^ [_1227671] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1227671)) = _1227671)], (23197 ^ _779530) ^ [_1227696, _1227698] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227696), _1227698))), -(_1227696 = _1227698), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227698), _1227696)))], (23207 ^ _779530) ^ [_1227764, _1227766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227764), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227766), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227764), _1227766)))], (23213 ^ _779530) ^ [_1227869, _1227871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227869), _1227871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227869), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1227871), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23229 ^ _779530) ^ [_1228113, _1228115] : [23230 ^ _779530 : [(23231 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228113), _1228115))], (23233 ^ _779530) ^ [] : [_1228113 = _1228115]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228115), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23219 ^ _779530) ^ [_1227995, _1227997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1227997), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227995), _1227997))), -(_1227995 = _1227997)], (23237 ^ _779530) ^ [_1228262, _1228264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228262), _1228264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228262), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1228264)))], (23243 ^ _779530) ^ [_1228386, _1228388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228386), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1228388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228386), _1228388)))], (23249 ^ _779530) ^ [_1228491, _1228493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228491), _1228493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228491), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1228493)))], (23255 ^ _779530) ^ [_1228617, _1228619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228619), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228617), _1228619)))], (23261 ^ _779530) ^ [_1228722, _1228724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228722), _1228724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228724), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (23267 ^ _779530) ^ [_1228833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228833)), -(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)), _1228833))))], (23273 ^ _779530) ^ [_1228934] : [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)), _1228934)), _1228934)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1228934), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23279 ^ _779530) ^ [_1229043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229043), 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)), _1229043)), _1229043)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23285 ^ _779530) ^ [_1229167] : [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)), _1229167)), _1229167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23287 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (23289 ^ _779530) ^ [] : [-(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))))], (23291 ^ _779530) ^ [_1229253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1229253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229253)))], (23297 ^ _779530) ^ [_1229332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1229332)))], (23303 ^ _779530) ^ [_1229432, _1229434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229432), _1229434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229432), _1229434)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23309 ^ _779530) ^ [_1229537, _1229539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1229537), _1229539)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229537), _1229539)))], (23315 ^ _779530) ^ [] : [-(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))], (23317 ^ _779530) ^ [_1229666] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229666) = _1229666)], (23319 ^ _779530) ^ [_1229692] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1229692), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1229692)], (23321 ^ _779530) ^ [_1229721] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1229721)), _1229721) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23323 ^ _779530) ^ [_1229753, _1229755, _1229757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229753), _1229755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1229757), _1229753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1229757), _1229755))))], (23333 ^ _779530) ^ [_1229934, _1229936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229934)), 23336 ^ _779530 : [(23337 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1229934), _1229936) = c_Groups_Oone__class_Oone(tc_Int_Oint), 23340 ^ _779530 : [(23341 ^ _779530) ^ [] : [-(_1229934 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23343 ^ _779530) ^ [] : [-(_1229936 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (23345 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1229934), _1229936) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1229934 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1229936 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (23355 ^ _779530) ^ [_1230235, _1230237, _1230239] : [class_Rings_Osemiring__1(_1230235), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1230235, _1230237, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1230239) = _1230239)], (23361 ^ _779530) ^ [_1230322, _1230324, _1230326, _1230328] : [class_Rings_Osemiring__1(_1230322), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1230322, _1230324, hAPP(c_Nat_OSuc, _1230326), _1230328) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1230322, _1230324, _1230326, hAPP(_1230324, _1230328)))], (23367 ^ _779530) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23369 ^ _779530) ^ [_1230451, _1230453, _1230455, _1230457, _1230459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1230451, _1230453)), hAPP(_1230451, _1230455))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1230457, _1230457)), hAPP(hAPP(c_Product__Type_OPair(_1230457, _1230457), _1230453), _1230455)), c_Wellfounded_Omlex__prod(_1230457, _1230451, _1230459))))], (23375 ^ _779530) ^ [_1230602, _1230604, _1230606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230602)), _1230602 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230602), _1230606)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230604), _1230602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1230606)))], (23389 ^ _779530) ^ [_1230831, _1230833, _1230835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230831)), _1230831 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1230831), _1230835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230835), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23403 ^ _779530) ^ [_1231060, _1231062, _1231064, _1231066, _1231068, _1231070] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231060), _1231062)), _1231064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231066), _1231068)), _1231070), 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), _1231066), _1231068)), _1231070)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231064), _1231060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231066), _1231060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231068), _1231062)))], (23429 ^ _779530) ^ [_1231565, _1231567, _1231569, _1231571, _1231573] : [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), _1231565), _1231567)), _1231569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231565), _1231571)), _1231573))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231573), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231565), _1231573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231565), _1231569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231571), _1231567)))], (23447 ^ _779530) ^ [_1231920, _1231922, _1231924, _1231926, _1231928, _1231930] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231920), _1231922)), _1231924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231926), _1231928)), _1231930), 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), _1231926), _1231928)), _1231930))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231930), _1231926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231926), _1231920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231922), _1231928)))], (23473 ^ _779530) ^ [_1232419, _1232421, _1232423] : [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), _1232419), _1232421)), _1232423))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232423), _1232419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232421)))], (23487 ^ _779530) ^ [_1232652, _1232654, _1232656] : [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), _1232652), _1232654)), _1232656)), 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)), _1232656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232654), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23501 ^ _779530) ^ [_1232891, _1232893, _1232895, _1232897, _1232899] : [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), _1232891), _1232893)), _1232895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232891), _1232897)), _1232899))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232895), _1232891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232899), _1232891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232893), _1232897)))], (23519 ^ _779530) ^ [_1233240] : [-(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)))), _1233240)) = 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), _1233240), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (23521 ^ _779530) ^ [] : [-(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)))], (23523 ^ _779530) ^ [_1233299, _1233301] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233299)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233301)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233299), _1233301)))], (23525 ^ _779530) ^ [_1233345, _1233347] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233345)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233347)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1233345), _1233347)))], (23527 ^ _779530) ^ [_1233406, _1233408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233406)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233406), _1233408)))], (23533 ^ _779530) ^ [_1233511, _1233513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233511), _1233513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1233513))))], (23539 ^ _779530) ^ [_1233637, _1233639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1233637), _1233639)), -(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)), _1233637)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233639))))], (23545 ^ _779530) ^ [_1233742, _1233744] : [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)), _1233742)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1233742), _1233744)))], (23551 ^ _779530) ^ [_1233868, _1233870] : [_1233868 = _1233870, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233868) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233870))], (23557 ^ _779530) ^ [_1233953, _1233955] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233953) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1233955), -(_1233953 = _1233955)], (23563 ^ _779530) ^ [_1234059, _1234061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1234059), _1234061)), -(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)), _1234059)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1234061))))], (23569 ^ _779530) ^ [_1234164, _1234166] : [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)), _1234164)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1234166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1234164), _1234166)))], (23575 ^ _779530) ^ [_1234290, _1234292] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234290) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234292), -(_1234290 = _1234292)], (23581 ^ _779530) ^ [_1234375, _1234377] : [_1234375 = _1234377, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234375) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234377))], (23587 ^ _779530) ^ [] : [-(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))))], (23589 ^ _779530) ^ [_1234499, _1234501] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1234499), _1234501)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234499)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1234501))))], (23595 ^ _779530) ^ [_1234604, _1234606] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234604)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1234606))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1234604), _1234606)))], (23601 ^ _779530) ^ [] : [-(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))))], (23603 ^ _779530) ^ [_1234733] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1234733) = 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)), _1234733)))], (23605 ^ _779530) ^ [_1234777] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1234777)), -(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)), _1234777))))], (23611 ^ _779530) ^ [_1234862] : [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)), _1234862))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1234862)))], (23617 ^ _779530) ^ [] : [-(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)))], (23619 ^ _779530) ^ [_1234971, _1234973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234973)), -(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), _1234971), _1234973))))], (23629 ^ _779530) ^ [_1235136] : [23631 ^ _779530 : [(23632 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23630 ^ [_1235136])))], (23634 ^ _779530) ^ [] : [hBOOL(hAPP(_1235136, 23630 ^ [_1235136]))]], 23635 ^ _779530 : [(23636 ^ _779530) ^ [_1235263] : [-(hBOOL(hAPP(_1235136, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235263))))]]], (23638 ^ _779530) ^ [_1235293] : [hBOOL(hAPP(_1235293, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23639 ^ [_1235293]))), 23642 ^ _779530 : [(23643 ^ _779530) ^ [_1235393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235393)), -(hBOOL(hAPP(_1235293, _1235393)))]]], (23660 ^ _779530) ^ [_1235666] : [23661 ^ _779530 : [(23662 ^ _779530) ^ [_1235723] : [hBOOL(hAPP(_1235666, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235723)))]], 23664 ^ _779530 : [(23665 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23663 ^ [_1235666])))], (23667 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1235666, 23663 ^ [_1235666])))]]], (23649 ^ _779530) ^ [_1235496] : [-(hBOOL(hAPP(_1235496, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23656 ^ [_1235496])))), 23650 ^ _779530 : [(23651 ^ _779530) ^ [_1235548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235548)), hBOOL(hAPP(_1235496, _1235548))]]], (23669 ^ _779530) ^ [_1235815] : [-(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), _1235815))))], (23671 ^ _779530) ^ [] : [-(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))))], (23673 ^ _779530) ^ [_1235861, _1235863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235863)), -(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), _1235861), _1235863))))], (23683 ^ _779530) ^ [_1236029, _1236031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236029)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236029), _1236031)))], (23689 ^ _779530) ^ [_1236134, _1236136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236134), _1236136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236134)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236136))))], (23695 ^ _779530) ^ [_1236245] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1236245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1236245)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23697 ^ _779530) ^ [_1236295, _1236297, _1236299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236295), _1236297)), -(c_Smallcheck_Osmall_H(_1236299, _1236295, _1236297) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (23703 ^ _779530) ^ [_1236386, _1236388, _1236390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236386), _1236388))), -(c_Smallcheck_Osmall_H(_1236390, _1236386, _1236388) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1236390, _1236386, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1236388), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1236390, _1236388)))], (23709 ^ _779530) ^ [_1236456, _1236458, _1236460, _1236462, _1236464] : [class_Groups_Oordered__ab__semigroup__add(_1236456), class_Rings_Osemiring__1(_1236456), 23719 ^ _779530 : [(23720 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1236458), 23718 ^ [_1236456, _1236458, _1236460, _1236462, _1236464]), _1236460)))], (23722 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236456), hAPP(_1236462, 23718 ^ [_1236456, _1236458, _1236460, _1236462, _1236464])), _1236464))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236456), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1236458, _1236456), _1236462), _1236460)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236456), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1236456), hAPP(c_Finite__Set_Ocard(_1236458), _1236460))), _1236464))))], (23726 ^ _779530) ^ [_1236855, _1236857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236855), _1236857)), -(c_Nat__Transfer_Otsub(_1236857, _1236855) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236857), _1236855))], (23732 ^ _779530) ^ [_1236954, _1236956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236954), _1236956))), -(c_Nat__Transfer_Otsub(_1236956, _1236954) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23738 ^ _779530) ^ [_1237000, _1237002] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1237000)), hAPP(c_Option_Ooption_OSome(_1237000), _1237002)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23740 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (23742 ^ _779530) ^ [_1237061] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1237061) = _1237061)], (23744 ^ _779530) ^ [] : [-(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))], (23746 ^ _779530) ^ [_1237105, _1237107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1237105, _1237107))))], (23756 ^ _779530) ^ [_1237252, _1237254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237252), _1237254)), -(c_Nat__Transfer_Otsub(_1237254, _1237252) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1237254), _1237252))], (23762 ^ _779530) ^ [_1237357, _1237359] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237357), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1237359)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237357), _1237359)))], (23764 ^ _779530) ^ [_1237400] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1237400)), c_Option_Ooption_ONone(_1237400)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23766 ^ _779530) ^ [_1237432, _1237434, _1237436] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1237432), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1237434), _1237436)))), 23769 ^ _779530 : [(23770 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237434), _1237436)), -(c_Smallcheck_Osmall_H(_1237432, _1237434, _1237436) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (23776 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237434), _1237436))), -(c_Smallcheck_Osmall_H(_1237432, _1237434, _1237436) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1237432, _1237434, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237436), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1237432, _1237436)))]]], (23782 ^ _779530) ^ [_1237730, _1237732, _1237734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237730), _1237732)), -(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)), _1237730)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1237734), _1237732)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237734), _1237730)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237732), _1237730)))], (23788 ^ _779530) ^ [_1237882, _1237884, _1237886] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237882), _1237884))), 23791 ^ _779530 : [(23792 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237886), _1237884)), -(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)), _1237882)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1237886), _1237884)) = 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))))], (23798 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237886), _1237884))), -(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)), _1237882)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1237886), _1237884)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (23804 ^ _779530) ^ [_1238184, _1238186, _1238188, _1238190, _1238192, _1238194, _1238196, _1238198] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1238184, _1238186), tc_prod(_1238184, _1238186))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1238184, _1238186), tc_prod(_1238184, _1238186)), hAPP(hAPP(c_Product__Type_OPair(_1238184, _1238186), _1238188), _1238190)), hAPP(hAPP(c_Product__Type_OPair(_1238184, _1238186), _1238192), _1238194))), c_Wellfounded_Olex__prod(_1238184, _1238186, _1238196, _1238198))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1238184, _1238184)), hAPP(hAPP(c_Product__Type_OPair(_1238184, _1238184), _1238188), _1238192)), _1238196))), 23811 ^ _779530 : [(23812 ^ _779530) ^ [] : [-(_1238188 = _1238192)], (23814 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1238186, _1238186)), hAPP(hAPP(c_Product__Type_OPair(_1238186, _1238186), _1238190), _1238194)), _1238198)))]]], (23816 ^ _779530) ^ [_1238509, _1238511, _1238513, _1238515, _1238517, _1238519, _1238521, _1238523] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1238509, _1238511), tc_prod(_1238509, _1238511))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1238509, _1238511), tc_prod(_1238509, _1238511)), hAPP(hAPP(c_Product__Type_OPair(_1238509, _1238511), _1238513), _1238515)), hAPP(hAPP(c_Product__Type_OPair(_1238509, _1238511), _1238517), _1238519))), c_Wellfounded_Olex__prod(_1238509, _1238511, _1238521, _1238523)))), 23817 ^ _779530 : [(23818 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1238509, _1238509)), hAPP(hAPP(c_Product__Type_OPair(_1238509, _1238509), _1238513), _1238517)), _1238521))], (23820 ^ _779530) ^ [] : [_1238513 = _1238517, hBOOL(hAPP(hAPP(c_member(tc_prod(_1238511, _1238511)), hAPP(hAPP(c_Product__Type_OPair(_1238511, _1238511), _1238515), _1238519)), _1238523))]]], (23828 ^ _779530) ^ [_1238884, _1238886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1238884), _1238886)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1238884, tc_HOL_Obool)), hAPP(c_Set_OPow(_1238884), _1238886)) = 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(_1238884), _1238886)))], (23844 ^ _779530) ^ [_1239231, _1239233, _1239235, _1239237] : [23845 ^ _779530 : [(23846 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1239231), _1239233)))], (23848 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1239235), _1239237)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1239231, _1239235)), c_Sum__Type_OPlus(_1239231, _1239235, _1239233, _1239237)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23834 ^ _779530) ^ [_1239026, _1239028, _1239030, _1239032] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1239026, _1239030)), c_Sum__Type_OPlus(_1239026, _1239030, _1239028, _1239032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1239026), _1239028)), hAPP(c_Finite__Set_Ocard(_1239030), _1239032))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1239026), _1239028)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1239030), _1239032))], (23852 ^ _779530) ^ [_1239331, _1239333] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1239331), _1239333))))], (23854 ^ _779530) ^ [_1239364, _1239366, _1239368, _1239370] : [class_Rings_Ocomm__semiring__1(_1239364), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1239364), hAPP(hAPP(c_Power_Opower__class_Opower(_1239364), _1239366), _1239368)), _1239370) = hAPP(hAPP(c_Power_Opower__class_Opower(_1239364), _1239366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239368), _1239370)))], (23860 ^ _779530) ^ [_1239503, _1239505, _1239507, _1239509] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1239503, _1239505), _1239507)), hBOOL(hAPP(hAPP(_1239505, _1239509), _1239507)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1239503, _1239505), _1239509)))], (23880 ^ _779530) ^ [_1239874, _1239876, _1239878] : [23882 ^ _779530 : [(23883 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1239876, 23881 ^ [_1239874, _1239876, _1239878]), _1239878)))], (23885 ^ _779530) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1239874, _1239876), 23881 ^ [_1239874, _1239876, _1239878]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1239874, _1239876), _1239878)))], (23870 ^ _779530) ^ [_1239688, _1239690, _1239692] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1239688, _1239690), _1239692)), 23873 ^ _779530 : [(23874 ^ _779530) ^ [_1239773] : [hBOOL(hAPP(hAPP(_1239690, _1239773), _1239692)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1239688, _1239690), _1239773)))]]], (23899 ^ _779530) ^ [_1240264, _1240266, _1240268] : [23901 ^ _779530 : [(23902 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1240266, 23900 ^ [_1240264, _1240266, _1240268]), _1240268)))], (23904 ^ _779530) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1240264, _1240266), 23900 ^ [_1240264, _1240266, _1240268]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1240264, _1240266), _1240268)))], (23889 ^ _779530) ^ [_1240078, _1240080, _1240082] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1240078, _1240080), _1240082)), 23892 ^ _779530 : [(23893 ^ _779530) ^ [_1240163] : [hBOOL(hAPP(hAPP(_1240080, _1240163), _1240082)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1240078, _1240080), _1240163)))]]], (23908 ^ _779530) ^ [_1240450, _1240452, _1240454, _1240456] : [class_Rings_Ocomm__semiring__1(_1240450), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240450), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240450), _1240452), _1240454)), _1240456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240450), hAPP(hAPP(c_Power_Opower__class_Opower(_1240450), _1240452), _1240456)), hAPP(hAPP(c_Power_Opower__class_Opower(_1240450), _1240454), _1240456)))], (23914 ^ _779530) ^ [_1240609, _1240611] : [class_Rings_Ocomm__semiring__1(_1240609), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1240609), _1240611), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1240611)], (23920 ^ _779530) ^ [_1240700, _1240702, _1240704, _1240706, _1240708] : [class_Orderings_Olinorder(_1240700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240700), _1240702), _1240704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240700), _1240706), _1240708)), 23931 ^ _779530 : [(23932 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1240700, _1240702), _1240704) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1240700, _1240706), _1240708), 23935 ^ _779530 : [(23936 ^ _779530) ^ [] : [-(_1240702 = _1240706)], (23938 ^ _779530) ^ [] : [-(_1240704 = _1240708)]]], (23940 ^ _779530) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1240700, _1240702), _1240704) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1240700, _1240706), _1240708)), _1240702 = _1240706, _1240704 = _1240708]]], (23950 ^ _779530) ^ [_1241181, _1241183, _1241185, _1241187, _1241189] : [class_Orderings_Olinorder(_1241181), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241181, _1241183), _1241185) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241181, _1241187), _1241189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241181), _1241183), _1241185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241181), _1241187), _1241189)), -(_1241183 = _1241187)], (23968 ^ _779530) ^ [_1241488, _1241490, _1241492, _1241494, _1241496] : [class_Orderings_Olinorder(_1241488), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241488, _1241490), _1241492) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1241488, _1241494), _1241496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241488), _1241490), _1241492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241488), _1241494), _1241496)), -(_1241492 = _1241496)], (23986 ^ _779530) ^ [_1241795, _1241797, _1241799] : [class_Rings_Ocomm__semiring__1(_1241795), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241795), hAPP(hAPP(c_Power_Opower__class_Opower(_1241795), _1241797), _1241799)), _1241797) = hAPP(hAPP(c_Power_Opower__class_Opower(_1241795), _1241797), hAPP(c_Nat_OSuc, _1241799)))], (23992 ^ _779530) ^ [_1241926, _1241928, _1241930] : [class_Rings_Ocomm__semiring__1(_1241926), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241926), _1241928), hAPP(hAPP(c_Power_Opower__class_Opower(_1241926), _1241928), _1241930)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1241926), _1241928), hAPP(c_Nat_OSuc, _1241930)))], (23998 ^ _779530) ^ [_1242057, _1242059, _1242061] : [class_Rings_Ocomm__semiring__1(_1242057), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1242057), _1242059), hAPP(c_Nat_OSuc, _1242061)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242057), _1242059), hAPP(hAPP(c_Power_Opower__class_Opower(_1242057), _1242059), _1242061)))], (24004 ^ _779530) ^ [_1242188, _1242190] : [class_Rings_Ocomm__semiring__1(_1242188), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1242188), _1242190), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1242188))], (24010 ^ _779530) ^ [_1242283, _1242285, _1242287, _1242289] : [class_Rings_Ocomm__semiring__1(_1242283), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242283), hAPP(hAPP(c_Power_Opower__class_Opower(_1242283), _1242285), _1242287)), hAPP(hAPP(c_Power_Opower__class_Opower(_1242283), _1242285), _1242289)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1242283), _1242285), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1242287), _1242289)))], (24016 ^ _779530) ^ [_1242438, _1242440, _1242442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242438), _1242440)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1242440), _1242442)) = 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, _1242438), _1242440)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242440), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1242440), _1242442))))], (24022 ^ _779530) ^ [_1242599] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242599), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24024 ^ _779530) ^ [_1242628, _1242630, _1242632] : [class_Rings_Oring__1(_1242628), hBOOL(hAPP(hAPP(c_member(_1242628), _1242630), c_Int_Oring__1__class_OInts(_1242628))), -(hBOOL(hAPP(hAPP(c_member(_1242628), hAPP(hAPP(c_Power_Opower__class_Opower(_1242628), _1242630), _1242632)), c_Int_Oring__1__class_OInts(_1242628))))], (24034 ^ _779530) ^ [_1242811] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242811) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1242811))], (24036 ^ _779530) ^ [_1242840, _1242842] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242840), _1242842)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242842), _1242840))], (24038 ^ _779530) ^ [_1242880, _1242882] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1242880), _1242882)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1242880)), hAPP(c_Nat_OSuc, _1242882)))], (24040 ^ _779530) ^ [_1242926, _1242928, _1242930] : [class_Orderings_Oorder(_1242926), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242926), _1242928), _1242930)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1242926, _1242930), _1242928) = c_Orderings_Obot__class_Obot(tc_fun(_1242926, tc_HOL_Obool)))], (24050 ^ _779530) ^ [_1243093, _1243095, _1243097] : [class_Orderings_Oorder(_1243093), 24053 ^ _779530 : [(24054 ^ _779530) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1243093, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243093, _1243095), _1243097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243093), _1243095), _1243097))], (24060 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243093), _1243095), _1243097))), -(c_Orderings_Obot__class_Obot(tc_fun(_1243093, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243093, _1243095), _1243097))]]], (24066 ^ _779530) ^ [_1243318, _1243320, _1243322] : [class_Orderings_Oorder(_1243318), 24069 ^ _779530 : [(24070 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243318, _1243320), _1243322) = c_Orderings_Obot__class_Obot(tc_fun(_1243318, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243318), _1243320), _1243322))], (24076 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243318), _1243320), _1243322))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243318, _1243320), _1243322) = c_Orderings_Obot__class_Obot(tc_fun(_1243318, tc_HOL_Obool)))]]], (24082 ^ _779530) ^ [_1243543, _1243545, _1243547, _1243549, _1243551] : [class_Orderings_Olinorder(_1243543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1243543, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243543, _1243545), _1243547)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243543, _1243549), _1243551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243543), _1243547), _1243545))), 24093 ^ _779530 : [(24094 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243543), _1243549), _1243545)))], (24096 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243543), _1243547), _1243551)))]]], (24098 ^ _779530) ^ [_1243824, _1243826, _1243828, _1243830] : [class_Groups_Ocomm__monoid__add(_1243824), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243824), _1243826), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1243828)), hAPP(c_Nat_OSuc, _1243830))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1243824), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1243824, tc_Nat_Onat), _1243826), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243828), _1243830)))], (24104 ^ _779530) ^ [_1243995, _1243997, _1243999, _1244001] : [class_Orderings_Olinorder(_1243995), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243995), _1243997), _1243999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243995), _1243999), _1244001)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1243995, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243995, _1243997), _1243999)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243995, _1243999), _1244001)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1243995, _1243997), _1244001))], (24118 ^ _779530) ^ [_1244272, _1244274, _1244276, _1244278, _1244280] : [class_Groups_Ocomm__monoid__add(_1244272), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244272), _1244274), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244276), _1244278)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244280), _1244278))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244272), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1244272, tc_Nat_Onat), _1244274), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1244278))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244276), _1244280)))], (24124 ^ _779530) ^ [_1244463, _1244465, _1244467, _1244469] : [class_Orderings_Olinorder(_1244463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1244463), _1244465), _1244467)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1244463, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244463, _1244465), _1244469)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244463, _1244465), _1244467)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244463, _1244467), _1244469))], (24134 ^ _779530) ^ [_1244670, _1244672, _1244674, _1244676] : [class_Orderings_Oorder(_1244670), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1244670, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244670, _1244672), _1244674)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244670, _1244674), _1244676)) = c_Orderings_Obot__class_Obot(tc_fun(_1244670, tc_HOL_Obool)))], (24140 ^ _779530) ^ [_1244805, _1244807, _1244809] : [-(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)), _1244805)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244807), _1244809)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244807), _1244805)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1244809), _1244805)))], (24142 ^ _779530) ^ [_1244866, _1244868, _1244870, _1244872, _1244874] : [class_Groups_Ocomm__monoid__add(_1244866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244868), _1244870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244870), _1244872)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1244866), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244866), _1244874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244868), _1244870))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244866), _1244874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244870), _1244872))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1244866), _1244874), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1244868), _1244872)))], (24156 ^ _779530) ^ [_1245189, _1245191, _1245193, _1245195, _1245197] : [class_Groups_Oab__group__add(_1245189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245191), _1245193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245193), _1245195)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1245189), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245189), _1245197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245191), _1245195))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245189), _1245197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245191), _1245193))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245189), _1245197), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245193), _1245195)))], (24170 ^ _779530) ^ [_1245512, _1245514, _1245516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245512, tc_fun(_1245512, tc_HOL_Obool))), _1245514), _1245516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245512, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1245512, _1245516)), c_Wellfounded_Oaccp(_1245512, _1245514))))], (24176 ^ _779530) ^ [_1245649] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245649), hAPP(c_Nat_OSuc, _1245649)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1245649), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (24178 ^ _779530) ^ [_1245687, _1245689] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1245687, 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(_1245687, tc_HOL_Obool)), tc_fun(_1245687, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1245687, tc_HOL_Obool)), tc_fun(_1245687, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1245687, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1245689)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1245687, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1245689))], (24180 ^ _779530) ^ [_1245783, _1245785, _1245787] : [class_Orderings_Olinorder(_1245783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245783), _1245785), _1245787)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245783, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1245783), _1245785)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1245783, _1245785), _1245787)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1245783), _1245787))], (24190 ^ _779530) ^ [_1245982, _1245984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1245982), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245984), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1245982))))), -(_1245982 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1245984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245984), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1245982))))], (24196 ^ _779530) ^ [_1246129, _1246131, _1246133] : [class_Orderings_Oorder(_1246129), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1246129, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1246129), _1246131)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1246129, _1246131), _1246133)) = c_Orderings_Obot__class_Obot(tc_fun(_1246129, tc_HOL_Obool)))], (24202 ^ _779530) ^ [_1246260, _1246262, _1246264] : [class_Groups_Ocomm__monoid__add(_1246260), hAPP(_1246262, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1246260), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246260), _1246262), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1246264)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246260), _1246262), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1246264)))], (24212 ^ _779530) ^ [_1246449, _1246451, _1246453, _1246455] : [class_Groups_Ocomm__monoid__add(_1246449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246451), _1246453)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246449), _1246455), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246451), _1246453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1246449), hAPP(_1246455, _1246451)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1246449), _1246455), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1246451)), _1246453))))], (24222 ^ _779530) ^ [_1246691, _1246693] : [_1246691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1246693), _1246691) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24228 ^ _779530) ^ [_1246774, _1246776] : [-(_1246774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1246776), _1246774) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246776), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1246776), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246774), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (24234 ^ _779530) ^ [_1246845, _1246847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246845), _1246847)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246845), hAPP(c_Nat_OSuc, _1246847)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1246847), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246845), _1246847)))], (24240 ^ _779530) ^ [_1246968, _1246970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246968), _1246970))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246968), hAPP(c_Nat_OSuc, _1246970)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24246 ^ _779530) ^ [_1247020, _1247022, _1247024, _1247026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1247020, _1247022)), c_Sum__Type_OPlus(_1247020, _1247022, _1247024, _1247026))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1247022), _1247026)))], (24252 ^ _779530) ^ [_1247133, _1247135, _1247137, _1247139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1247133, _1247135)), c_Sum__Type_OPlus(_1247133, _1247135, _1247137, _1247139))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1247133), _1247137)))], (24258 ^ _779530) ^ [_1247246, _1247248, _1247250, _1247252] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1247246), _1247248)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247250), _1247252)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1247246, _1247250)), c_Sum__Type_OPlus(_1247246, _1247250, _1247248, _1247252))))], (24268 ^ _779530) ^ [_1247444, _1247446, _1247448, _1247450] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1247444, _1247446)), c_Sum__Type_OPlus(_1247444, _1247446, _1247448, _1247450))), 24271 ^ _779530 : [(24272 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1247444), _1247448)))], (24274 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1247446), _1247450)))]]], (24276 ^ _779530) ^ [_1247587, _1247589, _1247591, _1247593] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1247587, _1247589)), c_Sum__Type_OPlus(_1247587, _1247589, _1247591, _1247593)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247587), _1247591)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247589), _1247593))], (24286 ^ _779530) ^ [_1247766, _1247768, _1247770, _1247772] : [class_Groups_Ocomm__monoid__add(_1247766), 24289 ^ _779530 : [(24290 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247768), _1247770)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1247766), _1247772), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247770), hAPP(c_Nat_OSuc, _1247768))) = c_Groups_Ozero__class_Ozero(_1247766))], (24296 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247768), _1247770))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1247766), _1247772), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247770), hAPP(c_Nat_OSuc, _1247768))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247766), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1247766), _1247772), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247770), _1247768))), hAPP(_1247772, _1247768)))]]], (24302 ^ _779530) ^ [_1248096, _1248098, _1248100, _1248102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1248096), _1248098)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248100), _1248102)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1248096, _1248100)), c_Sum__Type_OPlus(_1248096, _1248100, _1248098, _1248102)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1248096), _1248098)), hAPP(c_Finite__Set_Ocard(_1248100), _1248102)))], (24312 ^ _779530) ^ [_1248307, _1248309, _1248311, _1248313] : [class_Rings_Olinordered__semidom(_1248307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248307), _1248309), _1248311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248307), c_Groups_Ozero__class_Ozero(_1248307)), _1248309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248307), hAPP(hAPP(c_Power_Opower__class_Opower(_1248307), _1248309), _1248313)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248307), _1248311), _1248313))))], (24330 ^ _779530) ^ [_1248636, _1248638, _1248640] : [class_Rings_Olinordered__semidom(_1248636), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248636), c_Groups_Oone__class_Oone(_1248636)), _1248638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248636), c_Groups_Oone__class_Oone(_1248636)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248636), _1248638), _1248640))))], (24344 ^ _779530) ^ [_1248877, _1248879, _1248881, _1248883] : [class_Rings_Olinordered__semidom(_1248877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248877), c_Groups_Oone__class_Oone(_1248877)), _1248879)), 24351 ^ _779530 : [(24352 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248877), hAPP(hAPP(c_Power_Opower__class_Opower(_1248877), _1248879), _1248881)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248877), _1248879), _1248883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1248881), _1248883)))], (24358 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1248881), _1248883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248877), hAPP(hAPP(c_Power_Opower__class_Opower(_1248877), _1248879), _1248881)), hAPP(hAPP(c_Power_Opower__class_Opower(_1248877), _1248879), _1248883))))]]], (24364 ^ _779530) ^ [_1249252, _1249254, _1249256, _1249258] : [class_Rings_Olinordered__semidom(_1249252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249252), c_Groups_Oone__class_Oone(_1249252)), _1249254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249252), hAPP(hAPP(c_Power_Opower__class_Opower(_1249252), _1249254), _1249256)), hAPP(hAPP(c_Power_Opower__class_Opower(_1249252), _1249254), _1249258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1249256), _1249258)))], (24378 ^ _779530) ^ [_1249517, _1249519, _1249521, _1249523] : [class_Rings_Olinordered__semidom(_1249517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1249519), _1249521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249517), c_Groups_Ozero__class_Ozero(_1249517)), _1249523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249517), _1249523), c_Groups_Oone__class_Oone(_1249517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249517), hAPP(hAPP(c_Power_Opower__class_Opower(_1249517), _1249523), _1249521)), hAPP(hAPP(c_Power_Opower__class_Opower(_1249517), _1249523), _1249519))))], (24396 ^ _779530) ^ [_1249856, _1249858] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1249856), _1249858))))], (24398 ^ _779530) ^ [_1249889, _1249891, _1249893] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1249889), _1249891)), _1249893) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1249889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249891), _1249893)))], (24400 ^ _779530) ^ [_1249940, _1249942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249940)), -(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), _1249940), _1249942))))], (24406 ^ _779530) ^ [_1250037, _1250039, _1250041] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1250037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1250039), _1250041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1250037), _1250039)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1250037), _1250041)))], (24408 ^ _779530) ^ [_1250094, _1250096] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250094)), _1250096) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250094), _1250096)))], (24410 ^ _779530) ^ [_1250137, _1250139] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250137), _1250139)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250137)), _1250139))], (24412 ^ _779530) ^ [_1250180, _1250182] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1250180)), _1250182) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1250180), _1250182)))], (24414 ^ _779530) ^ [_1250223] : [-(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)), _1250223))))], (24416 ^ _779530) ^ [_1250251, _1250253] : [-(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)), _1250251)), 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), _1250253), _1250251))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1250251), _1250253))], (24418 ^ _779530) ^ [_1250301, _1250303, _1250305] : [class_Rings_Oring__1__no__zero__divisors(_1250301), -(_1250303 = c_Groups_Ozero__class_Ozero(_1250301)), hAPP(hAPP(c_Power_Opower__class_Opower(_1250301), _1250303), _1250305) = c_Groups_Ozero__class_Ozero(_1250301)], (24428 ^ _779530) ^ [_1250460, _1250462, _1250464] : [class_Groups_Omonoid__mult(_1250460), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250460), hAPP(hAPP(c_Power_Opower__class_Opower(_1250460), _1250462), _1250464)), _1250462) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250460), _1250462), hAPP(hAPP(c_Power_Opower__class_Opower(_1250460), _1250462), _1250464)))], (24434 ^ _779530) ^ [_1250601, _1250603, _1250605, _1250607] : [class_Groups_Ocomm__monoid__mult(_1250601), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250601), _1250603), _1250605)), _1250607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250601), hAPP(hAPP(c_Power_Opower__class_Opower(_1250601), _1250603), _1250607)), hAPP(hAPP(c_Power_Opower__class_Opower(_1250601), _1250605), _1250607)))], (24440 ^ _779530) ^ [_1250760, _1250762] : [class_Groups_Omonoid__mult(_1250760), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250760), c_Groups_Oone__class_Oone(_1250760)), _1250762) = c_Groups_Oone__class_Oone(_1250760))], (24446 ^ _779530) ^ [_1250859, _1250861, _1250863, _1250865] : [class_Groups_Omonoid__mult(_1250859), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250859), _1250861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250863), _1250865)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1250859), hAPP(hAPP(c_Power_Opower__class_Opower(_1250859), _1250861), _1250863)), _1250865))], (24452 ^ _779530) ^ [_1250998, _1251000] : [class_Groups_Omonoid__mult(_1250998), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1250998), _1251000), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1251000)], (24458 ^ _779530) ^ [_1251089, _1251091, _1251093, _1251095] : [class_Rings_Olinordered__semidom(_1251089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251089), _1251091), _1251093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251089), c_Groups_Ozero__class_Ozero(_1251089)), _1251091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251089), hAPP(hAPP(c_Power_Opower__class_Opower(_1251089), _1251091), _1251095)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251089), _1251093), _1251095))))], (24472 ^ _779530) ^ [_1251358, _1251360, _1251362] : [class_Rings_Olinordered__semidom(_1251358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251358), c_Groups_Ozero__class_Ozero(_1251358)), _1251360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251358), c_Groups_Ozero__class_Ozero(_1251358)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251358), _1251360), _1251362))))], (24482 ^ _779530) ^ [_1251541, _1251543, _1251545] : [class_Rings_Olinordered__semidom(_1251541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251541), c_Groups_Ozero__class_Ozero(_1251541)), _1251543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251541), c_Groups_Ozero__class_Ozero(_1251541)), hAPP(hAPP(c_Power_Opower__class_Opower(_1251541), _1251543), _1251545))))], (24492 ^ _779530) ^ [_1251724, _1251726, _1251728] : [class_Power_Opower(_1251724), class_Rings_Omult__zero(_1251724), class_Rings_Ono__zero__divisors(_1251724), class_Rings_Ozero__neq__one(_1251724), 24507 ^ _779530 : [(24508 ^ _779530) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1251724), _1251726), _1251728) = c_Groups_Ozero__class_Ozero(_1251724), 24511 ^ _779530 : [(24512 ^ _779530) ^ [] : [-(_1251726 = c_Groups_Ozero__class_Ozero(_1251724))], (24514 ^ _779530) ^ [] : [_1251728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (24516 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1251724), _1251726), _1251728) = c_Groups_Ozero__class_Ozero(_1251724)), _1251726 = c_Groups_Ozero__class_Ozero(_1251724), -(_1251728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24526 ^ _779530) ^ [_1252216, _1252218, _1252220] : [class_Rings_Olinordered__semidom(_1252216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252216), c_Groups_Oone__class_Oone(_1252216)), _1252218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252216), c_Groups_Oone__class_Oone(_1252216)), hAPP(hAPP(c_Power_Opower__class_Opower(_1252216), _1252218), _1252220))))], (24536 ^ _779530) ^ [_1252399, _1252401] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1252399), c_Groups_Ozero__class_Ozero(_1252399)), hAPP(c_Nat_OSuc, _1252401)) = c_Groups_Ozero__class_Ozero(_1252399)), class_Power_Opower(_1252399), class_Rings_Osemiring__0(_1252399)], (24546 ^ _779530) ^ [_1252554, _1252556, _1252558, _1252560] : [class_Rings_Olinordered__semidom(_1252554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252554), c_Groups_Oone__class_Oone(_1252554)), _1252556)), 24553 ^ _779530 : [(24554 ^ _779530) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1252554), _1252556), _1252558) = hAPP(hAPP(c_Power_Opower__class_Opower(_1252554), _1252556), _1252560), -(_1252558 = _1252560)], (24560 ^ _779530) ^ [] : [_1252558 = _1252560, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252554), _1252556), _1252558) = hAPP(hAPP(c_Power_Opower__class_Opower(_1252554), _1252556), _1252560))]]], (24566 ^ _779530) ^ [_1252893, _1252895, _1252897] : [class_Groups_Omonoid__mult(_1252893), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252893), _1252895), hAPP(c_Nat_OSuc, _1252897)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252893), hAPP(hAPP(c_Power_Opower__class_Opower(_1252893), _1252895), _1252897)), _1252895))], (24572 ^ _779530) ^ [_1253024, _1253026, _1253028] : [class_Power_Opower(_1253024), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1253024), _1253026), hAPP(c_Nat_OSuc, _1253028)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253024), _1253026), hAPP(hAPP(c_Power_Opower__class_Opower(_1253024), _1253026), _1253028)))], (24578 ^ _779530) ^ [_1253155, _1253157] : [class_Power_Opower(_1253155), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1253155), _1253157), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1253155))], (24584 ^ _779530) ^ [_1253250, _1253252, _1253254, _1253256] : [class_Groups_Omonoid__mult(_1253250), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1253250), _1253252), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1253254), _1253256)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253250), hAPP(hAPP(c_Power_Opower__class_Opower(_1253250), _1253252), _1253254)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253250), _1253252), _1253256)))], (24590 ^ _779530) ^ [_1253405] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1253405) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24602 ^ _779530) ^ [_1253544, _1253546] : [24603 ^ _779530 : [(24604 ^ _779530) ^ [] : [_1253546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24606 ^ _779530) ^ [] : [_1253544 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1253544), _1253546) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24592 ^ _779530) ^ [_1253446, _1253448] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1253446), _1253448) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1253448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1253446 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24620 ^ _779530) ^ [_1253794, _1253796] : [24621 ^ _779530 : [(24622 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1253794))], (24624 ^ _779530) ^ [] : [_1253796 = 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), _1253794), _1253796))))], (24610 ^ _779530) ^ [_1253688, _1253690] : [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), _1253688), _1253690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1253688))), -(_1253690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24628 ^ _779530) ^ [_1253931, _1253933, _1253935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1253931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1253931), _1253933)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1253931), _1253935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253933), _1253935)))], (24638 ^ _779530) ^ [_1254112, _1254114, _1254116] : [class_Rings_Osemiring__1(_1254112), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1254112), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1254114), _1254116)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1254112), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1254112), _1254114)), _1254116))], (24644 ^ _779530) ^ [_1254237, _1254239, _1254241, _1254243] : [class_Rings_Olinordered__semidom(_1254237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254237), hAPP(hAPP(c_Power_Opower__class_Opower(_1254237), _1254239), _1254241)), hAPP(hAPP(c_Power_Opower__class_Opower(_1254237), _1254243), _1254241))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254237), c_Groups_Ozero__class_Ozero(_1254237)), _1254243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254237), _1254239), _1254243)))], (24658 ^ _779530) ^ [_1254506, _1254508, _1254510, _1254512] : [class_Rings_Olinordered__semidom(_1254506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254506), hAPP(hAPP(c_Power_Opower__class_Opower(_1254506), _1254508), hAPP(c_Nat_OSuc, _1254510))), hAPP(hAPP(c_Power_Opower__class_Opower(_1254506), _1254512), hAPP(c_Nat_OSuc, _1254510)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254506), c_Groups_Ozero__class_Ozero(_1254506)), _1254512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254506), _1254508), _1254512)))], (24672 ^ _779530) ^ [_1254787, _1254789, _1254791, _1254793] : [class_Rings_Olinordered__semidom(_1254787), hAPP(hAPP(c_Power_Opower__class_Opower(_1254787), _1254789), hAPP(c_Nat_OSuc, _1254791)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1254787), _1254793), hAPP(c_Nat_OSuc, _1254791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254787), c_Groups_Ozero__class_Ozero(_1254787)), _1254789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254787), c_Groups_Ozero__class_Ozero(_1254787)), _1254793)), -(_1254789 = _1254793)], (24690 ^ _779530) ^ [_1255114, _1255116, _1255118] : [class_Rings_Olinordered__semidom(_1255114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255114), c_Groups_Oone__class_Oone(_1255114)), _1255116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255114), hAPP(hAPP(c_Power_Opower__class_Opower(_1255114), _1255116), _1255118)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255114), _1255116), hAPP(hAPP(c_Power_Opower__class_Opower(_1255114), _1255116), _1255118)))))], (24700 ^ _779530) ^ [_1255325, _1255327, _1255329] : [class_Rings_Olinordered__semidom(_1255325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255325), c_Groups_Oone__class_Oone(_1255325)), _1255327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255325), c_Groups_Oone__class_Oone(_1255325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255325), _1255327), hAPP(hAPP(c_Power_Opower__class_Opower(_1255325), _1255327), _1255329)))))], (24710 ^ _779530) ^ [_1255524, _1255526] : [class_Power_Opower(_1255524), class_Rings_Osemiring__0(_1255524), 24717 ^ _779530 : [(24718 ^ _779530) ^ [] : [_1255526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1255524), c_Groups_Ozero__class_Ozero(_1255524)), _1255526) = c_Groups_Oone__class_Oone(_1255524))], (24724 ^ _779530) ^ [] : [-(_1255526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1255524), c_Groups_Ozero__class_Ozero(_1255524)), _1255526) = c_Groups_Ozero__class_Ozero(_1255524))]]], (24730 ^ _779530) ^ [_1255798, _1255800, _1255802] : [class_Rings_Olinordered__semidom(_1255798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255798), c_Groups_Oone__class_Oone(_1255798)), _1255800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255798), c_Groups_Oone__class_Oone(_1255798)), hAPP(hAPP(c_Power_Opower__class_Opower(_1255798), _1255800), hAPP(c_Nat_OSuc, _1255802)))))], (24740 ^ _779530) ^ [_1255987, _1255989, _1255991, _1255993] : [class_Rings_Olinordered__semidom(_1255987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255987), c_Groups_Oone__class_Oone(_1255987)), _1255989)), 24747 ^ _779530 : [(24748 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255987), hAPP(hAPP(c_Power_Opower__class_Opower(_1255987), _1255989), _1255991)), hAPP(hAPP(c_Power_Opower__class_Opower(_1255987), _1255989), _1255993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255991), _1255993)))], (24754 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255991), _1255993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255987), hAPP(hAPP(c_Power_Opower__class_Opower(_1255987), _1255989), _1255991)), hAPP(hAPP(c_Power_Opower__class_Opower(_1255987), _1255989), _1255993))))]]], (24760 ^ _779530) ^ [_1256362, _1256364, _1256366, _1256368] : [class_Rings_Olinordered__semidom(_1256362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256362), c_Groups_Oone__class_Oone(_1256362)), _1256364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256362), hAPP(hAPP(c_Power_Opower__class_Opower(_1256362), _1256364), _1256366)), hAPP(hAPP(c_Power_Opower__class_Opower(_1256362), _1256364), _1256368))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256366), _1256368)))], (24774 ^ _779530) ^ [_1256627, _1256629, _1256631, _1256633] : [class_Rings_Olinordered__semidom(_1256627), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256629), _1256631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256627), c_Groups_Oone__class_Oone(_1256627)), _1256633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256627), hAPP(hAPP(c_Power_Opower__class_Opower(_1256627), _1256633), _1256629)), hAPP(hAPP(c_Power_Opower__class_Opower(_1256627), _1256633), _1256631))))], (24788 ^ _779530) ^ [_1256892, _1256894, _1256896, _1256898] : [class_Rings_Olinordered__semidom(_1256892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1256894), _1256896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256892), c_Groups_Oone__class_Oone(_1256892)), _1256898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256892), hAPP(hAPP(c_Power_Opower__class_Opower(_1256892), _1256898), _1256894)), hAPP(hAPP(c_Power_Opower__class_Opower(_1256892), _1256898), _1256896))))], (24802 ^ _779530) ^ [_1257157, _1257159, _1257161] : [class_Rings_Oring__1(_1257157), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257157), hAPP(c_Groups_Ouminus__class_Ouminus(_1257157), _1257159)), _1257161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257157), hAPP(hAPP(c_Power_Opower__class_Opower(_1257157), hAPP(c_Groups_Ouminus__class_Ouminus(_1257157), c_Groups_Oone__class_Oone(_1257157))), _1257161)), hAPP(hAPP(c_Power_Opower__class_Opower(_1257157), _1257159), _1257161)))], (24808 ^ _779530) ^ [_1257322, _1257324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257322)), -(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), _1257322), _1257324))))], (24814 ^ _779530) ^ [_1257419, _1257421, _1257423] : [class_Rings_Olinordered__semidom(_1257419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257419), c_Groups_Ozero__class_Ozero(_1257419)), _1257421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257419), _1257421), c_Groups_Oone__class_Oone(_1257419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257419), _1257421), hAPP(hAPP(c_Power_Opower__class_Opower(_1257419), _1257421), _1257423))), hAPP(hAPP(c_Power_Opower__class_Opower(_1257419), _1257421), _1257423))))], (24828 ^ _779530) ^ [_1257702, _1257704, _1257706, _1257708] : [class_Rings_Olinordered__semidom(_1257702), hAPP(hAPP(c_Power_Opower__class_Opower(_1257702), _1257704), _1257706) = hAPP(hAPP(c_Power_Opower__class_Opower(_1257702), _1257708), _1257706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257702), c_Groups_Ozero__class_Ozero(_1257702)), _1257704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257702), c_Groups_Ozero__class_Ozero(_1257702)), _1257708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257706)), -(_1257704 = _1257708)], (24850 ^ _779530) ^ [_1258077, _1258079, _1258081] : [class_Rings_Olinordered__semidom(_1258077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258077), c_Groups_Ozero__class_Ozero(_1258077)), _1258079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258077), _1258079), c_Groups_Oone__class_Oone(_1258077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258077), hAPP(hAPP(c_Power_Opower__class_Opower(_1258077), _1258079), hAPP(c_Nat_OSuc, _1258081))), c_Groups_Oone__class_Oone(_1258077))))], (24864 ^ _779530) ^ [_1258338, _1258340, _1258342, _1258344] : [class_Rings_Olinordered__semidom(_1258338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258340), _1258342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258338), c_Groups_Ozero__class_Ozero(_1258338)), _1258344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258338), _1258344), c_Groups_Oone__class_Oone(_1258338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258338), hAPP(hAPP(c_Power_Opower__class_Opower(_1258338), _1258344), _1258342)), hAPP(hAPP(c_Power_Opower__class_Opower(_1258338), _1258344), _1258340))))], (24882 ^ _779530) ^ [_1258677, _1258679] : [-(c_Sum__Type_OPlus(_1258677, _1258679, c_Orderings_Otop__class_Otop(tc_fun(_1258677, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1258679, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1258677, _1258679), tc_HOL_Obool)))], (24884 ^ _779530) ^ [_1258725, _1258727, _1258729, _1258731] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1258725), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1258727), _1258729)))), -(hBOOL(hAPP(hAPP(hAPP(_1258731, _1258725), _1258727), _1258729))), 24892 ^ _779530 : [(24893 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 24889 ^ [_1258725, _1258727, _1258729, _1258731]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 24890 ^ [_1258725, _1258727, _1258729, _1258731]), 24891 ^ [_1258725, _1258727, _1258729, _1258731])))))], (24905 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1258731, 24889 ^ [_1258725, _1258727, _1258729, _1258731]), 24890 ^ [_1258725, _1258727, _1258729, _1258731]), 24891 ^ [_1258725, _1258727, _1258729, _1258731]))], (24895 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24890 ^ [_1258725, _1258727, _1258729, _1258731]), 24891 ^ [_1258725, _1258727, _1258729, _1258731]))), hAPP(24889 ^ [_1258725, _1258727, _1258729, _1258731], 24891 ^ [_1258725, _1258727, _1258729, _1258731]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1258731, 24889 ^ [_1258725, _1258727, _1258729, _1258731]), 24890 ^ [_1258725, _1258727, _1258729, _1258731]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24891 ^ [_1258725, _1258727, _1258729, _1258731]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (24909 ^ _779530) ^ [_1259464, _1259466, _1259468, _1259470, _1259472, _1259474, _1259476] : [hBOOL(hAPP(_1259464, _1259466)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1259468, _1259468)), hAPP(hAPP(c_Product__Type_OPair(_1259468, _1259468), _1259470), _1259472)), hAPP(_1259474, _1259466))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1259476, _1259468), tc_prod(_1259476, _1259468))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1259476, _1259468), tc_prod(_1259476, _1259468)), hAPP(hAPP(c_Product__Type_OPair(_1259476, _1259468), _1259466), _1259470)), hAPP(hAPP(c_Product__Type_OPair(_1259476, _1259468), _1259466), _1259472))), c_Recdef_Osame__fst(_1259476, _1259468, _1259464, _1259474))))], (24919 ^ _779530) ^ [_1259784, _1259786] : [24927 ^ _779530 : [(24928 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24926 ^ [_1259784, _1259786]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259784))))], (24930 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1259786, 24926 ^ [_1259784, _1259786])))]], 24920 ^ _779530 : [(24921 ^ _779530) ^ [_1259852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1259852), _1259784)), hBOOL(hAPP(_1259786, _1259852))]]], (24932 ^ _779530) ^ [_1260012, _1260014] : [24940 ^ _779530 : [(24941 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24939 ^ [_1260012, _1260014]), _1260012)))], (24943 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1260014, 24939 ^ [_1260012, _1260014])))]], 24933 ^ _779530 : [(24934 ^ _779530) ^ [_1260080] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1260080), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260012))), hBOOL(hAPP(_1260014, _1260080))]]], (24945 ^ _779530) ^ [_1260264, _1260266] : [24947 ^ _779530 : [(24948 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24946 ^ [_1260264, _1260266]), _1260264)))], (24950 ^ _779530) ^ [] : [hBOOL(hAPP(_1260266, 24946 ^ [_1260264, _1260266]))]], 24951 ^ _779530 : [(24952 ^ _779530) ^ [_1260414] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1260414), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260264))), -(hBOOL(hAPP(_1260266, _1260414)))]]], (24958 ^ _779530) ^ [_1260515, _1260517] : [24960 ^ _779530 : [(24961 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24959 ^ [_1260515, _1260517]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260515))))], (24963 ^ _779530) ^ [] : [hBOOL(hAPP(_1260517, 24959 ^ [_1260515, _1260517]))]], 24964 ^ _779530 : [(24965 ^ _779530) ^ [_1260668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1260668), _1260515)), -(hBOOL(hAPP(_1260517, _1260668)))]]], (24971 ^ _779530) ^ [_1260790, _1260792, _1260794, _1260796] : [c_Sum__Type_OPlus(_1260790, _1260792, _1260794, _1260796) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1260790, _1260792), tc_HOL_Obool)), 24974 ^ _779530 : [(24975 ^ _779530) ^ [] : [-(_1260794 = c_Orderings_Obot__class_Obot(tc_fun(_1260790, tc_HOL_Obool)))], (24977 ^ _779530) ^ [] : [-(_1260796 = c_Orderings_Obot__class_Obot(tc_fun(_1260792, tc_HOL_Obool)))]]], (24979 ^ _779530) ^ [_1260939, _1260941, _1260943, _1260945] : [-(c_Sum__Type_OPlus(_1260939, _1260941, _1260943, _1260945) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1260939, _1260941), tc_HOL_Obool))), _1260943 = c_Orderings_Obot__class_Obot(tc_fun(_1260939, tc_HOL_Obool)), _1260945 = c_Orderings_Obot__class_Obot(tc_fun(_1260941, tc_HOL_Obool))], (24989 ^ _779530) ^ [_1261124, _1261126, _1261128, _1261130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261124, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261124, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24990 ^ [_1261124, _1261126, _1261128, _1261130])), _1261126)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261124, 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), 24990 ^ [_1261124, _1261126, _1261128, _1261130]), _1261128))), _1261130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261124, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261124, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1261126)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1261124, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1261130))))], (24996 ^ _779530) ^ [_1261454] : [class_Power_Opower(_1261454), -(c_Power_Opower__class_Opower(_1261454) = c_Power_Opower_Opower(_1261454, c_Groups_Oone__class_Oone(_1261454), c_Groups_Otimes__class_Otimes(_1261454)))], (25002 ^ _779530) ^ [_1261547, _1261549, _1261551, _1261553] : [_1261547 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1261549), _1261551)), _1261553), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1261547, _1261549), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1261551), _1261553)))), 25009 ^ _779530 : [(25010 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261549)))], (25012 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261553), _1261549))]], 25017 ^ _779530 : [(25018 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261549))], (25020 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261549), _1261553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261553), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (25028 ^ _779530) ^ [_1262009, _1262011, _1262013, _1262015] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262009, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25029 ^ [_1262009, _1262011, _1262013, _1262015])), _1262011) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262009, 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), 25029 ^ [_1262009, _1262011, _1262013, _1262015]), _1262013))), _1262015), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262009, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1262011) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262009, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1262015))], (25035 ^ _779530) ^ [_1262289, _1262291, _1262293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262289, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262289, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25036 ^ [_1262289, _1262291, _1262293])), _1262291)), _1262293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1262289, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1262289, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1262291)), _1262293)))], (25042 ^ _779530) ^ [_1262515, _1262517, _1262519, _1262521, _1262523, _1262525] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1262515, _1262517), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1262519), _1262521))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1262515, _1262517), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1262523), _1262525))), -(_1262517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1262521 = _1262525)], (25056 ^ _779530) ^ [_1262719, _1262721, _1262723, _1262725, _1262727, _1262729] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1262719, _1262721), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1262723), _1262725))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1262719, _1262721), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1262727), _1262729))), -(_1262721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1262723 = _1262727)], (25070 ^ _779530) ^ [_1262923, _1262925, _1262927] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1262923, _1262923), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1262925), _1262927))), -(_1262923 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1262927 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25080 ^ _779530) ^ [_1263035] : [-(_1263035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1263035), 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)))))], (25086 ^ _779530) ^ [_1263074, _1263076, _1263078, _1263080] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1263074, _1263076, _1263078), _1263080), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1263076)], (25088 ^ _779530) ^ [_1263113, _1263115, _1263117, _1263119, _1263121] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1263113, _1263115, _1263117), _1263119), hAPP(c_Nat_OSuc, _1263121)) = hAPP(hAPP(_1263117, _1263119), hAPP(hAPP(c_Power_Opower_Opower(_1263113, _1263115, _1263117), _1263119), _1263121)))], (25090 ^ _779530) ^ [_1263173, _1263175, _1263177] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1263173, _1263173), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1263175), _1263177))), -(_1263173 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1263175 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25100 ^ _779530) ^ [_1263289, _1263291, _1263293, _1263295] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1263289, _1263291), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1263293), _1263295))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263289), _1263291), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1263295), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263293)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1263293)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1263295), 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), _1263291), _1263295))))))], (25106 ^ _779530) ^ [_1263516, _1263518, _1263520] : [class_Orderings_Olinorder(_1263516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263516), _1263518), _1263520)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263516, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1263516), _1263518), c_Orderings_Obot__class_Obot(tc_fun(_1263516, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1263516, _1263518, _1263520)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1263516, _1263518), _1263520))], (25116 ^ _779530) ^ [_1263729, _1263731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1263729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1263731)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1263731), _1263729)), _1263731) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1263731), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1263729), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (25126 ^ _779530) ^ [_1263932, _1263934, _1263936] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1263932, tc_HOL_Obool), tc_fun(_1263932, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1263932, tc_HOL_Obool), tc_fun(_1263932, tc_HOL_Obool)), _1263934), _1263936)), c_Wellfounded_Ofinite__psubset(_1263932))), 25129 ^ _779530 : [(25130 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1263932, tc_HOL_Obool)), _1263934), _1263936)))], (25132 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263932), _1263936)))]]], (25134 ^ _779530) ^ [_1264127, _1264129, _1264131] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1264127, tc_HOL_Obool), tc_fun(_1264127, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1264127, tc_HOL_Obool), tc_fun(_1264127, tc_HOL_Obool)), _1264129), _1264131)), c_Wellfounded_Ofinite__psubset(_1264127)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1264127, tc_HOL_Obool)), _1264129), _1264131)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264127), _1264131))], (25144 ^ _779530) ^ [_1264356, _1264358, _1264360] : [class_Orderings_Olinorder(_1264356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264356), _1264358)), hBOOL(hAPP(hAPP(c_member(_1264356), _1264360), _1264358)), 25155 ^ _779530 : [(25156 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264356, tc_HOL_Obool)), _1264358), hAPP(hAPP(c_Set_Oinsert(_1264356), _1264360), c_Orderings_Obot__class_Obot(tc_fun(_1264356, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1264356, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1264356, c_Orderings_Oord__class_Omin(_1264356), _1264358) = _1264360)], (25162 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264356, tc_HOL_Obool)), _1264358), hAPP(hAPP(c_Set_Oinsert(_1264356), _1264360), c_Orderings_Obot__class_Obot(tc_fun(_1264356, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1264356, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1264356, c_Orderings_Oord__class_Omin(_1264356), _1264358) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1264356), _1264360), c_Big__Operators_Olattice_OInf__fin(_1264356, c_Orderings_Oord__class_Omin(_1264356), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264356, tc_HOL_Obool)), _1264358), hAPP(hAPP(c_Set_Oinsert(_1264356), _1264360), c_Orderings_Obot__class_Obot(tc_fun(_1264356, tc_HOL_Obool)))))))]]], (25168 ^ _779530) ^ [_1264880, _1264882] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1264880, _1264882)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1264880)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1264882))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25170 ^ _779530) ^ [_1264929, _1264931] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1264929, _1264931))))], (25172 ^ _779530) ^ [_1264960, _1264962] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1264960, _1264962))))], (25174 ^ _779530) ^ [_1264991] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1264991) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25176 ^ _779530) ^ [_1265017, _1265019] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265017), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1265019)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1265017)), _1265019))], (25178 ^ _779530) ^ [_1265060, _1265062] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1265060)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1265062)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265060), _1265062))], (25180 ^ _779530) ^ [_1265103, _1265105] : [class_Divides_Osemiring__div(_1265103), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265103), _1265105), c_Groups_Ozero__class_Ozero(_1265103)) = c_Groups_Ozero__class_Ozero(_1265103))], (25186 ^ _779530) ^ [_1265202, _1265204] : [class_Divides_Osemiring__div(_1265202), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265202), c_Groups_Ozero__class_Ozero(_1265202)), _1265204) = c_Groups_Ozero__class_Ozero(_1265202))], (25192 ^ _779530) ^ [_1265301, _1265303] : [class_Divides_Osemiring__div(_1265301), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1265301), _1265303), c_Groups_Oone__class_Oone(_1265301)) = _1265303)], (25198 ^ _779530) ^ [_1265396, _1265398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265398)), -(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), _1265396), _1265398))))], (25208 ^ _779530) ^ [_1265549, _1265551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265549), 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)), _1265551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265549), _1265551)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25218 ^ _779530) ^ [_1265714, _1265716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265714), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25221 ^ _779530 : [(25222 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265716), _1265714)), 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)), _1265716)))], (25228 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265716), _1265714)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25234 ^ _779530) ^ [_1265970, _1265972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265970)), 25237 ^ _779530 : [(25238 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1265972), _1265970)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265972), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25244 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265972), 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), _1265972), _1265970)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25250 ^ _779530) ^ [_1266225] : [-(_1266225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1266225), _1266225) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25256 ^ _779530) ^ [_1266265, _1266267, _1266269, _1266271] : [class_Divides_Osemiring__div(_1266265), 25259 ^ _779530 : [(25260 ^ _779530) ^ [] : [_1266267 = c_Groups_Ozero__class_Ozero(_1266265), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266265), _1266267), _1266269)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266265), _1266267), _1266271)) = c_Groups_Ozero__class_Ozero(_1266265))], (25266 ^ _779530) ^ [] : [-(_1266267 = c_Groups_Ozero__class_Ozero(_1266265)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266265), _1266267), _1266269)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266265), _1266267), _1266271)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266265), _1266269), _1266271))]]], (25272 ^ _779530) ^ [_1266571, _1266573, _1266575] : [class_Divides_Osemiring__div(_1266571), -(_1266573 = c_Groups_Ozero__class_Ozero(_1266571)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266571), _1266575), _1266573)), _1266573) = _1266575)], (25282 ^ _779530) ^ [_1266699, _1266701, _1266703] : [class_Divides_Osemiring__div(_1266699), -(_1266701 = c_Groups_Ozero__class_Ozero(_1266699)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266699), _1266701), _1266703)), _1266701) = _1266703)], (25292 ^ _779530) ^ [_1266827, _1266829, _1266831, _1266833] : [class_Divides_Osemiring__div(_1266827), -(_1266829 = c_Groups_Ozero__class_Ozero(_1266827)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266827), _1266831), _1266829)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266827), _1266833), _1266829)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266827), _1266831), _1266833))], (25302 ^ _779530) ^ [_1266989, _1266991, _1266993, _1266995] : [class_Divides_Osemiring__div(_1266989), -(_1266991 = c_Groups_Ozero__class_Ozero(_1266989)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266989), _1266991), _1266993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266989), _1266991), _1266995)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1266989), _1266993), _1266995))], (25312 ^ _779530) ^ [_1267151, _1267153] : [class_Divides_Osemiring__div(_1267151), -(_1267153 = c_Groups_Ozero__class_Ozero(_1267151)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1267151), _1267153), _1267153) = c_Groups_Oone__class_Oone(_1267151))], (25322 ^ _779530) ^ [_1267265, _1267267, _1267269] : [class_Orderings_Oorder(_1267265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267265), _1267267), _1267269)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1267265, _1267269, _1267267) = c_Orderings_Obot__class_Obot(tc_fun(_1267265, tc_HOL_Obool)))], (25332 ^ _779530) ^ [_1267428, _1267430, _1267432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267428), _1267430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267432), 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), _1267430), _1267432)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267428), _1267432))))], (25342 ^ _779530) ^ [_1267615, _1267617, _1267619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267615), _1267617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1267619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267615), _1267619)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267617), _1267619))))], (25352 ^ _779530) ^ [_1267796, _1267798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267796), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267798), _1267796)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267796), _1267798) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25362 ^ _779530) ^ [_1267957, _1267959, _1267961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1267957), 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)), _1267959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1267959), _1267961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267957), _1267959)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1267957), _1267961))))], (25376 ^ _779530) ^ [_1268202, _1268204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268202), 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)), _1268204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268202), _1268204)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25386 ^ _779530) ^ [_1268367, _1268369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268367), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25389 ^ _779530 : [(25390 ^ _779530) ^ [] : [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), _1268369), _1268367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268369), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25396 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268369), 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), _1268369), _1268367))))]]], (25402 ^ _779530) ^ [_1268623, _1268625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268623)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268623), _1268625)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268623), _1268625) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25412 ^ _779530) ^ [_1268778, _1268780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1268780), 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), _1268778), _1268780)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25422 ^ _779530) ^ [_1268943, _1268945, _1268947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1268945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1268945), _1268947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268943), _1268947)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1268943), _1268945))))], (25436 ^ _779530) ^ [_1269182, _1269184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269182)), 25439 ^ _779530 : [(25440 ^ _779530) ^ [] : [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), _1269182), _1269184))), 25443 ^ _779530 : [(25444 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269184), _1269182)))], (25446 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269184)))]]], (25448 ^ _779530) ^ [] : [-(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), _1269182), _1269184)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269184), _1269182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269184))]]], (25458 ^ _779530) ^ [_1269510, _1269512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269510)), 25461 ^ _779530 : [(25462 ^ _779530) ^ [] : [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), _1269512), _1269510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269510), _1269512)))], (25468 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1269510), _1269512)), -(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), _1269512), _1269510))))]]], (25474 ^ _779530) ^ [_1269760, _1269762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269760)), 25477 ^ _779530 : [(25478 ^ _779530) ^ [] : [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), _1269762), _1269760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269762)))], (25484 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1269762)), -(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), _1269762), _1269760))))]]], (25490 ^ _779530) ^ [_1270016, _1270018] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270016), _1270018) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1270018 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25499 ^ _779530 : [(25500 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1270016)))], (25502 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270016), _1270018)))]], 25503 ^ _779530 : [(25504 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270016), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25506 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270018), _1270016)))]]], (25508 ^ _779530) ^ [_1270247, _1270249] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270247), _1270249) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25509 ^ _779530 : [(25510 ^ _779530) ^ [] : [_1270249 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25512 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1270247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270247), _1270249))], (25518 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1270247), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1270249), _1270247))]]], (25526 ^ _779530) ^ [_1270542, _1270544] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1270542)), _1270544) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1270542, _1270544))], (25528 ^ _779530) ^ [_1270580, _1270582, _1270584] : [class_Groups_Oordered__ab__group__add(_1270580), -(hAPP(c_Set_Oimage(_1270580, _1270580, c_Groups_Ouminus__class_Ouminus(_1270580)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1270580, _1270582, _1270584)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1270580, hAPP(c_Groups_Ouminus__class_Ouminus(_1270580), _1270584), hAPP(c_Groups_Ouminus__class_Ouminus(_1270580), _1270582)))], (25534 ^ _779530) ^ [_1270711, _1270713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1270711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1270713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270711), _1270713)), _1270711)))], (25544 ^ _779530) ^ [_1270870, _1270872, _1270874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1270870)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1270874), _1270870)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1270872), _1270874)), _1270870))], (25550 ^ _779530) ^ [_1271001, _1271003, _1271005, _1271007] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1271001, _1271003), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1271005), _1271007))), -(_1271003 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1271001), _1271003) = _1271005)], (25560 ^ _779530) ^ [_1271131, _1271133, _1271135, _1271137] : [class_Divides_Osemiring__div(_1271131), -(_1271133 = c_Groups_Ozero__class_Ozero(_1271131)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271131), _1271135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271131), _1271133), _1271137))), _1271133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271131), _1271137), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271131), _1271135), _1271133)))], (25570 ^ _779530) ^ [_1271309, _1271311, _1271313, _1271315] : [class_Divides_Osemiring__div(_1271309), -(_1271311 = c_Groups_Ozero__class_Ozero(_1271309)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271309), _1271313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271309), _1271315), _1271311))), _1271311) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271309), _1271315), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271309), _1271313), _1271311)))], (25580 ^ _779530) ^ [_1271487, _1271489, _1271491] : [class_Divides_Osemiring__div(_1271487), -(_1271489 = c_Groups_Ozero__class_Ozero(_1271487)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271487), _1271489), _1271491)), _1271489) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271487), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271487), _1271491), _1271489)), c_Groups_Oone__class_Oone(_1271487)))], (25590 ^ _779530) ^ [_1271651, _1271653, _1271655] : [class_Divides_Osemiring__div(_1271651), -(_1271653 = c_Groups_Ozero__class_Ozero(_1271651)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271651), _1271655), _1271653)), _1271653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1271651), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1271651), _1271655), _1271653)), c_Groups_Oone__class_Oone(_1271651)))], (25600 ^ _779530) ^ [_1271815, _1271817, _1271819] : [class_Orderings_Olinorder(_1271815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271815), _1271817)), hBOOL(hAPP(hAPP(c_member(_1271815), _1271819), _1271817)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1271815), _1271819), c_Big__Operators_Olattice_OInf__fin(_1271815, c_Orderings_Oord__class_Omin(_1271815), _1271817)) = c_Big__Operators_Olattice_OInf__fin(_1271815, c_Orderings_Oord__class_Omin(_1271815), _1271817))], (25614 ^ _779530) ^ [_1272062, _1272064] : [class_Orderings_Olinorder(_1272062), -(c_Big__Operators_Olattice_OInf__fin(_1272062, c_Orderings_Oord__class_Omin(_1272062), hAPP(hAPP(c_Set_Oinsert(_1272062), _1272064), c_Orderings_Obot__class_Obot(tc_fun(_1272062, tc_HOL_Obool)))) = _1272064)], (25620 ^ _779530) ^ [_1272175, _1272177] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_1272175, _1272177)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25622 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25624 ^ _779530) ^ [_1272224, _1272226, _1272228, _1272230] : [class_Orderings_Oorder(_1272224), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1272224, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1272224, _1272226, _1272228)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1272224, _1272228), _1272230)) = c_Orderings_Obot__class_Obot(tc_fun(_1272224, tc_HOL_Obool)))], (25630 ^ _779530) ^ [_1272355, _1272357] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1272355, _1272357)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1272357), hAPP(c_Nat_OSuc, _1272355)))], (25632 ^ _779530) ^ [_1272396, _1272398, _1272400] : [class_Orderings_Olinorder(_1272396), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272396), _1272398)), -(_1272398 = c_Orderings_Obot__class_Obot(tc_fun(_1272396, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1272396, c_Orderings_Oord__class_Omin(_1272396), hAPP(hAPP(c_Set_Oinsert(_1272396), _1272400), _1272398)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1272396), _1272400), c_Big__Operators_Olattice_OInf__fin(_1272396, c_Orderings_Oord__class_Omin(_1272396), _1272398)))], (25646 ^ _779530) ^ [_1272616, _1272618, _1272620] : [class_Orderings_Olinorder(_1272616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272616), _1272618)), -(_1272620 = c_Orderings_Obot__class_Obot(tc_fun(_1272616, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1272616, tc_HOL_Obool)), _1272620), _1272618)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1272616), c_Big__Operators_Olattice_OInf__fin(_1272616, c_Orderings_Oord__class_Omin(_1272616), _1272620)), c_Big__Operators_Olattice_OInf__fin(_1272616, c_Orderings_Oord__class_Omin(_1272616), _1272618)) = c_Big__Operators_Olattice_OInf__fin(_1272616, c_Orderings_Oord__class_Omin(_1272616), _1272618))], (25664 ^ _779530) ^ [_1272948, _1272950, _1272952] : [class_Orderings_Olinorder(_1272948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272948), _1272950)), -(_1272950 = c_Orderings_Obot__class_Obot(tc_fun(_1272948, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272948), _1272952)), -(_1272952 = c_Orderings_Obot__class_Obot(tc_fun(_1272948, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1272948, c_Orderings_Oord__class_Omin(_1272948), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272948, tc_HOL_Obool)), _1272950), _1272952)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1272948), c_Big__Operators_Olattice_OInf__fin(_1272948, c_Orderings_Oord__class_Omin(_1272948), _1272950)), c_Big__Operators_Olattice_OInf__fin(_1272948, c_Orderings_Oord__class_Omin(_1272948), _1272952)))], (25686 ^ _779530) ^ [_1273315, _1273317] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1273315), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1273317) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1273315, _1273317))], (25688 ^ _779530) ^ [_1273356, _1273358, _1273360, _1273362] : [_1273356 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1273358), _1273360)), _1273362), -(_1273358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1273356), _1273358) = _1273360), 25695 ^ _779530 : [(25696 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273358)))], (25698 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273362), _1273358))]], 25703 ^ _779530 : [(25704 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273358))], (25706 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273358), _1273362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1273362), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (25764 ^ _779530) ^ [_1274803, _1274805, _1274807] : [-(hBOOL(hAPP(_1274803, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1274805), _1274807)))), 25767 ^ _779530 : [(25768 ^ _779530) ^ [] : [-(_1274807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25770 ^ _779530) ^ [] : [hBOOL(hAPP(_1274803, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 25773 ^ _779530 : [(25774 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274807)))], (25778 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25776 ^ [_1274803, _1274805, _1274807])))], (25780 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25776 ^ [_1274803, _1274805, _1274807]), _1274807)))], (25782 ^ _779530) ^ [] : [-(_1274805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274807), 25775 ^ [_1274803, _1274805, _1274807])), 25776 ^ [_1274803, _1274805, _1274807]))], (25784 ^ _779530) ^ [] : [hBOOL(hAPP(_1274803, 25775 ^ [_1274803, _1274805, _1274807]))]], 25785 ^ _779530 : [(25786 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274807), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25790 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274807), 25788 ^ [_1274803, _1274805, _1274807])))], (25792 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25788 ^ [_1274803, _1274805, _1274807]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25794 ^ _779530) ^ [] : [-(_1274805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1274807), 25787 ^ [_1274803, _1274805, _1274807])), 25788 ^ [_1274803, _1274805, _1274807]))], (25796 ^ _779530) ^ [] : [hBOOL(hAPP(_1274803, 25787 ^ [_1274803, _1274805, _1274807]))]]], (25718 ^ _779530) ^ [_1273843, _1273845, _1273847] : [hBOOL(hAPP(_1273843, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1273845), _1273847))), 25721 ^ _779530 : [(25722 ^ _779530) ^ [] : [_1273847 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1273843, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25728 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1273847)), 25731 ^ _779530 : [(25732 ^ _779530) ^ [_1274177] : [-(hBOOL(hAPP(_1273843, _1274177))), 25733 ^ _779530 : [(25734 ^ _779530) ^ [_1274248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1274248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1274248), _1273847)), _1273845 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1273847), _1274177)), _1274248)]]]]], (25746 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273847), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25749 ^ _779530 : [(25750 ^ _779530) ^ [_1274507] : [-(hBOOL(hAPP(_1273843, _1274507))), 25751 ^ _779530 : [(25752 ^ _779530) ^ [_1274581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1273847), _1274581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1274581), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1273845 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1273847), _1274507)), _1274581)]]]]]]], (25800 ^ _779530) ^ [_1275517, _1275519, _1275521] : [class_Orderings_Olinorder(_1275517), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275517), _1275519)), -(hBOOL(hAPP(hAPP(c_member(_1275517), _1275521), _1275519))), -(_1275519 = c_Orderings_Obot__class_Obot(tc_fun(_1275517, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1275517, c_Orderings_Oord__class_Omin(_1275517), hAPP(hAPP(c_Set_Oinsert(_1275517), _1275521), _1275519)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1275517), _1275521), c_Big__Operators_Olattice_OInf__fin(_1275517, c_Orderings_Oord__class_Omin(_1275517), _1275519)))], (25818 ^ _779530) ^ [_1275766, _1275768, _1275770, _1275772] : [class_Orderings_Olinorder(_1275766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275766), _1275768), _1275770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275766), _1275770), _1275772)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275766, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1275766, _1275768, _1275770)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1275766, _1275770), _1275772)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1275766, _1275768, _1275772))], (25832 ^ _779530) ^ [_1276035, _1276037, _1276039] : [class_Orderings_Olinorder(_1276035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276035), _1276037)), 25839 ^ _779530 : [(25840 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1276035, tc_HOL_Obool)), _1276037), hAPP(hAPP(c_Set_Oinsert(_1276035), _1276039), c_Orderings_Obot__class_Obot(tc_fun(_1276035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1276035, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1276035, c_Orderings_Oord__class_Omin(_1276035), hAPP(hAPP(c_Set_Oinsert(_1276035), _1276039), _1276037)) = _1276039)], (25846 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1276035, tc_HOL_Obool)), _1276037), hAPP(hAPP(c_Set_Oinsert(_1276035), _1276039), c_Orderings_Obot__class_Obot(tc_fun(_1276035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1276035, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1276035, c_Orderings_Oord__class_Omin(_1276035), hAPP(hAPP(c_Set_Oinsert(_1276035), _1276039), _1276037)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1276035), _1276039), c_Big__Operators_Olattice_OInf__fin(_1276035, c_Orderings_Oord__class_Omin(_1276035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1276035, tc_HOL_Obool)), _1276037), hAPP(hAPP(c_Set_Oinsert(_1276035), _1276039), c_Orderings_Obot__class_Obot(tc_fun(_1276035, tc_HOL_Obool)))))))]]], (25852 ^ _779530) ^ [_1276523, _1276525, _1276527] : [class_Orderings_Olinorder(_1276523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276523), _1276525)), -(_1276525 = c_Orderings_Obot__class_Obot(tc_fun(_1276523, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276523), _1276527)), -(_1276527 = c_Orderings_Obot__class_Obot(tc_fun(_1276523, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1276523, tc_HOL_Obool)), _1276525), _1276527) = c_Orderings_Obot__class_Obot(tc_fun(_1276523, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1276523, c_Orderings_Oord__class_Omin(_1276523), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276523, tc_HOL_Obool)), _1276525), _1276527)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1276523), c_Big__Operators_Olattice_OInf__fin(_1276523, c_Orderings_Oord__class_Omin(_1276523), _1276525)), c_Big__Operators_Olattice_OInf__fin(_1276523, c_Orderings_Oord__class_Omin(_1276523), _1276527)))], (25878 ^ _779530) ^ [_1277018, _1277020, _1277022] : [class_Orderings_Olinorder(_1277018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277018), _1277020)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277018), _1277022)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277018, tc_HOL_Obool)), _1277020), _1277022) = c_Orderings_Obot__class_Obot(tc_fun(_1277018, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277018), c_Big__Operators_Olattice_OInf__fin(_1277018, c_Orderings_Oord__class_Omin(_1277018), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277018, tc_HOL_Obool)), _1277020), _1277022))), c_Big__Operators_Olattice_OInf__fin(_1277018, c_Orderings_Oord__class_Omin(_1277018), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277018, tc_HOL_Obool)), _1277020), _1277022))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277018), c_Big__Operators_Olattice_OInf__fin(_1277018, c_Orderings_Oord__class_Omin(_1277018), _1277020)), c_Big__Operators_Olattice_OInf__fin(_1277018, c_Orderings_Oord__class_Omin(_1277018), _1277022)))], (25896 ^ _779530) ^ [_1277390, _1277392] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1277390, _1277392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1277392)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25898 ^ _779530) ^ [_1277430, _1277432, _1277434] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1277430, _1277432, _1277434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1277432)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1277434))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25900 ^ _779530) ^ [_1277482, _1277484, _1277486] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1277482, _1277484, _1277486)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1277486)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25902 ^ _779530) ^ [_1277534, _1277536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277534)), -(c_SMT_Oz3div(_1277536, _1277534) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1277536), _1277534))], (25908 ^ _779530) ^ [_1277627, _1277629] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1277627))), -(c_SMT_Oz3div(_1277629, _1277627) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1277629), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277627))))], (25914 ^ _779530) ^ [_1277691, _1277693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1277691), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1277693, _1277691) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277693), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1277691)))], (25920 ^ _779530) ^ [_1277797, _1277799] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1277797), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 25923 ^ _779530 : [(25924 ^ _779530) ^ [] : [25925 ^ _779530 : [(25926 ^ _779530) ^ [] : [_1277799 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25928 ^ _779530) ^ [] : [_1277797 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1277799, _1277797) = 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)))], (25932 ^ _779530) ^ [] : [-(c_Nitpick_Onorm__frac(_1277799, _1277797) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1277799), _1277797)), 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), _1277799))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1277797)))), -(_1277799 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1277797 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25942 ^ _779530) ^ [_1278095, _1278097] : [class_Orderings_Olinorder(_1278095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278095), _1278097)), -(_1278097 = c_Orderings_Obot__class_Obot(tc_fun(_1278095, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1278095), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1278095), 25955 ^ [_1278095, _1278097]), 25956 ^ [_1278095, _1278097])), hAPP(hAPP(c_Set_Oinsert(_1278095), 25955 ^ [_1278095, _1278097]), hAPP(hAPP(c_Set_Oinsert(_1278095), 25956 ^ [_1278095, _1278097]), c_Orderings_Obot__class_Obot(tc_fun(_1278095, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1278095), c_Big__Operators_Olattice_OInf__fin(_1278095, c_Orderings_Oord__class_Omin(_1278095), _1278097)), _1278097)))], (25962 ^ _779530) ^ [_1278545, _1278547, _1278549, _1278551, _1278553] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1278545, _1278547), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1278549), _1278551))), -(_1278547 = 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)), _1278553)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1278545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1278547), _1278553)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1278549), _1278553)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1278547), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1278549, _1278553))), _1278551)))))], (25976 ^ _779530) ^ [_1278851, _1278853, _1278855] : [class_Orderings_Olinorder(_1278851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278851), _1278853)), -(_1278853 = c_Orderings_Obot__class_Obot(tc_fun(_1278851, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278851), _1278855), c_Big__Operators_Olattice_OInf__fin(_1278851, c_Orderings_Oord__class_Omin(_1278851), _1278853)) = c_Big__Operators_Olattice_OInf__fin(_1278851, c_Orderings_Oord__class_Omin(_1278851), hAPP(c_Set_OCollect(_1278851), hAPP(hAPP(c_COMBB(tc_fun(_1278851, tc_HOL_Obool), tc_HOL_Obool, _1278851), c_HOL_OEx(_1278851)), hAPP(hAPP(c_COMBC(_1278851, tc_fun(_1278851, tc_HOL_Obool), tc_fun(_1278851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278851, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1278851, tc_HOL_Obool), tc_fun(_1278851, tc_HOL_Obool)), _1278851), c_COMBS(_1278851, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278851, tc_HOL_Obool), tc_fun(_1278851, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1278851), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1278851), c_fconj)), hAPP(hAPP(c_COMBC(_1278851, tc_fun(_1278851, _1278851), tc_fun(_1278851, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1278851, tc_HOL_Obool), tc_fun(tc_fun(_1278851, _1278851), tc_fun(_1278851, tc_HOL_Obool)), _1278851), c_COMBB(_1278851, tc_HOL_Obool, _1278851)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1278851), _1278855))))), hAPP(hAPP(c_COMBC(_1278851, tc_fun(_1278851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1278851)), _1278853))))))], (25990 ^ _779530) ^ [_1279349, _1279351, _1279353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1279349), _1279351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1279349), _1279353)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1279351), _1279353))))], (25996 ^ _779530) ^ [_1279472, _1279474] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1279472), _1279474)), _1279472)))], (25998 ^ _779530) ^ [_1279508, _1279510, _1279512] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1279508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1279510), _1279512)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1279508), _1279510)), _1279512))], (26000 ^ _779530) ^ [_1279559, _1279561, _1279563, _1279565] : [class_Orderings_Olinorder(_1279559), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279559), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279559), _1279561), _1279563)), _1279565) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279559), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279559), _1279561), _1279565)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279559), _1279563), _1279565)))], (26006 ^ _779530) ^ [_1279718, _1279720, _1279722, _1279724] : [class_Orderings_Olinorder(_1279718), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279718), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279718), _1279720), _1279722)), _1279724) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279718), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279718), _1279720), _1279724)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279718), _1279722), _1279724)))], (26012 ^ _779530) ^ [_1279877, _1279879, _1279881, _1279883] : [class_Orderings_Olinorder(_1279877), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279877), _1279879), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279877), _1279881), _1279883)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279877), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279877), _1279879), _1279881)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279877), _1279879), _1279883)))], (26018 ^ _779530) ^ [_1280036, _1280038, _1280040, _1280042] : [class_Orderings_Olinorder(_1280036), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280036), _1280038), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1280036), _1280040), _1280042)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1280036), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280036), _1280038), _1280040)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280036), _1280038), _1280042)))], (26024 ^ _779530) ^ [_1280195, _1280197, _1280199] : [class_Orderings_Olinorder(_1280195), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1280195), _1280197), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280195), _1280197), _1280199)) = _1280197)], (26030 ^ _779530) ^ [_1280304, _1280306, _1280308] : [class_Orderings_Olinorder(_1280304), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280304), _1280306), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1280304), _1280306), _1280308)) = _1280306)], (26036 ^ _779530) ^ [_1280413, _1280415, _1280417, _1280419] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1280413), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280413), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280413), _1280415), _1280417)), _1280419) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280413), _1280415), _1280419)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280413), _1280417), _1280419)))], (26042 ^ _779530) ^ [_1280572, _1280574, _1280576, _1280578] : [class_Groups_Oordered__ab__group__add(_1280572), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280572), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280572), _1280574), _1280576)), _1280578) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280572), _1280574), _1280578)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280572), _1280576), _1280578)))], (26048 ^ _779530) ^ [_1280731] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1280731), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1280731)], (26050 ^ _779530) ^ [_1280760] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1280760) = _1280760)], (26052 ^ _779530) ^ [_1280786, _1280788] : [class_Orderings_Olinorder(_1280786), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280786), _1280788), _1280788) = _1280788)], (26058 ^ _779530) ^ [_1280877, _1280879, _1280881] : [class_Orderings_Olinorder(_1280877), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280877), _1280879), _1280881) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280877), _1280881), _1280879))], (26064 ^ _779530) ^ [_1280986, _1280988, _1280990] : [class_Orderings_Olinorder(_1280986), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280986), _1280988), _1280990) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280986), _1280990), _1280988))], (26070 ^ _779530) ^ [_1281095, _1281097, _1281099] : [class_Orderings_Olinorder(_1281095), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281095), _1281097), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281095), _1281097), _1281099)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281095), _1281097), _1281099))], (26076 ^ _779530) ^ [_1281220, _1281222, _1281224] : [class_Orderings_Olinorder(_1281220), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281220), _1281222), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281220), _1281222), _1281224)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281220), _1281222), _1281224))], (26082 ^ _779530) ^ [_1281345, _1281347, _1281349, _1281351] : [class_Orderings_Olinorder(_1281345), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281345), _1281347), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281345), _1281349), _1281351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281345), _1281349), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281345), _1281347), _1281351)))], (26088 ^ _779530) ^ [_1281488, _1281490, _1281492, _1281494] : [class_Orderings_Olinorder(_1281488), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281488), _1281490), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281488), _1281492), _1281494)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281488), _1281492), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281488), _1281490), _1281494)))], (26094 ^ _779530) ^ [_1281631, _1281633, _1281635, _1281637] : [class_Orderings_Olinorder(_1281631), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281631), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281631), _1281633), _1281635)), _1281637) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281631), _1281633), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281631), _1281635), _1281637)))], (26100 ^ _779530) ^ [_1281774, _1281776, _1281778, _1281780] : [class_Orderings_Olinorder(_1281774), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281774), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281774), _1281776), _1281778)), _1281780) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281774), _1281776), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281774), _1281778), _1281780)))], (26106 ^ _779530) ^ [_1281917, _1281919] : [class_Orderings_Olinorder(_1281917), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281917), _1281919), _1281919) = _1281919)], (26112 ^ _779530) ^ [_1282008, _1282010] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1282008)), hAPP(c_Nat_OSuc, _1282010)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1282008), _1282010)))], (26114 ^ _779530) ^ [_1282054, _1282056, _1282058] : [class_Divides_Osemiring__div(_1282054), -(c_Divides_Odiv__class_Omod(_1282054, c_Divides_Odiv__class_Omod(_1282054, _1282056, _1282058), _1282058) = c_Divides_Odiv__class_Omod(_1282054, _1282056, _1282058))], (26120 ^ _779530) ^ [_1282155] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1282155, _1282155) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26122 ^ _779530) ^ [_1282182, _1282184] : [class_Divides_Osemiring__div(_1282182), -(c_Divides_Odiv__class_Omod(_1282182, _1282184, _1282184) = c_Groups_Ozero__class_Ozero(_1282182))], (26128 ^ _779530) ^ [_1282269, _1282271] : [class_Divides_Osemiring__div(_1282269), -(c_Divides_Odiv__class_Omod(_1282269, _1282271, c_Groups_Ozero__class_Ozero(_1282269)) = _1282271)], (26134 ^ _779530) ^ [_1282356] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1282356) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26136 ^ _779530) ^ [_1282383, _1282385] : [class_Divides_Osemiring__div(_1282383), -(c_Divides_Odiv__class_Omod(_1282383, c_Groups_Ozero__class_Ozero(_1282383), _1282385) = c_Groups_Ozero__class_Ozero(_1282383))], (26142 ^ _779530) ^ [_1282474, _1282476, _1282478, _1282480, _1282482, _1282484] : [class_Divides_Osemiring__div(_1282474), c_Divides_Odiv__class_Omod(_1282474, _1282476, _1282478) = c_Divides_Odiv__class_Omod(_1282474, _1282480, _1282478), c_Divides_Odiv__class_Omod(_1282474, _1282482, _1282478) = c_Divides_Odiv__class_Omod(_1282474, _1282484, _1282478), -(c_Divides_Odiv__class_Omod(_1282474, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282474), _1282476), _1282482), _1282478) = c_Divides_Odiv__class_Omod(_1282474, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282474), _1282480), _1282484), _1282478))], (26156 ^ _779530) ^ [_1282757, _1282759, _1282761, _1282763] : [class_Divides_Osemiring__div(_1282757), -(c_Divides_Odiv__class_Omod(_1282757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282757), c_Divides_Odiv__class_Omod(_1282757, _1282759, _1282761)), _1282763), _1282761) = c_Divides_Odiv__class_Omod(_1282757, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282757), _1282759), _1282763), _1282761))], (26162 ^ _779530) ^ [_1282892, _1282894, _1282896, _1282898] : [class_Divides_Osemiring__div(_1282892), -(c_Divides_Odiv__class_Omod(_1282892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282892), _1282894), _1282896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282892), _1282898), _1282896)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282892), c_Divides_Odiv__class_Omod(_1282892, _1282894, _1282898)), _1282896))], (26168 ^ _779530) ^ [_1283035, _1283037, _1283039, _1283041] : [class_Divides_Osemiring__div(_1283035), -(c_Divides_Odiv__class_Omod(_1283035, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283035), _1283037), _1283039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283035), _1283037), _1283041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283035), _1283037), c_Divides_Odiv__class_Omod(_1283035, _1283039, _1283041)))], (26174 ^ _779530) ^ [_1283178, _1283180, _1283182, _1283184] : [class_Divides_Osemiring__div(_1283178), -(c_Divides_Odiv__class_Omod(_1283178, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283178), _1283180), _1283182), _1283184) = c_Divides_Odiv__class_Omod(_1283178, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283178), c_Divides_Odiv__class_Omod(_1283178, _1283180, _1283184)), c_Divides_Odiv__class_Omod(_1283178, _1283182, _1283184)), _1283184))], (26180 ^ _779530) ^ [_1283321, _1283323, _1283325, _1283327] : [class_Divides_Osemiring__div(_1283321), -(c_Divides_Odiv__class_Omod(_1283321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283321), _1283323), _1283325), _1283327) = c_Divides_Odiv__class_Omod(_1283321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283321), c_Divides_Odiv__class_Omod(_1283321, _1283323, _1283327)), _1283325), _1283327))], (26186 ^ _779530) ^ [_1283456, _1283458, _1283460, _1283462] : [class_Divides_Osemiring__div(_1283456), -(c_Divides_Odiv__class_Omod(_1283456, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283456), _1283458), _1283460), _1283462) = c_Divides_Odiv__class_Omod(_1283456, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283456), _1283458), c_Divides_Odiv__class_Omod(_1283456, _1283460, _1283462)), _1283462))], (26192 ^ _779530) ^ [_1283591, _1283593, _1283595, _1283597, _1283599, _1283601] : [class_Divides_Osemiring__div(_1283591), c_Divides_Odiv__class_Omod(_1283591, _1283593, _1283595) = c_Divides_Odiv__class_Omod(_1283591, _1283597, _1283595), c_Divides_Odiv__class_Omod(_1283591, _1283599, _1283595) = c_Divides_Odiv__class_Omod(_1283591, _1283601, _1283595), -(c_Divides_Odiv__class_Omod(_1283591, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1283591), _1283593), _1283599), _1283595) = c_Divides_Odiv__class_Omod(_1283591, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1283591), _1283597), _1283601), _1283595))], (26206 ^ _779530) ^ [_1283874, _1283876, _1283878, _1283880] : [class_Divides_Osemiring__div(_1283874), -(c_Divides_Odiv__class_Omod(_1283874, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1283874), c_Divides_Odiv__class_Omod(_1283874, _1283876, _1283878)), _1283880), _1283878) = c_Divides_Odiv__class_Omod(_1283874, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1283874), _1283876), _1283880), _1283878))], (26212 ^ _779530) ^ [_1284009, _1284011, _1284013, _1284015] : [class_Divides_Osemiring__div(_1284009), -(c_Divides_Odiv__class_Omod(_1284009, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284009), _1284011), c_Divides_Odiv__class_Omod(_1284009, _1284013, _1284015)), _1284015) = c_Divides_Odiv__class_Omod(_1284009, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284009), _1284011), _1284013), _1284015))], (26218 ^ _779530) ^ [_1284144, _1284146, _1284148, _1284150] : [class_Divides_Osemiring__div(_1284144), -(c_Divides_Odiv__class_Omod(_1284144, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284144), _1284146), _1284148), _1284150) = c_Divides_Odiv__class_Omod(_1284144, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284144), c_Divides_Odiv__class_Omod(_1284144, _1284146, _1284150)), c_Divides_Odiv__class_Omod(_1284144, _1284148, _1284150)), _1284150))], (26224 ^ _779530) ^ [_1284287, _1284289, _1284291, _1284293] : [class_Divides_Osemiring__div(_1284287), -(c_Divides_Odiv__class_Omod(_1284287, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284287), _1284289), _1284291), _1284293) = c_Divides_Odiv__class_Omod(_1284287, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284287), c_Divides_Odiv__class_Omod(_1284287, _1284289, _1284293)), _1284291), _1284293))], (26230 ^ _779530) ^ [_1284422, _1284424, _1284426, _1284428] : [class_Divides_Osemiring__div(_1284422), -(c_Divides_Odiv__class_Omod(_1284422, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284422), _1284424), _1284426), _1284428) = c_Divides_Odiv__class_Omod(_1284422, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284422), _1284424), c_Divides_Odiv__class_Omod(_1284422, _1284426, _1284428)), _1284428))], (26236 ^ _779530) ^ [_1284557, _1284559, _1284561] : [class_Divides_Osemiring__div(_1284557), -(c_Divides_Odiv__class_Omod(_1284557, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284557), _1284559), _1284561), _1284559) = c_Divides_Odiv__class_Omod(_1284557, _1284561, _1284559))], (26242 ^ _779530) ^ [_1284666, _1284668, _1284670] : [class_Divides_Osemiring__div(_1284666), -(c_Divides_Odiv__class_Omod(_1284666, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284666), _1284668), _1284670), _1284670) = c_Divides_Odiv__class_Omod(_1284666, _1284668, _1284670))], (26248 ^ _779530) ^ [_1284775, _1284777, _1284779, _1284781] : [class_Divides_Oring__div(_1284775), c_Divides_Odiv__class_Omod(_1284775, _1284777, _1284779) = c_Divides_Odiv__class_Omod(_1284775, _1284781, _1284779), -(c_Divides_Odiv__class_Omod(_1284775, hAPP(c_Groups_Ouminus__class_Ouminus(_1284775), _1284777), _1284779) = c_Divides_Odiv__class_Omod(_1284775, hAPP(c_Groups_Ouminus__class_Ouminus(_1284775), _1284781), _1284779))], (26258 ^ _779530) ^ [_1284962, _1284964, _1284966] : [class_Divides_Oring__div(_1284962), -(c_Divides_Odiv__class_Omod(_1284962, hAPP(c_Groups_Ouminus__class_Ouminus(_1284962), _1284964), _1284966) = c_Divides_Odiv__class_Omod(_1284962, hAPP(c_Groups_Ouminus__class_Ouminus(_1284962), c_Divides_Odiv__class_Omod(_1284962, _1284964, _1284966)), _1284966))], (26264 ^ _779530) ^ [_1285083, _1285085, _1285087, _1285089] : [class_Divides_Oring__div(_1285083), -(c_Divides_Odiv__class_Omod(_1285083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285083), _1285085), _1285087), _1285089) = c_Divides_Odiv__class_Omod(_1285083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285083), _1285085), c_Divides_Odiv__class_Omod(_1285083, _1285087, _1285089)), _1285089))], (26270 ^ _779530) ^ [_1285218, _1285220, _1285222, _1285224] : [class_Divides_Oring__div(_1285218), -(c_Divides_Odiv__class_Omod(_1285218, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285218), _1285220), _1285222), _1285224) = c_Divides_Odiv__class_Omod(_1285218, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285218), c_Divides_Odiv__class_Omod(_1285218, _1285220, _1285224)), _1285222), _1285224))], (26276 ^ _779530) ^ [_1285353, _1285355, _1285357, _1285359] : [class_Divides_Oring__div(_1285353), -(c_Divides_Odiv__class_Omod(_1285353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285353), _1285355), _1285357), _1285359) = c_Divides_Odiv__class_Omod(_1285353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285353), c_Divides_Odiv__class_Omod(_1285353, _1285355, _1285359)), c_Divides_Odiv__class_Omod(_1285353, _1285357, _1285359)), _1285359))], (26282 ^ _779530) ^ [_1285496, _1285498, _1285500, _1285502, _1285504, _1285506] : [class_Divides_Oring__div(_1285496), c_Divides_Odiv__class_Omod(_1285496, _1285498, _1285500) = c_Divides_Odiv__class_Omod(_1285496, _1285502, _1285500), c_Divides_Odiv__class_Omod(_1285496, _1285504, _1285500) = c_Divides_Odiv__class_Omod(_1285496, _1285506, _1285500), -(c_Divides_Odiv__class_Omod(_1285496, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285496), _1285498), _1285504), _1285500) = c_Divides_Odiv__class_Omod(_1285496, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1285496), _1285502), _1285506), _1285500))], (26296 ^ _779530) ^ [_1285779, _1285781, _1285783, _1285785] : [class_Orderings_Olinorder(_1285779), 26299 ^ _779530 : [(26300 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285779), _1285781), _1285783)), _1285785)), 26303 ^ _779530 : [(26304 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), _1285781), _1285785)))], (26306 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), _1285783), _1285785)))]]], (26308 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285779), _1285781), _1285783)), _1285785))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), _1285781), _1285785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285779), _1285783), _1285785))]]], (26318 ^ _779530) ^ [_1286159, _1286161, _1286163, _1286165] : [class_Orderings_Olinorder(_1286159), 26321 ^ _779530 : [(26332 ^ _779530) ^ [] : [26333 ^ _779530 : [(26334 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), _1286163))], (26336 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), _1286165))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286159), _1286163), _1286165))))], (26322 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286159), _1286163), _1286165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), _1286163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286159), _1286161), _1286165)))]]], (26340 ^ _779530) ^ [_1286508, _1286510, _1286512, _1286514] : [class_Orderings_Olinorder(_1286508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286508), _1286510), _1286512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286508), _1286510), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286508), _1286514), _1286512))))], (26350 ^ _779530) ^ [_1286687, _1286689, _1286691, _1286693] : [class_Orderings_Olinorder(_1286687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286687), _1286689), _1286691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286687), _1286689), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286687), _1286691), _1286693))))], (26360 ^ _779530) ^ [_1286866, _1286868, _1286870, _1286872] : [class_Orderings_Olinorder(_1286866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286866), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286866), _1286868), _1286870)), _1286872)), 26367 ^ _779530 : [(26368 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286866), _1286868), _1286872)))], (26370 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286866), _1286870), _1286872)))]]], (26372 ^ _779530) ^ [_1287089, _1287091, _1287093, _1287095, _1287097] : [class_Orderings_Olinorder(_1287089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287089), _1287091), _1287093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287089), _1287095), _1287097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287089), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287089), _1287091), _1287095)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287089), _1287093), _1287097))))], (26386 ^ _779530) ^ [_1287360, _1287362, _1287364, _1287366] : [class_Orderings_Olinorder(_1287360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287360), _1287362), _1287364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287360), _1287366), _1287364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287360), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287360), _1287362), _1287366)), _1287364)))], (26400 ^ _779530) ^ [_1287609, _1287611, _1287613, _1287615] : [class_Orderings_Olinorder(_1287609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287609), _1287611), _1287613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287609), _1287615), _1287613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287609), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287609), _1287611), _1287615)), _1287613)))], (26414 ^ _779530) ^ [_1287858, _1287860, _1287862] : [class_Orderings_Olinorder(_1287858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287858), _1287860), _1287862)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1287858), _1287862), _1287860) = _1287862)], (26424 ^ _779530) ^ [_1288019, _1288021, _1288023] : [class_Orderings_Olinorder(_1288019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288019), _1288021), _1288023)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288019), _1288021), _1288023) = _1288023)], (26434 ^ _779530) ^ [_1288180, _1288182, _1288184, _1288186] : [class_Orderings_Olinorder(_1288180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288180), _1288182), _1288184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288180), _1288182), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288180), _1288186), _1288184))))], (26444 ^ _779530) ^ [_1288359, _1288361, _1288363, _1288365] : [class_Orderings_Olinorder(_1288359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288359), _1288361), _1288363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288359), _1288361), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288359), _1288363), _1288365))))], (26454 ^ _779530) ^ [_1288538, _1288540, _1288542, _1288544] : [class_Orderings_Olinorder(_1288538), 26457 ^ _779530 : [(26458 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288538), _1288540), _1288542)), _1288544)), 26461 ^ _779530 : [(26462 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), _1288540), _1288544)))], (26464 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), _1288542), _1288544)))]]], (26466 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288538), _1288540), _1288542)), _1288544))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), _1288540), _1288544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288538), _1288542), _1288544))]]], (26476 ^ _779530) ^ [_1288918, _1288920, _1288922] : [class_Orderings_Olinorder(_1288918), 26479 ^ _779530 : [(26480 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288918), _1288920), _1288922)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288918), _1288920), _1288922) = _1288922)], (26486 ^ _779530) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288918), _1288920), _1288922) = _1288922, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288918), _1288920), _1288922)))]]], (26492 ^ _779530) ^ [_1289174, _1289176, _1289178] : [class_Orderings_Olinorder(_1289174), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289174), _1289176), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289174), _1289178), _1289176))))], (26498 ^ _779530) ^ [_1289281, _1289283, _1289285] : [class_Orderings_Olinorder(_1289281), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289281), _1289283), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289281), _1289283), _1289285))))], (26504 ^ _779530) ^ [_1289388, _1289390, _1289392, _1289394] : [class_Orderings_Olinorder(_1289388), 26507 ^ _779530 : [(26518 ^ _779530) ^ [] : [26519 ^ _779530 : [(26520 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), _1289392))], (26522 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), _1289394))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289388), _1289392), _1289394))))], (26508 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289388), _1289392), _1289394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), _1289392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289388), _1289390), _1289394)))]]], (26526 ^ _779530) ^ [_1289737, _1289739] : [-(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, _1289737, _1289739)), _1289739) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1289737), _1289739))], (26528 ^ _779530) ^ [_1289780, _1289782] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1289780), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1289782)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1289780, _1289782)))], (26530 ^ _779530) ^ [_1289822, _1289824] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1289822, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1289824)) = 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), _1289822), _1289824)))], (26532 ^ _779530) ^ [_1289864, _1289866, _1289868] : [-(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, _1289864, _1289866)), _1289868), _1289866) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1289864), _1289868), _1289866))], (26534 ^ _779530) ^ [_1289915, _1289917, _1289919] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1289915), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1289917, _1289919)), _1289919) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1289915), _1289917), _1289919))], (26536 ^ _779530) ^ [_1289966, _1289968, _1289970] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1289966), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1289968, _1289970)), _1289970) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1289966), _1289968), _1289970))], (26538 ^ _779530) ^ [_1290017, _1290019, _1290021] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1290017), _1290019), _1290021) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1290017), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1290019, _1290021)), _1290021))], (26540 ^ _779530) ^ [_1290068] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1290068) = c_Orderings_Oord__class_Omax(_1290068)), class_Lattices_Osemilattice__sup(_1290068), class_Orderings_Olinorder(_1290068)], (26550 ^ _779530) ^ [_1290197, _1290199, _1290201, _1290203, _1290205] : [class_Orderings_Olinorder(_1290197), class_Orderings_Olinorder(_1290199), c_Orderings_Oorder__class_Omono(_1290199, _1290197, _1290201), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290197), hAPP(_1290201, _1290203)), hAPP(_1290201, _1290205)) = hAPP(_1290201, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290199), _1290203), _1290205)))], (26564 ^ _779530) ^ [_1290446, _1290448, _1290450] : [-(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, _1290446, _1290448)), _1290450), _1290448) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1290446), _1290450), _1290448))], (26566 ^ _779530) ^ [_1290497] : [class_Orderings_Olinorder(_1290497), -(c_Finite__Set_Ofun__left__comm__idem(_1290497, _1290497, c_Orderings_Oord__class_Omax(_1290497)))], (26572 ^ _779530) ^ [_1290576, _1290578, _1290580] : [class_Divides_Osemiring__div(_1290576), -(c_Divides_Odiv__class_Omod(_1290576, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290576), _1290578), _1290580), _1290578) = c_Groups_Ozero__class_Ozero(_1290576))], (26578 ^ _779530) ^ [_1290681, _1290683, _1290685] : [class_Divides_Osemiring__div(_1290681), -(c_Divides_Odiv__class_Omod(_1290681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290681), _1290683), _1290685), _1290685) = c_Groups_Ozero__class_Ozero(_1290681))], (26584 ^ _779530) ^ [_1290786, _1290788, _1290790, _1290792] : [class_Divides_Osemiring__div(_1290786), -(c_Divides_Odiv__class_Omod(_1290786, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1290786), _1290788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290786), _1290790), _1290792)), _1290792) = c_Divides_Odiv__class_Omod(_1290786, _1290788, _1290792))], (26590 ^ _779530) ^ [_1290913, _1290915, _1290917, _1290919] : [class_Divides_Osemiring__div(_1290913), -(c_Divides_Odiv__class_Omod(_1290913, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1290913), _1290915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290913), _1290917), _1290919)), _1290917) = c_Divides_Odiv__class_Omod(_1290913, _1290915, _1290917))], (26596 ^ _779530) ^ [_1291040, _1291042] : [class_Divides_Osemiring__div(_1291040), -(c_Divides_Odiv__class_Omod(_1291040, _1291042, c_Groups_Oone__class_Oone(_1291040)) = c_Groups_Ozero__class_Ozero(_1291040))], (26602 ^ _779530) ^ [_1291131, _1291133, _1291135] : [class_Divides_Osemiring__div(_1291131), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1291131), c_Divides_Odiv__class_Omod(_1291131, _1291133, _1291135)), _1291135) = c_Groups_Ozero__class_Ozero(_1291131))], (26608 ^ _779530) ^ [_1291236] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1291236), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1291236)], (26610 ^ _779530) ^ [_1291265, _1291267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1291265), _1291267)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1291265), _1291267) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26616 ^ _779530) ^ [_1291376, _1291378, _1291380] : [_1291376 = 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), _1291376), _1291378)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1291376), _1291380)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26622 ^ _779530) ^ [_1291485, _1291487, _1291489] : [-(_1291485 = 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), _1291485), _1291487)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1291485), _1291489)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1291487), _1291489))], (26628 ^ _779530) ^ [_1291549, _1291551, _1291553, _1291555] : [class_Orderings_Olinorder(_1291549), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291549), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291549), _1291551), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291549), _1291553), _1291555))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291549), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291549), _1291551), _1291553)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291549), _1291551), _1291555)))))], (26634 ^ _779530) ^ [_1291722, _1291724, _1291726, _1291728] : [class_Orderings_Olinorder(_1291722), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291722), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291722), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291722), _1291724), _1291726)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291722), _1291724), _1291728))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291722), _1291724), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291722), _1291726), _1291728)))))], (26640 ^ _779530) ^ [_1291895, _1291897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291897)), -(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, _1291895, _1291897))))], (26650 ^ _779530) ^ [_1292044, _1292046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292044, _1292046)), _1292044)))], (26656 ^ _779530) ^ [_1292143, _1292145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292145, _1292143)), _1292143)))], (26662 ^ _779530) ^ [_1292242, _1292244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292242), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292242), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292244, _1292242))))], (26668 ^ _779530) ^ [_1292347, _1292349, _1292351] : [class_Groups_Olinordered__ab__group__add(_1292347), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292347), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292347), _1292349), _1292351)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292347), hAPP(c_Groups_Ouminus__class_Ouminus(_1292347), _1292349)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292347), _1292351)))], (26674 ^ _779530) ^ [_1292486, _1292488, _1292490] : [class_Groups_Olinordered__ab__group__add(_1292486), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292486), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292486), _1292488), _1292490)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292486), hAPP(c_Groups_Ouminus__class_Ouminus(_1292486), _1292488)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292486), _1292490)))], (26680 ^ _779530) ^ [_1292625, _1292627] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292625), _1292627)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292625)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292627)))], (26682 ^ _779530) ^ [_1292671, _1292673] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292671)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292673)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1292671), _1292673)))], (26684 ^ _779530) ^ [_1292717, _1292719] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1292717), _1292719)), _1292719) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1292717), _1292719))], (26686 ^ _779530) ^ [_1292775, _1292777] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292775, _1292777) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1292775 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1292777), 26689 ^ [_1292775, _1292777]))], (26693 ^ _779530) ^ [_1292880, _1292882] : [26694 ^ _779530 : [(26695 ^ _779530) ^ [_1292929] : [_1292880 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1292882), _1292929)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292880, _1292882) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26699 ^ _779530) ^ [_1292991, _1292993] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1292991), _1292993) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1292991, _1292993) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (26705 ^ _779530) ^ [_1293081, _1293083] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293081, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1293083)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293081, _1293083) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (26711 ^ _779530) ^ [_1293172, _1293174] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293172, _1293174)), _1293174) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26713 ^ _779530) ^ [_1293205] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1293205), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26715 ^ _779530) ^ [_1293231] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293231, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1293231)], (26717 ^ _779530) ^ [_1293260, _1293262, _1293264] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1293260), _1293262)), _1293264) = 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), _1293260), _1293264)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1293262), _1293264))), 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, _1293260, _1293264)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1293262, _1293264))), _1293264)))], (26719 ^ _779530) ^ [_1293343, _1293345, _1293347, _1293349] : [class_Divides_Osemiring__div(_1293343), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293343), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293343), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1293343), _1293345), _1293347)), _1293347)), c_Divides_Odiv__class_Omod(_1293343, _1293345, _1293347))), _1293349) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293343), _1293345), _1293349))], (26725 ^ _779530) ^ [_1293510, _1293512, _1293514, _1293516] : [class_Divides_Osemiring__div(_1293510), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293510), _1293512), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1293510), _1293514), _1293512))), c_Divides_Odiv__class_Omod(_1293510, _1293514, _1293512))), _1293516) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293510), _1293514), _1293516))], (26731 ^ _779530) ^ [_1293677, _1293679, _1293681] : [class_Divides_Osemiring__div(_1293677), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293677), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1293677), _1293679), _1293681)), _1293681)), c_Divides_Odiv__class_Omod(_1293677, _1293679, _1293681)) = _1293679)], (26737 ^ _779530) ^ [_1293810, _1293812, _1293814] : [class_Divides_Osemiring__div(_1293810), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293810), _1293812), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1293810), _1293814), _1293812))), c_Divides_Odiv__class_Omod(_1293810, _1293814, _1293812)) = _1293814)], (26743 ^ _779530) ^ [_1293943, _1293945, _1293947] : [class_Divides_Osemiring__div(_1293943), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1293943), c_Divides_Odiv__class_Omod(_1293943, _1293945, _1293947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1293943), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1293943), _1293945), _1293947)), _1293947)) = _1293945)], (26749 ^ _779530) ^ [_1294076, _1294078, _1294080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294076), _1294078)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1294080), _1294078)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1294080), _1294076))))], (26759 ^ _779530) ^ [_1294257, _1294259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294257)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294259), _1294257)), _1294257) = _1294259)], (26765 ^ _779530) ^ [_1294362, _1294364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294362)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294362), _1294364)), _1294362) = _1294364)], (26771 ^ _779530) ^ [_1294467, _1294469, _1294471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294467)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294467), _1294469)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1294467), _1294471)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1294469), _1294471))], (26777 ^ _779530) ^ [_1294598, _1294600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1294598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1294600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1294600), _1294598)), _1294600)))], (26787 ^ _779530) ^ [_1294757, _1294759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1294757)), -(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, _1294759, _1294757))))], (26793 ^ _779530) ^ [_1294850, _1294852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1294850)), 26796 ^ _779530 : [(26797 ^ _779530) ^ [] : [-(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, _1294852, _1294850))))], (26799 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294852, _1294850)), _1294850)))]]], (26801 ^ _779530) ^ [_1294987, _1294989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1294987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1294987), _1294989)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1294987, _1294989) = _1294987)], (26811 ^ _779530) ^ [_1295138, _1295140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295138), 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, _1295140, _1295138)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26817 ^ _779530) ^ [_1295243, _1295245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295243), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 26820 ^ _779530 : [(26821 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1295245, _1295243)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26823 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295243), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1295245, _1295243))))]]], (26825 ^ _779530) ^ [_1295392, _1295394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295392), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295394), _1295392)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1295392, _1295394) = _1295392)], (26835 ^ _779530) ^ [_1295549] : [class_Orderings_Oord(_1295549), -(c_Orderings_Oord__class_Omax(_1295549) = c_Orderings_Oord_Omax(_1295549, c_Orderings_Oord__class_Oless__eq(_1295549)))], (26841 ^ _779530) ^ [_1295636, _1295638, _1295640] : [class_Orderings_Olinorder(_1295636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295636), _1295638)), hBOOL(hAPP(hAPP(c_member(_1295636), _1295640), _1295638)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295636), _1295640), c_Big__Operators_Olinorder__class_OMax(_1295636, _1295638)) = c_Big__Operators_Olinorder__class_OMax(_1295636, _1295638))], (26855 ^ _779530) ^ [_1295871, _1295873, _1295875, _1295877, _1295879] : [class_Lattices_Osemilattice__sup(_1295871), class_Orderings_Olinorder(_1295873), c_Orderings_Oorder__class_Omono(_1295873, _1295871, _1295875), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295871), hAPP(_1295875, _1295877)), hAPP(_1295875, _1295879))), hAPP(_1295875, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1295873), _1295877), _1295879)))))], (26869 ^ _779530) ^ [_1296134, _1296136, _1296138, _1296140, _1296142] : [class_Orderings_Olinorder(_1296134), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296134, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1296134, _1296136), _1296138)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1296134, _1296140), _1296142)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1296134, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1296134), _1296136), _1296140)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296134), _1296138), _1296142)))], (26875 ^ _779530) ^ [_1296314, _1296316] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296314, _1296316) = 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), _1296314), _1296316) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26881 ^ _779530) ^ [_1296407, _1296409] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296407, _1296409) = 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), _1296407), _1296409) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296409), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296407, _1296409)))], (26887 ^ _779530) ^ [_1296475, _1296477] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296475, _1296477) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296475, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1296477)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26893 ^ _779530) ^ [_1296568, _1296570] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296568, _1296570) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296568, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1296570)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296568, _1296570)), _1296570))], (26899 ^ _779530) ^ [_1296627, _1296629, _1296631] : [-(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), _1296627), _1296629)), _1296629)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296627, _1296629))), _1296631) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296627), _1296631))], (26901 ^ _779530) ^ [_1296688, _1296690, _1296692] : [-(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), _1296688), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1296690), _1296688))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296690, _1296688))), _1296692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296690), _1296692))], (26903 ^ _779530) ^ [_1296749, _1296751, _1296753] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1296749), _1296751)), _1296753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1296749), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1296751), _1296753))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1296749), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296751, _1296753))), _1296753)))], (26905 ^ _779530) ^ [_1296822, _1296824] : [-(_1296822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1296824), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1296822), _1296824))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296822, _1296824)))], (26907 ^ _779530) ^ [_1296869, _1296871] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1296869), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1296871), _1296869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296871), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296871, _1296869)))], (26909 ^ _779530) ^ [_1296916, _1296918] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1296916, _1296918) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1296916), _1296918)), _1296918)))], (26911 ^ _779530) ^ [_1296963, _1296965, _1296967, _1296969, _1296971] : [class_Orderings_Olinorder(_1296963), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296963, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1296963, _1296965, _1296967)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1296963, _1296969, _1296971)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1296963, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1296963), _1296965), _1296969), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1296963), _1296967), _1296971)))], (26917 ^ _779530) ^ [_1297122, _1297124, _1297126, _1297128] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1297122, _1297124), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1297126), _1297128))), -(_1297124 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1297122, _1297124) = _1297128)], (26927 ^ _779530) ^ [_1297248] : [class_Orderings_Olinorder(_1297248), -(c_Orderings_Oord_Omin(_1297248, hAPP(c_COMBC(_1297248, _1297248, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1297248))) = c_Orderings_Oord__class_Omax(_1297248))], (26933 ^ _779530) ^ [_1297349, _1297351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1297349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1297351), _1297349))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1297351), _1297349) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1297351), _1297349)), _1297349)))], (26943 ^ _779530) ^ [_1297497, _1297499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1297497)), 26946 ^ _779530 : [(26947 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1297499), _1297497)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1297499), _1297497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26953 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1297499), _1297497))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1297499), _1297497) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1297499), _1297497)), _1297497)))]]], (26983 ^ _779530) ^ [_1298206, _1298208, _1298210] : [-(hBOOL(hAPP(_1298206, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1298208), _1298210)))), 26986 ^ _779530 : [(26987 ^ _779530) ^ [] : [-(_1298210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26989 ^ _779530) ^ [] : [hBOOL(hAPP(_1298206, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 26990 ^ _779530 : [(26991 ^ _779530) ^ [] : [_1298210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26995 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26993 ^ [_1298206, _1298208, _1298210]), _1298210)))], (26997 ^ _779530) ^ [] : [-(_1298208 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1298210), 26992 ^ [_1298206, _1298208, _1298210])), 26993 ^ [_1298206, _1298208, _1298210]))], (26999 ^ _779530) ^ [] : [hBOOL(hAPP(_1298206, 26992 ^ [_1298206, _1298208, _1298210]))]]], (26959 ^ _779530) ^ [_1297769, _1297771, _1297773] : [hBOOL(hAPP(_1297769, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1297771), _1297773))), 26962 ^ _779530 : [(26963 ^ _779530) ^ [] : [_1297773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1297769, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26969 ^ _779530) ^ [] : [-(_1297773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26972 ^ _779530 : [(26973 ^ _779530) ^ [_1298021, _1298023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1298021), _1297773)), _1297771 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1297773), _1298023)), _1298021), -(hBOOL(hAPP(_1297769, _1298023)))]]]]], (27003 ^ _779530) ^ [_1298628, _1298630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298628), _1298630)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1298628, _1298630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298628), _1298630))], (27013 ^ _779530) ^ [_1298803, _1298805, _1298807] : [class_Orderings_Olinorder(_1298803), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298803), _1298805)), -(_1298805 = c_Orderings_Obot__class_Obot(tc_fun(_1298803, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1298803, hAPP(hAPP(c_Set_Oinsert(_1298803), _1298807), _1298805)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298803), _1298807), c_Big__Operators_Olinorder__class_OMax(_1298803, _1298805)))], (27027 ^ _779530) ^ [_1299011, _1299013, _1299015] : [class_Orderings_Olinorder(_1299011), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299011), _1299013)), -(_1299015 = c_Orderings_Obot__class_Obot(tc_fun(_1299011, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299011, tc_HOL_Obool)), _1299015), _1299013)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299011), c_Big__Operators_Olinorder__class_OMax(_1299011, _1299015)), c_Big__Operators_Olinorder__class_OMax(_1299011, _1299013)) = c_Big__Operators_Olinorder__class_OMax(_1299011, _1299013))], (27045 ^ _779530) ^ [_1299325, _1299327, _1299329] : [class_Orderings_Olinorder(_1299325), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299325), _1299327)), hBOOL(hAPP(hAPP(c_member(_1299325), _1299329), _1299327)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299325), _1299329), c_Big__Operators_Olattice_OInf__fin(_1299325, c_Orderings_Oord__class_Omin(_1299325), _1299327)) = _1299329)], (27059 ^ _779530) ^ [_1299560, _1299562, _1299564] : [class_Orderings_Olinorder(_1299560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299560), _1299562)), -(_1299562 = c_Orderings_Obot__class_Obot(tc_fun(_1299560, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299560), _1299564)), -(_1299564 = c_Orderings_Obot__class_Obot(tc_fun(_1299560, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1299560, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299560, tc_HOL_Obool)), _1299562), _1299564)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299560), c_Big__Operators_Olinorder__class_OMax(_1299560, _1299562)), c_Big__Operators_Olinorder__class_OMax(_1299560, _1299564)))], (27081 ^ _779530) ^ [_1299905, _1299907] : [-(_1299905 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1299907, _1299905), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1299907), _1299905)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1299907, _1299905)))))], (27087 ^ _779530) ^ [_1299962, _1299964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1299962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1299962), _1299964)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1299964), _1299962) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1299964), _1299962)), _1299962)))], (27097 ^ _779530) ^ [_1300165, _1300167, _1300169] : [hBOOL(hAPP(_1300165, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1300167), _1300169))), 27102 ^ _779530 : [(27103 ^ _779530) ^ [] : [-(_1300169 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27105 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1300165, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 27107 ^ _779530 : [(27108 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300169), 27106 ^ [_1300165, _1300167, _1300169])), _1300167)))], (27110 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300169), hAPP(c_Nat_OSuc, 27106 ^ [_1300165, _1300167, _1300169])))))], (27112 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1300165, 27106 ^ [_1300165, _1300167, _1300169])))]]], (27114 ^ _779530) ^ [_1300469, _1300471, _1300473] : [-(hBOOL(hAPP(_1300469, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1300471), _1300473)))), 27115 ^ _779530 : [(27116 ^ _779530) ^ [] : [_1300473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1300469, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27122 ^ _779530) ^ [_1300637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300473), _1300637)), _1300471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300473), hAPP(c_Nat_OSuc, _1300637)))), hBOOL(hAPP(_1300469, _1300637))]]], (27134 ^ _779530) ^ [_1300867, _1300869, _1300871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1300867)), 27137 ^ _779530 : [(27148 ^ _779530) ^ [] : [_1300869 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1300871), _1300867), 27151 ^ _779530 : [(27152 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300867), _1300869)), _1300871)))], (27154 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300867), hAPP(c_Nat_OSuc, _1300869)))))]]], (27138 ^ _779530) ^ [] : [-(_1300869 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1300871), _1300867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300867), _1300869)), _1300871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1300871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1300867), hAPP(c_Nat_OSuc, _1300869))))]]], (27156 ^ _779530) ^ [_1301251, _1301253, _1301255] : [class_Orderings_Olinorder(_1301251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301251), _1301253)), -(hBOOL(hAPP(hAPP(c_member(_1301251), _1301255), _1301253))), -(_1301253 = c_Orderings_Obot__class_Obot(tc_fun(_1301251, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1301251, hAPP(hAPP(c_Set_Oinsert(_1301251), _1301255), _1301253)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301251), _1301255), c_Big__Operators_Olinorder__class_OMax(_1301251, _1301253)))], (27220 ^ _779530) ^ [_1302383, _1302385, _1302387] : [-(hBOOL(hAPP(_1302383, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1302385, _1302387)))), 27223 ^ _779530 : [(27224 ^ _779530) ^ [] : [-(_1302387 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27226 ^ _779530) ^ [] : [hBOOL(hAPP(_1302383, _1302385))]], 27229 ^ _779530 : [(27230 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302387)))], (27234 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27232 ^ [_1302383, _1302385, _1302387])))], (27236 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27232 ^ [_1302383, _1302385, _1302387]), _1302387)))], (27238 ^ _779530) ^ [] : [-(_1302385 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1302387), 27231 ^ [_1302383, _1302385, _1302387])), 27232 ^ [_1302383, _1302385, _1302387]))], (27240 ^ _779530) ^ [] : [hBOOL(hAPP(_1302383, 27232 ^ [_1302383, _1302385, _1302387]))]], 27241 ^ _779530 : [(27242 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302387), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27246 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302387), 27244 ^ [_1302383, _1302385, _1302387])))], (27248 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27244 ^ [_1302383, _1302385, _1302387]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27250 ^ _779530) ^ [] : [-(_1302385 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1302387), 27243 ^ [_1302383, _1302385, _1302387])), 27244 ^ [_1302383, _1302385, _1302387]))], (27252 ^ _779530) ^ [] : [hBOOL(hAPP(_1302383, 27244 ^ [_1302383, _1302385, _1302387]))]]], (27174 ^ _779530) ^ [_1301506, _1301508, _1301510] : [hBOOL(hAPP(_1301506, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1301508, _1301510))), 27177 ^ _779530 : [(27178 ^ _779530) ^ [] : [_1301510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1301506, _1301508)))], (27184 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301510)), 27187 ^ _779530 : [(27188 ^ _779530) ^ [_1301836, _1301838] : [-(hBOOL(hAPP(_1301506, _1301836))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301836), _1301510)), _1301508 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1301510), _1301838)), _1301836)]]], (27202 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301510), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 27205 ^ _779530 : [(27206 ^ _779530) ^ [_1302128, _1302130] : [-(hBOOL(hAPP(_1301506, _1302128))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301510), _1302128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1302128), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1301508 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1301510), _1302130)), _1302128)]]]]], (27256 ^ _779530) ^ [_1303095, _1303097, _1303099, _1303101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303097), _1303099)), -(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), _1303099), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303101, _1303095))), _1303097))))], (27270 ^ _779530) ^ [_1303342, _1303344, _1303346, _1303348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303344), _1303346)), -(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), _1303346), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303348, _1303342))), _1303344)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1303346), _1303342))))], (27284 ^ _779530) ^ [_1303607, _1303609, _1303611, _1303613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303609), _1303611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1303611), 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), _1303609), _1303607)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1303609), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303613, _1303607))), _1303611))))], (27298 ^ _779530) ^ [_1303878, _1303880, _1303882, _1303884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303880), _1303882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1303882), 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), _1303880), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1303884, _1303878))), _1303882)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27312 ^ _779530) ^ [_1304137, _1304139, _1304141, _1304143] : [_1304137 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1304139), _1304141)), _1304143), -(_1304139 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1304137, _1304139) = _1304143), 27319 ^ _779530 : [(27320 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304139)))], (27322 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1304143), _1304139))]], 27327 ^ _779530 : [(27328 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1304139))], (27330 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1304139), _1304143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1304143), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (27342 ^ _779530) ^ [_1304602, _1304604, _1304606] : [class_Orderings_Olinorder(_1304602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304602), _1304604)), 27349 ^ _779530 : [(27350 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304602, tc_HOL_Obool)), _1304604), hAPP(hAPP(c_Set_Oinsert(_1304602), _1304606), c_Orderings_Obot__class_Obot(tc_fun(_1304602, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1304602, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1304602, hAPP(hAPP(c_Set_Oinsert(_1304602), _1304606), _1304604)) = _1304606)], (27356 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304602, tc_HOL_Obool)), _1304604), hAPP(hAPP(c_Set_Oinsert(_1304602), _1304606), c_Orderings_Obot__class_Obot(tc_fun(_1304602, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1304602, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1304602, hAPP(hAPP(c_Set_Oinsert(_1304602), _1304606), _1304604)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1304602), _1304606), c_Big__Operators_Olinorder__class_OMax(_1304602, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304602, tc_HOL_Obool)), _1304604), hAPP(hAPP(c_Set_Oinsert(_1304602), _1304606), c_Orderings_Obot__class_Obot(tc_fun(_1304602, tc_HOL_Obool)))))))]]], (27362 ^ _779530) ^ [_1305072, _1305074, _1305076] : [class_Orderings_Olinorder(_1305072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305072), _1305074)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305072), _1305076)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305072, tc_HOL_Obool)), _1305074), _1305076) = c_Orderings_Obot__class_Obot(tc_fun(_1305072, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305072), c_Big__Operators_Olinorder__class_OMax(_1305072, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305072, tc_HOL_Obool)), _1305074), _1305076))), c_Big__Operators_Olinorder__class_OMax(_1305072, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305072, tc_HOL_Obool)), _1305074), _1305076))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305072), c_Big__Operators_Olinorder__class_OMax(_1305072, _1305074)), c_Big__Operators_Olinorder__class_OMax(_1305072, _1305076)))], (27380 ^ _779530) ^ [_1305420, _1305422, _1305424] : [class_Orderings_Olinorder(_1305420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305420), _1305422)), -(_1305422 = c_Orderings_Obot__class_Obot(tc_fun(_1305420, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305420), _1305424)), -(_1305424 = c_Orderings_Obot__class_Obot(tc_fun(_1305420, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305420, tc_HOL_Obool)), _1305422), _1305424) = c_Orderings_Obot__class_Obot(tc_fun(_1305420, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1305420, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305420, tc_HOL_Obool)), _1305422), _1305424)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305420), c_Big__Operators_Olinorder__class_OMax(_1305420, _1305422)), c_Big__Operators_Olinorder__class_OMax(_1305420, _1305424)))], (27406 ^ _779530) ^ [_1305897, _1305899, _1305901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305897)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305899, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1305901), _1305897)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1305901), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1305899), _1305901), _1305897))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1305899, _1305901)))], (27412 ^ _779530) ^ [_1306051, _1306053] : [-(_1306051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27415 ^ _779530 : [(27416 ^ _779530) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306053, _1306051) = 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), _1306053)), _1306051) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306053), _1306051)))], (27422 ^ _779530) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306053, _1306051) = 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), _1306053)), _1306051) = 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), _1306053), _1306051))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (27428 ^ _779530) ^ [_1306324, _1306326] : [-(_1306324 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27431 ^ _779530 : [(27432 ^ _779530) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306326, _1306324) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306326), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1306324)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306326), _1306324)))], (27438 ^ _779530) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1306326, _1306324) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1306326), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1306324)) = 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), _1306326), _1306324))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (27444 ^ _779530) ^ [_1306598, _1306600, _1306602, _1306604, _1306606, _1306608, _1306610] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1306598, _1306600), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1306602), _1306604))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1306606, _1306600), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1306608), _1306610))), -(_1306600 = 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), _1306598), _1306606), _1306600), 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), _1306602), _1306608)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306604), _1306610)), _1306600))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306604), _1306610), _1306600)))))], (27458 ^ _779530) ^ [_1306908, _1306910, _1306912] : [class_Orderings_Olinorder(_1306908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306908), _1306910)), hBOOL(hAPP(hAPP(c_member(_1306908), _1306912), _1306910)), 27469 ^ _779530 : [(27470 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306908, tc_HOL_Obool)), _1306910), hAPP(hAPP(c_Set_Oinsert(_1306908), _1306912), c_Orderings_Obot__class_Obot(tc_fun(_1306908, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1306908, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1306908, _1306910) = _1306912)], (27476 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306908, tc_HOL_Obool)), _1306910), hAPP(hAPP(c_Set_Oinsert(_1306908), _1306912), c_Orderings_Obot__class_Obot(tc_fun(_1306908, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1306908, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306908, _1306910) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306908), _1306912), c_Big__Operators_Olinorder__class_OMax(_1306908, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306908, tc_HOL_Obool)), _1306910), hAPP(hAPP(c_Set_Oinsert(_1306908), _1306912), c_Orderings_Obot__class_Obot(tc_fun(_1306908, tc_HOL_Obool)))))))]]], (27482 ^ _779530) ^ [_1307414, _1307416, _1307418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307414)), 27485 ^ _779530 : [(27504 ^ _779530) ^ [] : [27507 ^ _779530 : [(27508 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27506 ^ [_1307414, _1307416, _1307418])))], (27510 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 27506 ^ [_1307414, _1307416, _1307418]), _1307414)))], (27512 ^ _779530) ^ [] : [-(_1307418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1307414), 27505 ^ [_1307414, _1307416, _1307418])), 27506 ^ [_1307414, _1307416, _1307418]))], (27514 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1307416, 27505 ^ [_1307414, _1307416, _1307418]), 27506 ^ [_1307414, _1307416, _1307418]))]], -(hBOOL(hAPP(hAPP(_1307416, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1307418), _1307414)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1307418, _1307414))))], (27486 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1307416, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1307418), _1307414)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1307418, _1307414))), 27489 ^ _779530 : [(27490 ^ _779530) ^ [_1307615, _1307617] : [-(hBOOL(hAPP(hAPP(_1307416, _1307617), _1307615))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307615), _1307414)), _1307418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1307414), _1307617)), _1307615)]]]]], (27518 ^ _779530) ^ [_1308129, _1308131, _1308133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 27521 ^ _779530 : [(27540 ^ _779530) ^ [] : [27543 ^ _779530 : [(27544 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308129), 27542 ^ [_1308129, _1308131, _1308133])))], (27546 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 27542 ^ [_1308129, _1308131, _1308133]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27548 ^ _779530) ^ [] : [-(_1308133 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308129), 27541 ^ [_1308129, _1308131, _1308133])), 27542 ^ [_1308129, _1308131, _1308133]))], (27550 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1308131, 27541 ^ [_1308129, _1308131, _1308133]), 27542 ^ [_1308129, _1308131, _1308133]))]], -(hBOOL(hAPP(hAPP(_1308131, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308133), _1308129)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1308133, _1308129))))], (27522 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1308131, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1308133), _1308129)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1308133, _1308129))), 27525 ^ _779530 : [(27526 ^ _779530) ^ [_1308339, _1308341] : [-(hBOOL(hAPP(hAPP(_1308131, _1308341), _1308339))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1308129), _1308339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1308339), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1308133 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308129), _1308341)), _1308339)]]]]], (27554 ^ _779530) ^ [_1308862, _1308864, _1308866, _1308868, _1308870] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1308862, _1308864), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1308866), _1308868))), -(_1308864 = 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), _1308870), _1308862), _1308864), 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), _1308870), _1308866)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308870), _1308868)), _1308864))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1308870), _1308868), _1308864)))))], (27564 ^ _779530) ^ [_1309084, _1309086, _1309088] : [class_Orderings_Olinorder(_1309084), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309084), _1309086)), -(_1309086 = c_Orderings_Obot__class_Obot(tc_fun(_1309084, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309084), _1309088)), -(_1309088 = c_Orderings_Obot__class_Obot(tc_fun(_1309084, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309084), c_Big__Operators_Olattice_OInf__fin(_1309084, c_Orderings_Oord__class_Omin(_1309084), _1309086)), c_Big__Operators_Olattice_OInf__fin(_1309084, c_Orderings_Oord__class_Omin(_1309084), _1309088)) = c_Big__Operators_Olattice_OInf__fin(_1309084, c_Orderings_Oord__class_Omin(_1309084), hAPP(c_Set_OCollect(_1309084), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_HOL_Obool), tc_HOL_Obool, _1309084), c_HOL_OEx(_1309084)), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool)), tc_fun(_1309084, tc_HOL_Obool), _1309084), hAPP(c_COMBB(tc_fun(_1309084, tc_HOL_Obool), tc_HOL_Obool, _1309084), c_HOL_OEx(_1309084))), hAPP(hAPP(c_COMBC(_1309084, tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool)), tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_fun(tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool))), tc_fun(tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool)), tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool))), _1309084), c_COMBS(_1309084, tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_fun(_1309084, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1309084, tc_fun(tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool))), _1309084), hAPP(c_COMBB(tc_fun(_1309084, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool)), _1309084), c_COMBS(_1309084, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool)), tc_fun(_1309084, tc_fun(_1309084, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1309084), hAPP(c_COMBB(tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1309084), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1309084), c_fconj))), hAPP(hAPP(c_COMBC(_1309084, tc_fun(_1309084, tc_fun(_1309084, _1309084)), tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1309084, _1309084), tc_fun(_1309084, tc_HOL_Obool)), tc_fun(tc_fun(_1309084, tc_fun(_1309084, _1309084)), tc_fun(_1309084, tc_fun(_1309084, tc_HOL_Obool))), _1309084), c_COMBB(tc_fun(_1309084, _1309084), tc_fun(_1309084, tc_HOL_Obool), _1309084)), hAPP(hAPP(c_COMBB(tc_fun(_1309084, tc_HOL_Obool), tc_fun(tc_fun(_1309084, _1309084), tc_fun(_1309084, tc_HOL_Obool)), _1309084), c_COMBB(_1309084, tc_HOL_Obool, _1309084)), c_fequal))), c_Orderings_Oord__class_Omax(_1309084)))))), hAPP(hAPP(c_COMBC(_1309084, tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1309084, tc_HOL_Obool), tc_fun(_1309084, tc_HOL_Obool)), _1309084), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1309084)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1309084), c_fconj), hAPP(hAPP(c_COMBC(_1309084, tc_fun(_1309084, tc_HOL_Obool), tc_HOL_Obool), c_member(_1309084)), _1309086)))), hAPP(hAPP(c_COMBC(_1309084, tc_fun(_1309084, tc_HOL_Obool), tc_HOL_Obool), c_member(_1309084)), _1309088))))))))], (27586 ^ _779530) ^ [_1310201, _1310203] : [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), _1310201), _1310203))), 27589 ^ _779530 : [(27590 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310203), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1310201, _1310203) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310201), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310203)))], (27596 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1310203), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 27599 ^ _779530 : [(27600 ^ _779530) ^ [] : [27601 ^ _779530 : [(27602 ^ _779530) ^ [] : [_1310201 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (27604 ^ _779530) ^ [] : [_1310203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1310201, _1310203) = 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)))], (27608 ^ _779530) ^ [] : [-(c_Nitpick_Onorm__frac(_1310201, _1310203) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1310201), _1310203)), 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), _1310201))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1310203)))), -(_1310201 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1310203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (27618 ^ _779530) ^ [_1310702, _1310704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310702)), -(c_SMT_Oz3mod(_1310704, _1310702) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1310704, _1310702))], (27624 ^ _779530) ^ [_1310791, _1310793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310791))), -(c_SMT_Oz3mod(_1310793, _1310791) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1310793, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1310791)))], (27630 ^ _779530) ^ [_1310841, _1310843, _1310845] : [class_Orderings_Olinorder(_1310841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310841), _1310843)), -(_1310843 = c_Orderings_Obot__class_Obot(tc_fun(_1310841, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310841), _1310845)), -(_1310845 = c_Orderings_Obot__class_Obot(tc_fun(_1310841, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310841), c_Big__Operators_Olattice_OSup__fin(_1310841, c_Orderings_Oord__class_Omax(_1310841), _1310843)), c_Big__Operators_Olattice_OSup__fin(_1310841, c_Orderings_Oord__class_Omax(_1310841), _1310845)) = c_Big__Operators_Olattice_OSup__fin(_1310841, c_Orderings_Oord__class_Omax(_1310841), hAPP(c_Set_OCollect(_1310841), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_HOL_Obool), tc_HOL_Obool, _1310841), c_HOL_OEx(_1310841)), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool)), tc_fun(_1310841, tc_HOL_Obool), _1310841), hAPP(c_COMBB(tc_fun(_1310841, tc_HOL_Obool), tc_HOL_Obool, _1310841), c_HOL_OEx(_1310841))), hAPP(hAPP(c_COMBC(_1310841, tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool)), tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_fun(tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool))), tc_fun(tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool)), tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool))), _1310841), c_COMBS(_1310841, tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_fun(_1310841, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1310841, tc_fun(tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool))), _1310841), hAPP(c_COMBB(tc_fun(_1310841, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool)), _1310841), c_COMBS(_1310841, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool)), tc_fun(_1310841, tc_fun(_1310841, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1310841), hAPP(c_COMBB(tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1310841), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1310841), c_fconj))), hAPP(hAPP(c_COMBC(_1310841, tc_fun(_1310841, tc_fun(_1310841, _1310841)), tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1310841, _1310841), tc_fun(_1310841, tc_HOL_Obool)), tc_fun(tc_fun(_1310841, tc_fun(_1310841, _1310841)), tc_fun(_1310841, tc_fun(_1310841, tc_HOL_Obool))), _1310841), c_COMBB(tc_fun(_1310841, _1310841), tc_fun(_1310841, tc_HOL_Obool), _1310841)), hAPP(hAPP(c_COMBB(tc_fun(_1310841, tc_HOL_Obool), tc_fun(tc_fun(_1310841, _1310841), tc_fun(_1310841, tc_HOL_Obool)), _1310841), c_COMBB(_1310841, tc_HOL_Obool, _1310841)), c_fequal))), c_Orderings_Oord__class_Omin(_1310841)))))), hAPP(hAPP(c_COMBC(_1310841, tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1310841, tc_HOL_Obool), tc_fun(_1310841, tc_HOL_Obool)), _1310841), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1310841)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1310841), c_fconj), hAPP(hAPP(c_COMBC(_1310841, tc_fun(_1310841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1310841)), _1310843)))), hAPP(hAPP(c_COMBC(_1310841, tc_fun(_1310841, tc_HOL_Obool), tc_HOL_Obool), c_member(_1310841)), _1310845))))))))], (27652 ^ _779530) ^ [_1311958, _1311960, _1311962] : [class_Orderings_Olinorder(_1311958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311958), _1311960)), -(_1311960 = c_Orderings_Obot__class_Obot(tc_fun(_1311958, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311958), _1311962), c_Big__Operators_Olattice_OSup__fin(_1311958, c_Orderings_Oord__class_Omax(_1311958), _1311960)) = c_Big__Operators_Olattice_OSup__fin(_1311958, c_Orderings_Oord__class_Omax(_1311958), hAPP(c_Set_OCollect(_1311958), hAPP(hAPP(c_COMBB(tc_fun(_1311958, tc_HOL_Obool), tc_HOL_Obool, _1311958), c_HOL_OEx(_1311958)), hAPP(hAPP(c_COMBC(_1311958, tc_fun(_1311958, tc_HOL_Obool), tc_fun(_1311958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1311958, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1311958, tc_HOL_Obool), tc_fun(_1311958, tc_HOL_Obool)), _1311958), c_COMBS(_1311958, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1311958, tc_HOL_Obool), tc_fun(_1311958, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1311958), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1311958), c_fconj)), hAPP(hAPP(c_COMBC(_1311958, tc_fun(_1311958, _1311958), tc_fun(_1311958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1311958, tc_HOL_Obool), tc_fun(tc_fun(_1311958, _1311958), tc_fun(_1311958, tc_HOL_Obool)), _1311958), c_COMBB(_1311958, tc_HOL_Obool, _1311958)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1311958), _1311962))))), hAPP(hAPP(c_COMBC(_1311958, tc_fun(_1311958, tc_HOL_Obool), tc_HOL_Obool), c_member(_1311958)), _1311960))))))], (27666 ^ _779530) ^ [_1312456, _1312458] : [class_Orderings_Olinorder(_1312456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312456), _1312458)), -(_1312458 = c_Orderings_Obot__class_Obot(tc_fun(_1312456, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1312456), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312456), 27679 ^ [_1312456, _1312458]), 27680 ^ [_1312456, _1312458])), hAPP(hAPP(c_Set_Oinsert(_1312456), 27679 ^ [_1312456, _1312458]), hAPP(hAPP(c_Set_Oinsert(_1312456), 27680 ^ [_1312456, _1312458]), c_Orderings_Obot__class_Obot(tc_fun(_1312456, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1312456), c_Big__Operators_Olinorder__class_OMax(_1312456, _1312458)), _1312458)))], (27686 ^ _779530) ^ [_1312900, _1312902, _1312904] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1312900), _1312902)), _1312904) = 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), _1312900), _1312904)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1312902), _1312904))), 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, _1312900, _1312904)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1312902, _1312904))), _1312904)))], (27688 ^ _779530) ^ [_1312983, _1312985, _1312987] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1312983, _1312985)), _1312987) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1312983), _1312987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1312985), _1312987)))], (27690 ^ _779530) ^ [_1313036, _1313038, _1313040] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1313036), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313038, _1313040)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1313036), _1313038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1313036), _1313040)))], (27692 ^ _779530) ^ [_1313089, _1313091] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1313089), _1313091) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313089, _1313091)), _1313091))], (27694 ^ _779530) ^ [_1313132, _1313134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313132), _1313134)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313132, _1313134) = _1313132)], (27700 ^ _779530) ^ [_1313227, _1313229] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313227, _1313229)), _1313227)))], (27702 ^ _779530) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (27704 ^ _779530) ^ [_1313288, _1313290] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313288, _1313290)) = _1313290, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1313288), _1313290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27710 ^ _779530) ^ [_1313387, _1313389] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313387, _1313389)) = _1313389), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1313387), _1313389) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313387, _1313389)))], (27716 ^ _779530) ^ [_1313446] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313446, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27718 ^ _779530) ^ [_1313473, _1313475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1313473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313475, _1313473)), _1313473)))], (27724 ^ _779530) ^ [_1313587, _1313589] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313587, _1313589) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1313587 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1313589), 27727 ^ [_1313587, _1313589]))], (27731 ^ _779530) ^ [_1313692, _1313694] : [27732 ^ _779530 : [(27733 ^ _779530) ^ [_1313741] : [_1313692 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1313694), _1313741)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313692, _1313694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27737 ^ _779530) ^ [_1313813, _1313815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313813), _1313815)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313813, _1313815) = _1313813)], (27743 ^ _779530) ^ [_1313902, _1313904] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313902), _1313904))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313902, _1313904) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1313902), _1313904), _1313904))], (27749 ^ _779530) ^ [_1313955, _1313957] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1313955), _1313957))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1313955, _1313957) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1313955), _1313957), _1313957))], (27755 ^ _779530) ^ [_1314010, _1314012, _1314014] : [-(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), _1314010), _1314012)), _1314014), _1314012) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314014, _1314012))], (27757 ^ _779530) ^ [_1314057, _1314059, _1314061] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314057), _1314059)), _1314061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314057), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1314059), _1314061))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314057), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314059, _1314061))), _1314061)))], (27759 ^ _779530) ^ [_1314130, _1314132, _1314134] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314130, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314132), _1314134)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314132), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1314130), _1314132), _1314134))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314130, _1314132)))], (27761 ^ _779530) ^ [_1314193, _1314195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1314193), _1314195)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314195, _1314193) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1314195), _1314193), _1314193))], (27767 ^ _779530) ^ [_1314308, _1314310] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1314308), _1314310)), _1314310) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1314308), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314308, _1314310)))], (27769 ^ _779530) ^ [_1314355, _1314357] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1314355), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1314357), _1314355)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1314357), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314357, _1314355)))], (27771 ^ _779530) ^ [_1314402, _1314404] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314402, _1314404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1314402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1314402), _1314404)), _1314404)))], (27773 ^ _779530) ^ [_1314449, _1314451] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1314449), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1314451)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314449, _1314451)))], (27775 ^ _779530) ^ [_1314491, _1314493] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314491, _1314493)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1314491), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1314493)))], (27777 ^ _779530) ^ [_1314533, _1314535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1314533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1314535, _1314533)), _1314533)))], (27783 ^ _779530) ^ [_1314632, _1314634, _1314636] : [-(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), _1314632), _1314634)), _1314636)), _1314634) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1314636), _1314634))], (27785 ^ _779530) ^ [_1314685, _1314687, _1314689] : [class_Orderings_Olinorder(_1314685), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314685), _1314687)), hBOOL(hAPP(hAPP(c_member(_1314685), _1314689), _1314687)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1314685), _1314689), c_Big__Operators_Olattice_OSup__fin(_1314685, c_Orderings_Oord__class_Omax(_1314685), _1314687)) = c_Big__Operators_Olattice_OSup__fin(_1314685, c_Orderings_Oord__class_Omax(_1314685), _1314687))], (27799 ^ _779530) ^ [_1314932, _1314934] : [class_Orderings_Olinorder(_1314932), -(c_Big__Operators_Olattice_OSup__fin(_1314932, c_Orderings_Oord__class_Omax(_1314932), hAPP(hAPP(c_Set_Oinsert(_1314932), _1314934), c_Orderings_Obot__class_Obot(tc_fun(_1314932, tc_HOL_Obool)))) = _1314934)], (27829 ^ _779530) ^ [_1315496, _1315498, _1315500] : [-(hBOOL(hAPP(_1315496, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1315498, _1315500)))), 27832 ^ _779530 : [(27833 ^ _779530) ^ [] : [-(_1315500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27835 ^ _779530) ^ [] : [hBOOL(hAPP(_1315496, _1315498))]], 27836 ^ _779530 : [(27837 ^ _779530) ^ [] : [_1315500 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27841 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27839 ^ [_1315496, _1315498, _1315500]), _1315500)))], (27843 ^ _779530) ^ [] : [-(_1315498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1315500), 27838 ^ [_1315496, _1315498, _1315500])), 27839 ^ [_1315496, _1315498, _1315500]))], (27845 ^ _779530) ^ [] : [hBOOL(hAPP(_1315496, 27839 ^ [_1315496, _1315498, _1315500]))]]], (27805 ^ _779530) ^ [_1315063, _1315065, _1315067] : [hBOOL(hAPP(_1315063, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1315065, _1315067))), 27808 ^ _779530 : [(27809 ^ _779530) ^ [] : [_1315067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1315063, _1315065)))], (27815 ^ _779530) ^ [] : [-(_1315067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 27818 ^ _779530 : [(27819 ^ _779530) ^ [_1315311, _1315313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315311), _1315067)), _1315065 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1315067), _1315313)), _1315311), -(hBOOL(hAPP(_1315063, _1315311)))]]]]], (27849 ^ _779530) ^ [_1315905, _1315907, _1315909, _1315911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1315905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1315907), _1315909)), -(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), _1315909), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1315911, _1315905))), _1315907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1315909), _1315905))))], (27859 ^ _779530) ^ [_1316110, _1316112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1316110)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1316110), _1316112)), _1316110) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27865 ^ _779530) ^ [_1316217, _1316219, _1316221] : [class_Orderings_Olinorder(_1316217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316217), _1316219)), -(_1316219 = c_Orderings_Obot__class_Obot(tc_fun(_1316217, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1316217, c_Orderings_Oord__class_Omax(_1316217), hAPP(hAPP(c_Set_Oinsert(_1316217), _1316221), _1316219)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316217), _1316221), c_Big__Operators_Olattice_OSup__fin(_1316217, c_Orderings_Oord__class_Omax(_1316217), _1316219)))], (27879 ^ _779530) ^ [_1316437, _1316439, _1316441] : [class_Orderings_Olinorder(_1316437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316437), _1316439)), -(_1316441 = c_Orderings_Obot__class_Obot(tc_fun(_1316437, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316437, tc_HOL_Obool)), _1316441), _1316439)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316437), c_Big__Operators_Olattice_OSup__fin(_1316437, c_Orderings_Oord__class_Omax(_1316437), _1316441)), c_Big__Operators_Olattice_OSup__fin(_1316437, c_Orderings_Oord__class_Omax(_1316437), _1316439)) = c_Big__Operators_Olattice_OSup__fin(_1316437, c_Orderings_Oord__class_Omax(_1316437), _1316439))], (27897 ^ _779530) ^ [_1316769, _1316771, _1316773] : [class_Orderings_Olinorder(_1316769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316769), _1316771)), hBOOL(hAPP(hAPP(c_member(_1316769), _1316773), _1316771)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316769), _1316773), c_Big__Operators_Olattice_OSup__fin(_1316769, c_Orderings_Oord__class_Omax(_1316769), _1316771)) = _1316773)], (27911 ^ _779530) ^ [_1317004, _1317006, _1317008] : [class_Orderings_Olinorder(_1317004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317004), _1317006)), -(_1317006 = c_Orderings_Obot__class_Obot(tc_fun(_1317004, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317004), _1317008)), -(_1317008 = c_Orderings_Obot__class_Obot(tc_fun(_1317004, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1317004, c_Orderings_Oord__class_Omax(_1317004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317004, tc_HOL_Obool)), _1317006), _1317008)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317004), c_Big__Operators_Olattice_OSup__fin(_1317004, c_Orderings_Oord__class_Omax(_1317004), _1317006)), c_Big__Operators_Olattice_OSup__fin(_1317004, c_Orderings_Oord__class_Omax(_1317004), _1317008)))], (27933 ^ _779530) ^ [_1317371, _1317373, _1317375] : [class_Orderings_Olinorder(_1317371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317371), _1317373)), -(hBOOL(hAPP(hAPP(c_member(_1317371), _1317375), _1317373))), -(_1317373 = c_Orderings_Obot__class_Obot(tc_fun(_1317371, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1317371, c_Orderings_Oord__class_Omax(_1317371), hAPP(hAPP(c_Set_Oinsert(_1317371), _1317375), _1317373)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317371), _1317375), c_Big__Operators_Olattice_OSup__fin(_1317371, c_Orderings_Oord__class_Omax(_1317371), _1317373)))], (27951 ^ _779530) ^ [_1317620, _1317622, _1317624] : [class_Orderings_Olinorder(_1317620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317620), _1317622)), 27958 ^ _779530 : [(27959 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317620, tc_HOL_Obool)), _1317622), hAPP(hAPP(c_Set_Oinsert(_1317620), _1317624), c_Orderings_Obot__class_Obot(tc_fun(_1317620, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1317620, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1317620, c_Orderings_Oord__class_Omax(_1317620), hAPP(hAPP(c_Set_Oinsert(_1317620), _1317624), _1317622)) = _1317624)], (27965 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317620, tc_HOL_Obool)), _1317622), hAPP(hAPP(c_Set_Oinsert(_1317620), _1317624), c_Orderings_Obot__class_Obot(tc_fun(_1317620, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1317620, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1317620, c_Orderings_Oord__class_Omax(_1317620), hAPP(hAPP(c_Set_Oinsert(_1317620), _1317624), _1317622)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1317620), _1317624), c_Big__Operators_Olattice_OSup__fin(_1317620, c_Orderings_Oord__class_Omax(_1317620), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1317620, tc_HOL_Obool)), _1317622), hAPP(hAPP(c_Set_Oinsert(_1317620), _1317624), c_Orderings_Obot__class_Obot(tc_fun(_1317620, tc_HOL_Obool)))))))]]], (27971 ^ _779530) ^ [_1318108, _1318110, _1318112] : [class_Orderings_Olinorder(_1318108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318108), _1318110)), -(_1318110 = c_Orderings_Obot__class_Obot(tc_fun(_1318108, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318108), _1318112)), -(_1318112 = c_Orderings_Obot__class_Obot(tc_fun(_1318108, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318108, tc_HOL_Obool)), _1318110), _1318112) = c_Orderings_Obot__class_Obot(tc_fun(_1318108, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1318108, c_Orderings_Oord__class_Omax(_1318108), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318108, tc_HOL_Obool)), _1318110), _1318112)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318108), c_Big__Operators_Olattice_OSup__fin(_1318108, c_Orderings_Oord__class_Omax(_1318108), _1318110)), c_Big__Operators_Olattice_OSup__fin(_1318108, c_Orderings_Oord__class_Omax(_1318108), _1318112)))], (27997 ^ _779530) ^ [_1318603, _1318605, _1318607] : [class_Orderings_Olinorder(_1318603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318603), _1318605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318603), _1318607)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318603, tc_HOL_Obool)), _1318605), _1318607) = c_Orderings_Obot__class_Obot(tc_fun(_1318603, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318603), c_Big__Operators_Olattice_OSup__fin(_1318603, c_Orderings_Oord__class_Omax(_1318603), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318603, tc_HOL_Obool)), _1318605), _1318607))), c_Big__Operators_Olattice_OSup__fin(_1318603, c_Orderings_Oord__class_Omax(_1318603), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318603, tc_HOL_Obool)), _1318605), _1318607))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318603), c_Big__Operators_Olattice_OSup__fin(_1318603, c_Orderings_Oord__class_Omax(_1318603), _1318605)), c_Big__Operators_Olattice_OSup__fin(_1318603, c_Orderings_Oord__class_Omax(_1318603), _1318607)))], (28015 ^ _779530) ^ [_1318975, _1318977, _1318979] : [class_Orderings_Olinorder(_1318975), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318975), _1318977)), hBOOL(hAPP(hAPP(c_member(_1318975), _1318979), _1318977)), 28026 ^ _779530 : [(28027 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318975, tc_HOL_Obool)), _1318977), hAPP(hAPP(c_Set_Oinsert(_1318975), _1318979), c_Orderings_Obot__class_Obot(tc_fun(_1318975, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318975, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1318975, c_Orderings_Oord__class_Omax(_1318975), _1318977) = _1318979)], (28033 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318975, tc_HOL_Obool)), _1318977), hAPP(hAPP(c_Set_Oinsert(_1318975), _1318979), c_Orderings_Obot__class_Obot(tc_fun(_1318975, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1318975, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1318975, c_Orderings_Oord__class_Omax(_1318975), _1318977) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318975), _1318979), c_Big__Operators_Olattice_OSup__fin(_1318975, c_Orderings_Oord__class_Omax(_1318975), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1318975, tc_HOL_Obool)), _1318977), hAPP(hAPP(c_Set_Oinsert(_1318975), _1318979), c_Orderings_Obot__class_Obot(tc_fun(_1318975, tc_HOL_Obool)))))))]]], (28039 ^ _779530) ^ [_1319499, _1319501] : [class_Orderings_Olinorder(_1319499), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319499), _1319501)), -(_1319501 = c_Orderings_Obot__class_Obot(tc_fun(_1319499, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319499), c_Big__Operators_Olattice_OInf__fin(_1319499, c_Orderings_Oord__class_Omin(_1319499), _1319501)), c_Big__Operators_Olattice_OSup__fin(_1319499, c_Orderings_Oord__class_Omax(_1319499), _1319501))))], (28053 ^ _779530) ^ [_1319697, _1319699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1319697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1319697), _1319699)), -(c_Divides_Odivmod__nat(_1319699, _1319697) = 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), _1319699), _1319697)), _1319697))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1319699), _1319697), _1319697)))], (28063 ^ _779530) ^ [_1319908, _1319910, _1319912] : [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), _1319908), _1319910))), -(hBOOL(hAPP(hAPP(_1319912, _1319908), _1319910))), 28070 ^ _779530 : [(28071 ^ _779530) ^ [] : [-(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), 28068 ^ [_1319908, _1319910, _1319912]), 28069 ^ [_1319908, _1319910, _1319912]))))], (28079 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1319912, 28068 ^ [_1319908, _1319910, _1319912]), 28069 ^ [_1319908, _1319910, _1319912]))], (28073 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 28069 ^ [_1319908, _1319910, _1319912]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1319912, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 28068 ^ [_1319908, _1319910, _1319912])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 28069 ^ [_1319908, _1319910, _1319912]))))]]], (28083 ^ _779530) ^ [_1320381, _1320383, _1320385, _1320387, _1320389] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1320381, _1320383), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1320385), _1320387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1320383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1320389)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1320381, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1320383), _1320389)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1320385), _1320389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1320383), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1320385, _1320389))), _1320387)))))], (28097 ^ _779530) ^ [_1320688, _1320690, _1320692, _1320694, _1320696] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1320688, _1320690), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1320692), _1320694))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1320690)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1320696), _1320688), _1320690), 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), _1320696), _1320692)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1320696), _1320694)), _1320690))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1320696), _1320694), _1320690)))))], (28107 ^ _779530) ^ [_1320957, _1320959, _1320961, _1320963] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1320957, _1320959), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1320961), _1320963))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1320957, _1320959) = _1320963)], (28113 ^ _779530) ^ [_1321068, _1321070] : [-(c_Divides_Odivmod__nat(_1321068, _1321070) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1321068, _1321070)))], (28115 ^ _779530) ^ [_1321102, _1321104] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321102, _1321104), c_Divides_Odivmod__nat(_1321102, _1321104))))], (28117 ^ _779530) ^ [_1321135, _1321137, _1321139] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321135, _1321137), _1321139)), -(c_Divides_Odivmod__nat(_1321135, _1321137) = _1321139)], (28123 ^ _779530) ^ [_1321230, _1321232, _1321234, _1321236] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321230, _1321232), _1321234)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321230, _1321232), _1321236)), -(_1321234 = _1321236)], (28133 ^ _779530) ^ [_1321387, _1321389] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321387, _1321389), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1321387), _1321389)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1321387, _1321389)))))], (28135 ^ _779530) ^ [_1321433, _1321435, _1321437, _1321439] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321433, _1321435), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1321437), _1321439))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1321433), _1321435) = _1321437)], (28141 ^ _779530) ^ [_1321548] : [-(c_Divides_Odivmod__nat(_1321548, 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)), _1321548))], (28143 ^ _779530) ^ [_1321577, _1321579] : [-(c_Divides_Odivmod__nat(_1321577, _1321579) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1321577), _1321579)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1321577, _1321579)))], (28145 ^ _779530) ^ [_1321621, _1321623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1321621), _1321623)), -(c_Divides_Odivmod__nat(_1321621, _1321623) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1321621))], (28151 ^ _779530) ^ [_1321720, _1321722, _1321724, _1321726, _1321728, _1321730, _1321732] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321720, _1321722), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1321724), _1321726))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1321728, _1321722), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1321730), _1321732))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1321722)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1321720), _1321728), _1321722), 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), _1321724), _1321730)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1321726), _1321732)), _1321722))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1321726), _1321732), _1321722)))))], (28165 ^ _779530) ^ [_1322081, _1322083] : [class_Orderings_Olinorder(_1322081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322081), _1322083)), -(_1322083 = c_Orderings_Obot__class_Obot(tc_fun(_1322081, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1322081), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322081), 28178 ^ [_1322081, _1322083]), 28179 ^ [_1322081, _1322083])), hAPP(hAPP(c_Set_Oinsert(_1322081), 28178 ^ [_1322081, _1322083]), hAPP(hAPP(c_Set_Oinsert(_1322081), 28179 ^ [_1322081, _1322083]), c_Orderings_Obot__class_Obot(tc_fun(_1322081, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1322081), c_Big__Operators_Olattice_OSup__fin(_1322081, c_Orderings_Oord__class_Omax(_1322081), _1322083)), _1322083)))], (28185 ^ _779530) ^ [_1322531, _1322533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1322531), 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)), _1322533)), -(c_Divides_OnegDivAlg(_1322531, _1322533) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1322531), _1322533)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322531, _1322533)))], (28195 ^ _779530) ^ [_1322721, _1322723] : [28196 ^ _779530 : [(28197 ^ _779530) ^ [] : [_1322721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28199 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1322723), _1322721))]], -(c_Divides_Odivmod__nat(_1322723, _1322721) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1322723))], (28203 ^ _779530) ^ [_1322852, _1322854] : [-(c_Divides_Odivmod__nat(_1322854, _1322852) = 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), _1322854), _1322852), _1322852))), -(_1322852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1322854), _1322852)))], (28213 ^ _779530) ^ [_1322917, _1322919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1322917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1322919)), -(c_Divides_OposDivAlg(_1322917, _1322919) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1322917), _1322919)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322917, _1322919)))], (28223 ^ _779530) ^ [_1323092] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1323092) = 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)))], (28225 ^ _779530) ^ [_1323118, _1323120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1323118), 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)), _1323120)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1323118, _1323120), c_Divides_OnegDivAlg(_1323118, _1323120))))], (28235 ^ _779530) ^ [_1323277, _1323279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323279)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1323277, _1323279), c_Divides_OposDivAlg(_1323277, _1323279))))], (28245 ^ _779530) ^ [_1323430, _1323432, _1323434, _1323436, _1323438, _1323440, _1323442] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1323430, _1323432)), hAPP(hAPP(c_Product__Type_OPair(_1323430, _1323432), _1323434), _1323436)), _1323438)), -(hBOOL(hAPP(hAPP(c_member(_1323440), hAPP(hAPP(_1323442, _1323434), _1323436)), hAPP(c_Set_Oimage(tc_prod(_1323430, _1323432), _1323440, hAPP(c_Product__Type_Oprod_Oprod__case(_1323430, _1323432, _1323440), _1323442)), _1323438))))], (28251 ^ _779530) ^ [_1323615, _1323617, _1323619, _1323621, _1323623, _1323625, _1323627, _1323629] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1323615, _1323617, _1323619), _1323621), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1323623, _1323625, tc_prod(_1323615, _1323617)), _1323627), _1323629)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1323623, _1323625, _1323619), hAPP(hAPP(c_COMBB(tc_fun(_1323625, tc_prod(_1323615, _1323617)), tc_fun(_1323625, _1323619), _1323623), hAPP(c_COMBB(tc_prod(_1323615, _1323617), _1323619, _1323625), hAPP(c_Product__Type_Oprod_Oprod__case(_1323615, _1323617, _1323619), _1323621))), _1323627)), _1323629))], (28253 ^ _779530) ^ [_1323721, _1323723, _1323725] : [-(c_Fun_Oinj__on(tc_prod(_1323721, _1323723), tc_prod(_1323723, _1323721), hAPP(c_Product__Type_Oprod_Oprod__case(_1323721, _1323723, tc_prod(_1323723, _1323721)), hAPP(c_COMBC(_1323723, _1323721, tc_prod(_1323723, _1323721)), c_Product__Type_OPair(_1323723, _1323721))), _1323725))], (28255 ^ _779530) ^ [_1323779, _1323781, _1323783, _1323785] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1323779, _1323781, _1323783), hAPP(hAPP(c_COMBB(tc_fun(_1323781, tc_prod(_1323779, _1323781)), tc_fun(_1323781, _1323783), _1323779), hAPP(c_COMBB(tc_prod(_1323779, _1323781), _1323783, _1323781), _1323785)), c_Product__Type_OPair(_1323779, _1323781))) = _1323785)], (28257 ^ _779530) ^ [_1323847, _1323849, _1323851, _1323853, _1323855] : [hBOOL(hAPP(hAPP(_1323847, _1323849), _1323851)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1323853, _1323855, tc_HOL_Obool), _1323847), hAPP(hAPP(c_Product__Type_OPair(_1323853, _1323855), _1323849), _1323851))))], (28263 ^ _779530) ^ [_1323976, _1323978, _1323980, _1323982, _1323984] : [hBOOL(hAPP(hAPP(_1323976, _1323978), _1323980)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1323982, _1323984, tc_HOL_Obool), _1323976), hAPP(hAPP(c_Product__Type_OPair(_1323982, _1323984), _1323978), _1323980))))], (28269 ^ _779530) ^ [_1324105, _1324107, _1324109, _1324111, _1324113, _1324115, _1324117] : [hBOOL(hAPP(hAPP(c_member(_1324105), _1324107), hAPP(hAPP(_1324109, _1324111), _1324113))), -(hBOOL(hAPP(hAPP(c_member(_1324105), _1324107), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1324115, _1324117, tc_fun(_1324105, tc_HOL_Obool)), _1324109), hAPP(hAPP(c_Product__Type_OPair(_1324115, _1324117), _1324111), _1324113)))))], (28275 ^ _779530) ^ [_1324276, _1324278, _1324280, _1324282, _1324284] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1324276, _1324278, tc_HOL_Obool), _1324280), hAPP(hAPP(c_Product__Type_OPair(_1324276, _1324278), _1324282), _1324284))), -(hBOOL(hAPP(hAPP(_1324280, _1324282), _1324284)))], (28281 ^ _779530) ^ [_1324405, _1324407, _1324409, _1324411, _1324413, _1324415, _1324417] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1324405, _1324407, tc_fun(_1324409, tc_HOL_Obool)), _1324411), hAPP(hAPP(c_Product__Type_OPair(_1324405, _1324407), _1324413), _1324415)), _1324417)), -(hBOOL(hAPP(hAPP(hAPP(_1324411, _1324413), _1324415), _1324417)))], (28287 ^ _779530) ^ [_1324556, _1324558] : [-(c_Relation_OId__on(_1324556, _1324558) = hAPP(c_Product__Type_Oprod_Oprod__case(_1324556, _1324556, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1324556, tc_HOL_Obool, tc_fun(_1324556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324556, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1324556, tc_HOL_Obool)), _1324556), c_COMBC(_1324556, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1324556, tc_HOL_Obool), tc_fun(_1324556, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1324556), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1324556), c_fconj)), c_fequal))), _1324558)))], (28289 ^ _779530) ^ [_1324650, _1324652, _1324654] : [-(c_HOL_OThe(tc_prod(_1324650, _1324652), _1324654) = c_HOL_OThe(tc_prod(_1324650, _1324652), hAPP(c_Product__Type_Oprod_Oprod__case(_1324650, _1324652, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1324652, tc_prod(_1324650, _1324652)), tc_fun(_1324652, tc_HOL_Obool), _1324650), hAPP(c_COMBB(tc_prod(_1324650, _1324652), tc_HOL_Obool, _1324652), _1324654)), c_Product__Type_OPair(_1324650, _1324652)))))], (28291 ^ _779530) ^ [_1324728, _1324730, _1324732, _1324734] : [-(c_HOL_OThe(tc_prod(_1324728, _1324730), hAPP(c_Product__Type_Oprod_Oprod__case(_1324728, _1324730, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1324728, tc_fun(_1324730, tc_HOL_Obool), tc_fun(_1324730, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1324730, tc_HOL_Obool), tc_fun(_1324730, tc_HOL_Obool)), _1324728), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1324730)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1324728), c_fconj), hAPP(c_fequal, _1324732)))), hAPP(c_fequal, _1324734)))) = hAPP(hAPP(c_Product__Type_OPair(_1324728, _1324730), _1324732), _1324734))], (28293 ^ _779530) ^ [_1324834, _1324836] : [-(c_Fun_Oinj__on(tc_fun(_1324834, _1324836), tc_fun(tc_prod(_1324834, _1324836), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1324834, _1324836), tc_HOL_Obool), tc_fun(tc_prod(_1324834, _1324836), tc_HOL_Obool), tc_fun(_1324834, _1324836)), c_Set_OCollect(tc_prod(_1324834, _1324836))), hAPP(hAPP(c_COMBB(tc_fun(_1324834, tc_fun(_1324836, tc_HOL_Obool)), tc_fun(tc_prod(_1324834, _1324836), tc_HOL_Obool), tc_fun(_1324834, _1324836)), c_Product__Type_Oprod_Oprod__case(_1324834, _1324836, tc_HOL_Obool)), hAPP(c_COMBB(_1324836, tc_fun(_1324836, tc_HOL_Obool), _1324834), hAPP(c_COMBC(_1324836, _1324836, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1324834, _1324836), tc_HOL_Obool))))], (28295 ^ _779530) ^ [_1324954, _1324956, _1324958, _1324960, _1324962, _1324964] : [hAPP(hAPP(c_Product__Type_OPair(_1324954, _1324956), _1324958), _1324960) = hAPP(hAPP(c_Product__Type_OPair(_1324954, _1324956), _1324962), _1324964), 28298 ^ _779530 : [(28299 ^ _779530) ^ [] : [-(_1324958 = _1324962)], (28301 ^ _779530) ^ [] : [-(_1324960 = _1324964)]]], (28303 ^ _779530) ^ [_1325132, _1325134, _1325136, _1325138, _1325140, _1325142] : [hAPP(hAPP(c_Product__Type_OPair(_1325132, _1325134), _1325136), _1325138) = hAPP(hAPP(c_Product__Type_OPair(_1325132, _1325134), _1325140), _1325142), 28306 ^ _779530 : [(28307 ^ _779530) ^ [] : [-(_1325136 = _1325140)], (28309 ^ _779530) ^ [] : [-(_1325138 = _1325142)]]], (28311 ^ _779530) ^ [_1325275, _1325277, _1325279, _1325281, _1325283, _1325285] : [-(hAPP(hAPP(c_Product__Type_OPair(_1325275, _1325277), _1325279), _1325281) = hAPP(hAPP(c_Product__Type_OPair(_1325275, _1325277), _1325283), _1325285)), _1325279 = _1325283, _1325281 = _1325285], (28321 ^ _779530) ^ [_1325476, _1325478, _1325480] : [hBOOL(hAPP(_1325476, 28322 ^ [_1325476, _1325478, _1325480])), 28325 ^ _779530 : [(28326 ^ _779530) ^ [_1325587, _1325589] : [-(hBOOL(hAPP(_1325476, hAPP(hAPP(c_Product__Type_OPair(_1325478, _1325480), _1325589), _1325587))))]]], (28328 ^ _779530) ^ [_1325623, _1325625, _1325627] : [hBOOL(hAPP(_1325623, hAPP(hAPP(c_Product__Type_OPair(_1325625, _1325627), 28329 ^ [_1325623, _1325625, _1325627]), 28330 ^ [_1325623, _1325625, _1325627]))), 28333 ^ _779530 : [(28334 ^ _779530) ^ [_1325770] : [-(hBOOL(hAPP(_1325623, _1325770)))]]], (28336 ^ _779530) ^ [_1325801, _1325803, _1325805, _1325807, _1325809, _1325811] : [_1325801 = _1325803, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1325805, _1325807, _1325809), _1325811), _1325801) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1325805, _1325807, _1325809), _1325811), _1325803))], (28342 ^ _779530) ^ [_1325926] : [-(c_Wellfounded_Ofinite__psubset(_1325926) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1325926, tc_HOL_Obool), tc_fun(_1325926, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1325926, tc_HOL_Obool), tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1325926, tc_HOL_Obool), tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1325926, tc_HOL_Obool)), c_COMBS(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1325926, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1325926, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1325926, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1325926, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1325926)))))], (28344 ^ _779530) ^ [_1326086, _1326088] : [-(c_Divides_Odivmod__int__rel(_1326086, _1326088) = 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, _1326086))), 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), _1326088)))))), 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)), _1326088))), 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)), _1326088))))), 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)), _1326088)))), 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), _1326088))), 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))))))))], (28346 ^ _779530) ^ [_1326201, _1326203, _1326205, _1326207, _1326209, _1326211] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1326201, _1326203, _1326205), _1326207), hAPP(hAPP(c_Product__Type_OPair(_1326201, _1326203), _1326209), _1326211)) = hAPP(hAPP(_1326207, _1326209), _1326211))], (28348 ^ _779530) ^ [_1326259, _1326261, _1326263, _1326265, _1326267, _1326269] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1326259, _1326261, _1326263), _1326265), hAPP(hAPP(c_Product__Type_OPair(_1326259, _1326261), _1326267), _1326269)) = hAPP(hAPP(_1326265, _1326267), _1326269))], (28350 ^ _779530) ^ [] : [-(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)))))], (28352 ^ _779530) ^ [_1326335] : [-(c_Int_Oint__ge__less__than(_1326335) = 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), _1326335)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (28354 ^ _779530) ^ [_1326381] : [-(c_Int_Oint__ge__less__than2(_1326381) = 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), _1326381)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (28356 ^ _779530) ^ [_1326427, _1326429, _1326431, _1326433] : [-(c_Nitpick_Oprod(_1326427, _1326429, _1326431, _1326433) = hAPP(c_Set_OCollect(tc_prod(_1326427, _1326429)), hAPP(c_Product__Type_Oprod_Oprod__case(_1326427, _1326429, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1326427, tc_fun(_1326429, tc_HOL_Obool), tc_fun(_1326429, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1326429, tc_HOL_Obool), tc_fun(_1326429, tc_HOL_Obool)), _1326427), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1326429)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1326427), c_fconj), hAPP(hAPP(c_COMBC(_1326427, tc_fun(_1326427, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326427)), _1326431)))), hAPP(hAPP(c_COMBC(_1326429, tc_fun(_1326429, tc_HOL_Obool), tc_HOL_Obool), c_member(_1326429)), _1326433)))))], (28358 ^ _779530) ^ [_1326555, _1326557, _1326559, _1326561] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1326555, _1326557), _1326559), _1326561) = hAPP(c_Set_OCollect(tc_prod(_1326557, _1326557)), hAPP(c_Product__Type_Oprod_Oprod__case(_1326557, _1326557, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1326557, tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_fun(_1326557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326557, tc_fun(tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_fun(_1326557, tc_HOL_Obool)), _1326557), c_COMBC(_1326557, tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1326557, tc_prod(_1326555, _1326555)), tc_fun(_1326557, tc_fun(tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_HOL_Obool)), _1326557), hAPP(c_COMBB(tc_prod(_1326555, _1326555), tc_fun(tc_fun(tc_prod(_1326555, _1326555), tc_HOL_Obool), tc_HOL_Obool), _1326557), c_member(tc_prod(_1326555, _1326555)))), hAPP(hAPP(c_COMBC(_1326557, tc_fun(_1326557, _1326555), tc_fun(_1326557, tc_prod(_1326555, _1326555))), hAPP(hAPP(c_COMBB(tc_fun(_1326555, tc_prod(_1326555, _1326555)), tc_fun(tc_fun(_1326557, _1326555), tc_fun(_1326557, tc_prod(_1326555, _1326555))), _1326557), c_COMBB(_1326555, tc_prod(_1326555, _1326555), _1326557)), hAPP(hAPP(c_COMBB(_1326555, tc_fun(_1326555, tc_prod(_1326555, _1326555)), _1326557), c_Product__Type_OPair(_1326555, _1326555)), _1326561))), _1326561)))), _1326559))))], (28360 ^ _779530) ^ [_1326796, _1326798, _1326800, _1326802, _1326804, _1326806] : [-(c_Product__Type_Oprod_Oprod__rec(_1326796, _1326798, _1326800, _1326802, hAPP(hAPP(c_Product__Type_OPair(_1326796, _1326798), _1326804), _1326806)) = hAPP(hAPP(_1326802, _1326804), _1326806))], (28362 ^ _779530) ^ [_1326850, _1326852, _1326854, _1326856, _1326858, _1326860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1326850, _1326852)), hAPP(hAPP(c_Product__Type_OPair(_1326850, _1326852), _1326854), _1326856)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1326850, _1326852), tc_HOL_Obool), _1326858))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1326850, _1326852), tc_HOL_Obool), tc_fun(tc_prod(_1326850, _1326852), tc_HOL_Obool), _1326858), 28373 ^ _779530 : [(28374 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1326850, _1326852)), hAPP(hAPP(c_Product__Type_OPair(_1326850, _1326852), 28371 ^ [_1326850, _1326852, _1326854, _1326856, _1326858, _1326860]), 28372 ^ [_1326850, _1326852, _1326854, _1326856, _1326858, _1326860])), hAPP(_1326858, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1326850, _1326852), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1326850, _1326852), tc_HOL_Obool), _1326858)), hAPP(c_Set_OCollect(tc_prod(_1326850, _1326852)), hAPP(c_Product__Type_Oprod_Oprod__case(_1326850, _1326852, tc_HOL_Obool), _1326860)))))))], (28376 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1326860, 28371 ^ [_1326850, _1326852, _1326854, _1326856, _1326858, _1326860]), 28372 ^ [_1326850, _1326852, _1326854, _1326856, _1326858, _1326860]))]], -(hBOOL(hAPP(hAPP(_1326860, _1326854), _1326856)))], (28406 ^ _779530) ^ [_1327804, _1327806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327804))), 28409 ^ _779530 : [(28410 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327806)), -(c_Divides_Odivmod__int(_1327804, _1327806) = c_Divides_OnegDivAlg(_1327804, _1327806))], (28416 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327806))), -(c_Divides_Odivmod__int(_1327804, _1327806) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327804), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327806))))]]], (28380 ^ _779530) ^ [_1327434, _1327436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327434)), 28383 ^ _779530 : [(28384 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327436)), -(c_Divides_Odivmod__int(_1327434, _1327436) = c_Divides_OposDivAlg(_1327434, _1327436))], (28390 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327436))), 28393 ^ _779530 : [(28394 ^ _779530) ^ [] : [_1327434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1327434, _1327436) = 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)))], (28400 ^ _779530) ^ [] : [-(_1327434 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1327434, _1327436) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327434), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327436))))]]]]], (28422 ^ _779530) ^ [_1328059, _1328061, _1328063, _1328065, _1328067, _1328069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1328059, _1328059)), hAPP(hAPP(c_Product__Type_OPair(_1328059, _1328059), _1328061), _1328063)), hAPP(hAPP(c_Relation_Oinv__image(_1328065, _1328059), _1328067), _1328069))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1328065, _1328065)), hAPP(hAPP(c_Product__Type_OPair(_1328065, _1328065), hAPP(_1328069, _1328061)), hAPP(_1328069, _1328063))), _1328067)))], (28428 ^ _779530) ^ [_1328246, _1328248, _1328250, _1328252, _1328254, _1328256] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1328252, _1328252)), hAPP(hAPP(c_Product__Type_OPair(_1328252, _1328252), hAPP(_1328256, _1328248)), hAPP(_1328256, _1328250))), _1328254)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1328246, _1328246)), hAPP(hAPP(c_Product__Type_OPair(_1328246, _1328246), _1328248), _1328250)), hAPP(hAPP(c_Relation_Oinv__image(_1328252, _1328246), _1328254), _1328256))))], (28434 ^ _779530) ^ [_1328439, _1328441] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1328439), _1328441)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1328439), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1328441)))], (28436 ^ _779530) ^ [_1328482, _1328484, _1328486] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1328482), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1328484)), _1328486)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1328482, _1328484), hAPP(c_Divides_OnegateSnd, _1328486))))], (28442 ^ _779530) ^ [_1328595, _1328597] : [-(_1328595 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1328597, _1328595), c_Divides_Odivmod__int(_1328597, _1328595))))], (28448 ^ _779530) ^ [_1328639, _1328641] : [-(c_Divides_Odivmod__int(_1328639, _1328641) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1328639), _1328641)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328639, _1328641)))], (28450 ^ _779530) ^ [_1328683, _1328685] : [-(c_FunDef_Orp__inv__image(_1328683, _1328685) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))))), tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))), tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)), tc_fun(tc_fun(_1328685, _1328683), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool)), c_COMBS(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)), tc_fun(tc_fun(_1328685, _1328683), tc_fun(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), tc_fun(tc_prod(_1328683, _1328683), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool))), tc_fun(_1328685, _1328683)), c_Product__Type_OPair(tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool), tc_fun(tc_prod(_1328685, _1328685), tc_HOL_Obool)))), c_Relation_Oinv__image(_1328683, _1328685))))), c_Relation_Oinv__image(_1328683, _1328685))))], (28452 ^ _779530) ^ [_1329196, _1329198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329196), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329198), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329196, _1329198) = 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), _1329196), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329198)))))], (28462 ^ _779530) ^ [_1329383, _1329385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329383), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329385), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329383), _1329385) = 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), _1329383), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329385)))))], (28472 ^ _779530) ^ [_1329574, _1329576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329574)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329576), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329574, _1329576) = 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), _1329574), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329576)))))], (28482 ^ _779530) ^ [_1329755, _1329757, _1329759, _1329761] : [hAPP(c_Product__Type_Ofst(_1329755, _1329757), _1329759) = hAPP(c_Product__Type_Ofst(_1329755, _1329757), _1329761), hAPP(c_Product__Type_Osnd(_1329755, _1329757), _1329759) = hAPP(c_Product__Type_Osnd(_1329755, _1329757), _1329761), -(_1329759 = _1329761)], (28492 ^ _779530) ^ [_1329961, _1329963, _1329965, _1329967] : [_1329961 = _1329963, 28495 ^ _779530 : [(28496 ^ _779530) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1329965, _1329967), _1329961) = hAPP(c_Product__Type_Ofst(_1329965, _1329967), _1329963))], (28498 ^ _779530) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1329965, _1329967), _1329961) = hAPP(c_Product__Type_Osnd(_1329965, _1329967), _1329963))]]], (28500 ^ _779530) ^ [_1330112, _1330114, _1330116, _1330118] : [-(_1330112 = _1330114), hAPP(c_Product__Type_Ofst(_1330116, _1330118), _1330112) = hAPP(c_Product__Type_Ofst(_1330116, _1330118), _1330114), hAPP(c_Product__Type_Osnd(_1330116, _1330118), _1330112) = hAPP(c_Product__Type_Osnd(_1330116, _1330118), _1330114)], (28510 ^ _779530) ^ [_1330299, _1330301, _1330303, _1330305, _1330307] : [hAPP(c_Product__Type_Osnd(_1330299, _1330301), hAPP(hAPP(c_Product__Type_OPair(_1330299, _1330301), _1330303), _1330305)) = _1330307, -(_1330305 = _1330307)], (28516 ^ _779530) ^ [_1330412, _1330414, _1330416, _1330418, _1330420] : [hAPP(c_Product__Type_Ofst(_1330412, _1330414), hAPP(hAPP(c_Product__Type_OPair(_1330412, _1330414), _1330416), _1330418)) = _1330420, -(_1330416 = _1330420)], (28522 ^ _779530) ^ [_1330525, _1330527, _1330529] : [-(hAPP(hAPP(c_Product__Type_OPair(_1330525, _1330527), hAPP(c_Product__Type_Ofst(_1330525, _1330527), _1330529)), hAPP(c_Product__Type_Osnd(_1330525, _1330527), _1330529)) = _1330529)], (28524 ^ _779530) ^ [_1330573, _1330575, _1330577, _1330579] : [-(hAPP(c_Product__Type_Osnd(_1330573, _1330575), hAPP(hAPP(c_Product__Type_OPair(_1330573, _1330575), _1330577), _1330579)) = _1330579)], (28526 ^ _779530) ^ [_1330617, _1330619, _1330621, _1330623] : [-(hAPP(c_Product__Type_Ofst(_1330617, _1330619), hAPP(hAPP(c_Product__Type_OPair(_1330617, _1330619), _1330621), _1330623)) = _1330621)], (28528 ^ _779530) ^ [_1330661, _1330663, _1330665] : [-(_1330661 = hAPP(hAPP(c_Product__Type_OPair(_1330663, _1330665), hAPP(c_Product__Type_Ofst(_1330663, _1330665), _1330661)), hAPP(c_Product__Type_Osnd(_1330663, _1330665), _1330661)))], (28530 ^ _779530) ^ [_1330709, _1330711, _1330713, _1330715, _1330717, _1330719, _1330721] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1330709, _1330711, _1330713), hAPP(c_Fun_Ocomp(_1330715, tc_fun(_1330711, _1330713), _1330709, _1330717), _1330719)), _1330721) = hAPP(hAPP(_1330717, hAPP(_1330719, hAPP(c_Product__Type_Ofst(_1330709, _1330711), _1330721))), hAPP(c_Product__Type_Osnd(_1330709, _1330711), _1330721)))], (28532 ^ _779530) ^ [_1330786, _1330788, _1330790, _1330792, _1330794] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1330786, _1330788, _1330790), _1330792), _1330794) = hAPP(hAPP(_1330792, hAPP(c_Product__Type_Ofst(_1330786, _1330788), _1330794)), hAPP(c_Product__Type_Osnd(_1330786, _1330788), _1330794)))], (28534 ^ _779530) ^ [_1330845, _1330847, _1330849, _1330851, _1330853] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1330845, _1330847, _1330849), _1330851), _1330853) = hAPP(hAPP(_1330851, hAPP(c_Product__Type_Ofst(_1330845, _1330847), _1330853)), hAPP(c_Product__Type_Osnd(_1330845, _1330847), _1330853)))], (28536 ^ _779530) ^ [_1330904, _1330906, _1330908, _1330910, _1330912, _1330914] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1330904, _1330906), _1330906, _1330908), hAPP(hAPP(c_COMBB(_1330910, tc_fun(_1330906, _1330908), tc_prod(_1330904, _1330906)), _1330912), hAPP(hAPP(c_COMBB(_1330904, _1330910, tc_prod(_1330904, _1330906)), _1330914), c_Product__Type_Ofst(_1330904, _1330906)))), c_Product__Type_Osnd(_1330904, _1330906)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1330904, _1330906, _1330908), hAPP(hAPP(c_COMBB(_1330910, tc_fun(_1330906, _1330908), _1330904), _1330912), _1330914)))], (28538 ^ _779530) ^ [_1331005, _1331007, _1331009, _1331011, _1331013] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1331005, _1331007, _1331009), _1331011), _1331013) = hAPP(hAPP(_1331011, hAPP(c_Product__Type_Ofst(_1331005, _1331007), _1331013)), hAPP(c_Product__Type_Osnd(_1331005, _1331007), _1331013)))], (28540 ^ _779530) ^ [_1331064, _1331066, _1331068] : [-(c_HOL_OThe(tc_prod(_1331064, _1331066), hAPP(c_Product__Type_Oprod_Oprod__case(_1331064, _1331066, tc_HOL_Obool), _1331068)) = c_HOL_OThe(tc_prod(_1331064, _1331066), hAPP(hAPP(c_COMBS(tc_prod(_1331064, _1331066), _1331066, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1331064, tc_fun(_1331066, tc_HOL_Obool), tc_prod(_1331064, _1331066)), _1331068), c_Product__Type_Ofst(_1331064, _1331066))), c_Product__Type_Osnd(_1331064, _1331066))))], (28542 ^ _779530) ^ [_1331145, _1331147, _1331149] : [-(hAPP(c_Product__Type_Ofst(_1331145, _1331147), _1331149) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1331145, _1331147, _1331145), c_COMBK(_1331145, _1331147)), _1331149))], (28544 ^ _779530) ^ [_1331191, _1331193, _1331195] : [-(hAPP(c_Product__Type_Osnd(_1331191, _1331193), _1331195) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1331191, _1331193, _1331193), hAPP(c_COMBK(tc_fun(_1331193, _1331193), _1331191), c_COMBI(_1331193))), _1331195))], (28546 ^ _779530) ^ [_1331245, _1331247] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331245), _1331247) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1331245, _1331247)))], (28548 ^ _779530) ^ [_1331282, _1331284] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331282, _1331284) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1331282, _1331284)))], (28550 ^ _779530) ^ [_1331317, _1331319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331317), 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)), _1331319)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331317), _1331319) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1331317, _1331319)))], (28560 ^ _779530) ^ [_1331484, _1331486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331484), 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)), _1331486)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331484, _1331486) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1331484, _1331486)))], (28570 ^ _779530) ^ [_1331647, _1331649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331649)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331647), _1331649) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1331647, _1331649)))], (28580 ^ _779530) ^ [_1331808, _1331810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331810)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331808, _1331810) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1331808, _1331810)))], (28590 ^ _779530) ^ [_1331965, _1331967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331967), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1331965), _1331967) = 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), _1331965), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1331967)))))], (28600 ^ _779530) ^ [_1332150, _1332152, _1332154, _1332156, _1332158] : [-(c_Product__Type_Oprod_Oprod__size(_1332150, _1332152, _1332154, _1332156, _1332158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1332154, hAPP(c_Product__Type_Ofst(_1332150, _1332152), _1332158))), hAPP(_1332156, hAPP(c_Product__Type_Osnd(_1332150, _1332152), _1332158)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (28602 ^ _779530) ^ [_1332217, _1332219, _1332221, _1332223, _1332225, _1332227] : [hBOOL(hAPP(_1332217, _1332219)), hBOOL(hAPP(_1332221, _1332223)), 28609 ^ _779530 : [(28610 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1332217, hAPP(c_Product__Type_Ofst(_1332225, _1332227), hAPP(hAPP(c_Product__Type_OPair(_1332225, _1332227), _1332219), _1332223)))))], (28612 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1332221, hAPP(c_Product__Type_Osnd(_1332225, _1332227), hAPP(hAPP(c_Product__Type_OPair(_1332225, _1332227), _1332219), _1332223)))))]]], (28614 ^ _779530) ^ [_1332464, _1332466, _1332468, _1332470, _1332472] : [hBOOL(hAPP(hAPP(_1332464, _1332466), _1332468)), -(hBOOL(hAPP(hAPP(_1332464, hAPP(c_Product__Type_Osnd(_1332470, _1332472), hAPP(hAPP(c_Product__Type_OPair(_1332470, _1332472), _1332468), _1332466))), hAPP(c_Product__Type_Ofst(_1332470, _1332472), hAPP(hAPP(c_Product__Type_OPair(_1332470, _1332472), _1332468), _1332466)))))], (28620 ^ _779530) ^ [_1332627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1332627)), 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), _1332627)) = 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), _1332627))))))], (28626 ^ _779530) ^ [_1332760, _1332762] : [class_Int_Onumber__ring(_1332760), 28629 ^ _779530 : [(28630 ^ _779530) ^ [] : [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), _1332762))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1332760), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332762)) = hAPP(c_Int_Onumber__class_Onumber__of(_1332760), _1332762))], (28636 ^ _779530) ^ [] : [-(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), _1332762)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1332760), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332762)) = c_Groups_Ozero__class_Ozero(_1332760))]]], (28642 ^ _779530) ^ [_1333000] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333000)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333000)))], (28644 ^ _779530) ^ [_1333035, _1333037] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333037)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333035), _1333037)))], (28646 ^ _779530) ^ [_1333081] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333081) = _1333081)], (28648 ^ _779530) ^ [_1333107, _1333109, _1333111] : [class_Int_Onumber(_1333107), 28651 ^ _779530 : [(28652 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1333107), _1333109) = _1333111, -(_1333111 = hAPP(c_Int_Onumber__class_Onumber__of(_1333107), _1333109))], (28658 ^ _779530) ^ [] : [_1333111 = hAPP(c_Int_Onumber__class_Onumber__of(_1333107), _1333109), -(hAPP(c_Int_Onumber__class_Onumber__of(_1333107), _1333109) = _1333111)]]], (28664 ^ _779530) ^ [_1333348, _1333350, _1333352] : [class_Int_Onumber__ring(_1333348), class_Int_Oring__char__0(_1333348), 28671 ^ _779530 : [(28672 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1333348), _1333350) = hAPP(c_Int_Onumber__class_Onumber__of(_1333348), _1333352), -(_1333350 = _1333352)], (28678 ^ _779530) ^ [] : [_1333350 = _1333352, -(hAPP(c_Int_Onumber__class_Onumber__of(_1333348), _1333350) = hAPP(c_Int_Onumber__class_Onumber__of(_1333348), _1333352))]]], (28684 ^ _779530) ^ [_1333643, _1333645] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333643)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333645)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333643), _1333645)))], (28686 ^ _779530) ^ [_1333704, _1333706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333704)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333704), _1333706)))], (28692 ^ _779530) ^ [_1333809, _1333811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1333809), _1333811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333809)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333811))))], (28698 ^ _779530) ^ [_1333935, _1333937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333935)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1333937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1333935), _1333937)))], (28704 ^ _779530) ^ [_1334040, _1334042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334040), _1334042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1334040)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1334042))))], (28710 ^ _779530) ^ [_1334151, _1334153, _1334155] : [class_Int_Onumber(_1334151), class_Orderings_Olinorder(_1334151), 28717 ^ _779530 : [(28718 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334151), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334153)), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334155))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334151), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334155)), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334153)))], (28724 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334151), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334155)), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334153)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334151), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334153)), hAPP(c_Int_Onumber__class_Onumber__of(_1334151), _1334155))))]]], (28730 ^ _779530) ^ [_1334478, _1334480, _1334482, _1334484] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334478), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334478), _1334480), _1334482)), hAPP(c_Int_Onumber__class_Onumber__of(_1334478), _1334484)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334478), _1334480), hAPP(c_Int_Onumber__class_Onumber__of(_1334478), _1334484))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334478), _1334482), hAPP(c_Int_Onumber__class_Onumber__of(_1334478), _1334484)))), class_Int_Onumber(_1334478), class_Rings_Osemiring(_1334478)], (28740 ^ _779530) ^ [_1334721, _1334723, _1334725, _1334727] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334721), hAPP(c_Int_Onumber__class_Onumber__of(_1334721), _1334723)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334721), _1334725), _1334727)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1334721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334721), hAPP(c_Int_Onumber__class_Onumber__of(_1334721), _1334723)), _1334725)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334721), hAPP(c_Int_Onumber__class_Onumber__of(_1334721), _1334723)), _1334727))), class_Int_Onumber(_1334721), class_Rings_Osemiring(_1334721)], (28750 ^ _779530) ^ [_1334964, _1334966, _1334968, _1334970] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334964), _1334966), _1334968)), hAPP(c_Int_Onumber__class_Onumber__of(_1334964), _1334970)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1334964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334964), _1334966), hAPP(c_Int_Onumber__class_Onumber__of(_1334964), _1334970))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1334964), _1334968), hAPP(c_Int_Onumber__class_Onumber__of(_1334964), _1334970)))), class_Int_Onumber(_1334964), class_Rings_Oring(_1334964)], (28760 ^ _779530) ^ [_1335207, _1335209, _1335211, _1335213] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335207), hAPP(c_Int_Onumber__class_Onumber__of(_1335207), _1335209)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1335207), _1335211), _1335213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1335207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335207), hAPP(c_Int_Onumber__class_Onumber__of(_1335207), _1335209)), _1335211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335207), hAPP(c_Int_Onumber__class_Onumber__of(_1335207), _1335209)), _1335213))), class_Int_Onumber(_1335207), class_Rings_Oring(_1335207)], (28770 ^ _779530) ^ [_1335450, _1335452, _1335454] : [class_Int_Onumber__ring(_1335450), class_Rings_Olinordered__idom(_1335450), 28777 ^ _779530 : [(28778 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335450), hAPP(c_Int_Onumber__class_Onumber__of(_1335450), _1335452)), hAPP(c_Int_Onumber__class_Onumber__of(_1335450), _1335454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335452), _1335454)))], (28784 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335452), _1335454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335450), hAPP(c_Int_Onumber__class_Onumber__of(_1335450), _1335452)), hAPP(c_Int_Onumber__class_Onumber__of(_1335450), _1335454))))]]], (28790 ^ _779530) ^ [_1335781, _1335783, _1335785] : [class_Int_Onumber__ring(_1335781), class_Rings_Olinordered__idom(_1335781), 28797 ^ _779530 : [(28798 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335781), hAPP(c_Int_Onumber__class_Onumber__of(_1335781), _1335783)), hAPP(c_Int_Onumber__class_Onumber__of(_1335781), _1335785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335783), _1335785)))], (28804 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335783), _1335785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335781), hAPP(c_Int_Onumber__class_Onumber__of(_1335781), _1335783)), hAPP(c_Int_Onumber__class_Onumber__of(_1335781), _1335785))))]]], (28810 ^ _779530) ^ [_1336112, _1336114, _1336116] : [class_Int_Onumber(_1336112), class_Orderings_Oord(_1336112), 28817 ^ _779530 : [(28818 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336112), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336114)), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336116))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336112), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336114)), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336116)) = hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336114))], (28824 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336112), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336114)), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336116)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1336112), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336114)), hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336116)) = hAPP(c_Int_Onumber__class_Onumber__of(_1336112), _1336116))]]], (28830 ^ _779530) ^ [_1336504, _1336506, _1336508] : [class_Int_Onumber(_1336504), class_Orderings_Oord(_1336504), 28837 ^ _779530 : [(28838 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336504), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336506)), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336508))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336504), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336506)), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336508)) = hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336508))], (28844 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1336504), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336506)), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336508)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1336504), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336506)), hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336508)) = hAPP(c_Int_Onumber__class_Onumber__of(_1336504), _1336506))]]], (28850 ^ _779530) ^ [_1336896, _1336898, _1336900, _1336902] : [class_Int_Onumber__ring(_1336896), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336896), hAPP(c_Int_Onumber__class_Onumber__of(_1336896), _1336898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336896), hAPP(c_Int_Onumber__class_Onumber__of(_1336896), _1336900)), _1336902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1336896), hAPP(c_Int_Onumber__class_Onumber__of(_1336896), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1336898), _1336900))), _1336902))], (28856 ^ _779530) ^ [_1337065, _1337067, _1337069] : [class_Int_Onumber__ring(_1337065), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337065), hAPP(c_Int_Onumber__class_Onumber__of(_1337065), _1337067)), hAPP(c_Int_Onumber__class_Onumber__of(_1337065), _1337069)) = hAPP(c_Int_Onumber__class_Onumber__of(_1337065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337067), _1337069)))], (28862 ^ _779530) ^ [_1337200, _1337202, _1337204] : [class_Int_Onumber__ring(_1337200), -(hAPP(c_Int_Onumber__class_Onumber__of(_1337200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337202), _1337204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1337200), hAPP(c_Int_Onumber__class_Onumber__of(_1337200), _1337202)), hAPP(c_Int_Onumber__class_Onumber__of(_1337200), _1337204)))], (28868 ^ _779530) ^ [_1337335, _1337337, _1337339, _1337341] : [class_Int_Onumber__ring(_1337335), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337335), hAPP(c_Int_Onumber__class_Onumber__of(_1337335), _1337337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337335), hAPP(c_Int_Onumber__class_Onumber__of(_1337335), _1337339)), _1337341)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337335), hAPP(c_Int_Onumber__class_Onumber__of(_1337335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337337), _1337339))), _1337341))], (28874 ^ _779530) ^ [_1337504, _1337506, _1337508] : [class_Int_Onumber__ring(_1337504), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337504), hAPP(c_Int_Onumber__class_Onumber__of(_1337504), _1337506)), hAPP(c_Int_Onumber__class_Onumber__of(_1337504), _1337508)) = hAPP(c_Int_Onumber__class_Onumber__of(_1337504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337506), _1337508)))], (28880 ^ _779530) ^ [_1337639, _1337641, _1337643] : [class_Int_Onumber__ring(_1337639), -(hAPP(c_Int_Onumber__class_Onumber__of(_1337639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1337641), _1337643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337639), hAPP(c_Int_Onumber__class_Onumber__of(_1337639), _1337641)), hAPP(c_Int_Onumber__class_Onumber__of(_1337639), _1337643)))], (28886 ^ _779530) ^ [_1337774, _1337776, _1337778] : [class_Int_Onumber__ring(_1337774), -(hAPP(c_Int_Onumber__class_Onumber__of(_1337774), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337776), _1337778)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1337774), hAPP(c_Int_Onumber__class_Onumber__of(_1337774), _1337776)), hAPP(c_Int_Onumber__class_Onumber__of(_1337774), _1337778)))], (28892 ^ _779530) ^ [_1337909, _1337911] : [class_Int_Onumber__ring(_1337909), -(hAPP(c_Int_Onumber__class_Onumber__of(_1337909), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1337911)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1337909), hAPP(c_Int_Onumber__class_Onumber__of(_1337909), _1337911)))], (28898 ^ _779530) ^ [_1338020, _1338022] : [class_Int_Onumber__ring(_1338020), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1338020), hAPP(c_Int_Onumber__class_Onumber__of(_1338020), _1338022)) = hAPP(c_Int_Onumber__class_Onumber__of(_1338020), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1338022)))], (28904 ^ _779530) ^ [_1338131, _1338133] : [class_Int_Onumber__ring(_1338131), -(hBOOL(hAPP(hAPP(c_member(_1338131), hAPP(c_Int_Onumber__class_Onumber__of(_1338131), _1338133)), c_Int_Oring__1__class_OInts(_1338131))))], (28910 ^ _779530) ^ [_1338234, _1338236] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338234), _1338236) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1338234, _1338236)))], (28912 ^ _779530) ^ [_1338271, _1338273] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338271, _1338273) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1338271, _1338273)))], (28914 ^ _779530) ^ [_1338306, _1338308, _1338310, _1338312] : [class_Int_Onumber__ring(_1338306), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1338306), hAPP(c_Int_Onumber__class_Onumber__of(_1338306), _1338308)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1338306), hAPP(c_Int_Onumber__class_Onumber__of(_1338306), _1338310)), _1338312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1338306), hAPP(c_Int_Onumber__class_Onumber__of(_1338306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338308), _1338310))), _1338312))], (28920 ^ _779530) ^ [_1338475, _1338477, _1338479] : [class_Int_Onumber__ring(_1338475), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338475), hAPP(c_Groups_Ouminus__class_Ouminus(_1338475), hAPP(c_Int_Onumber__class_Onumber__of(_1338475), _1338477))), _1338479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338475), hAPP(c_Int_Onumber__class_Onumber__of(_1338475), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1338477))), _1338479))], (28926 ^ _779530) ^ [_1338620, _1338622, _1338624] : [class_Int_Onumber__ring(_1338620), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1338620), hAPP(c_Int_Onumber__class_Onumber__of(_1338620), _1338622)), hAPP(c_Int_Onumber__class_Onumber__of(_1338620), _1338624)) = hAPP(c_Int_Onumber__class_Onumber__of(_1338620), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338622), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1338624))))], (28964 ^ _779530) ^ [_1339315, _1339317, _1339319] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1339315, _1339317), _1339319))), _1339315 = 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), _1339319)), _1339317)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1339319)), 28971 ^ _779530 : [(28972 ^ _779530) ^ [] : [-(_1339317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28974 ^ _779530) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1339319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 28975 ^ _779530 : [(28976 ^ _779530) ^ [] : [_1339317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (28978 ^ _779530) ^ [] : [28979 ^ _779530 : [(28980 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1339317)))], (28982 ^ _779530) ^ [] : [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), _1339319))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1339319)), _1339317))]], 28987 ^ _779530 : [(28988 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1339317))], (28990 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1339317), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1339319))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1339319)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (28932 ^ _779530) ^ [_1338779, _1338781, _1338783] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1338779, _1338781), _1338783)), 28935 ^ _779530 : [(28936 ^ _779530) ^ [] : [-(_1338779 = 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), _1338783)), _1338781)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1338783)))], (28938 ^ _779530) ^ [] : [_1338781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1338783) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28944 ^ _779530) ^ [] : [-(_1338781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28947 ^ _779530 : [(28948 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338781)), 28951 ^ _779530 : [(28952 ^ _779530) ^ [] : [-(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), _1338783))))], (28954 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1338783)), _1338781)))]]], (28956 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338781))), 28959 ^ _779530 : [(28960 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1338781), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1338783))))], (28962 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1338783)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (28998 ^ _779530) ^ [_1339924, _1339926] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1339924)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1339926)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1339924), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339926))))], (29000 ^ _779530) ^ [_1339973, _1339975, _1339977, _1339979] : [class_Int_Onumber__ring(_1339973), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1339973), hAPP(c_Int_Onumber__class_Onumber__of(_1339973), _1339975)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1339973), _1339977), hAPP(c_Int_Onumber__class_Onumber__of(_1339973), _1339979))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1339973), hAPP(c_Int_Onumber__class_Onumber__of(_1339973), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1339975), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1339979)))), _1339977))], (29006 ^ _779530) ^ [_1340148] : [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), _1340148))), -(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), _1340148)) = 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), _1340148))))], (29012 ^ _779530) ^ [_1340265] : [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), _1340265))), -(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), _1340265)) = 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), _1340265))))], (29018 ^ _779530) ^ [_1340380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1340380)), 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), _1340380)) = 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), _1340380))))))], (29024 ^ _779530) ^ [_1340515, _1340517, _1340519] : [class_Int_Onumber__ring(_1340515), 29027 ^ _779530 : [(29028 ^ _779530) ^ [] : [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), _1340517))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1340515), hAPP(c_Int_Onumber__class_Onumber__of(_1340515), _1340519)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1340517))) = hAPP(hAPP(c_HOL_OLet(_1340515, _1340515), hAPP(hAPP(c_Power_Opower__class_Opower(_1340515), hAPP(c_Int_Onumber__class_Onumber__of(_1340515), _1340519)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1340517))), hAPP(hAPP(c_COMBS(_1340515, _1340515, _1340515), hAPP(hAPP(c_COMBB(_1340515, tc_fun(_1340515, _1340515), _1340515), c_Groups_Otimes__class_Otimes(_1340515)), hAPP(c_Groups_Otimes__class_Otimes(_1340515), hAPP(c_Int_Onumber__class_Onumber__of(_1340515), _1340519)))), c_COMBI(_1340515))))], (29034 ^ _779530) ^ [] : [-(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), _1340517)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1340515), hAPP(c_Int_Onumber__class_Onumber__of(_1340515), _1340519)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1340517))) = c_Groups_Oone__class_Oone(_1340515))]]], (29040 ^ _779530) ^ [_1340913, _1340915, _1340917] : [class_Orderings_Olinorder(_1340913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340913), _1340915), _1340917)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340913, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1340913, _1340915, _1340917)), hAPP(hAPP(c_Set_Oinsert(_1340913), _1340917), c_Orderings_Obot__class_Obot(tc_fun(_1340913, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1340913, _1340915, _1340917))], (29050 ^ _779530) ^ [_1341122, _1341124, _1341126, _1341128, _1341130, _1341132] : [class_Groups_Ocomm__monoid__mult(_1341122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341124), _1341126)), 29057 ^ _779530 : [(29058 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1341124), _1341128), _1341126)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341124, _1341122), hAPP(hAPP(c_COMBC(_1341124, _1341122, _1341122), hAPP(hAPP(c_COMBS(_1341124, _1341122, tc_fun(_1341122, _1341122)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1341122, tc_fun(_1341122, _1341122)), _1341124), c_If(_1341122)), hAPP(hAPP(c_COMBC(_1341124, _1341124, tc_HOL_Obool), c_fequal), _1341128))), _1341130)), _1341132)), _1341126) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341122), hAPP(_1341130, _1341128)), hAPP(hAPP(c_Power_Opower__class_Opower(_1341122), _1341132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1341124), _1341126)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (29064 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341124), _1341128), _1341126))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341124, _1341122), hAPP(hAPP(c_COMBC(_1341124, _1341122, _1341122), hAPP(hAPP(c_COMBS(_1341124, _1341122, tc_fun(_1341122, _1341122)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1341122, tc_fun(_1341122, _1341122)), _1341124), c_If(_1341122)), hAPP(hAPP(c_COMBC(_1341124, _1341124, tc_HOL_Obool), c_fequal), _1341128))), _1341130)), _1341132)), _1341126) = hAPP(hAPP(c_Power_Opower__class_Opower(_1341122), _1341132), hAPP(c_Finite__Set_Ocard(_1341124), _1341126)))]]], (29070 ^ _779530) ^ [_1341734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341734)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1341734) = 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, _1341734))))], (29076 ^ _779530) ^ [_1341837, _1341839] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1341837, _1341839))))], (29078 ^ _779530) ^ [_1341868, _1341870] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1341868, _1341870))))], (29080 ^ _779530) ^ [_1341899] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1341899) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1341899)))], (29082 ^ _779530) ^ [_1341931] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1341931)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1341931))], (29084 ^ _779530) ^ [_1341963, _1341965] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1341963, _1341965)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1341965), _1341963)))], (29086 ^ _779530) ^ [_1342019, _1342021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1342019)), c_Int_OBit1(_1342021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342019), _1342021)))], (29092 ^ _779530) ^ [_1342120, _1342122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342120), _1342122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1342120)), c_Int_OBit1(_1342122))))], (29098 ^ _779530) ^ [_1342242, _1342244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1342242)), c_Int_OBit1(_1342244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342242), _1342244)))], (29104 ^ _779530) ^ [_1342343, _1342345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1342343), _1342345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1342343)), c_Int_OBit1(_1342345))))], (29110 ^ _779530) ^ [_1342465, _1342467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1342465)), c_Int_OBit1(_1342467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342465), _1342467)))], (29116 ^ _779530) ^ [_1342566, _1342568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342566), _1342568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1342566)), c_Int_OBit1(_1342568))))], (29122 ^ _779530) ^ [_1342688, _1342690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1342688)), c_Int_OBit1(_1342690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342688), _1342690)))], (29128 ^ _779530) ^ [_1342789, _1342791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342789), _1342791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1342789)), c_Int_OBit1(_1342791))))], (29134 ^ _779530) ^ [_1342896] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1342896)) = _1342896)], (29136 ^ _779530) ^ [_1342940, _1342942] : [c_Int_OBit1(_1342940) = c_Int_OBit1(_1342942), -(_1342940 = _1342942)], (29142 ^ _779530) ^ [_1343021, _1343023] : [_1343021 = _1343023, -(c_Int_OBit1(_1343021) = c_Int_OBit1(_1343023))], (29148 ^ _779530) ^ [_1343108, _1343110, _1343112, _1343114, _1343116] : [class_Groups_Ocomm__monoid__mult(_1343108), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343110, _1343108), hAPP(hAPP(c_COMBS(_1343110, _1343108, _1343108), hAPP(hAPP(c_COMBB(_1343108, tc_fun(_1343108, _1343108), _1343110), c_Groups_Otimes__class_Otimes(_1343108)), _1343112)), _1343114)), _1343116) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343108), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343110, _1343108), _1343112), _1343116)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343110, _1343108), _1343114), _1343116)))], (29154 ^ _779530) ^ [_1343309, _1343311, _1343313] : [class_Groups_Ocomm__monoid__mult(_1343309), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343311, _1343309), hAPP(c_COMBK(_1343309, _1343311), c_Groups_Oone__class_Oone(_1343309))), _1343313) = c_Groups_Oone__class_Oone(_1343309))], (29160 ^ _779530) ^ [_1343424, _1343426, _1343428] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343424, tc_Nat_Onat), _1343426), _1343428) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343424, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1343424), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1343426)), _1343428)))], (29162 ^ _779530) ^ [_1343482, _1343484, _1343486, _1343488] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1343482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343484, tc_Nat_Onat), _1343486), _1343488)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343484, _1343482), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1343482, _1343484), c_Nat_Osemiring__1__class_Oof__nat(_1343482)), _1343486)), _1343488)), class_Groups_Ocomm__monoid__mult(_1343482), class_Rings_Osemiring__1(_1343482)], (29172 ^ _779530) ^ [_1343685, _1343687, _1343689] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343685, tc_Nat_Onat), _1343687), _1343689)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343685, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1343685), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1343687)), _1343689))], (29174 ^ _779530) ^ [_1343743, _1343745, _1343747] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1343743), _1343745), _1343747) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1343743), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1343743, tc_Int_Oint), _1343745), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1343747))), class_Groups_Ocomm__monoid__add(_1343743), class_Groups_Ocomm__monoid__mult(_1343743)], (29184 ^ _779530) ^ [_1343934, _1343936, _1343938, _1343940] : [class_Rings_Ocomm__semiring__1(_1343934), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343936), _1343938)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343936, _1343934), _1343940), _1343938) = c_Groups_Ozero__class_Ozero(_1343934)), 29193 ^ _779530 : [(29194 ^ _779530) ^ [_1344115] : [hBOOL(hAPP(hAPP(c_member(_1343936), _1344115), _1343938)), hAPP(_1343940, _1344115) = c_Groups_Ozero__class_Ozero(_1343934)]]], (29202 ^ _779530) ^ [_1344264, _1344266, _1344268, _1344270] : [class_Rings_Ocomm__semiring__1(_1344264), class_Rings_Ono__zero__divisors(_1344264), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344266), _1344268)), 29213 ^ _779530 : [(29214 ^ _779530) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344266, _1344264), _1344270), _1344268) = c_Groups_Ozero__class_Ozero(_1344264), 29218 ^ _779530 : [(29219 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344266), 29217 ^ [_1344264, _1344266, _1344268, _1344270]), _1344268)))], (29221 ^ _779530) ^ [] : [-(hAPP(_1344270, 29217 ^ [_1344264, _1344266, _1344268, _1344270]) = c_Groups_Ozero__class_Ozero(_1344264))]]], (29223 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344266, _1344264), _1344270), _1344268) = c_Groups_Ozero__class_Ozero(_1344264)), 29224 ^ _779530 : [(29225 ^ _779530) ^ [_1344642] : [hBOOL(hAPP(hAPP(c_member(_1344266), _1344642), _1344268)), hAPP(_1344270, _1344642) = c_Groups_Ozero__class_Ozero(_1344264)]]]]], (29233 ^ _779530) ^ [_1344797, _1344799, _1344801] : [class_Groups_Ocomm__monoid__mult(_1344797), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344799, _1344797), _1344801), c_Orderings_Obot__class_Obot(tc_fun(_1344799, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1344797))], (29239 ^ _779530) ^ [_1344906, _1344908, _1344910] : [class_Groups_Ocomm__monoid__mult(_1344906), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1344908, _1344906), _1344910), c_Orderings_Obot__class_Obot(tc_fun(_1344908, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1344906))], (29245 ^ _779530) ^ [_1345015, _1345017, _1345019, _1345021] : [class_Groups_Ocomm__monoid__mult(_1345015), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345017), _1345019))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345017, _1345015), _1345021), _1345019) = c_Groups_Oone__class_Oone(_1345015))], (29255 ^ _779530) ^ [_1345139, _1345141, _1345143, _1345145] : [class_Groups_Ocomm__monoid__mult(_1345139), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345141), _1345143))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345141, _1345139), _1345145), _1345143) = c_Groups_Oone__class_Oone(_1345139))], (29265 ^ _779530) ^ [_1345263, _1345265, _1345267] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345263), _1345265)), 29268 ^ _779530 : [(29279 ^ _779530) ^ [] : [29281 ^ _779530 : [(29282 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345263), 29280 ^ [_1345263, _1345265, _1345267]), _1345265)))], (29284 ^ _779530) ^ [] : [hAPP(_1345267, 29280 ^ [_1345263, _1345265, _1345267]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345263, tc_Nat_Onat), _1345267), _1345265) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29269 ^ _779530) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1345263, tc_Nat_Onat), _1345267), _1345265) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 29272 ^ _779530 : [(29273 ^ _779530) ^ [_1345425] : [hBOOL(hAPP(hAPP(c_member(_1345263), _1345425), _1345265)), -(hAPP(_1345267, _1345425) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (29288 ^ _779530) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29290 ^ _779530) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29292 ^ _779530) ^ [_1345731] : [29293 ^ _779530 : [(29294 ^ _779530) ^ [_1345788] : [hBOOL(hAPP(_1345731, _1345788))]], 29296 ^ _779530 : [(29297 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29295 ^ [_1345731])))], (29299 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1345731, hAPP(c_Int_Onat, 29295 ^ [_1345731]))))]]], (29301 ^ _779530) ^ [_1345874] : [-(hBOOL(hAPP(_1345874, 29308 ^ [_1345874]))), 29302 ^ _779530 : [(29303 ^ _779530) ^ [_1345926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1345926)), hBOOL(hAPP(_1345874, hAPP(c_Int_Onat, _1345926)))]]], (29323 ^ _779530) ^ [_1346250] : [29325 ^ _779530 : [(29326 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29324 ^ [_1346250])))], (29328 ^ _779530) ^ [] : [hBOOL(hAPP(_1346250, hAPP(c_Int_Onat, 29324 ^ [_1346250])))]], 29329 ^ _779530 : [(29330 ^ _779530) ^ [_1346383] : [-(hBOOL(hAPP(_1346250, _1346383)))]]], (29312 ^ _779530) ^ [_1346065] : [hBOOL(hAPP(_1346065, 29313 ^ [_1346065])), 29316 ^ _779530 : [(29317 ^ _779530) ^ [_1346159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346159)), -(hBOOL(hAPP(_1346065, hAPP(c_Int_Onat, _1346159))))]]], (29332 ^ _779530) ^ [_1346416, _1346418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346418)), 29339 ^ _779530 : [(29340 ^ _779530) ^ [] : [hAPP(c_Int_Onat, _1346416) = hAPP(c_Int_Onat, _1346418), -(_1346416 = _1346418)], (29346 ^ _779530) ^ [] : [_1346416 = _1346418, -(hAPP(c_Int_Onat, _1346416) = hAPP(c_Int_Onat, _1346418))]]], (29352 ^ _779530) ^ [_1346701, _1346703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1346703)), 29359 ^ _779530 : [(29360 ^ _779530) ^ [] : [hAPP(c_Int_Onat, _1346701) = hAPP(c_Int_Onat, _1346703), -(_1346701 = _1346703)], (29366 ^ _779530) ^ [] : [_1346701 = _1346703, -(hAPP(c_Int_Onat, _1346701) = hAPP(c_Int_Onat, _1346703))]]], (29372 ^ _779530) ^ [_1346998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1346998)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1346998), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29378 ^ _779530) ^ [_1347093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1347093), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1347093)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29384 ^ _779530) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29386 ^ _779530) ^ [_1347212] : [-(c_Int_OBit1(_1347212) = 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)), _1347212)), _1347212))], (29388 ^ _779530) ^ [_1347246, _1347248, _1347250, _1347252, _1347254] : [class_Groups_Ocomm__monoid__mult(_1347246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347248), _1347250)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347248, _1347246), hAPP(hAPP(c_COMBS(_1347248, _1347246, _1347246), hAPP(hAPP(c_COMBB(_1347246, tc_fun(_1347246, _1347246), _1347248), c_Groups_Otimes__class_Otimes(_1347246)), _1347252)), _1347254)), _1347250) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347246), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347248, _1347246), _1347252), _1347250)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347248, _1347246), _1347254), _1347250)))], (29398 ^ _779530) ^ [_1347513, _1347515] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1347513), _1347515) = 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)), _1347513)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1347515))))], (29400 ^ _779530) ^ [_1347559] : [-(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)), _1347559)) = _1347559)], (29402 ^ _779530) ^ [_1347588, _1347590, _1347592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1347588), _1347590)), 29405 ^ _779530 : [(29416 ^ _779530) ^ [] : [29418 ^ _779530 : [(29419 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347588), 29417 ^ [_1347588, _1347590, _1347592]), _1347590)))], (29421 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1347592, 29417 ^ [_1347588, _1347590, _1347592])))]], -(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(_1347588, tc_Nat_Onat), _1347592), _1347590))))], (29406 ^ _779530) ^ [] : [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(_1347588, tc_Nat_Onat), _1347592), _1347590))), 29409 ^ _779530 : [(29410 ^ _779530) ^ [_1347756] : [hBOOL(hAPP(hAPP(c_member(_1347588), _1347756), _1347590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1347592, _1347756))))]]]]], (29425 ^ _779530) ^ [_1348024, _1348026, _1348028] : [class_Orderings_Oorder(_1348024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348024), _1348026), _1348028)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1348024, _1348028, _1348026) = c_Orderings_Obot__class_Obot(tc_fun(_1348024, tc_HOL_Obool)))], (29435 ^ _779530) ^ [_1348187, _1348189, _1348191, _1348193, _1348195, _1348197] : [class_Groups_Ocomm__monoid__mult(_1348187), c_Fun_Oinj__on(_1348189, _1348191, _1348193, _1348195), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1348191, _1348187), _1348197), hAPP(c_Set_Oimage(_1348189, _1348191, _1348193), _1348195)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1348189, _1348187), hAPP(c_Fun_Ocomp(_1348191, _1348187, _1348189, _1348197), _1348193)), _1348195))], (29445 ^ _779530) ^ [_1348400, _1348402, _1348404, _1348406, _1348408, _1348410, _1348412, _1348414] : [class_Groups_Ocomm__monoid__mult(_1348400), c_Fun_Oinj__on(_1348402, _1348404, _1348406, _1348408), _1348410 = hAPP(c_Set_Oimage(_1348402, _1348404, _1348406), _1348408), _1348412 = hAPP(c_Fun_Ocomp(_1348404, _1348400, _1348402, _1348414), _1348406), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1348404, _1348400), _1348414), _1348410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1348402, _1348400), _1348412), _1348408))], (29463 ^ _779530) ^ [_1348749, _1348751, _1348753] : [class_Orderings_Oorder(_1348749), 29466 ^ _779530 : [(29467 ^ _779530) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1348749, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1348749, _1348751, _1348753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348749), _1348751), _1348753))], (29473 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348749), _1348751), _1348753))), -(c_Orderings_Obot__class_Obot(tc_fun(_1348749, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1348749, _1348751, _1348753))]]], (29479 ^ _779530) ^ [_1348968, _1348970, _1348972] : [class_Orderings_Oorder(_1348968), 29482 ^ _779530 : [(29483 ^ _779530) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1348968, _1348970, _1348972) = c_Orderings_Obot__class_Obot(tc_fun(_1348968, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348968), _1348970), _1348972))], (29489 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348968), _1348970), _1348972))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1348968, _1348970, _1348972) = c_Orderings_Obot__class_Obot(tc_fun(_1348968, tc_HOL_Obool)))]]], (29495 ^ _779530) ^ [_1349187, _1349189, _1349191, _1349193] : [class_Orderings_Olinorder(_1349187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349187), _1349189), _1349191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349187), _1349191), _1349193)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1349187, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349187, _1349189, _1349191)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349187, _1349191, _1349193)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1349187, _1349189, _1349193))], (29509 ^ _779530) ^ [] : [-(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))))], (29511 ^ _779530) ^ [_1349470, _1349472, _1349474, _1349476] : [class_Orderings_Oorder(_1349470), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349470, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349470, _1349472, _1349474)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1349470, _1349474, _1349476)) = c_Orderings_Obot__class_Obot(tc_fun(_1349470, tc_HOL_Obool)))], (29517 ^ _779530) ^ [_1349597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1349597), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1349597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29523 ^ _779530) ^ [_1349700] : [hAPP(c_Int_Onat, _1349700) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1349700), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29529 ^ _779530) ^ [_1349787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1349787), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1349787) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29535 ^ _779530) ^ [_1349880] : [-(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), _1349880)) = 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), _1349880))))], (29537 ^ _779530) ^ [_1349933, _1349935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1349933)), hAPP(c_Int_Onat, _1349935))), 29540 ^ _779530 : [(29541 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1349935)))], (29543 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1349933), _1349935)))]]], (29545 ^ _779530) ^ [_1350068, _1350070] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1350068)), hAPP(c_Int_Onat, _1350070)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350068), _1350070))], (29555 ^ _779530) ^ [_1350235, _1350237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350235)), 29558 ^ _779530 : [(29559 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1350237)), hAPP(c_Int_Onat, _1350235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350237), _1350235)))], (29565 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350237), _1350235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1350237)), hAPP(c_Int_Onat, _1350235))))]]], (29571 ^ _779530) ^ [_1350494, _1350496] : [class_Int_Onumber__ring(_1350494), -(hAPP(c_Int_Onumber__class_Onumber__of(_1350494), c_Int_OBit1(_1350496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350494), c_Groups_Oone__class_Oone(_1350494)), hAPP(c_Int_Onumber__class_Onumber__of(_1350494), _1350496))), hAPP(c_Int_Onumber__class_Onumber__of(_1350494), _1350496)))], (29577 ^ _779530) ^ [_1350639, _1350641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350641)), 29584 ^ _779530 : [(29585 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1350639)), hAPP(c_Int_Onat, _1350641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1350639), _1350641)))], (29591 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1350639), _1350641)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1350639)), hAPP(c_Int_Onat, _1350641))))]]], (29597 ^ _779530) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29599 ^ _779530) ^ [_1350972, _1350974, _1350976, _1350978, _1350980] : [class_Groups_Ocomm__monoid__mult(_1350972), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350974), _1350976)), 29606 ^ _779530 : [(29607 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1350974), _1350978), _1350976)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1350974, _1350972), hAPP(hAPP(c_COMBC(_1350974, _1350972, _1350972), hAPP(hAPP(c_COMBS(_1350974, _1350972, tc_fun(_1350972, _1350972)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1350972, tc_fun(_1350972, _1350972)), _1350974), c_If(_1350972)), hAPP(c_fequal, _1350978))), _1350980)), c_Groups_Oone__class_Oone(_1350972))), _1350976) = hAPP(_1350980, _1350978))], (29613 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1350974), _1350978), _1350976))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1350974, _1350972), hAPP(hAPP(c_COMBC(_1350974, _1350972, _1350972), hAPP(hAPP(c_COMBS(_1350974, _1350972, tc_fun(_1350972, _1350972)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1350972, tc_fun(_1350972, _1350972)), _1350974), c_If(_1350972)), hAPP(c_fequal, _1350978))), _1350980)), c_Groups_Oone__class_Oone(_1350972))), _1350976) = c_Groups_Oone__class_Oone(_1350972))]]], (29619 ^ _779530) ^ [_1351482, _1351484, _1351486, _1351488, _1351490] : [class_Groups_Ocomm__monoid__mult(_1351482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351484), _1351486)), 29626 ^ _779530 : [(29627 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1351484), _1351488), _1351486)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351484, _1351482), hAPP(hAPP(c_COMBC(_1351484, _1351482, _1351482), hAPP(hAPP(c_COMBS(_1351484, _1351482, tc_fun(_1351482, _1351482)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1351482, tc_fun(_1351482, _1351482)), _1351484), c_If(_1351482)), hAPP(hAPP(c_COMBC(_1351484, _1351484, tc_HOL_Obool), c_fequal), _1351488))), _1351490)), c_Groups_Oone__class_Oone(_1351482))), _1351486) = hAPP(_1351490, _1351488))], (29633 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1351484), _1351488), _1351486))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351484, _1351482), hAPP(hAPP(c_COMBC(_1351484, _1351482, _1351482), hAPP(hAPP(c_COMBS(_1351484, _1351482, tc_fun(_1351482, _1351482)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1351482, tc_fun(_1351482, _1351482)), _1351484), c_If(_1351482)), hAPP(hAPP(c_COMBC(_1351484, _1351484, tc_HOL_Obool), c_fequal), _1351488))), _1351490)), c_Groups_Oone__class_Oone(_1351482))), _1351486) = c_Groups_Oone__class_Oone(_1351482))]]], (29639 ^ _779530) ^ [_1352020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352020)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1352020)) = _1352020)], (29645 ^ _779530) ^ [_1352126, _1352128] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352126) = _1352128, 29648 ^ _779530 : [(29649 ^ _779530) ^ [] : [-(_1352126 = hAPP(c_Int_Onat, _1352128))], (29651 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352128)))]]], (29653 ^ _779530) ^ [_1352241, _1352243] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352241) = _1352243), _1352241 = hAPP(c_Int_Onat, _1352243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352243))], (29663 ^ _779530) ^ [_1352394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352394)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1352394)) = _1352394)], (29669 ^ _779530) ^ [_1352479] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352479))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1352479)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29675 ^ _779530) ^ [_1352538, _1352540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1352538), hAPP(c_Int_Onat, _1352540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352538)), _1352540)))], (29681 ^ _779530) ^ [_1352643, _1352645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352643)), _1352645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1352643), hAPP(c_Int_Onat, _1352645))))], (29687 ^ _779530) ^ [_1352754] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1352754))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29689 ^ _779530) ^ [_1352786, _1352788, _1352790] : [class_Int_Onumber__ring(_1352786), 29692 ^ _779530 : [(29693 ^ _779530) ^ [] : [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), _1352788))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1352786), _1352790), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1352788))) = hAPP(hAPP(c_HOL_OLet(_1352786, _1352786), hAPP(hAPP(c_Power_Opower__class_Opower(_1352786), _1352790), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1352788))), hAPP(hAPP(c_COMBS(_1352786, _1352786, _1352786), hAPP(hAPP(c_COMBB(_1352786, tc_fun(_1352786, _1352786), _1352786), c_Groups_Otimes__class_Otimes(_1352786)), hAPP(c_Groups_Otimes__class_Otimes(_1352786), _1352790))), c_COMBI(_1352786))))], (29699 ^ _779530) ^ [] : [-(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), _1352788)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1352786), _1352790), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1352788))) = c_Groups_Oone__class_Oone(_1352786))]]], (29705 ^ _779530) ^ [_1353144, _1353146] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1353144, _1353146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1353146), _1353144))], (29707 ^ _779530) ^ [_1353182, _1353184, _1353186, _1353188] : [class_Groups_Ocomm__monoid__mult(_1353182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353184), _1353186)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1353184, _1353182), hAPP(c_COMBK(_1353182, _1353184), _1353188)), _1353186) = hAPP(hAPP(c_Power_Opower__class_Opower(_1353182), _1353188), hAPP(c_Finite__Set_Ocard(_1353184), _1353186)))], (29717 ^ _779530) ^ [_1353390, _1353392] : [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), _1353390))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1353392), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1353390))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1353392), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1353390))), 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), _1353392))), c_COMBI(tc_Int_Oint))))], (29723 ^ _779530) ^ [_1353547, _1353549] : [-(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), _1353547)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1353549), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1353547))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (29729 ^ _779530) ^ [_1353601, _1353603, _1353605, _1353607, _1353609] : [class_Groups_Ocomm__monoid__mult(_1353601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353603), _1353605)), -(hBOOL(hAPP(hAPP(c_member(_1353603), _1353607), _1353605))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1353603, _1353601), _1353609), hAPP(hAPP(c_Set_Oinsert(_1353603), _1353607), _1353605)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353601), hAPP(_1353609, _1353607)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1353603, _1353601), _1353609), _1353605)))], (29743 ^ _779530) ^ [_1353851, _1353853, _1353855, _1353857, _1353859] : [class_Groups_Ocomm__monoid__mult(_1353851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353853), _1353855)), -(hBOOL(hAPP(hAPP(c_member(_1353853), _1353857), _1353855))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1353853, _1353851), _1353859), hAPP(hAPP(c_Set_Oinsert(_1353853), _1353857), _1353855)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353851), hAPP(_1353859, _1353857)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1353853, _1353851), _1353859), _1353855)))], (29757 ^ _779530) ^ [_1354101, _1354103, _1354105, _1354107, _1354109] : [class_Groups_Ocomm__monoid__mult(_1354101), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354103), _1354105)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354103), _1354107)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354101), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354103, _1354101), _1354109), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354103, tc_HOL_Obool)), _1354105), _1354107))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354103, _1354101), _1354109), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354103, tc_HOL_Obool)), _1354105), _1354107))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354101), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354103, _1354101), _1354109), _1354105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354103, _1354101), _1354109), _1354107)))], (29771 ^ _779530) ^ [_1354462, _1354464, _1354466, _1354468, _1354470] : [class_Groups_Ocomm__monoid__mult(_1354462), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354464), _1354466)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354464), _1354468)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354462), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354464, _1354462), _1354470), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1354464, tc_HOL_Obool)), _1354466), _1354468))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354464, _1354462), _1354470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1354464, tc_HOL_Obool)), _1354466), _1354468))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354462), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354464, _1354462), _1354470), _1354466)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354464, _1354462), _1354470), _1354468)))], (29785 ^ _779530) ^ [_1354823, _1354825, _1354827, _1354829, _1354831] : [class_Groups_Ocomm__monoid__mult(_1354823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354825), _1354827)), c_Fun_Oinj__on(_1354825, _1354825, _1354829, _1354827), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354825, _1354823), _1354831), hAPP(c_Set_Oimage(_1354825, _1354825, _1354829), _1354827)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354825, _1354823), hAPP(c_Fun_Ocomp(_1354825, _1354823, _1354825, _1354831), _1354829)), _1354827))], (29799 ^ _779530) ^ [_1355098, _1355100, _1355102] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355098), _1355100), _1355102) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1355098), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1355098, tc_Int_Oint), _1355100), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1355102))), class_Groups_Ocomm__monoid__add(_1355098), class_Groups_Ocomm__monoid__mult(_1355098)], (29809 ^ _779530) ^ [_1355289, _1355291, _1355293, _1355295] : [class_Groups_Ocomm__monoid__mult(_1355289), 29812 ^ _779530 : [(29813 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1355291), _1355293)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1355291, _1355289), _1355295), _1355293) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1355289, _1355291, c_Groups_Otimes__class_Otimes(_1355289)), _1355295), c_Groups_Oone__class_Oone(_1355289)), _1355293))], (29819 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1355291), _1355293))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1355291, _1355289), _1355295), _1355293) = c_Groups_Oone__class_Oone(_1355289))]]], (29825 ^ _779530) ^ [_1355561, _1355563, _1355565, _1355567] : [class_Groups_Ocomm__monoid__mult(_1355561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355563), _1355565)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1355563, _1355561), _1355567), _1355565) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1355561, _1355563, c_Groups_Otimes__class_Otimes(_1355561)), _1355567), c_Groups_Oone__class_Oone(_1355561)), _1355565))], (29835 ^ _779530) ^ [_1355756] : [-(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)), _1355756)) = hAPP(c_Int_Onat, _1355756))], (29837 ^ _779530) ^ [_1355788, _1355790] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1355788), _1355790)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1355790), _1355788)))], (29839 ^ _779530) ^ [_1355843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1355843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355843)))], (29845 ^ _779530) ^ [_1355928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1355928))))], (29851 ^ _779530) ^ [_1356019, _1356021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356021)), 29858 ^ _779530 : [(29859 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1356019)), hAPP(c_Int_Onat, _1356021))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356019), _1356021)))], (29865 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356019), _1356021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1356019)), hAPP(c_Int_Onat, _1356021))))]]], (29871 ^ _779530) ^ [_1356334, _1356336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356334)), 29874 ^ _779530 : [(29875 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1356334)), hAPP(c_Int_Onat, _1356336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356334), _1356336)))], (29881 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1356334), _1356336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1356334)), hAPP(c_Int_Onat, _1356336))))]]], (29903 ^ _779530) ^ [_1356800, _1356802] : [-(_1356800 = hAPP(c_Int_Onat, _1356802)), 29906 ^ _779530 : [(29907 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356802)))], (29909 ^ _779530) ^ [] : [_1356802 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1356800)]], 29910 ^ _779530 : [(29911 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356802))], (29913 ^ _779530) ^ [] : [_1356800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29887 ^ _779530) ^ [_1356608, _1356610] : [_1356608 = hAPP(c_Int_Onat, _1356610), 29890 ^ _779530 : [(29891 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356610)), -(_1356610 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1356608))], (29897 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356610))), -(_1356608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29933 ^ _779530) ^ [_1357231, _1357233] : [-(hAPP(c_Int_Onat, _1357231) = _1357233), 29936 ^ _779530 : [(29937 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357231)))], (29939 ^ _779530) ^ [] : [_1357231 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1357233)]], 29940 ^ _779530 : [(29941 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357231))], (29943 ^ _779530) ^ [] : [_1357233 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29917 ^ _779530) ^ [_1357039, _1357041] : [hAPP(c_Int_Onat, _1357039) = _1357041, 29920 ^ _779530 : [(29921 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357039)), -(_1357039 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1357041))], (29927 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357039))), -(_1357041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29947 ^ _779530) ^ [_1357455, _1357457] : [29948 ^ _779530 : [(29949 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357455))], (29951 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1357457))]], 29952 ^ _779530 : [(29953 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1357455)), hAPP(c_Int_Onat, _1357457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357455), _1357457)))], (29959 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357455), _1357457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1357455)), hAPP(c_Int_Onat, _1357457))))]]], (29981 ^ _779530) ^ [_1358034, _1358036] : [-(hBOOL(hAPP(_1358034, hAPP(c_Int_Onat, _1358036)))), 29985 ^ _779530 : [(29986 ^ _779530) ^ [] : [-(_1358036 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 29984 ^ [_1358034, _1358036]))], (29988 ^ _779530) ^ [] : [hBOOL(hAPP(_1358034, 29984 ^ [_1358034, _1358036]))]], 29989 ^ _779530 : [(29990 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1358036), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29992 ^ _779530) ^ [] : [hBOOL(hAPP(_1358034, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (29965 ^ _779530) ^ [_1357771, _1357773] : [hBOOL(hAPP(_1357771, hAPP(c_Int_Onat, _1357773))), 29968 ^ _779530 : [(29969 ^ _779530) ^ [_1357871] : [_1357773 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1357871), -(hBOOL(hAPP(_1357771, _1357871)))], (29975 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357773), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1357771, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (29996 ^ _779530) ^ [_1358297, _1358299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358297)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358299)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1358297)), hAPP(c_Int_Onat, _1358299)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358297), _1358299)))], (30006 ^ _779530) ^ [_1358476, _1358478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358476)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358478)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1358476), _1358478)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1358476)), hAPP(c_Int_Onat, _1358478)))], (30016 ^ _779530) ^ [_1358670, _1358672] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358670) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1358672), 30019 ^ _779530 : [(30020 ^ _779530) ^ [] : [-(_1358670 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1358672)))], (30022 ^ _779530) ^ [] : [-(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), _1358672))))]]], (30024 ^ _779530) ^ [_1358803, _1358805] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358803) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1358805)), _1358803 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1358805)), 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), _1358805)))], (30034 ^ _779530) ^ [_1358968, _1358970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1358970)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1358968)), hAPP(c_Int_Onat, _1358970)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1358968), _1358970)))], (30044 ^ _779530) ^ [_1359147, _1359149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359147)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359147), _1359149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1359147)), hAPP(c_Int_Onat, _1359149)))], (30050 ^ _779530) ^ [_1359270, _1359272] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1359270), _1359272) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1359270)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1359272))))], (30052 ^ _779530) ^ [_1359316, _1359318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1359316), _1359318)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1359318), _1359316)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1359318)), hAPP(c_Int_Onat, _1359316)))], (30062 ^ _779530) ^ [_1359501, _1359503, _1359505] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359501, tc_Nat_Onat), _1359503), _1359505) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359501, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1359501), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1359503)), _1359505)))], (30064 ^ _779530) ^ [_1359559, _1359561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359561)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1359559), hAPP(c_Int_Onat, _1359561)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359559, _1359561)))], (30074 ^ _779530) ^ [_1359730, _1359732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359732)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359730, _1359732)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1359730), hAPP(c_Int_Onat, _1359732)))], (30084 ^ _779530) ^ [_1359901, _1359903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1359903)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1359901)), hAPP(c_Int_Onat, _1359903)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1359901), _1359903)))], (30094 ^ _779530) ^ [_1360080, _1360082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360080)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1360080), _1360082)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1360080)), hAPP(c_Int_Onat, _1360082)))], (30100 ^ _779530) ^ [_1360203, _1360205, _1360207, _1360209, _1360211] : [class_Orderings_Olinorder(_1360203), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360203, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360203, _1360205, _1360207)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360203, _1360209, _1360211)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1360203, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360203), _1360205), _1360209), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1360203), _1360207), _1360211)))], (30106 ^ _779530) ^ [_1360362, _1360364, _1360366] : [class_Groups_Oordered__ab__group__add(_1360362), -(hAPP(c_Set_Oimage(_1360362, _1360362, c_Groups_Ouminus__class_Ouminus(_1360362)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1360362, _1360364), _1360366)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1360362, hAPP(c_Groups_Ouminus__class_Ouminus(_1360362), _1360366), hAPP(c_Groups_Ouminus__class_Ouminus(_1360362), _1360364)))], (30112 ^ _779530) ^ [_1360497, _1360499, _1360501] : [class_Groups_Oordered__ab__group__add(_1360497), -(hAPP(c_Set_Oimage(_1360497, _1360497, c_Groups_Ouminus__class_Ouminus(_1360497)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360497, _1360499, _1360501)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1360497, hAPP(c_Groups_Ouminus__class_Ouminus(_1360497), _1360501)), hAPP(c_Groups_Ouminus__class_Ouminus(_1360497), _1360499)))], (30118 ^ _779530) ^ [_1360632, _1360634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360632)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1360632)), _1360634) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1360632), _1360634)))], (30124 ^ _779530) ^ [_1360749, _1360751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360749)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1360749), _1360751)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1360749)), _1360751))], (30130 ^ _779530) ^ [_1360866, _1360868, _1360870, _1360872] : [class_Orderings_Oorder(_1360866), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360866, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360866, _1360868, _1360870)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1360866, _1360870, _1360872)) = c_Orderings_Obot__class_Obot(tc_fun(_1360866, tc_HOL_Obool)))], (30136 ^ _779530) ^ [_1360993, _1360995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360995)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1360993)), hAPP(c_Int_Onat, _1360995)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1360993, _1360995)))], (30146 ^ _779530) ^ [_1361166, _1361168, _1361170, _1361172, _1361174] : [class_Groups_Ocomm__monoid__mult(_1361166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361168), _1361170)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361168, _1361166), _1361172), hAPP(hAPP(c_Set_Oinsert(_1361168), _1361174), _1361170)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361166), hAPP(_1361172, _1361174)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361168, _1361166), _1361172), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1361168, tc_HOL_Obool)), _1361170), hAPP(hAPP(c_Set_Oinsert(_1361168), _1361174), c_Orderings_Obot__class_Obot(tc_fun(_1361168, tc_HOL_Obool)))))))], (30156 ^ _779530) ^ [_1361435, _1361437, _1361439, _1361441, _1361443] : [class_Groups_Ocomm__monoid__mult(_1361435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361437), _1361439)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361437), _1361441)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361437, tc_HOL_Obool)), _1361439), _1361441) = c_Orderings_Obot__class_Obot(tc_fun(_1361437, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361437, _1361435), _1361443), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361437, tc_HOL_Obool)), _1361439), _1361441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361435), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361437, _1361435), _1361443), _1361439)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361437, _1361435), _1361443), _1361441)))], (30174 ^ _779530) ^ [_1361830, _1361832, _1361834, _1361836, _1361838] : [class_Groups_Ocomm__monoid__mult(_1361830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361832), _1361834)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361832), _1361836)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361832, tc_HOL_Obool)), _1361834), _1361836) = c_Orderings_Obot__class_Obot(tc_fun(_1361832, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361832, _1361830), _1361838), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361832, tc_HOL_Obool)), _1361834), _1361836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361830), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361832, _1361830), _1361838), _1361834)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1361832, _1361830), _1361838), _1361836)))], (30192 ^ _779530) ^ [_1362237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1362237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1362237)))], (30198 ^ _779530) ^ [_1362322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1362322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1362322))))], (30204 ^ _779530) ^ [_1362413, _1362415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362413)), 30207 ^ _779530 : [(30208 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1362413)), _1362415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362413), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1362415))))], (30214 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362413), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1362415))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1362413)), _1362415)))]]], (30220 ^ _779530) ^ [_1362672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362672)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1362672)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1362672)))], (30226 ^ _779530) ^ [_1362775, _1362777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362775), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1362775), _1362777)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1362775))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1362777))))], (30232 ^ _779530) ^ [_1362916] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1362916) = 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), _1362916), c_Int_Onat)))))], (30234 ^ _779530) ^ [_1362957] : [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), _1362957))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362957) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362957)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (30240 ^ _779530) ^ [_1363072, _1363074, _1363076, _1363078, _1363080] : [class_Groups_Ocomm__monoid__mult(_1363072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363074), _1363076)), hBOOL(hAPP(hAPP(c_member(_1363074), _1363078), _1363076)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1363074, _1363072), _1363080), _1363076) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363072), hAPP(_1363080, _1363078)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1363074, _1363072), _1363080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363074, tc_HOL_Obool)), _1363076), hAPP(hAPP(c_Set_Oinsert(_1363074), _1363078), c_Orderings_Obot__class_Obot(tc_fun(_1363074, tc_HOL_Obool)))))))], (30254 ^ _779530) ^ [_1363397, _1363399, _1363401, _1363403] : [class_Orderings_Olinorder(_1363397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363397), _1363399), _1363401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363397), _1363401), _1363403)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363397, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1363397, _1363399, _1363401)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1363397, _1363401, _1363403)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1363397, _1363399, _1363403))], (30268 ^ _779530) ^ [_1363662, _1363664] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1363662, _1363664)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1363664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1363662), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (30270 ^ _779530) ^ [_1363709, _1363711] : [-(c_Int_Onat__aux(_1363709, _1363711) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1363709)), _1363711))], (30272 ^ _779530) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30274 ^ _779530) ^ [_1363770] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1363770))), -(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), _1363770)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30280 ^ _779530) ^ [_1363863] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1363863)))), -(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), _1363863)) = 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), _1363863))))], (30286 ^ _779530) ^ [_1363921] : [-(hAPP(c_Int_Onat, _1363921) = 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, _1363921)), 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)))))))], (30288 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30290 ^ _779530) ^ [_1363998, _1364000] : [hAPP(c_Int_ORep__Integ, _1363998) = hAPP(c_Int_ORep__Integ, _1364000), -(_1363998 = _1364000)], (30296 ^ _779530) ^ [_1364083, _1364085] : [_1364083 = _1364085, -(hAPP(c_Int_ORep__Integ, _1364083) = hAPP(c_Int_ORep__Integ, _1364085))], (30302 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30304 ^ _779530) ^ [_1364207] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364207)))], (30306 ^ _779530) ^ [_1364241] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364241))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364241)))], (30312 ^ _779530) ^ [_1364275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1364275)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364275))], (30318 ^ _779530) ^ [_1364373] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364373), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30324 ^ _779530) ^ [_1364458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1364458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364458)))], (30330 ^ _779530) ^ [_1364549] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364549)), -(hAPP(c_Int_Onat, _1364549) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30336 ^ _779530) ^ [_1364646] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1364646)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364646))))], (30342 ^ _779530) ^ [_1364741] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364741))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1364741)))))], (30348 ^ _779530) ^ [_1364838] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1364838))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1364838)) = _1364838)], (30354 ^ _779530) ^ [_1364880] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364880))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364880) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30360 ^ _779530) ^ [_1364971] : [-(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, _1364971))))))], (30388 ^ _779530) ^ [_1365405, _1365407] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365405) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365407)), 30391 ^ _779530 : [(30392 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365405))))], (30394 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365407)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 30395 ^ _779530 : [(30396 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365405)))], (30398 ^ _779530) ^ [] : [30399 ^ _779530 : [(30400 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365407))))], (30402 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365405) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 30403 ^ _779530 : [(30404 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365407)))], (30406 ^ _779530) ^ [] : [_1365405 = _1365407]]]]], (30362 ^ _779530) ^ [_1365020, _1365022] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365020) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365022), 30365 ^ _779530 : [(30366 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365022)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30372 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365020)))), 30375 ^ _779530 : [(30376 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365022))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365020) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30382 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365022)))), -(_1365020 = _1365022)]]]]], (30410 ^ _779530) ^ [_1365818, _1365820, _1365822] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365818))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365820)), _1365822)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365820)), _1365822))], (30416 ^ _779530) ^ [_1365956, _1365958, _1365960] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365956)))), 30419 ^ _779530 : [(30420 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365958))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365958)), _1365960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365956)), _1365960))], (30426 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1365958)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365958)), _1365960)) = 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), _1365956), _1365958))), _1365960))]]], (30432 ^ _779530) ^ [_1366287] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366287))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366287)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30438 ^ _779530) ^ [_1366378] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366378)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366378)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366378))], (30444 ^ _779530) ^ [_1366437, _1366439] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1366437)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1366439)), hAPP(c_Int_Onat, _1366437)) = hAPP(c_Int_Onat, _1366439))], (30450 ^ _779530) ^ [_1366542, _1366544] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1366542))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1366544)), hAPP(c_Int_Onat, _1366542)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1366544), _1366542)), 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)))], (30456 ^ _779530) ^ [_1366606, _1366608] : [class_Int_Onumber__ring(_1366606), 30459 ^ _779530 : [(30460 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366608))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1366606), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366608)) = c_Groups_Ozero__class_Ozero(_1366606))], (30466 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366608)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1366606), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366608)) = hAPP(c_Int_Onumber__class_Onumber__of(_1366606), _1366608))]]], (30472 ^ _779530) ^ [_1366855, _1366857] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366855))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366855), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366857)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30478 ^ _779530) ^ [_1366957, _1366959] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366957)))), 30481 ^ _779530 : [(30482 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366959))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366957), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366957))], (30488 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366959)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366957), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366959)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366957), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1366959))))]]], (30494 ^ _779530) ^ [_1367239, _1367241] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367239))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367239)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367241)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30500 ^ _779530) ^ [_1367344, _1367346] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367344)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367344)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367346)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367344)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367346))))], (30506 ^ _779530) ^ [_1367420] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367420))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1367420)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30512 ^ _779530) ^ [_1367509] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367509)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1367509)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367509)), 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)))))], (30518 ^ _779530) ^ [_1367573, _1367575] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367573))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367573)), _1367575) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1367575))], (30524 ^ _779530) ^ [_1367678, _1367680] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367678)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367678)), _1367680) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367678)), _1367680)))], (30530 ^ _779530) ^ [_1367751, _1367753] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367751))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367751)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367753)) = 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), _1367753)))], (30536 ^ _779530) ^ [_1367868, _1367870] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367868)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367868)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367870)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1367868)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367870))))], (30542 ^ _779530) ^ [_1367938, _1367940] : [c_Nat__Transfer_Onat__set(_1367938), c_Nat__Transfer_Onat__set(_1367940), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1367938), _1367940) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1367938)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1367940))))], (30552 ^ _779530) ^ [_1368105, _1368107] : [c_Nat__Transfer_Onat__set(_1368105), c_Nat__Transfer_Onat__set(_1368107), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1368105), _1368107) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1368105)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1368107))))], (30562 ^ _779530) ^ [_1368281, _1368283] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1368281))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368281)), _1368283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1368283))], (30568 ^ _779530) ^ [_1368392, _1368394] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1368392)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368392)), _1368394)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1368392))), _1368394))], (30574 ^ _779530) ^ [_1368467, _1368469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368467), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368469)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368467)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368469))], (30580 ^ _779530) ^ [_1368578, _1368580] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368578), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368580)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368578)) = 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), _1368580), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1368578)))), 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)))], (30586 ^ _779530) ^ [_1368651] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1368651) = c_Int_OPls)], (30588 ^ _779530) ^ [_1368677] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1368677), c_Int_OPls) = _1368677)], (30590 ^ _779530) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (30592 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (30594 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (30596 ^ _779530) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30598 ^ _779530) ^ [_1368784] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1368784) = _1368784)], (30600 ^ _779530) ^ [_1368810] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1368810), c_Int_OPls) = _1368810)], (30602 ^ _779530) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (30604 ^ _779530) ^ [_1368866] : [c_Int_OPls = c_Int_OBit1(_1368866)], (30606 ^ _779530) ^ [_1368900] : [c_Int_OBit1(_1368900) = c_Int_OPls], (30608 ^ _779530) ^ [_1368925] : [class_Int_Onumber__ring(_1368925), -(c_Groups_Ozero__class_Ozero(_1368925) = hAPP(c_Int_Onumber__class_Onumber__of(_1368925), c_Int_OPls))], (30614 ^ _779530) ^ [_1369012] : [class_Int_Onumber__ring(_1369012), -(hAPP(c_Int_Onumber__class_Onumber__of(_1369012), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1369012))], (30620 ^ _779530) ^ [_1369099, _1369101] : [class_Int_Onumber__ring(_1369099), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369099), _1369101), hAPP(c_Int_Onumber__class_Onumber__of(_1369099), c_Int_OPls)) = _1369101)], (30626 ^ _779530) ^ [_1369200, _1369202] : [class_Int_Onumber__ring(_1369200), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369200), hAPP(c_Int_Onumber__class_Onumber__of(_1369200), c_Int_OPls)), _1369202) = _1369202)], (30632 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30634 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30636 ^ _779530) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (30638 ^ _779530) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (30640 ^ _779530) ^ [_1369391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1369391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1369391)))], (30646 ^ _779530) ^ [_1369474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1369474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1369474))))], (30652 ^ _779530) ^ [_1369575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1369575)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369575), c_Int_OPls)))], (30658 ^ _779530) ^ [_1369670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369670), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1369670)), c_Int_OPls)))], (30664 ^ _779530) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (30666 ^ _779530) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (30668 ^ _779530) ^ [_1369813, _1369815] : [c_Nat__Transfer_Onat__set(_1369813), c_Nat__Transfer_Onat__set(_1369815), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1369813), _1369815)))], (30678 ^ _779530) ^ [_1369948, _1369950] : [c_Nat__Transfer_Onat__set(_1369948), c_Nat__Transfer_Onat__set(_1369950), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1369948), _1369950)))], (30688 ^ _779530) ^ [_1370089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370089), 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), _1370089)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30694 ^ _779530) ^ [_1370180] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370180), 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), _1370180)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1370180)))], (30700 ^ _779530) ^ [_1370238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370238), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370238)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30706 ^ _779530) ^ [_1370335] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370335), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370335)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1370335)))], (30722 ^ _779530) ^ [_1370559] : [30724 ^ _779530 : [(30725 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30723 ^ [_1370559]), _1370559)))], (30727 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30723 ^ [_1370559]))]], -(c_Nat__Transfer_Onat__set(_1370559))], (30712 ^ _779530) ^ [_1370402] : [c_Nat__Transfer_Onat__set(_1370402), 30715 ^ _779530 : [(30716 ^ _779530) ^ [_1370468] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1370468), _1370402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370468)))]]], (30731 ^ _779530) ^ [_1370707] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1370707)))], (30733 ^ _779530) ^ [_1370732, _1370734] : [c_Nat__Transfer_Onat__set(_1370732), c_Nat__Transfer_Onat__set(_1370734), 30740 ^ _779530 : [(30741 ^ _779530) ^ [] : [_1370732 = _1370734, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1370732) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1370734))], (30747 ^ _779530) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1370732) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1370734), -(_1370732 = _1370734)]]], (30753 ^ _779530) ^ [_1371005, _1371007] : [class_Int_Onumber__ring(_1371005), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1371005), hAPP(c_Int_Onumber__class_Onumber__of(_1371005), c_Int_OBit1(c_Int_OPls))), _1371007) = _1371007)], (30759 ^ _779530) ^ [_1371106, _1371108] : [class_Int_Onumber__ring(_1371106), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1371106), _1371108), hAPP(c_Int_Onumber__class_Onumber__of(_1371106), c_Int_OBit1(c_Int_OPls))) = _1371108)], (30765 ^ _779530) ^ [_1371207] : [class_Int_Onumber__ring(_1371207), -(c_Groups_Oone__class_Oone(_1371207) = hAPP(c_Int_Onumber__class_Onumber__of(_1371207), c_Int_OBit1(c_Int_OPls)))], (30771 ^ _779530) ^ [_1371294] : [class_Int_Onumber__ring(_1371294), -(hAPP(c_Int_Onumber__class_Onumber__of(_1371294), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1371294))], (30777 ^ _779530) ^ [_1371393] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371393), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371393), c_Int_OPls)))], (30783 ^ _779530) ^ [_1371480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371480), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371480))], (30789 ^ _779530) ^ [_1371585] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371585) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371585), c_Int_OPls)))], (30795 ^ _779530) ^ [_1371672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371672), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1371672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30801 ^ _779530) ^ [] : [-(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))))], (30803 ^ _779530) ^ [_1371795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1371795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1371795)))], (30809 ^ _779530) ^ [_1371878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1371878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1371878))))], (30815 ^ _779530) ^ [_1371979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1371979)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371979), c_Int_OPls)))], (30821 ^ _779530) ^ [_1372074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372074), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1372074)), c_Int_OPls)))], (30827 ^ _779530) ^ [_1372190, _1372192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372190)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372192))), 30830 ^ _779530 : [(30837 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372190), _1372192)))], (30831 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372190), _1372192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1372192)))]]], (30839 ^ _779530) ^ [_1372393, _1372395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372393)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372395)))), 30842 ^ _779530 : [(30843 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372393), _1372395)))], (30845 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1372395))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372393), _1372395))], (30861 ^ _779530) ^ [_1372748, _1372750] : [30862 ^ _779530 : [(30863 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372748), _1372750))], (30865 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372748), 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), _1372748)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372750))))], (30851 ^ _779530) ^ [_1372618, _1372620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372618)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1372620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372618), _1372620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372618), c_Int_OPls)))], (30869 ^ _779530) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (30871 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30873 ^ _779530) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (30875 ^ _779530) ^ [_1372963] : [-(c_Int_Osucc(_1372963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1372963), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30877 ^ _779530) ^ [_1372994, _1372996] : [class_Int_Onumber__ring(_1372994), class_Rings_Olinordered__idom(_1372994), 30884 ^ _779530 : [(30885 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372994), c_Groups_Ozero__class_Ozero(_1372994)), hAPP(c_Int_Onumber__class_Onumber__of(_1372994), _1372996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1372996)))], (30891 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1372996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1372994), c_Groups_Ozero__class_Ozero(_1372994)), hAPP(c_Int_Onumber__class_Onumber__of(_1372994), _1372996))))]]], (30897 ^ _779530) ^ [_1373299, _1373301] : [class_Int_Onumber__ring(_1373299), class_Rings_Olinordered__idom(_1373299), 30904 ^ _779530 : [(30905 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373299), hAPP(c_Int_Onumber__class_Onumber__of(_1373299), _1373301)), c_Groups_Ozero__class_Ozero(_1373299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1373301), c_Int_OPls)))], (30911 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1373301), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373299), hAPP(c_Int_Onumber__class_Onumber__of(_1373299), _1373301)), c_Groups_Ozero__class_Ozero(_1373299))))]]], (30917 ^ _779530) ^ [_1373613, _1373615] : [class_Int_Onumber__ring(_1373613), class_Rings_Olinordered__idom(_1373613), 30924 ^ _779530 : [(30925 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373613), hAPP(c_Int_Onumber__class_Onumber__of(_1373613), _1373615)), c_Groups_Ozero__class_Ozero(_1373613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373615), c_Int_OPls)))], (30931 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373615), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373613), hAPP(c_Int_Onumber__class_Onumber__of(_1373613), _1373615)), c_Groups_Ozero__class_Ozero(_1373613))))]]], (30937 ^ _779530) ^ [_1373927, _1373929] : [class_Int_Onumber__ring(_1373927), class_Rings_Olinordered__idom(_1373927), 30944 ^ _779530 : [(30945 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373927), c_Groups_Ozero__class_Ozero(_1373927)), hAPP(c_Int_Onumber__class_Onumber__of(_1373927), _1373929))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1373929)))], (30951 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1373929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373927), c_Groups_Ozero__class_Ozero(_1373927)), hAPP(c_Int_Onumber__class_Onumber__of(_1373927), _1373929))))]]], (30957 ^ _779530) ^ [_1374244] : [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), _1374244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1374244)))], (30963 ^ _779530) ^ [_1374329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1374329)), -(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), _1374329))))], (30969 ^ _779530) ^ [] : [-(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)))], (30971 ^ _779530) ^ [] : [-(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)))))], (30973 ^ _779530) ^ [_1374456, _1374458] : [class_Groups_Omonoid__mult(_1374456), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1374456), _1374458), 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(_1374456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374456), _1374458), _1374458)), _1374458))], (30979 ^ _779530) ^ [] : [-(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))))))], (30981 ^ _779530) ^ [_1374597] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1374597))) = 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)))), _1374597))], (30983 ^ _779530) ^ [_1374641, _1374643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374641), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374641)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374643)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374643))], (30989 ^ _779530) ^ [_1374753, _1374755] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374753), c_Int_OPls))), 30992 ^ _779530 : [(30993 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374755), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374753)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374755)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374753))], (30999 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374755), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374753)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1374755)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1374753), _1374755)))]]], (31005 ^ _779530) ^ [] : [-(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)))))], (31007 ^ _779530) ^ [] : [-(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)))))], (31009 ^ _779530) ^ [_1375062, _1375064] : [c_Nat__Transfer_Onat__set(_1375062), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1375064), _1375062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375064)))], (31019 ^ _779530) ^ [_1375203, _1375205] : [class_Int_Onumber__ring(_1375203), -(hAPP(c_Int_Onumber__class_Onumber__of(_1375203), c_Int_Osucc(_1375205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1375203), c_Groups_Oone__class_Oone(_1375203)), hAPP(c_Int_Onumber__class_Onumber__of(_1375203), _1375205)))], (31025 ^ _779530) ^ [_1375322] : [-(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)))), _1375322))))], (31027 ^ _779530) ^ [_1375350, _1375352] : [class_Int_Onumber__ring(_1375350), class_Rings_Olinordered__idom(_1375350), 31034 ^ _779530 : [(31035 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375350), hAPP(c_Int_Onumber__class_Onumber__of(_1375350), _1375352)), c_Groups_Oone__class_Oone(_1375350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375352), c_Int_OBit1(c_Int_OPls))))], (31041 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375352), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375350), hAPP(c_Int_Onumber__class_Onumber__of(_1375350), _1375352)), c_Groups_Oone__class_Oone(_1375350))))]]], (31047 ^ _779530) ^ [_1375664, _1375666] : [class_Int_Onumber__ring(_1375664), class_Rings_Olinordered__idom(_1375664), 31054 ^ _779530 : [(31055 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375664), c_Groups_Oone__class_Oone(_1375664)), hAPP(c_Int_Onumber__class_Onumber__of(_1375664), _1375666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375666)))], (31061 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375664), c_Groups_Oone__class_Oone(_1375664)), hAPP(c_Int_Onumber__class_Onumber__of(_1375664), _1375666))))]]], (31067 ^ _779530) ^ [_1375969, _1375971] : [class_Int_Onumber__ring(_1375969), class_Rings_Olinordered__idom(_1375969), 31074 ^ _779530 : [(31075 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375969), c_Groups_Oone__class_Oone(_1375969)), hAPP(c_Int_Onumber__class_Onumber__of(_1375969), _1375971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375971)))], (31081 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1375971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375969), c_Groups_Oone__class_Oone(_1375969)), hAPP(c_Int_Onumber__class_Onumber__of(_1375969), _1375971))))]]], (31087 ^ _779530) ^ [_1376274, _1376276] : [class_Int_Onumber__ring(_1376274), class_Rings_Olinordered__idom(_1376274), 31094 ^ _779530 : [(31095 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376274), hAPP(c_Int_Onumber__class_Onumber__of(_1376274), _1376276)), c_Groups_Oone__class_Oone(_1376274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376276), c_Int_OBit1(c_Int_OPls))))], (31101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376276), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376274), hAPP(c_Int_Onumber__class_Onumber__of(_1376274), _1376276)), c_Groups_Oone__class_Oone(_1376274))))]]], (31107 ^ _779530) ^ [_1376588, _1376590] : [class_Int_Onumber__ring(_1376588), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376588), hAPP(c_Int_Onumber__class_Onumber__of(_1376588), _1376590)), c_Groups_Oone__class_Oone(_1376588)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1376590), c_Int_OBit1(c_Int_OPls))))], (31113 ^ _779530) ^ [_1376715, _1376717] : [class_Int_Onumber__ring(_1376715), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1376715), c_Groups_Oone__class_Oone(_1376715)), hAPP(c_Int_Onumber__class_Onumber__of(_1376715), _1376717)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376715), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1376717)))], (31119 ^ _779530) ^ [_1376836, _1376838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1376836)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1376838)), _1376836) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1376838), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1376836), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (31125 ^ _779530) ^ [_1376968, _1376970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376968), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376968)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376970)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31131 ^ _779530) ^ [_1377073, _1377075] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377073), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377073)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377075)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1377073), _1377075)))], (31137 ^ _779530) ^ [_1377149, _1377151, _1377153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377149), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377149)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377151)), _1377153)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31143 ^ _779530) ^ [_1377268, _1377270, _1377272] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377268), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377268)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377270)), _1377272)) = 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), _1377268), _1377270))), _1377272))], (31149 ^ _779530) ^ [_1377346, _1377348] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377346))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377348)) = 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)))), _1377346), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377348)))], (31151 ^ _779530) ^ [_1377397, _1377399] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377397))), _1377399) = 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)))), _1377397), _1377399))], (31153 ^ _779530) ^ [_1377442, _1377444] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377442, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377444)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1377442, 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)))), _1377444)))], (31155 ^ _779530) ^ [_1377487, _1377489] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377487)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377489)) = 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)))), _1377487)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377489)))], (31157 ^ _779530) ^ [_1377542, _1377544] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377542)))), _1377544) = 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)))), _1377542)), _1377544))], (31159 ^ _779530) ^ [_1377591, _1377593] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377591), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1377593)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377591), 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)))), _1377593)))], (31161 ^ _779530) ^ [_1377640] : [c_Nat__Transfer_Onat__set(_1377640), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1377640)) = _1377640)], (31167 ^ _779530) ^ [_1377725, _1377727] : [class_Int_Onumber__ring(_1377725), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377725), hAPP(c_Int_Onumber__class_Onumber__of(_1377725), _1377727)), c_Groups_Oone__class_Oone(_1377725)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377725), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1377727), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (31173 ^ _779530) ^ [_1377852, _1377854] : [class_Int_Onumber__ring(_1377852), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1377852), c_Groups_Oone__class_Oone(_1377852)), hAPP(c_Int_Onumber__class_Onumber__of(_1377852), _1377854)) = hAPP(c_Int_Onumber__class_Onumber__of(_1377852), 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), _1377854))))], (31179 ^ _779530) ^ [_1377979] : [c_Nat__Transfer_Onat__set(_1377979), 31182 ^ _779530 : [(31183 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1377979)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1377979))))], (31189 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1377979))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1377979)))]]], (31195 ^ _779530) ^ [_1378199] : [c_Nat__Transfer_Onat__set(_1378199), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1378199) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378199)))], (31201 ^ _779530) ^ [_1378290, _1378292] : [c_Nat__Transfer_Onat__set(_1378290), c_Nat__Transfer_Onat__set(_1378292), 31208 ^ _779530 : [(31209 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1378290), _1378292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378290)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378292))))], (31215 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378290)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1378290), _1378292)))]]], (31221 ^ _779530) ^ [_1378593, _1378595] : [c_Nat__Transfer_Onat__set(_1378593), c_Nat__Transfer_Onat__set(_1378595), 31228 ^ _779530 : [(31229 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1378593), _1378595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378593)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378595))))], (31235 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378593)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1378593), _1378595)))]]], (31241 ^ _779530) ^ [_1378896, _1378898, _1378900] : [class_Groups_Ocomm__monoid__add(_1378896), class_Groups_Ocomm__monoid__mult(_1378896), c_Nat__Transfer_Onat__set(_1378898), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1378896), _1378900), _1378898) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1378896), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1378896, tc_Nat_Onat), _1378900), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1378898)))], (31255 ^ _779530) ^ [_1379147] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379147))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379147)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31261 ^ _779530) ^ [_1379238] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379238)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1379238)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1379238)))], (31267 ^ _779530) ^ [_1379290, _1379292, _1379294] : [class_Groups_Ocomm__monoid__add(_1379290), class_Groups_Ocomm__monoid__mult(_1379290), c_Nat__Transfer_Onat__set(_1379292), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1379290), _1379294), _1379292) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1379290), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1379290, tc_Nat_Onat), _1379294), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1379292)))], (31281 ^ _779530) ^ [_1379535, _1379537] : [class_Int_Onumber__ring(_1379535), 31284 ^ _779530 : [(31285 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1379535), _1379537) = c_Groups_Oone__class_Oone(_1379535), -(c_Int_Oiszero(_1379535, hAPP(c_Int_Onumber__class_Onumber__of(_1379535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1379537), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (31291 ^ _779530) ^ [] : [c_Int_Oiszero(_1379535, hAPP(c_Int_Onumber__class_Onumber__of(_1379535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1379537), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1379535), _1379537) = c_Groups_Oone__class_Oone(_1379535))]]], (31297 ^ _779530) ^ [_1379794, _1379796] : [class_Int_Onumber__ring(_1379794), 31300 ^ _779530 : [(31301 ^ _779530) ^ [] : [c_Groups_Oone__class_Oone(_1379794) = hAPP(c_Int_Onumber__class_Onumber__of(_1379794), _1379796), -(c_Int_Oiszero(_1379794, hAPP(c_Int_Onumber__class_Onumber__of(_1379794), 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), _1379796)))))], (31307 ^ _779530) ^ [] : [c_Int_Oiszero(_1379794, hAPP(c_Int_Onumber__class_Onumber__of(_1379794), 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), _1379796)))), -(c_Groups_Oone__class_Oone(_1379794) = hAPP(c_Int_Onumber__class_Onumber__of(_1379794), _1379796))]]], (31313 ^ _779530) ^ [_1380053, _1380055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1380053), 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)))), _1380055)), 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)))), _1380053)) = 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), _1380055), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1380053))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31319 ^ _779530) ^ [_1380213, _1380215] : [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), _1380213))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1380215)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1380213))) = 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), _1380215), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1380213)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31325 ^ _779530) ^ [_1380360, _1380362] : [-(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), _1380360)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1380362)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1380360))) = 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), _1380362)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1380360)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31331 ^ _779530) ^ [_1380454] : [c_Int_OBit0(_1380454) = c_Int_OPls, -(_1380454 = c_Int_OPls)], (31337 ^ _779530) ^ [_1380529] : [_1380529 = c_Int_OPls, -(c_Int_OBit0(_1380529) = c_Int_OPls)], (31343 ^ _779530) ^ [_1380622] : [c_Int_OPls = c_Int_OBit0(_1380622), -(c_Int_OPls = _1380622)], (31349 ^ _779530) ^ [_1380697] : [c_Int_OPls = _1380697, -(c_Int_OPls = c_Int_OBit0(_1380697))], (31355 ^ _779530) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (31357 ^ _779530) ^ [_1380796, _1380798] : [class_Int_Onumber__ring(_1380796), class_Int_Oring__char__0(_1380796), 31364 ^ _779530 : [(31365 ^ _779530) ^ [] : [c_Int_Oiszero(_1380796, hAPP(c_Int_Onumber__class_Onumber__of(_1380796), c_Int_OBit0(_1380798))), -(c_Int_Oiszero(_1380796, hAPP(c_Int_Onumber__class_Onumber__of(_1380796), _1380798)))], (31371 ^ _779530) ^ [] : [c_Int_Oiszero(_1380796, hAPP(c_Int_Onumber__class_Onumber__of(_1380796), _1380798)), -(c_Int_Oiszero(_1380796, hAPP(c_Int_Onumber__class_Onumber__of(_1380796), c_Int_OBit0(_1380798))))]]], (31377 ^ _779530) ^ [_1381101, _1381103] : [c_Int_OBit1(_1381101) = c_Int_OBit0(_1381103)], (31379 ^ _779530) ^ [_1381142, _1381144] : [c_Int_OBit0(_1381142) = c_Int_OBit1(_1381144)], (31381 ^ _779530) ^ [_1381171, _1381173] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1381171)), _1381173) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1381171), _1381173)))], (31383 ^ _779530) ^ [_1381212, _1381214] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1381212)), c_Int_OBit0(_1381214)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1381212), _1381214)))], (31385 ^ _779530) ^ [_1381255] : [-(c_Int_OBit0(_1381255) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1381255), _1381255))], (31387 ^ _779530) ^ [_1381301, _1381303] : [c_Int_OBit0(_1381301) = c_Int_OBit0(_1381303), -(_1381301 = _1381303)], (31393 ^ _779530) ^ [_1381382, _1381384] : [_1381382 = _1381384, -(c_Int_OBit0(_1381382) = c_Int_OBit0(_1381384))], (31399 ^ _779530) ^ [_1381484, _1381486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1381484)), c_Int_OBit0(_1381486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1381484), _1381486)))], (31405 ^ _779530) ^ [_1381585, _1381587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1381585), _1381587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1381585)), c_Int_OBit0(_1381587))))], (31411 ^ _779530) ^ [_1381707, _1381709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1381707)), c_Int_OBit0(_1381709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1381707), _1381709)))], (31417 ^ _779530) ^ [_1381808, _1381810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1381808), _1381810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1381808)), c_Int_OBit0(_1381810))))], (31423 ^ _779530) ^ [_1381930, _1381932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1381930)), c_Int_OBit0(_1381932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381930), _1381932)))], (31429 ^ _779530) ^ [_1382031, _1382033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382031), _1382033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1382031)), c_Int_OBit0(_1382033))))], (31435 ^ _779530) ^ [_1382153, _1382155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1382153)), c_Int_OBit0(_1382155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382153), _1382155)))], (31441 ^ _779530) ^ [_1382254, _1382256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382254), _1382256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1382254)), c_Int_OBit0(_1382256))))], (31447 ^ _779530) ^ [_1382361] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1382361)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1382361)))], (31449 ^ _779530) ^ [_1382394, _1382396] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1382394)), c_Int_OBit0(_1382396)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1382394), _1382396)))], (31451 ^ _779530) ^ [_1382437] : [class_Rings_Osemiring__1(_1382437), -(c_Int_Oiszero(_1382437, c_Groups_Ozero__class_Ozero(_1382437)))], (31457 ^ _779530) ^ [_1382514, _1382516] : [class_Rings_Osemiring__1(_1382514), 31460 ^ _779530 : [(31461 ^ _779530) ^ [] : [c_Int_Oiszero(_1382514, _1382516), -(_1382516 = c_Groups_Ozero__class_Ozero(_1382514))], (31467 ^ _779530) ^ [] : [_1382516 = c_Groups_Ozero__class_Ozero(_1382514), -(c_Int_Oiszero(_1382514, _1382516))]]], (31473 ^ _779530) ^ [_1382725] : [class_Rings_Osemiring__1(_1382725), c_Int_Oiszero(_1382725, c_Groups_Oone__class_Oone(_1382725))], (31479 ^ _779530) ^ [_1382815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1382815)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382815), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31485 ^ _779530) ^ [_1382910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382910), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1382910)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31491 ^ _779530) ^ [_1383023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1383023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1383023)))], (31497 ^ _779530) ^ [_1383106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1383106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1383106))))], (31503 ^ _779530) ^ [_1383207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383207)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383207), c_Int_OPls)))], (31509 ^ _779530) ^ [_1383302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383302), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383302)), c_Int_OPls)))], (31515 ^ _779530) ^ [_1383418, _1383420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383418)), c_Int_OBit1(_1383420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383418), _1383420)))], (31521 ^ _779530) ^ [_1383519, _1383521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383519), _1383521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383519)), c_Int_OBit1(_1383521))))], (31527 ^ _779530) ^ [_1383641, _1383643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383641)), c_Int_OBit1(_1383643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383641), _1383643)))], (31533 ^ _779530) ^ [_1383742, _1383744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383742), _1383744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1383742)), c_Int_OBit1(_1383744))))], (31539 ^ _779530) ^ [_1383861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1383861)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383861), c_Int_OPls)))], (31545 ^ _779530) ^ [_1383956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383956), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1383956)), c_Int_OPls)))], (31551 ^ _779530) ^ [_1384069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1384069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1384069)))], (31557 ^ _779530) ^ [_1384152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1384152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1384152))))], (31563 ^ _779530) ^ [_1384256, _1384258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1384256)), c_Int_OBit0(_1384258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384256), _1384258)))], (31569 ^ _779530) ^ [_1384357, _1384359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384357), _1384359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1384357)), c_Int_OBit0(_1384359))))], (31575 ^ _779530) ^ [_1384479, _1384481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1384479)), c_Int_OBit0(_1384481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384479), _1384481)))], (31581 ^ _779530) ^ [_1384580, _1384582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384580), _1384582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1384580)), c_Int_OBit0(_1384582))))], (31587 ^ _779530) ^ [_1384687, _1384689] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1384687)), c_Int_OBit0(_1384689)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384687), _1384689)))], (31589 ^ _779530) ^ [_1384730, _1384732] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1384730)), c_Int_OBit1(_1384732)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384730), _1384732)))], (31591 ^ _779530) ^ [_1384773] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1384773)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1384773)))], (31593 ^ _779530) ^ [_1384806, _1384808] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1384806)), c_Int_OBit1(_1384808)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1384806), _1384808)))], (31595 ^ _779530) ^ [_1384849, _1384851] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1384849)), c_Int_OBit0(_1384851)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1384849), _1384851)))], (31597 ^ _779530) ^ [_1384892, _1384894] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1384892))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1384894))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384892)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384894)))], (31599 ^ _779530) ^ [_1384957] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1384957)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384957))))], (31605 ^ _779530) ^ [_1385052] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385052))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1385052)))))], (31611 ^ _779530) ^ [_1385153] : [-(c_Int_Osucc(c_Int_OBit1(_1385153)) = c_Int_OBit0(c_Int_Osucc(_1385153)))], (31613 ^ _779530) ^ [_1385184] : [-(c_Int_Osucc(c_Int_OBit0(_1385184)) = c_Int_OBit1(_1385184))], (31615 ^ _779530) ^ [_1385213] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1385213)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385213)), 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))))], (31617 ^ _779530) ^ [_1385250, _1385252] : [class_Int_Onumber__ring(_1385250), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385250), c_Int_OBit0(_1385252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385250), c_Groups_Ozero__class_Ozero(_1385250)), hAPP(c_Int_Onumber__class_Onumber__of(_1385250), _1385252))), hAPP(c_Int_Onumber__class_Onumber__of(_1385250), _1385252)))], (31623 ^ _779530) ^ [_1385410, _1385412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1385410)), c_Int_OBit0(_1385412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385410), _1385412)))], (31629 ^ _779530) ^ [_1385511, _1385513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385511), _1385513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1385511)), c_Int_OBit0(_1385513))))], (31635 ^ _779530) ^ [_1385633, _1385635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1385633)), c_Int_OBit0(_1385635))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385633), _1385635)))], (31641 ^ _779530) ^ [_1385734, _1385736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385734), _1385736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1385734)), c_Int_OBit0(_1385736))))], (31647 ^ _779530) ^ [_1385856, _1385858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1385856)), c_Int_OBit1(_1385858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385856), _1385858)))], (31653 ^ _779530) ^ [_1385957, _1385959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385957), _1385959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1385957)), c_Int_OBit1(_1385959))))], (31659 ^ _779530) ^ [_1386079, _1386081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1386079)), c_Int_OBit1(_1386081))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1386079), _1386081)))], (31665 ^ _779530) ^ [_1386180, _1386182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1386180), _1386182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1386180)), c_Int_OBit1(_1386182))))], (31671 ^ _779530) ^ [] : [-(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))))], (31673 ^ _779530) ^ [_1386305, _1386307] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1386305)), _1386307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1386305), _1386307))), _1386307))], (31675 ^ _779530) ^ [_1386352, _1386354] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1386352)), c_Int_OBit1(_1386354)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1386352), c_Int_Osucc(_1386354))))], (31677 ^ _779530) ^ [_1386397, _1386399, _1386401] : [class_Int_Onumber__ring(_1386397), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1386397), _1386399), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1386401))) = hAPP(hAPP(c_HOL_OLet(_1386397, _1386397), hAPP(hAPP(c_Power_Opower__class_Opower(_1386397), _1386399), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1386401))), hAPP(hAPP(c_COMBS(_1386397, _1386397, _1386397), c_Groups_Otimes__class_Otimes(_1386397)), c_COMBI(_1386397))))], (31683 ^ _779530) ^ [_1386568, _1386570] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1386568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1386570))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1386568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1386570))), 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))))], (31685 ^ _779530) ^ [_1386619] : [class_Int_Onumber__ring(_1386619), -(c_Int_Oiszero(_1386619, hAPP(c_Int_Onumber__class_Onumber__of(_1386619), c_Int_OPls)))], (31691 ^ _779530) ^ [_1386702, _1386704] : [c_Int_Oiszero(_1386702, hAPP(c_Int_Onumber__class_Onumber__of(_1386702), c_Int_OBit1(_1386704))), class_Int_Onumber__ring(_1386702), class_Int_Oring__char__0(_1386702)], (31701 ^ _779530) ^ [_1386842, _1386844] : [class_Int_Onumber__ring(_1386842), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386842), c_Groups_Oone__class_Oone(_1386842)), c_Groups_Oone__class_Oone(_1386842))), hAPP(c_Int_Onumber__class_Onumber__of(_1386842), _1386844)) = hAPP(c_Int_Onumber__class_Onumber__of(_1386842), c_Int_OBit0(_1386844)))], (31707 ^ _779530) ^ [_1386981] : [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), _1386981))), 31710 ^ _779530 : [(31711 ^ _779530) ^ [] : [-(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(_1386981)))))], (31713 ^ _779530) ^ [] : [-(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(_1386981)))))]]], (31715 ^ _779530) ^ [_1387120, _1387122, _1387124] : [class_Int_Onumber__ring(_1387120), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1387120), hAPP(c_Int_Onumber__class_Onumber__of(_1387120), _1387122)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1387124))) = hAPP(hAPP(c_HOL_OLet(_1387120, _1387120), hAPP(hAPP(c_Power_Opower__class_Opower(_1387120), hAPP(c_Int_Onumber__class_Onumber__of(_1387120), _1387122)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1387124))), hAPP(hAPP(c_COMBS(_1387120, _1387120, _1387120), c_Groups_Otimes__class_Otimes(_1387120)), c_COMBI(_1387120))))], (31721 ^ _779530) ^ [_1387311, _1387313] : [class_Int_Onumber__ring(_1387311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387311), _1387313), hAPP(c_Int_Onumber__class_Onumber__of(_1387311), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387311), _1387313), _1387313))], (31727 ^ _779530) ^ [_1387428, _1387430] : [class_Int_Onumber__ring(_1387428), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387428), hAPP(c_Int_Onumber__class_Onumber__of(_1387428), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1387430) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387428), _1387430), _1387430))], (31733 ^ _779530) ^ [_1387545] : [class_Int_Onumber__ring(_1387545), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387545), c_Groups_Oone__class_Oone(_1387545)), c_Groups_Oone__class_Oone(_1387545)) = hAPP(c_Int_Onumber__class_Onumber__of(_1387545), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (31739 ^ _779530) ^ [_1387652, _1387654] : [class_Rings_Oring__1__no__zero__divisors(_1387652), 31742 ^ _779530 : [(31743 ^ _779530) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1387652), _1387654), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1387652), -(_1387654 = c_Groups_Ozero__class_Ozero(_1387652))], (31749 ^ _779530) ^ [] : [_1387654 = c_Groups_Ozero__class_Ozero(_1387652), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1387652), _1387654), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1387652))]]], (31755 ^ _779530) ^ [_1387893] : [class_Rings_Osemiring__1(_1387893), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1387893), c_Groups_Ozero__class_Ozero(_1387893)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1387893))], (31761 ^ _779530) ^ [] : [-(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))))], (31763 ^ _779530) ^ [] : [-(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))))], (31765 ^ _779530) ^ [_1388026, _1388028] : [class_Groups_Omonoid__mult(_1388026), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1388026), _1388028), 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(_1388026), _1388028), _1388028))], (31771 ^ _779530) ^ [_1388133, _1388135] : [class_Rings_Ocomm__semiring__1(_1388133), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388133), _1388135), _1388135) = hAPP(hAPP(c_Power_Opower__class_Opower(_1388133), _1388135), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31777 ^ _779530) ^ [] : [-(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))))))], (31779 ^ _779530) ^ [_1388258] : [-(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)))), _1388258) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1388258)))], (31781 ^ _779530) ^ [_1388290] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1388290), 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, _1388290)))], (31783 ^ _779530) ^ [_1388325] : [class_Rings_Osemiring__1(_1388325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1388325), c_Groups_Oone__class_Oone(_1388325)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1388325))], (31789 ^ _779530) ^ [_1388422, _1388424] : [class_Rings_Oring__1(_1388422), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1388422), hAPP(c_Groups_Ouminus__class_Ouminus(_1388422), _1388424)), 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(_1388422), _1388424), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31795 ^ _779530) ^ [_1388539] : [-(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)))), _1388539) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1388539), _1388539))], (31797 ^ _779530) ^ [_1388571] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1388571), 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), _1388571), _1388571))], (31799 ^ _779530) ^ [_1388606, _1388608, _1388610] : [class_Groups_Omonoid__mult(_1388606), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1388606), _1388608), 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)))), _1388610)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1388606), hAPP(hAPP(c_Power_Opower__class_Opower(_1388606), _1388608), _1388610)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31805 ^ _779530) ^ [] : [-(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)))))], (31807 ^ _779530) ^ [] : [-(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)))))], (31809 ^ _779530) ^ [] : [-(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))))], (31811 ^ _779530) ^ [_1388791] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1388791)), 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, _1388791, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31813 ^ _779530) ^ [_1388828] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1388828))), 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), _1388828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (31815 ^ _779530) ^ [_1388872, _1388874] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1388872)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1388874))) = 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), _1388872), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1388874))))], (31817 ^ _779530) ^ [_1388924] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1388924), _1388924)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1388924)], (31819 ^ _779530) ^ [_1388959] : [class_Int_Onumber__ring(_1388959), c_Int_Oiszero(_1388959, hAPP(c_Int_Onumber__class_Onumber__of(_1388959), c_Int_OBit1(c_Int_OPls)))], (31825 ^ _779530) ^ [_1389043, _1389045, _1389047] : [class_Int_Onumber__ring(_1389043), 31828 ^ _779530 : [(31829 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1389043), _1389045) = hAPP(c_Int_Onumber__class_Onumber__of(_1389043), _1389047), -(c_Int_Oiszero(_1389043, hAPP(c_Int_Onumber__class_Onumber__of(_1389043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389045), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1389047)))))], (31835 ^ _779530) ^ [] : [c_Int_Oiszero(_1389043, hAPP(c_Int_Onumber__class_Onumber__of(_1389043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1389045), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1389047)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1389043), _1389045) = hAPP(c_Int_Onumber__class_Onumber__of(_1389043), _1389047))]]], (31841 ^ _779530) ^ [_1389326, _1389328] : [class_Rings_Olinordered__idom(_1389326), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389326), c_Groups_Ozero__class_Ozero(_1389326)), hAPP(hAPP(c_Power_Opower__class_Opower(_1389326), _1389328), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (31847 ^ _779530) ^ [_1389435, _1389437, _1389439] : [class_Rings_Olinordered__semidom(_1389435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389435), hAPP(hAPP(c_Power_Opower__class_Opower(_1389435), _1389437), 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(_1389435), _1389439), 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(_1389435), c_Groups_Ozero__class_Ozero(_1389435)), _1389439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389435), _1389437), _1389439)))], (31861 ^ _779530) ^ [_1389698, _1389700, _1389702] : [class_Rings_Olinordered__semidom(_1389698), hAPP(hAPP(c_Power_Opower__class_Opower(_1389698), _1389700), 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(_1389698), _1389702), 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(_1389698), c_Groups_Ozero__class_Ozero(_1389698)), _1389700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389698), c_Groups_Ozero__class_Ozero(_1389698)), _1389702)), -(_1389700 = _1389702)], (31879 ^ _779530) ^ [_1390005, _1390007] : [class_Rings_Olinordered__idom(_1390005), 31882 ^ _779530 : [(31883 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390005), c_Groups_Ozero__class_Ozero(_1390005)), hAPP(hAPP(c_Power_Opower__class_Opower(_1390005), _1390007), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1390007 = c_Groups_Ozero__class_Ozero(_1390005)], (31889 ^ _779530) ^ [] : [-(_1390007 = c_Groups_Ozero__class_Ozero(_1390005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390005), c_Groups_Ozero__class_Ozero(_1390005)), hAPP(hAPP(c_Power_Opower__class_Opower(_1390005), _1390007), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (31895 ^ _779530) ^ [_1390229, _1390231] : [class_Rings_Olinordered__idom(_1390229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390229), hAPP(hAPP(c_Power_Opower__class_Opower(_1390229), _1390231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1390229)))], (31901 ^ _779530) ^ [_1390339, _1390341, _1390343] : [class_Rings_Olinordered__idom(_1390339), 31904 ^ _779530 : [(31905 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390339), hAPP(hAPP(c_Power_Opower__class_Opower(_1390339), _1390341), 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(_1390339), _1390343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1390339), 31908 ^ _779530 : [(31909 ^ _779530) ^ [] : [-(_1390341 = c_Groups_Ozero__class_Ozero(_1390339))], (31911 ^ _779530) ^ [] : [-(_1390343 = c_Groups_Ozero__class_Ozero(_1390339))]]], (31913 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390339), hAPP(hAPP(c_Power_Opower__class_Opower(_1390339), _1390341), 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(_1390339), _1390343), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1390339)), _1390341 = c_Groups_Ozero__class_Ozero(_1390339), _1390343 = c_Groups_Ozero__class_Ozero(_1390339)]]], (31923 ^ _779530) ^ [_1390714, _1390716] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1390714), hAPP(c_Int_Onumber__class_Onumber__of(_1390714), _1390716)), 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(_1390714), hAPP(c_Int_Onumber__class_Onumber__of(_1390714), _1390716)), hAPP(c_Int_Onumber__class_Onumber__of(_1390714), _1390716))), class_Groups_Omonoid__mult(_1390714), class_Int_Onumber(_1390714)], (31933 ^ _779530) ^ [_1390901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1390901), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1390901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1390901 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31943 ^ _779530) ^ [] : [-(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))))], (31945 ^ _779530) ^ [_1391017, _1391019] : [class_Rings_Oring__1__no__zero__divisors(_1391017), 31948 ^ _779530 : [(31959 ^ _779530) ^ [] : [31960 ^ _779530 : [(31961 ^ _779530) ^ [] : [_1391019 = c_Groups_Oone__class_Oone(_1391017)], (31963 ^ _779530) ^ [] : [_1391019 = hAPP(c_Groups_Ouminus__class_Ouminus(_1391017), c_Groups_Oone__class_Oone(_1391017))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1391017), _1391019), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1391017))], (31949 ^ _779530) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1391017), _1391019), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1391017), -(_1391019 = c_Groups_Oone__class_Oone(_1391017)), -(_1391019 = hAPP(c_Groups_Ouminus__class_Ouminus(_1391017), c_Groups_Oone__class_Oone(_1391017)))]]], (31967 ^ _779530) ^ [_1391324, _1391326, _1391328] : [class_Rings_Ocomm__semiring__1(_1391324), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1391324), _1391326), 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)))), _1391328)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391324), hAPP(hAPP(c_Power_Opower__class_Opower(_1391324), _1391326), _1391328)), hAPP(hAPP(c_Power_Opower__class_Opower(_1391324), _1391326), _1391328)))], (31973 ^ _779530) ^ [_1391471, _1391473, _1391475] : [class_Rings_Oring__1(_1391471), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1391471), hAPP(c_Groups_Ouminus__class_Ouminus(_1391471), _1391473)), 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)))), _1391475)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1391471), _1391473), 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)))), _1391475)))], (31979 ^ _779530) ^ [_1391602, _1391604, _1391606] : [class_Rings_Olinordered__semidom(_1391602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391602), hAPP(hAPP(c_Power_Opower__class_Opower(_1391602), _1391604), 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(_1391602), _1391606), 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(_1391602), c_Groups_Ozero__class_Ozero(_1391602)), _1391606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391602), _1391604), _1391606)))], (31993 ^ _779530) ^ [_1391865, _1391867, _1391869] : [class_Rings_Olinordered__idom(_1391865), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391865), c_Groups_Ozero__class_Ozero(_1391865)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391865), hAPP(hAPP(c_Power_Opower__class_Opower(_1391865), _1391867), 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(_1391865), _1391869), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (31999 ^ _779530) ^ [_1392008, _1392010, _1392012] : [class_Rings_Olinordered__idom(_1392008), 32002 ^ _779530 : [(32003 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392008), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392008), hAPP(hAPP(c_Power_Opower__class_Opower(_1392008), _1392010), 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(_1392008), _1392012), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1392008))), 32006 ^ _779530 : [(32007 ^ _779530) ^ [] : [-(_1392010 = c_Groups_Ozero__class_Ozero(_1392008))], (32009 ^ _779530) ^ [] : [-(_1392012 = c_Groups_Ozero__class_Ozero(_1392008))]]], (32011 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1392008), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392008), hAPP(hAPP(c_Power_Opower__class_Opower(_1392008), _1392010), 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(_1392008), _1392012), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1392008)))), _1392010 = c_Groups_Ozero__class_Ozero(_1392008), _1392012 = c_Groups_Ozero__class_Ozero(_1392008)]]], (32021 ^ _779530) ^ [_1392404, _1392406, _1392408] : [class_Rings_Olinordered__idom(_1392404), 32024 ^ _779530 : [(32035 ^ _779530) ^ [] : [32036 ^ _779530 : [(32037 ^ _779530) ^ [] : [-(_1392406 = c_Groups_Ozero__class_Ozero(_1392404))], (32039 ^ _779530) ^ [] : [-(_1392408 = c_Groups_Ozero__class_Ozero(_1392404))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392404), c_Groups_Ozero__class_Ozero(_1392404)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392404), hAPP(hAPP(c_Power_Opower__class_Opower(_1392404), _1392406), 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(_1392404), _1392408), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (32025 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392404), c_Groups_Ozero__class_Ozero(_1392404)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392404), hAPP(hAPP(c_Power_Opower__class_Opower(_1392404), _1392406), 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(_1392404), _1392408), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1392406 = c_Groups_Ozero__class_Ozero(_1392404), _1392408 = c_Groups_Ozero__class_Ozero(_1392404)]]], (32043 ^ _779530) ^ [_1392779, _1392781, _1392783] : [class_Rings_Olinordered__idom(_1392779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1392779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392779), hAPP(hAPP(c_Power_Opower__class_Opower(_1392779), _1392781), 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(_1392779), _1392783), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1392779)))], (32049 ^ _779530) ^ [_1392923, _1392925, _1392927] : [class_Int_Onumber__ring(_1392923), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1392923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392923), _1392925), _1392927)), 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(_1392923), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392923), hAPP(hAPP(c_Power_Opower__class_Opower(_1392923), _1392925), 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(_1392923), _1392927), 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(_1392923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392923), hAPP(c_Int_Onumber__class_Onumber__of(_1392923), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1392925)), _1392927)))], (32055 ^ _779530) ^ [_1393138, _1393140, _1393142] : [class_Rings_Olinordered__idom(_1393138), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393138), c_Groups_Ozero__class_Ozero(_1393138)), hAPP(hAPP(c_Power_Opower__class_Opower(_1393138), _1393140), 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)))), _1393142)))))], (32061 ^ _779530) ^ [_1393255, _1393257, _1393259] : [class_Groups_Omonoid__mult(_1393255), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1393255), _1393257), 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)))), _1393259))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393255), _1393257), hAPP(hAPP(c_Power_Opower__class_Opower(_1393255), hAPP(hAPP(c_Power_Opower__class_Opower(_1393255), _1393257), _1393259)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (32067 ^ _779530) ^ [_1393408, _1393410, _1393412] : [class_Rings_Ocomm__semiring__1(_1393408), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1393408), _1393410), 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)))), _1393412))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393408), _1393410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393408), hAPP(hAPP(c_Power_Opower__class_Opower(_1393408), _1393410), _1393412)), hAPP(hAPP(c_Power_Opower__class_Opower(_1393408), _1393410), _1393412))))], (32073 ^ _779530) ^ [_1393577, _1393579] : [class_Rings_Oring__1(_1393577), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1393577), hAPP(c_Groups_Ouminus__class_Ouminus(_1393577), c_Groups_Oone__class_Oone(_1393577))), 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)))), _1393579)) = c_Groups_Oone__class_Oone(_1393577))], (32079 ^ _779530) ^ [_1393701, _1393703] : [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), _1393701))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1393703))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1393701))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393703)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393701)))], (32085 ^ _779530) ^ [_1393838, _1393840] : [-(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), _1393838)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1393840))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1393838))) = 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), _1393840)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1393838)))], (32091 ^ _779530) ^ [_1393927] : [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, _1393927, 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, _1393927, 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))], (32097 ^ _779530) ^ [_1394018] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1394018, 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, _1394018, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32103 ^ _779530) ^ [_1394115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1394115)), -(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), _1394115), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32109 ^ _779530) ^ [_1394210, _1394212, _1394214] : [class_Int_Onumber__ring(_1394210), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1394210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1394210), _1394212), _1394214)), 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(_1394210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1394210), hAPP(hAPP(c_Power_Opower__class_Opower(_1394210), _1394212), 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(_1394210), _1394214), 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(_1394210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394210), hAPP(c_Int_Onumber__class_Onumber__of(_1394210), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1394212)), _1394214)))], (32115 ^ _779530) ^ [_1394425, _1394427, _1394429] : [class_Rings_Olinordered__idom(_1394425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394425), c_Groups_Ozero__class_Ozero(_1394425)), hAPP(hAPP(c_Power_Opower__class_Opower(_1394425), _1394427), 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)))), _1394429))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394425), c_Groups_Ozero__class_Ozero(_1394425)), _1394427)))], (32125 ^ _779530) ^ [_1394620, _1394622, _1394624] : [class_Rings_Olinordered__idom(_1394620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394620), _1394622), c_Groups_Ozero__class_Ozero(_1394620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394620), hAPP(hAPP(c_Power_Opower__class_Opower(_1394620), _1394622), 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)))), _1394624)))), c_Groups_Ozero__class_Ozero(_1394620))))], (32135 ^ _779530) ^ [_1394815, _1394817] : [class_Rings_Oring__1(_1394815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1394815), hAPP(c_Groups_Ouminus__class_Ouminus(_1394815), c_Groups_Oone__class_Oone(_1394815))), 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)))), _1394817))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1394815), c_Groups_Oone__class_Oone(_1394815)))], (32141 ^ _779530) ^ [_1394946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1394946)), -(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), _1394946), 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)))))))], (32147 ^ _779530) ^ [_1395053, _1395055] : [class_Int_Onumber__ring(_1395053), 32150 ^ _779530 : [(32151 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1395053) = hAPP(c_Int_Onumber__class_Onumber__of(_1395053), _1395055), -(c_Int_Oiszero(_1395053, hAPP(c_Int_Onumber__class_Onumber__of(_1395053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1395055)))))], (32157 ^ _779530) ^ [] : [c_Int_Oiszero(_1395053, hAPP(c_Int_Onumber__class_Onumber__of(_1395053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1395055)))), -(c_Groups_Ozero__class_Ozero(_1395053) = hAPP(c_Int_Onumber__class_Onumber__of(_1395053), _1395055))]]], (32163 ^ _779530) ^ [_1395312, _1395314] : [class_Int_Onumber__ring(_1395312), 32166 ^ _779530 : [(32167 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1395312), _1395314) = c_Groups_Ozero__class_Ozero(_1395312), -(c_Int_Oiszero(_1395312, hAPP(c_Int_Onumber__class_Onumber__of(_1395312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1395314), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (32173 ^ _779530) ^ [] : [c_Int_Oiszero(_1395312, hAPP(c_Int_Onumber__class_Onumber__of(_1395312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1395314), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1395312), _1395314) = c_Groups_Ozero__class_Ozero(_1395312))]]], (32179 ^ _779530) ^ [_1395571, _1395573] : [class_Rings_Osemiring__1(_1395571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395573)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1395571), 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)))), _1395573))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1395571), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1395571), hAPP(c_Int_Onat, _1395573))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1395571), hAPP(c_Int_Onat, _1395573))))], (32189 ^ _779530) ^ [_1395772, _1395774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395772)), -(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)))), _1395774)), 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)))), _1395772)) = 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, _1395774, _1395772))))], (32195 ^ _779530) ^ [_1395899, _1395901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395899), 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)))), _1395901))), 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)))), _1395899)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1395901), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1395899))], (32201 ^ _779530) ^ [_1396040, _1396042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396040)), -(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)))), _1396042))), 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)))), _1396040)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396042), _1396040))], (32207 ^ _779530) ^ [_1396163, _1396165, _1396167] : [-(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), _1396163)), 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))), _1396165))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1396167))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1396167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1396163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1396163), 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), _1396167), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1396165)))))], (32209 ^ _779530) ^ [_1396250] : [-(c_Divides_Oadjust(_1396250) = 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)), _1396250))))), 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)), _1396250))))), 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))))))))], (32211 ^ _779530) ^ [_1396311, _1396313, _1396315] : [-(hAPP(c_Divides_Oadjust(_1396311), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1396313), _1396315)) = 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), _1396315), _1396311)), 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)))), _1396313)), 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)))), _1396313)), _1396315))))], (32213 ^ _779530) ^ [_1396391] : [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), _1396391))), 32216 ^ _779530 : [(32217 ^ _779530) ^ [] : [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), _1396391))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396391)) = 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)))], (32223 ^ _779530) ^ [] : [-(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), _1396391)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396391)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1396391)), 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), _1396391)))))]]], (32229 ^ _779530) ^ [_1396660, _1396662] : [32230 ^ _779530 : [(32231 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396660), _1396662))], (32233 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396662), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1396660, _1396662) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396660))], (32237 ^ _779530) ^ [_1396801, _1396803] : [-(c_Divides_OposDivAlg(_1396801, _1396803) = hAPP(c_Divides_Oadjust(_1396803), c_Divides_OposDivAlg(_1396801, 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)))), _1396803)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396801), _1396803))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396803), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32247 ^ _779530) ^ [_1396870, _1396872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396870)), 32250 ^ _779530 : [(32251 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396872), _1396870)), -(c_Divides_OposDivAlg(_1396872, _1396870) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396872))], (32257 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396872), _1396870))), -(c_Divides_OposDivAlg(_1396872, _1396870) = hAPP(c_Divides_Oadjust(_1396870), c_Divides_OposDivAlg(_1396872, 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)))), _1396870))))]]], (32263 ^ _779530) ^ [_1397110, _1397112] : [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), _1397110))), 32266 ^ _779530 : [(32267 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397112)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397110))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397112), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397110)) = 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), _1397112)))], (32273 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397112)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397110)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397112), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397110)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397110)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397112), 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), _1397110)))))]]], (32279 ^ _779530) ^ [_1397428, _1397430] : [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), _1397428), _1397430))), 32282 ^ _779530 : [(32283 ^ _779530) ^ [] : [32284 ^ _779530 : [(32285 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397428), _1397430))], (32287 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1397430), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1397428, _1397430) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397428))], (32291 ^ _779530) ^ [] : [-(c_Divides_OposDivAlg(_1397428, _1397430) = hAPP(c_Divides_Oadjust(_1397430), c_Divides_OposDivAlg(_1397428, 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)))), _1397430)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397428), _1397430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1397430), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32301 ^ _779530) ^ [_1397751, _1397753] : [class_Rings_Oring__1(_1397751), 32304 ^ _779530 : [(32305 ^ _779530) ^ [] : [_1397753 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1397751), _1397753) = c_Groups_Ozero__class_Ozero(_1397751))], (32311 ^ _779530) ^ [] : [-(_1397753 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32314 ^ _779530 : [(32315 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397753), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1397751), _1397753) = hAPP(c_Groups_Ouminus__class_Ouminus(_1397751), hAPP(c_Int_Oring__1__class_Oof__int(_1397751), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1397753))))], (32321 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397753), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1397751), _1397753) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1397751), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1397751, _1397751)), tc_fun(tc_Int_Oint, _1397751)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1397751, _1397751), _1397751), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1397751, _1397751)), tc_fun(tc_Int_Oint, _1397751)), tc_Int_Oint), c_COMBB(tc_fun(_1397751, _1397751), _1397751, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1397751, tc_fun(tc_fun(_1397751, _1397751), _1397751), tc_Int_Oint), c_HOL_OLet(_1397751, _1397751)), c_Int_Oring__1__class_Oof__int(_1397751)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1397751, _1397751), tc_fun(_1397751, _1397751)), hAPP(hAPP(c_COMBB(tc_fun(_1397751, tc_fun(_1397751, _1397751)), tc_fun(tc_fun(_1397751, _1397751), tc_fun(_1397751, _1397751)), tc_Int_Oint), c_COMBS(_1397751, _1397751, _1397751)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1397751, _1397751), tc_fun(_1397751, tc_fun(_1397751, _1397751))), hAPP(hAPP(c_COMBB(tc_fun(_1397751, tc_fun(_1397751, _1397751)), tc_fun(tc_fun(_1397751, _1397751), tc_fun(_1397751, tc_fun(_1397751, _1397751))), tc_Int_Oint), c_COMBB(_1397751, tc_fun(_1397751, _1397751), _1397751)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1397751, tc_fun(_1397751, _1397751)), tc_Int_Oint), c_If(_1397751)), 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(_1397751, _1397751, _1397751), c_Groups_Oplus__class_Oplus(_1397751)), c_COMBI(_1397751))))), hAPP(hAPP(c_COMBC(_1397751, _1397751, _1397751), hAPP(hAPP(c_COMBB(_1397751, tc_fun(_1397751, _1397751), _1397751), c_Groups_Oplus__class_Oplus(_1397751)), hAPP(hAPP(c_COMBS(_1397751, _1397751, _1397751), c_Groups_Oplus__class_Oplus(_1397751)), c_COMBI(_1397751)))), c_Groups_Oone__class_Oone(_1397751))))), c_Divides_Odivmod__int(_1397753, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (32327 ^ _779530) ^ [_1398664] : [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), _1398664))), 32330 ^ _779530 : [(32331 ^ _779530) ^ [] : [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), _1398664)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398664)) = 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), _1398664))))], (32337 ^ _779530) ^ [] : [-(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), _1398664))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398664)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398664)), 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), _1398664)))))]]], (32343 ^ _779530) ^ [] : [c_Int_OPls = c_Int_OMin], (32345 ^ _779530) ^ [] : [c_Int_OMin = c_Int_OPls], (32347 ^ _779530) ^ [_1399002, _1399004] : [class_Int_Onumber__ring(_1399002), -(hAPP(c_Int_Onumber__class_Onumber__of(_1399002), _1399004) = hAPP(c_Int_Oring__1__class_Oof__int(_1399002), _1399004))], (32353 ^ _779530) ^ [_1399097] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399097) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1399097))], (32355 ^ _779530) ^ [_1399126] : [class_Int_Onumber__ring(_1399126), -(hAPP(c_Int_Oring__1__class_Oof__int(_1399126), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1399126), c_Int_OMin))], (32361 ^ _779530) ^ [_1399231] : [c_Int_OBit1(_1399231) = c_Int_OMin, -(_1399231 = c_Int_OMin)], (32367 ^ _779530) ^ [_1399306] : [_1399306 = c_Int_OMin, -(c_Int_OBit1(_1399306) = c_Int_OMin)], (32373 ^ _779530) ^ [_1399399] : [c_Int_OMin = c_Int_OBit1(_1399399), -(c_Int_OMin = _1399399)], (32379 ^ _779530) ^ [_1399474] : [c_Int_OMin = _1399474, -(c_Int_OMin = c_Int_OBit1(_1399474))], (32385 ^ _779530) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (32387 ^ _779530) ^ [_1399573] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1399573)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1399573))], (32389 ^ _779530) ^ [_1399605, _1399607, _1399609] : [class_Int_Oring__char__0(_1399605), 32392 ^ _779530 : [(32393 ^ _779530) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1399605), _1399607) = hAPP(c_Int_Oring__1__class_Oof__int(_1399605), _1399609), -(_1399607 = _1399609)], (32399 ^ _779530) ^ [] : [_1399607 = _1399609, -(hAPP(c_Int_Oring__1__class_Oof__int(_1399605), _1399607) = hAPP(c_Int_Oring__1__class_Oof__int(_1399605), _1399609))]]], (32405 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (32407 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (32409 ^ _779530) ^ [_1399897] : [c_Int_OBit0(_1399897) = c_Int_OMin], (32411 ^ _779530) ^ [_1399931] : [c_Int_OMin = c_Int_OBit0(_1399931)], (32413 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32415 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (32417 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (32419 ^ _779530) ^ [_1400028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1400028)))], (32425 ^ _779530) ^ [_1400111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1400111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400111))))], (32431 ^ _779530) ^ [_1400212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400212)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400212), c_Int_OMin)))], (32437 ^ _779530) ^ [_1400307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400307), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400307)), c_Int_OMin)))], (32443 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (32445 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (32447 ^ _779530) ^ [_1400462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400462)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400462), c_Int_OMin)))], (32453 ^ _779530) ^ [_1400557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400557), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400557)), c_Int_OMin)))], (32459 ^ _779530) ^ [_1400670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1400670)))], (32465 ^ _779530) ^ [_1400753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1400753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1400753))))], (32471 ^ _779530) ^ [_1400854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1400854)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400854), c_Int_OMin)))], (32477 ^ _779530) ^ [_1400949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400949), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1400949)), c_Int_OMin)))], (32483 ^ _779530) ^ [_1401062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1401062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1401062)))], (32489 ^ _779530) ^ [_1401145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1401145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1401145))))], (32495 ^ _779530) ^ [] : [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)], (32497 ^ _779530) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32499 ^ _779530) ^ [_1401276] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1401276) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1401276))], (32501 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (32503 ^ _779530) ^ [_1401323] : [class_Rings_Oring__1(_1401323), -(hAPP(c_Int_Oring__1__class_Oof__int(_1401323), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1401323))], (32509 ^ _779530) ^ [_1401410, _1401412] : [class_Int_Oring__char__0(_1401410), 32512 ^ _779530 : [(32513 ^ _779530) ^ [] : [c_Groups_Ozero__class_Ozero(_1401410) = hAPP(c_Int_Oring__1__class_Oof__int(_1401410), _1401412), -(_1401412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32519 ^ _779530) ^ [] : [_1401412 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1401410) = hAPP(c_Int_Oring__1__class_Oof__int(_1401410), _1401412))]]], (32525 ^ _779530) ^ [_1401636, _1401638] : [class_Int_Oring__char__0(_1401636), 32528 ^ _779530 : [(32529 ^ _779530) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1401636), _1401638) = c_Groups_Ozero__class_Ozero(_1401636), -(_1401638 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32535 ^ _779530) ^ [] : [_1401638 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1401636), _1401638) = c_Groups_Ozero__class_Ozero(_1401636))]]], (32541 ^ _779530) ^ [_1401862, _1401864, _1401866] : [class_Rings_Olinordered__idom(_1401862), 32544 ^ _779530 : [(32545 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401862), hAPP(c_Int_Oring__1__class_Oof__int(_1401862), _1401864)), hAPP(c_Int_Oring__1__class_Oof__int(_1401862), _1401866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401864), _1401866)))], (32551 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1401864), _1401866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401862), hAPP(c_Int_Oring__1__class_Oof__int(_1401862), _1401864)), hAPP(c_Int_Oring__1__class_Oof__int(_1401862), _1401866))))]]], (32557 ^ _779530) ^ [_1402139, _1402141, _1402143] : [class_Rings_Olinordered__idom(_1402139), 32560 ^ _779530 : [(32561 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402139), hAPP(c_Int_Oring__1__class_Oof__int(_1402139), _1402141)), hAPP(c_Int_Oring__1__class_Oof__int(_1402139), _1402143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402141), _1402143)))], (32567 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402141), _1402143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402139), hAPP(c_Int_Oring__1__class_Oof__int(_1402139), _1402141)), hAPP(c_Int_Oring__1__class_Oof__int(_1402139), _1402143))))]]], (32573 ^ _779530) ^ [_1402416] : [class_Int_Onumber__ring(_1402416), c_Int_Oiszero(_1402416, hAPP(c_Int_Onumber__class_Onumber__of(_1402416), c_Int_OMin))], (32579 ^ _779530) ^ [_1402500, _1402502, _1402504] : [class_Rings_Oring__1(_1402500), -(hAPP(c_Int_Oring__1__class_Oof__int(_1402500), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402502), _1402504)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1402500), hAPP(c_Int_Oring__1__class_Oof__int(_1402500), _1402502)), hAPP(c_Int_Oring__1__class_Oof__int(_1402500), _1402504)))], (32585 ^ _779530) ^ [_1402635, _1402637] : [class_Int_Onumber__ring(_1402635), -(hAPP(c_Int_Oring__1__class_Oof__int(_1402635), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402637)) = hAPP(c_Int_Onumber__class_Onumber__of(_1402635), _1402637))], (32591 ^ _779530) ^ [_1402736, _1402738, _1402740] : [class_Rings_Oring__1(_1402736), -(hAPP(c_Int_Oring__1__class_Oof__int(_1402736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1402738), _1402740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402736), hAPP(c_Int_Oring__1__class_Oof__int(_1402736), _1402738)), hAPP(c_Int_Oring__1__class_Oof__int(_1402736), _1402740)))], (32597 ^ _779530) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (32599 ^ _779530) ^ [_1402889] : [class_Rings_Oring__1(_1402889), -(hAPP(c_Int_Oring__1__class_Oof__int(_1402889), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1402889))], (32605 ^ _779530) ^ [_1402976, _1402978, _1402980] : [class_Rings_Oring__1(_1402976), -(hAPP(c_Int_Oring__1__class_Oof__int(_1402976), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1402978), _1402980)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1402976), hAPP(c_Int_Oring__1__class_Oof__int(_1402976), _1402978)), hAPP(c_Int_Oring__1__class_Oof__int(_1402976), _1402980)))], (32611 ^ _779530) ^ [_1403111] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1403111), c_Int_OMin) = c_Int_Osucc(_1403111))], (32613 ^ _779530) ^ [_1403142, _1403144] : [class_Rings_Oring__1(_1403142), -(hAPP(c_Int_Oring__1__class_Oof__int(_1403142), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1403144)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1403142), _1403144))], (32619 ^ _779530) ^ [_1403243, _1403245] : [class_Rings_Oring__1(_1403243), -(hAPP(c_Int_Oring__1__class_Oof__int(_1403243), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1403245)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1403243), hAPP(c_Int_Oring__1__class_Oof__int(_1403243), _1403245)))], (32625 ^ _779530) ^ [_1403354, _1403356] : [class_Rings_Oring__1(_1403354), -(hBOOL(hAPP(hAPP(c_member(_1403354), hAPP(c_Int_Oring__1__class_Oof__int(_1403354), _1403356)), c_Int_Oring__1__class_OInts(_1403354))))], (32631 ^ _779530) ^ [_1403457, _1403459, _1403461] : [class_Rings_Oring__1(_1403457), -(hAPP(c_Int_Oring__1__class_Oof__int(_1403457), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1403459), _1403461)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1403457), hAPP(c_Int_Oring__1__class_Oof__int(_1403457), _1403459)), _1403461))], (32637 ^ _779530) ^ [_1403582, _1403584] : [class_Int_Onumber__ring(_1403582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403582), hAPP(c_Int_Onumber__class_Onumber__of(_1403582), c_Int_OMin)), _1403584) = hAPP(c_Groups_Ouminus__class_Ouminus(_1403582), _1403584))], (32643 ^ _779530) ^ [_1403693, _1403695] : [class_Int_Onumber__ring(_1403693), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403693), _1403695), hAPP(c_Int_Onumber__class_Onumber__of(_1403693), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1403693), _1403695))], (32649 ^ _779530) ^ [_1403804] : [class_Int_Onumber__ring(_1403804), -(hAPP(c_Int_Onumber__class_Onumber__of(_1403804), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1403804), c_Groups_Oone__class_Oone(_1403804)))], (32655 ^ _779530) ^ [_1403901] : [class_Int_Onumber__ring(_1403901), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1403901), c_Groups_Oone__class_Oone(_1403901)) = hAPP(c_Int_Onumber__class_Onumber__of(_1403901), c_Int_OMin))], (32661 ^ _779530) ^ [_1404010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1404010)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404010), c_Int_OMin)))], (32667 ^ _779530) ^ [_1404105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404105), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1404105)), c_Int_OMin)))], (32673 ^ _779530) ^ [_1404218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1404218))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1404218)))], (32679 ^ _779530) ^ [_1404301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1404301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1404301))))], (32685 ^ _779530) ^ [_1404390] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1404390, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32687 ^ _779530) ^ [_1404417] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1404417)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1404417)))], (32689 ^ _779530) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (32691 ^ _779530) ^ [_1404483, _1404485] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1404483), _1404485) = c_Groups_Oone__class_Oone(tc_Int_Oint), 32696 ^ _779530 : [(32697 ^ _779530) ^ [] : [-(_1404483 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (32699 ^ _779530) ^ [] : [-(_1404485 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 32700 ^ _779530 : [(32701 ^ _779530) ^ [] : [-(_1404483 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (32703 ^ _779530) ^ [] : [-(_1404485 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (32705 ^ _779530) ^ [_1404667, _1404669] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1404667), _1404669) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 32706 ^ _779530 : [(32707 ^ _779530) ^ [] : [_1404667 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1404669 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (32713 ^ _779530) ^ [] : [_1404667 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1404669 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (32721 ^ _779530) ^ [_1404893, _1404895] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1404893), _1404895) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1404893 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1404893 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (32731 ^ _779530) ^ [_1404995] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1404995)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1404995)))], (32733 ^ _779530) ^ [_1405028] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1405028)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1405028)))], (32735 ^ _779530) ^ [_1405061] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1405061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1405061))], (32737 ^ _779530) ^ [_1405093, _1405095, _1405097, _1405099] : [class_Rings_Oring__1(_1405093), -(hAPP(c_Int_Oring__1__class_Oof__int(_1405093), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405095, tc_Int_Oint), _1405097), _1405099)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405095, _1405093), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1405093, _1405095), c_Int_Oring__1__class_Oof__int(_1405093)), _1405097)), _1405099))], (32743 ^ _779530) ^ [_1405242, _1405244, _1405246, _1405248] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1405242), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405244, tc_Int_Oint), _1405246), _1405248)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1405244, _1405242), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1405242, _1405244), c_Int_Oring__1__class_Oof__int(_1405242)), _1405246)), _1405248)), class_Groups_Ocomm__monoid__mult(_1405242), class_Rings_Oring__1(_1405242)], (32753 ^ _779530) ^ [_1405445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1405445)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1405445) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (32759 ^ _779530) ^ [_1405530, _1405532] : [class_Rings_Olinordered__idom(_1405530), 32762 ^ _779530 : [(32763 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405530), hAPP(c_Int_Oring__1__class_Oof__int(_1405530), _1405532)), c_Groups_Ozero__class_Ozero(_1405530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405532), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32769 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405532), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405530), hAPP(c_Int_Oring__1__class_Oof__int(_1405530), _1405532)), c_Groups_Ozero__class_Ozero(_1405530))))]]], (32775 ^ _779530) ^ [_1405792, _1405794] : [class_Rings_Olinordered__idom(_1405792), 32778 ^ _779530 : [(32779 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405792), c_Groups_Ozero__class_Ozero(_1405792)), hAPP(c_Int_Oring__1__class_Oof__int(_1405792), _1405794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1405794)))], (32785 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1405794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405792), c_Groups_Ozero__class_Ozero(_1405792)), hAPP(c_Int_Oring__1__class_Oof__int(_1405792), _1405794))))]]], (32791 ^ _779530) ^ [_1406045, _1406047] : [class_Rings_Olinordered__idom(_1406045), 32794 ^ _779530 : [(32795 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406045), c_Groups_Ozero__class_Ozero(_1406045)), hAPP(c_Int_Oring__1__class_Oof__int(_1406045), _1406047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1406047)))], (32801 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1406047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406045), c_Groups_Ozero__class_Ozero(_1406045)), hAPP(c_Int_Oring__1__class_Oof__int(_1406045), _1406047))))]]], (32807 ^ _779530) ^ [_1406298, _1406300] : [class_Rings_Olinordered__idom(_1406298), 32810 ^ _779530 : [(32811 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406298), hAPP(c_Int_Oring__1__class_Oof__int(_1406298), _1406300)), c_Groups_Ozero__class_Ozero(_1406298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32817 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406298), hAPP(c_Int_Oring__1__class_Oof__int(_1406298), _1406300)), c_Groups_Ozero__class_Ozero(_1406298))))]]], (32823 ^ _779530) ^ [_1406560, _1406562] : [class_Rings_Oring__1(_1406560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1406562)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1406560), hAPP(c_Int_Onat, _1406562)) = hAPP(c_Int_Oring__1__class_Oof__int(_1406560), _1406562))], (32833 ^ _779530) ^ [_1406717] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1406717) = 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), _1406717), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (32835 ^ _779530) ^ [_1406752, _1406754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1406752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1406752), _1406754)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1406752), _1406754) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (32845 ^ _779530) ^ [_1406919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1406919)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1406919) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1406919), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32851 ^ _779530) ^ [_1407018, _1407020] : [class_Rings_Oring__1(_1407018), 32854 ^ _779530 : [(32855 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407020), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1407018), _1407020) = hAPP(c_Groups_Ouminus__class_Ouminus(_1407018), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407018), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1407020)))))], (32861 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407020), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1407018), _1407020) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407018), hAPP(c_Int_Onat, _1407020)))]]], (32867 ^ _779530) ^ [_1407280, _1407282] : [class_Int_Onumber__ring(_1407280), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1407280), hAPP(c_Int_Onumber__class_Onumber__of(_1407280), 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)))), _1407282)) = c_Groups_Oone__class_Oone(_1407280))], (32873 ^ _779530) ^ [_1407391, _1407393] : [class_Int_Onumber__ring(_1407391), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1407391), hAPP(c_Int_Onumber__class_Onumber__of(_1407391), 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)))), _1407393))) = hAPP(c_Int_Onumber__class_Onumber__of(_1407391), c_Int_OMin))], (32879 ^ _779530) ^ [_1407523, _1407525] : [32880 ^ _779530 : [(32881 ^ _779530) ^ [] : [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), _1407523), _1407525)))], (32883 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407525), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1407523, _1407525) = 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), _1407523), _1407525)))], (32887 ^ _779530) ^ [_1407682, _1407684] : [-(c_Divides_OnegDivAlg(_1407682, _1407684) = hAPP(c_Divides_Oadjust(_1407684), c_Divides_OnegDivAlg(_1407682, 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)))), _1407684)))), -(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), _1407682), _1407684)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407684), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32897 ^ _779530) ^ [_1407754, _1407756] : [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), _1407754))), 32900 ^ _779530 : [(32901 ^ _779530) ^ [] : [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), _1407756)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407756), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754)) = 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), _1407756)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754))))], (32907 ^ _779530) ^ [] : [-(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), _1407756)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407756), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407754)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407756), 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), _1407754)))))]]], (32913 ^ _779530) ^ [_1408102, _1408104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1408102)), 32916 ^ _779530 : [(32917 ^ _779530) ^ [] : [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), _1408104), _1408102))), -(c_Divides_OnegDivAlg(_1408104, _1408102) = 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), _1408104), _1408102)))], (32923 ^ _779530) ^ [] : [-(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), _1408104), _1408102)))), -(c_Divides_OnegDivAlg(_1408104, _1408102) = hAPP(c_Divides_Oadjust(_1408102), c_Divides_OnegDivAlg(_1408104, 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)))), _1408102))))]]], (32929 ^ _779530) ^ [_1408366, _1408368] : [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), _1408366), _1408368))), 32932 ^ _779530 : [(32933 ^ _779530) ^ [] : [32934 ^ _779530 : [(32935 ^ _779530) ^ [] : [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), _1408366), _1408368)))], (32937 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1408368), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1408366, _1408368) = 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), _1408366), _1408368)))], (32941 ^ _779530) ^ [] : [-(c_Divides_OnegDivAlg(_1408366, _1408368) = hAPP(c_Divides_Oadjust(_1408368), c_Divides_OnegDivAlg(_1408366, 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)))), _1408368)))), -(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), _1408366), _1408368)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1408368), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32951 ^ _779530) ^ [_1408713, _1408715, _1408717] : [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), _1408713), _1408715))), -(hBOOL(hAPP(hAPP(_1408717, _1408713), _1408715))), 32958 ^ _779530 : [(32959 ^ _779530) ^ [] : [-(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), 32956 ^ [_1408713, _1408715, _1408717]), 32957 ^ [_1408713, _1408715, _1408717]))))], (32971 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1408717, 32956 ^ [_1408713, _1408715, _1408717]), 32957 ^ [_1408713, _1408715, _1408717]))], (32961 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1408717, 32956 ^ [_1408713, _1408715, _1408717]), 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)))), 32957 ^ [_1408713, _1408715, _1408717])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32956 ^ [_1408713, _1408715, _1408717]), 32957 ^ [_1408713, _1408715, _1408717]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 32957 ^ [_1408713, _1408715, _1408717]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (32975 ^ _779530) ^ [_1409205] : [_1409205 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1409205) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32981 ^ _779530) ^ [_1409281] : [-(_1409281 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 32984 ^ _779530 : [(32985 ^ _779530) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1409281, 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, _1409281) = 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), _1409281), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (32991 ^ _779530) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1409281, 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, _1409281) = 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), _1409281), 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)))]]], (32997 ^ _779530) ^ [] : [-(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))], (32999 ^ _779530) ^ [] : [-(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))], (33001 ^ _779530) ^ [] : [-(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)))], (33003 ^ _779530) ^ [_1409595, _1409597] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1409595, _1409597) = 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), _1409595), _1409597)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1409595, _1409597)))], (33005 ^ _779530) ^ [_1409639, _1409641, _1409643] : [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), _1409639), _1409641))), -(hBOOL(hAPP(hAPP(_1409643, _1409639), _1409641))), 33012 ^ _779530 : [(33013 ^ _779530) ^ [] : [-(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), 33010 ^ [_1409639, _1409641, _1409643]), 33011 ^ [_1409639, _1409641, _1409643]))))], (33025 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1409643, 33010 ^ [_1409639, _1409641, _1409643]), 33011 ^ [_1409639, _1409641, _1409643]))], (33015 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1409643, 33010 ^ [_1409639, _1409641, _1409643]), 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)))), 33011 ^ [_1409639, _1409641, _1409643])))), -(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), 33010 ^ [_1409639, _1409641, _1409643]), 33011 ^ [_1409639, _1409641, _1409643])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 33011 ^ [_1409639, _1409641, _1409643]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (33029 ^ _779530) ^ [_1410134, _1410136] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1410134), _1410136) = c_Smallcheck_Osmall_H(_1410134, hAPP(c_Code__Numeral_Oint__of, _1410136), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1410136))))], (33031 ^ _779530) ^ [_1410178, _1410180, _1410182, _1410184] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1410180, _1410178)), _1410182), _1410184) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1410180), hAPP(hAPP(c_COMBC(_1410180, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1410178, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1410180), c_Smallcheck_Osmall__class_Osmall(_1410178)), hAPP(hAPP(c_COMBB(tc_fun(_1410178, tc_prod(_1410180, _1410178)), tc_fun(_1410178, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1410180), hAPP(c_COMBB(tc_prod(_1410180, _1410178), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1410178), _1410182)), c_Product__Type_OPair(_1410180, _1410178)))), _1410184)), _1410184)), class_Smallcheck_Osmall(_1410178), class_Smallcheck_Osmall(_1410180)], (33041 ^ _779530) ^ [_1410472, _1410474] : [_1410472 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1410472, _1410474) = _1410474)], (33047 ^ _779530) ^ [_1410549, _1410551] : [-(_1410549 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1410549, _1410551) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1410549), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1410551)))], (33053 ^ _779530) ^ [_1410602, _1410604] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410602)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410604)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1410604))), 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), _1410602)), c_Int_Onat)))))], (33055 ^ _779530) ^ [_1410665, _1410667] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410665)), hAPP(c_Nat_OSuc, _1410667)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1410665))), 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)), _1410667)))))], (33057 ^ _779530) ^ [_1410722] : [-(c_Int_Osucc(c_Int_Opred(_1410722)) = _1410722)], (33059 ^ _779530) ^ [_1410764, _1410766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410764), _1410766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410764)), _1410766)))], (33065 ^ _779530) ^ [_1410861, _1410863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410861)), _1410863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410861), _1410863)))], (33071 ^ _779530) ^ [_1410964] : [-(c_Int_Opred(c_Int_OBit1(_1410964)) = c_Int_OBit0(_1410964))], (33073 ^ _779530) ^ [_1410993] : [-(c_Int_Opred(c_Int_OBit0(_1410993)) = c_Int_OBit1(c_Int_Opred(_1410993)))], (33075 ^ _779530) ^ [_1411024] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1411024)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1411024))))], (33077 ^ _779530) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (33079 ^ _779530) ^ [_1411077] : [-(c_Int_Opred(_1411077) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1411077), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33081 ^ _779530) ^ [_1411108] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1411108) = c_Int_Opred(_1411108))], (33083 ^ _779530) ^ [_1411136] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411136), c_Int_OMin) = c_Int_Opred(_1411136))], (33085 ^ _779530) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (33087 ^ _779530) ^ [_1411185, _1411187] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1411185)), c_Int_OBit1(_1411187)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1411185)), _1411187)))], (33089 ^ _779530) ^ [_1411230, _1411232] : [class_Int_Onumber__ring(_1411230), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411230), c_Int_Opred(_1411232)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411230), hAPP(c_Groups_Ouminus__class_Ouminus(_1411230), c_Groups_Oone__class_Oone(_1411230))), hAPP(c_Int_Onumber__class_Onumber__of(_1411230), _1411232)))], (33095 ^ _779530) ^ [_1411371] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1411371)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411371) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33101 ^ _779530) ^ [_1411462] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411462) = 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(_1411462)))))], (33107 ^ _779530) ^ [_1411559, _1411561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1411559)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1411561)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411559)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1411561), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1411559))))], (33113 ^ _779530) ^ [_1411701, _1411703] : [hAPP(c_Nat_OSuc, _1411701) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411703), -(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(_1411703))), 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)), _1411701))))))], (33119 ^ _779530) ^ [_1411824, _1411826] : [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(_1411826))), 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)), _1411824))))), -(hAPP(c_Nat_OSuc, _1411824) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411826))], (33125 ^ _779530) ^ [_1411968, _1411970] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411968) = hAPP(c_Nat_OSuc, _1411970), -(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(_1411968))), 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)), _1411970))))))], (33131 ^ _779530) ^ [_1412091, _1412093] : [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(_1412091))), 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)), _1412093))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412091) = hAPP(c_Nat_OSuc, _1412093))], (33137 ^ _779530) ^ [_1412226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412226), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412226)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33143 ^ _779530) ^ [_1412323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412323), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412323)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1412323)))], (33149 ^ _779530) ^ [_1412393, _1412395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412393)), hAPP(c_Nat_OSuc, _1412395))), -(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(_1412393))), 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)), _1412395)))))], (33155 ^ _779530) ^ [_1412520, _1412522] : [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(_1412520))), 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)), _1412522)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412520)), hAPP(c_Nat_OSuc, _1412522))))], (33161 ^ _779530) ^ [_1412668, _1412670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412668)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412670))), -(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(_1412670))), 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), _1412668)), c_Int_Onat))))))], (33167 ^ _779530) ^ [_1412813, _1412815] : [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(_1412815))), 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), _1412813)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412813)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412815))))], (33173 ^ _779530) ^ [_1412979, _1412981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1412979)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412981))), -(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(_1412981))), 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), _1412979)), c_Int_Onat))))))], (33179 ^ _779530) ^ [_1413124, _1413126] : [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(_1413126))), 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), _1413124)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413124)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413126))))], (33185 ^ _779530) ^ [_1413290, _1413292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413290)), hAPP(c_Nat_OSuc, _1413292))), -(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(_1413290))), 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)), _1413292)))))], (33191 ^ _779530) ^ [_1413417, _1413419] : [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(_1413417))), 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)), _1413419)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413417)), hAPP(c_Nat_OSuc, _1413419))))], (33197 ^ _779530) ^ [_1413550, _1413552] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413550)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413552)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413552))), 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, _1413550))), 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), _1413550)), c_Int_Onat)))))], (33199 ^ _779530) ^ [_1413622, _1413624] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413622)), hAPP(c_Nat_OSuc, _1413624)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413622))), 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, _1413624))), 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)), _1413624)))))], (33201 ^ _779530) ^ [_1413688, _1413690, _1413692, _1413694, _1413696] : [-(c_Nat_Onat_Onat__case(_1413688, _1413690, _1413692, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413694)), _1413696)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1413688), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413694))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1413688, _1413688), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1413688, tc_fun(_1413688, _1413688)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413688, tc_fun(_1413688, _1413688)), tc_Int_Oint), c_If(_1413688)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1413688, _1413690, _1413692, _1413696))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1413688, tc_Int_Oint), _1413692), 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)), _1413696)))))], (33203 ^ _779530) ^ [_1413806, _1413808, _1413810, _1413812] : [-(c_Nat_Onat_Onat__case(_1413806, _1413808, _1413810, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413812)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1413806), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413812))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1413806, _1413806), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1413806, tc_fun(_1413806, _1413806)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413806, tc_fun(_1413806, _1413806)), tc_Int_Oint), c_If(_1413806)), c_Nat__Numeral_Oneg)), _1413808)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1413806, tc_Int_Oint), _1413810), c_Int_Onat))))], (33205 ^ _779530) ^ [_1413908, _1413910, _1413912, _1413914, _1413916] : [-(hAPP(c_Nat_Onat_Onat__rec(_1413908, _1413910, _1413912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413914)), _1413916)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1413908), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413914))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1413908, _1413908), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1413908, tc_fun(_1413908, _1413908)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1413908, tc_fun(_1413908, _1413908)), tc_Int_Oint), c_If(_1413908)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1413908, _1413910, _1413912), _1413916))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1413908, _1413908), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1413908, _1413908), tc_Int_Oint), _1413912), 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)), _1413916))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1413908, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1413908, _1413910, _1413912)), 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)), _1413916))))))], (33207 ^ _779530) ^ [_1414060, _1414062, _1414064] : [-(hAPP(c_Nat_Onat_Onat__rec(_1414060, _1414062, _1414064), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1414062)], (33209 ^ _779530) ^ [_1414094, _1414096, _1414098, _1414100] : [-(hAPP(c_Nat_Onat_Onat__rec(_1414094, _1414096, _1414098), hAPP(c_Nat_OSuc, _1414100)) = hAPP(hAPP(_1414098, _1414100), hAPP(c_Nat_Onat_Onat__rec(_1414094, _1414096, _1414098), _1414100)))], (33211 ^ _779530) ^ [_1414146, _1414148, _1414150] : [-(c_Nat_Onat_Onat__case(_1414146, _1414148, _1414150, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1414148)], (33213 ^ _779530) ^ [_1414178, _1414180, _1414182, _1414184] : [-(c_Nat_Onat_Onat__case(_1414178, _1414180, _1414182, hAPP(c_Nat_OSuc, _1414184)) = hAPP(_1414182, _1414184))], (33215 ^ _779530) ^ [_1414218, _1414220] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414218)), _1414220) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1414218), 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), _1414218)), _1414220))], (33217 ^ _779530) ^ [_1414266, _1414268] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1414266), hAPP(c_Nat_OSuc, _1414268)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1414268), 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)), _1414268)), _1414266))], (33219 ^ _779530) ^ [_1414329, _1414331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414329)), _1414331)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1414329), _1414331)))], (33225 ^ _779530) ^ [_1414432, _1414434] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1414432), _1414434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414432)), _1414434)))], (33231 ^ _779530) ^ [_1414541, _1414543] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1414541), hAPP(c_Nat_OSuc, _1414543)) = 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), _1414541), _1414543)))], (33233 ^ _779530) ^ [_1414586, _1414588] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1414586)), _1414588) = 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), _1414586)), _1414588))], (33235 ^ _779530) ^ [_1414631, _1414633] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1414631), hAPP(c_Nat_OSuc, _1414633)) = 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)), _1414633)), _1414631))], (33237 ^ _779530) ^ [_1414676, _1414678, _1414680, _1414682] : [-(hAPP(c_Nat_Onat_Onat__rec(_1414676, _1414678, _1414680), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414682)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1414676), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414682))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1414676, _1414676), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1414676, tc_fun(_1414676, _1414676)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1414676, tc_fun(_1414676, _1414676)), tc_Int_Oint), c_If(_1414676)), c_Nat__Numeral_Oneg)), _1414678)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1414676, _1414676), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1414676, _1414676), tc_Int_Oint), _1414680), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1414676, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1414676, _1414678, _1414680)), c_Int_Onat)))))], (33239 ^ _779530) ^ [_1414807, _1414809] : [c_Nat__Transfer_Ois__nat(_1414807), c_Nat__Transfer_Onat__set(_1414809), 33246 ^ _779530 : [(33247 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1414807), _1414809)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1414807)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1414809))))], (33253 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1414807)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1414809))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1414807), _1414809)))]]], (33259 ^ _779530) ^ [_1415110, _1415112] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1415110, _1415112) = c_Smallcheck_Ofull__small_H(_1415110, hAPP(c_Code__Numeral_Oint__of, _1415112), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1415112))))], (33261 ^ _779530) ^ [_1415152, _1415154, _1415156, _1415158, _1415160] : [class_Groups_Ocomm__monoid__mult(_1415152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415154), _1415156)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415154), _1415158)), 33275 ^ _779530 : [(33276 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415154), 33274 ^ [_1415152, _1415154, _1415156, _1415158, _1415160]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415154, tc_HOL_Obool)), _1415156), _1415158))))], (33278 ^ _779530) ^ [] : [hAPP(_1415160, 33274 ^ [_1415152, _1415154, _1415156, _1415158, _1415160]) = c_Groups_Oone__class_Oone(_1415152)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415154, _1415152), _1415160), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415154, tc_HOL_Obool)), _1415156), _1415158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415152), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415154, _1415152), _1415160), _1415156)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1415154, _1415152), _1415160), _1415158)))], (33282 ^ _779530) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (33284 ^ _779530) ^ [_1415665, _1415667] : [c_Nat__Transfer_Ois__nat(_1415665), c_Nat__Transfer_Ois__nat(_1415667), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415665), _1415667)))], (33294 ^ _779530) ^ [_1415800, _1415802] : [c_Nat__Transfer_Ois__nat(_1415800), c_Nat__Transfer_Ois__nat(_1415802), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1415800), _1415802)))], (33304 ^ _779530) ^ [_1415935] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1415935)))], (33306 ^ _779530) ^ [_1415960, _1415962] : [c_Nat__Transfer_Ois__nat(_1415960), c_Nat__Transfer_Ois__nat(_1415962), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1415960, _1415962)))], (33316 ^ _779530) ^ [_1416091, _1416093] : [c_Nat__Transfer_Ois__nat(_1416091), c_Nat__Transfer_Ois__nat(_1416093), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1416091), _1416093)))], (33326 ^ _779530) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33328 ^ _779530) ^ [_1416244, _1416246] : [c_Nat__Transfer_Ois__nat(_1416244), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1416244), _1416246)))], (33334 ^ _779530) ^ [_1416329, _1416331] : [c_Nat__Transfer_Ois__nat(_1416329), c_Nat__Transfer_Ois__nat(_1416331), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1416329, _1416331)))], (33344 ^ _779530) ^ [_1416470] : [c_Nat__Transfer_Ois__nat(_1416470), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416470)))], (33350 ^ _779530) ^ [_1416543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1416543)), -(c_Nat__Transfer_Ois__nat(_1416543))], (33356 ^ _779530) ^ [_1416622, _1416624] : [c_Nat__Transfer_Onat__set(_1416622), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1416624), _1416622)), -(c_Nat__Transfer_Ois__nat(_1416624))], (33366 ^ _779530) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (33368 ^ _779530) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33370 ^ _779530) ^ [_1416793, _1416795, _1416797] : [33372 ^ _779530 : [(33373 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416793), 33371 ^ [_1416793, _1416795, _1416797]), _1416795)))], (33375 ^ _779530) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1416797, 33371 ^ [_1416793, _1416795, _1416797]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416793, tc_Int_Oint), _1416797), _1416795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1416793, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1416793), c_Int_Onat), _1416797)), _1416795)))], (33379 ^ _779530) ^ [_1417023, _1417025, _1417027] : [33381 ^ _779530 : [(33382 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417023), 33380 ^ [_1417023, _1417025, _1417027]), _1417025)))], (33384 ^ _779530) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1417027, 33380 ^ [_1417023, _1417025, _1417027]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417023, tc_Int_Oint), _1417027), _1417025) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417023, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1417023), c_Int_Onat), _1417027)), _1417025)))], (33388 ^ _779530) ^ [_1417253, _1417255, _1417257, _1417259, _1417261] : [class_Groups_Ocomm__monoid__mult(_1417253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417255), _1417257)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417255), _1417259)), 33402 ^ _779530 : [(33403 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417255), 33401 ^ [_1417253, _1417255, _1417257, _1417259, _1417261]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417255, tc_HOL_Obool)), _1417257), _1417259))))], (33405 ^ _779530) ^ [] : [hAPP(_1417261, 33401 ^ [_1417253, _1417255, _1417257, _1417259, _1417261]) = c_Groups_Oone__class_Oone(_1417253)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417255, _1417253), _1417261), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417255, tc_HOL_Obool)), _1417257), _1417259)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417253), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417255, _1417253), _1417261), _1417257)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417255, _1417253), _1417261), _1417259)))], (33409 ^ _779530) ^ [] : [-(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))], (33411 ^ _779530) ^ [_1417766, _1417768] : [class_Int_Onumber__ring(_1417766), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1417768)), -(hBOOL(hAPP(hAPP(c_member(_1417766), hAPP(c_Int_Onumber__class_Onumber__of(_1417766), _1417768)), c_Nat_Osemiring__1__class_ONats(_1417766))))], (33421 ^ _779530) ^ [_1417925, _1417927, _1417929, _1417931, _1417933] : [class_Fields_Ofield(_1417925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417927), _1417929)), -(hAPP(_1417931, _1417933) = c_Groups_Ozero__class_Ozero(_1417925)), 33432 ^ _779530 : [(33433 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1417927), _1417933), _1417929)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417927, _1417925), _1417931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417927, tc_HOL_Obool)), _1417929), hAPP(hAPP(c_Set_Oinsert(_1417927), _1417933), c_Orderings_Obot__class_Obot(tc_fun(_1417927, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417925), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417927, _1417925), _1417931), _1417929)), hAPP(_1417931, _1417933)))], (33439 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417927), _1417933), _1417929))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417927, _1417925), _1417931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417927, tc_HOL_Obool)), _1417929), hAPP(hAPP(c_Set_Oinsert(_1417927), _1417933), c_Orderings_Obot__class_Obot(tc_fun(_1417927, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1417927, _1417925), _1417931), _1417929))]]], (33445 ^ _779530) ^ [_1418466, _1418468, _1418470, _1418472] : [class_Rings_Odivision__ring(_1418466), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1418466), _1418468), _1418470)), _1418472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1418466), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418466), _1418468), _1418472)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418466), _1418470), _1418472)))], (33451 ^ _779530) ^ [_1418625, _1418627] : [class_Rings_Odivision__ring(_1418625), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418625), _1418627), c_Groups_Oone__class_Oone(_1418625)) = _1418627)], (33457 ^ _779530) ^ [_1418720, _1418722, _1418724] : [class_Rings_Odivision__ring(_1418720), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1418720), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418720), _1418722), _1418724)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418720), hAPP(c_Groups_Ouminus__class_Ouminus(_1418720), _1418722)), _1418724))], (33463 ^ _779530) ^ [_1418849, _1418851, _1418853, _1418855] : [class_Rings_Odivision__ring(_1418849), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418849), _1418851), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418849), _1418853), _1418855)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418849), _1418851), _1418853)), _1418855))], (33469 ^ _779530) ^ [_1418992, _1418994, _1418996, _1418998] : [class_Rings_Odivision__ring(_1418992), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418992), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418992), _1418994), _1418996)), _1418998) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1418992), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418992), _1418994), _1418998)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418992), _1418996), _1418998)))], (33475 ^ _779530) ^ [_1419151, _1419153, _1419155, _1419157] : [class_Fields_Ofield__inverse__zero(_1419151), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419151), _1419153), _1419155)), _1419157) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419151), hAPP(hAPP(c_Power_Opower__class_Opower(_1419151), _1419153), _1419157)), hAPP(hAPP(c_Power_Opower__class_Opower(_1419151), _1419155), _1419157)))], (33481 ^ _779530) ^ [_1419310, _1419312, _1419314, _1419316, _1419318] : [class_Fields_Ofield(_1419310), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419310), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419312, _1419310), _1419314), _1419316)), _1419318) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1419312, _1419310), hAPP(hAPP(c_COMBC(_1419312, _1419310, _1419310), hAPP(hAPP(c_COMBB(_1419310, tc_fun(_1419310, _1419310), _1419312), c_Rings_Oinverse__class_Odivide(_1419310)), _1419314)), _1419318)), _1419316))], (33487 ^ _779530) ^ [_1419493, _1419495] : [class_Rings_Odivision__ring(_1419493), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419493), c_Groups_Ozero__class_Ozero(_1419493)), _1419495) = c_Groups_Ozero__class_Ozero(_1419493))], (33493 ^ _779530) ^ [_1419592, _1419594] : [class_Rings_Odivision__ring__inverse__zero(_1419592), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419592), _1419594), c_Groups_Ozero__class_Ozero(_1419592)) = c_Groups_Ozero__class_Ozero(_1419592))], (33499 ^ _779530) ^ [_1419691, _1419693, _1419695, _1419697] : [class_Rings_Odivision__ring(_1419691), -(_1419693 = c_Groups_Ozero__class_Ozero(_1419691)), 33506 ^ _779530 : [(33507 ^ _779530) ^ [] : [_1419695 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419691), _1419697), _1419693), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1419691), _1419695), _1419693) = _1419697)], (33513 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1419691), _1419695), _1419693) = _1419697, -(_1419695 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1419691), _1419697), _1419693))]]], (33519 ^ _779530) ^ [_1420019, _1420021, _1420023, _1420025] : [class_Rings_Odivision__ring(_1420019), -(_1420021 = c_Groups_Ozero__class_Ozero(_1420019)), 33526 ^ _779530 : [(33527 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420019), _1420023), _1420021) = _1420025, -(_1420023 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420019), _1420025), _1420021))], (33533 ^ _779530) ^ [] : [_1420023 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420019), _1420025), _1420021), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420019), _1420023), _1420021) = _1420025)]]], (33539 ^ _779530) ^ [_1420347, _1420349, _1420351, _1420353] : [class_Rings_Odivision__ring(_1420347), -(_1420349 = c_Groups_Ozero__class_Ozero(_1420347)), _1420351 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420347), _1420353), _1420349), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420347), _1420351), _1420349) = _1420353)], (33553 ^ _779530) ^ [_1420577, _1420579, _1420581, _1420583] : [class_Rings_Odivision__ring(_1420577), -(_1420579 = c_Groups_Ozero__class_Ozero(_1420577)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420577), _1420581), _1420579) = _1420583, -(_1420581 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420577), _1420583), _1420579))], (33567 ^ _779530) ^ [_1420807, _1420809] : [class_Rings_Odivision__ring__inverse__zero(_1420807), 33570 ^ _779530 : [(33571 ^ _779530) ^ [] : [_1420809 = c_Groups_Ozero__class_Ozero(_1420807), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420807), _1420809), _1420809) = c_Groups_Ozero__class_Ozero(_1420807))], (33577 ^ _779530) ^ [] : [-(_1420809 = c_Groups_Ozero__class_Ozero(_1420807)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420807), _1420809), _1420809) = c_Groups_Oone__class_Oone(_1420807))]]], (33583 ^ _779530) ^ [_1421029, _1421031] : [class_Rings_Odivision__ring(_1421029), -(_1421031 = c_Groups_Ozero__class_Ozero(_1421029)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421029), _1421031), _1421031) = c_Groups_Oone__class_Oone(_1421029))], (33593 ^ _779530) ^ [_1421143, _1421145, _1421147] : [class_Rings_Odivision__ring(_1421143), -(_1421145 = c_Groups_Ozero__class_Ozero(_1421143)), 33600 ^ _779530 : [(33601 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421143), _1421147), _1421145) = c_Groups_Oone__class_Oone(_1421143), -(_1421147 = _1421145)], (33607 ^ _779530) ^ [] : [_1421147 = _1421145, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421143), _1421147), _1421145) = c_Groups_Oone__class_Oone(_1421143))]]], (33613 ^ _779530) ^ [_1421445, _1421447, _1421449] : [class_Rings_Odivision__ring(_1421445), -(_1421447 = c_Groups_Ozero__class_Ozero(_1421445)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421445), hAPP(c_Groups_Ouminus__class_Ouminus(_1421445), _1421449)), hAPP(c_Groups_Ouminus__class_Ouminus(_1421445), _1421447)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421445), _1421449), _1421447))], (33623 ^ _779530) ^ [_1421593, _1421595, _1421597] : [class_Rings_Odivision__ring(_1421593), -(_1421595 = c_Groups_Ozero__class_Ozero(_1421593)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1421593), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421593), _1421597), _1421595)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421593), _1421597), hAPP(c_Groups_Ouminus__class_Ouminus(_1421593), _1421595)))], (33633 ^ _779530) ^ [_1421741, _1421743, _1421745, _1421747] : [class_Fields_Ofield(_1421741), -(_1421743 = c_Groups_Ozero__class_Ozero(_1421741)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1421741), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421741), _1421745), _1421743)), _1421747) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421741), hAPP(hAPP(c_Power_Opower__class_Opower(_1421741), _1421745), _1421747)), hAPP(hAPP(c_Power_Opower__class_Opower(_1421741), _1421743), _1421747)))], (33643 ^ _779530) ^ [_1421919, _1421921, _1421923] : [class_Fields_Ofield__inverse__zero(_1421919), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421919), c_Groups_Oone__class_Oone(_1421919)), hAPP(hAPP(c_Power_Opower__class_Opower(_1421919), _1421921), _1421923)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1421919), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421919), c_Groups_Oone__class_Oone(_1421919)), _1421921)), _1421923))], (33649 ^ _779530) ^ [_1422068, _1422070, _1422072, _1422074, _1422076] : [class_Fields_Ofield__inverse__zero(_1422068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422070), _1422072)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422070, _1422068), hAPP(hAPP(c_COMBS(_1422070, _1422068, _1422068), hAPP(hAPP(c_COMBB(_1422068, tc_fun(_1422068, _1422068), _1422070), c_Rings_Oinverse__class_Odivide(_1422068)), _1422074)), _1422076)), _1422072) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422068), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422070, _1422068), _1422074), _1422072)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1422070, _1422068), _1422076), _1422072)))], (33659 ^ _779530) ^ [_1422335, _1422337, _1422339, _1422341] : [class_Fields_Ofield__inverse__zero(_1422335), class_Int_Onumber(_1422335), 33666 ^ _779530 : [(33683 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422335), _1422337), hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339)) = _1422341), 33686 ^ _779530 : [(33687 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339) = c_Groups_Ozero__class_Ozero(_1422335)], (33689 ^ _779530) ^ [] : [_1422337 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422335), _1422341), hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339))]], 33690 ^ _779530 : [(33691 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339) = c_Groups_Ozero__class_Ozero(_1422335))], (33693 ^ _779530) ^ [] : [_1422341 = c_Groups_Ozero__class_Ozero(_1422335)]]], (33667 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422335), _1422337), hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339)) = _1422341, 33670 ^ _779530 : [(33671 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339) = c_Groups_Ozero__class_Ozero(_1422335)), -(_1422337 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422335), _1422341), hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339)))], (33677 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1422335), _1422339) = c_Groups_Ozero__class_Ozero(_1422335), -(_1422341 = c_Groups_Ozero__class_Ozero(_1422335))]]]]], (33697 ^ _779530) ^ [_1422945, _1422947, _1422949, _1422951] : [class_Fields_Ofield__inverse__zero(_1422945), class_Int_Onumber(_1422945), 33704 ^ _779530 : [(33721 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422945), _1422947), _1422949) = hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951)), 33724 ^ _779530 : [(33725 ^ _779530) ^ [] : [_1422949 = c_Groups_Ozero__class_Ozero(_1422945)], (33727 ^ _779530) ^ [] : [_1422947 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422945), hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951)), _1422949)]], 33728 ^ _779530 : [(33729 ^ _779530) ^ [] : [-(_1422949 = c_Groups_Ozero__class_Ozero(_1422945))], (33731 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951) = c_Groups_Ozero__class_Ozero(_1422945)]]], (33705 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422945), _1422947), _1422949) = hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951), 33708 ^ _779530 : [(33709 ^ _779530) ^ [] : [-(_1422949 = c_Groups_Ozero__class_Ozero(_1422945)), -(_1422947 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422945), hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951)), _1422949))], (33715 ^ _779530) ^ [] : [_1422949 = c_Groups_Ozero__class_Ozero(_1422945), -(hAPP(c_Int_Onumber__class_Onumber__of(_1422945), _1422951) = c_Groups_Ozero__class_Ozero(_1422945))]]]]], (33735 ^ _779530) ^ [_1423540, _1423542, _1423544, _1423546] : [class_Fields_Ofield__inverse__zero(_1423540), class_Int_Onumber(_1423540), 33742 ^ _779530 : [(33759 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423540), _1423544), _1423546)), 33762 ^ _779530 : [(33763 ^ _779530) ^ [] : [_1423546 = c_Groups_Ozero__class_Ozero(_1423540)], (33765 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423540), hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542)), _1423546) = _1423544]], 33766 ^ _779530 : [(33767 ^ _779530) ^ [] : [-(_1423546 = c_Groups_Ozero__class_Ozero(_1423540))], (33769 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542) = c_Groups_Ozero__class_Ozero(_1423540)]]], (33743 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423540), _1423544), _1423546), 33746 ^ _779530 : [(33747 ^ _779530) ^ [] : [-(_1423546 = c_Groups_Ozero__class_Ozero(_1423540)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423540), hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542)), _1423546) = _1423544)], (33753 ^ _779530) ^ [] : [_1423546 = c_Groups_Ozero__class_Ozero(_1423540), -(hAPP(c_Int_Onumber__class_Onumber__of(_1423540), _1423542) = c_Groups_Ozero__class_Ozero(_1423540))]]]]], (33773 ^ _779530) ^ [_1424135, _1424137, _1424139, _1424141] : [class_Fields_Ofield__inverse__zero(_1424135), class_Int_Onumber(_1424135), 33780 ^ _779530 : [(33797 ^ _779530) ^ [] : [-(_1424137 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1424135), _1424139), hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141))), 33800 ^ _779530 : [(33801 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141) = c_Groups_Ozero__class_Ozero(_1424135)], (33803 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424135), _1424137), hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141)) = _1424139]], 33804 ^ _779530 : [(33805 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141) = c_Groups_Ozero__class_Ozero(_1424135))], (33807 ^ _779530) ^ [] : [_1424137 = c_Groups_Ozero__class_Ozero(_1424135)]]], (33781 ^ _779530) ^ [] : [_1424137 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1424135), _1424139), hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141)), 33784 ^ _779530 : [(33785 ^ _779530) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141) = c_Groups_Ozero__class_Ozero(_1424135)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424135), _1424137), hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141)) = _1424139)], (33791 ^ _779530) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1424135), _1424141) = c_Groups_Ozero__class_Ozero(_1424135), -(_1424137 = c_Groups_Ozero__class_Ozero(_1424135))]]]]], (33811 ^ _779530) ^ [_1424745, _1424747] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1424745), _1424747), hAPP(c_Int_Onumber__class_Onumber__of(_1424745), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1424745)), class_Fields_Ofield__inverse__zero(_1424745), class_Int_Onumber__ring(_1424745)], (33821 ^ _779530) ^ [_1424900, _1424902] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1424900), _1424902), hAPP(c_Int_Onumber__class_Onumber__of(_1424900), c_Int_OBit1(c_Int_OPls))) = _1424902), class_Fields_Ofield(_1424900), class_Int_Onumber__ring(_1424900)], (33831 ^ _779530) ^ [_1425051, _1425053] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1425051), _1425053), hAPP(c_Int_Onumber__class_Onumber__of(_1425051), c_Int_OBit1(c_Int_OPls))) = _1425053), class_Fields_Ofield(_1425051), class_Int_Onumber__ring(_1425051)], (33841 ^ _779530) ^ [_1425202, _1425204] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1425202), _1425204), hAPP(c_Int_Onumber__class_Onumber__of(_1425202), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1425202), _1425204)), class_Fields_Ofield__inverse__zero(_1425202), class_Int_Onumber__ring(_1425202)], (33851 ^ _779530) ^ [_1425363] : [class_Rings_Osemiring__1(_1425363), -(hBOOL(hAPP(hAPP(c_member(_1425363), c_Groups_Ozero__class_Ozero(_1425363)), c_Nat_Osemiring__1__class_ONats(_1425363))))], (33857 ^ _779530) ^ [_1425458, _1425460, _1425462] : [class_Rings_Osemiring__1(_1425458), hBOOL(hAPP(hAPP(c_member(_1425458), _1425460), c_Nat_Osemiring__1__class_ONats(_1425458))), hBOOL(hAPP(hAPP(c_member(_1425458), _1425462), c_Nat_Osemiring__1__class_ONats(_1425458))), -(hBOOL(hAPP(hAPP(c_member(_1425458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425458), _1425460), _1425462)), c_Nat_Osemiring__1__class_ONats(_1425458))))], (33871 ^ _779530) ^ [_1425713, _1425715, _1425717] : [class_Rings_Osemiring__1(_1425713), hBOOL(hAPP(hAPP(c_member(_1425713), _1425715), c_Nat_Osemiring__1__class_ONats(_1425713))), hBOOL(hAPP(hAPP(c_member(_1425713), _1425717), c_Nat_Osemiring__1__class_ONats(_1425713))), -(hBOOL(hAPP(hAPP(c_member(_1425713), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425713), _1425715), _1425717)), c_Nat_Osemiring__1__class_ONats(_1425713))))], (33885 ^ _779530) ^ [_1425968, _1425970, _1425972, _1425974] : [class_Fields_Olinordered__field__inverse__zero(_1425968), class_Int_Onumber(_1425968), 33892 ^ _779530 : [(33919 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425970), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1425968), _1425972), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))))), 33922 ^ _779530 : [(33923 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), c_Groups_Ozero__class_Ozero(_1425968)), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))))], (33925 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425968), _1425970), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))), _1425972))]], 33926 ^ _779530 : [(33927 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), c_Groups_Ozero__class_Ozero(_1425968)), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)))], (33929 ^ _779530) ^ [] : [33930 ^ _779530 : [(33931 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)), c_Groups_Ozero__class_Ozero(_1425968))))], (33933 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425968), _1425970), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))))]], 33934 ^ _779530 : [(33935 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)), c_Groups_Ozero__class_Ozero(_1425968)))], (33937 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425970), c_Groups_Ozero__class_Ozero(_1425968)))]]]]], (33893 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425970), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1425968), _1425972), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)))), 33896 ^ _779530 : [(33897 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), c_Groups_Ozero__class_Ozero(_1425968)), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425968), _1425970), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974))), _1425972)))], (33903 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), c_Groups_Ozero__class_Ozero(_1425968)), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)))), 33906 ^ _779530 : [(33907 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)), c_Groups_Ozero__class_Ozero(_1425968))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425968), _1425970), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)))))], (33913 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), hAPP(c_Int_Onumber__class_Onumber__of(_1425968), _1425974)), c_Groups_Ozero__class_Ozero(_1425968)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425968), _1425970), c_Groups_Ozero__class_Ozero(_1425968))))]]]]]]], (33941 ^ _779530) ^ [_1427082, _1427084, _1427086, _1427088] : [class_Fields_Olinordered__field__inverse__zero(_1427082), class_Int_Onumber(_1427082), 33948 ^ _779530 : [(33975 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1427082), _1427086), _1427088)))), 33978 ^ _779530 : [(33979 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), c_Groups_Ozero__class_Ozero(_1427082)), _1427088)))], (33981 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), _1427088)), _1427086))]], 33982 ^ _779530 : [(33983 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), c_Groups_Ozero__class_Ozero(_1427082)), _1427088))], (33985 ^ _779530) ^ [] : [33986 ^ _779530 : [(33987 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427088), c_Groups_Ozero__class_Ozero(_1427082))))], (33989 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), _1427088)))]], 33990 ^ _779530 : [(33991 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427088), c_Groups_Ozero__class_Ozero(_1427082)))], (33993 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), c_Groups_Ozero__class_Ozero(_1427082)))]]]]], (33949 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1427082), _1427086), _1427088))), 33952 ^ _779530 : [(33953 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), c_Groups_Ozero__class_Ozero(_1427082)), _1427088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), _1427088)), _1427086)))], (33959 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), c_Groups_Ozero__class_Ozero(_1427082)), _1427088))), 33962 ^ _779530 : [(33963 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427088), c_Groups_Ozero__class_Ozero(_1427082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), _1427088))))], (33969 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), _1427088), c_Groups_Ozero__class_Ozero(_1427082)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427082), hAPP(c_Int_Onumber__class_Onumber__of(_1427082), _1427084)), c_Groups_Ozero__class_Ozero(_1427082))))]]]]]]], (33997 ^ _779530) ^ [_1428151, _1428153, _1428155, _1428157] : [class_Fields_Olinordered__field__inverse__zero(_1428151), class_Int_Onumber(_1428151), 34004 ^ _779530 : [(34031 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1428151), _1428153), _1428155)), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)))), 34034 ^ _779530 : [(34035 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), _1428155)))], (34037 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428151), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)), _1428155)))]], 34038 ^ _779530 : [(34039 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), _1428155))], (34041 ^ _779530) ^ [] : [34042 ^ _779530 : [(34043 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428155), c_Groups_Ozero__class_Ozero(_1428151))))], (34045 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428151), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)), _1428155)), _1428153))]], 34046 ^ _779530 : [(34047 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428155), c_Groups_Ozero__class_Ozero(_1428151)))], (34049 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)))]]]]], (34005 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1428151), _1428153), _1428155)), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157))), 34008 ^ _779530 : [(34009 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), _1428155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428151), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)), _1428155))))], (34015 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), _1428155))), 34018 ^ _779530 : [(34019 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428155), c_Groups_Ozero__class_Ozero(_1428151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1428151), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157)), _1428155)), _1428153)))], (34025 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), _1428155), c_Groups_Ozero__class_Ozero(_1428151)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428151), c_Groups_Ozero__class_Ozero(_1428151)), hAPP(c_Int_Onumber__class_Onumber__of(_1428151), _1428157))))]]]]]]], (34053 ^ _779530) ^ [_1429220, _1429222, _1429224, _1429226] : [class_Fields_Olinordered__field__inverse__zero(_1429220), class_Int_Onumber(_1429220), 34060 ^ _779530 : [(34087 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1429220), _1429222), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))), _1429226))), 34090 ^ _779530 : [(34091 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))))], (34093 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), _1429222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429220), _1429226), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))))]], 34094 ^ _779530 : [(34095 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)))], (34097 ^ _779530) ^ [] : [34098 ^ _779530 : [(34099 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)), c_Groups_Ozero__class_Ozero(_1429220))))], (34101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429220), _1429226), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))), _1429222))]], 34102 ^ _779530 : [(34103 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)), c_Groups_Ozero__class_Ozero(_1429220)))], (34105 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), _1429226))]]]]], (34061 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1429220), _1429222), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))), _1429226)), 34064 ^ _779530 : [(34065 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), _1429222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429220), _1429226), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)))))], (34071 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)))), 34074 ^ _779530 : [(34075 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)), c_Groups_Ozero__class_Ozero(_1429220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1429220), _1429226), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224))), _1429222)))], (34081 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), hAPP(c_Int_Onumber__class_Onumber__of(_1429220), _1429224)), c_Groups_Ozero__class_Ozero(_1429220)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429220), c_Groups_Ozero__class_Ozero(_1429220)), _1429226)))]]]]]]], (34109 ^ _779530) ^ [_1430334] : [class_Rings_Osemiring__1(_1430334), -(hBOOL(hAPP(hAPP(c_member(_1430334), c_Groups_Oone__class_Oone(_1430334)), c_Nat_Osemiring__1__class_ONats(_1430334))))], (34115 ^ _779530) ^ [_1430429, _1430431] : [class_Rings_Osemiring__1(_1430429), -(hBOOL(hAPP(hAPP(c_member(_1430429), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1430429), _1430431)), c_Nat_Osemiring__1__class_ONats(_1430429))))], (34121 ^ _779530) ^ [_1430532, _1430534, _1430536, _1430538] : [class_Fields_Ofield(_1430532), -(_1430534 = c_Groups_Ozero__class_Ozero(_1430532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1430536), _1430538)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430532), _1430534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1430538), _1430536)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430532), hAPP(hAPP(c_Power_Opower__class_Opower(_1430532), _1430534), _1430538)), hAPP(hAPP(c_Power_Opower__class_Opower(_1430532), _1430534), _1430536)))], (34135 ^ _779530) ^ [_1430816, _1430818] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430816), hAPP(c_Int_Onumber__class_Onumber__of(_1430816), c_Int_OMin)), _1430818) = hAPP(c_Groups_Ouminus__class_Ouminus(_1430816), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430816), c_Groups_Oone__class_Oone(_1430816)), _1430818))), class_Fields_Ofield__inverse__zero(_1430816), class_Int_Onumber__ring(_1430816)], (34145 ^ _779530) ^ [_1430997, _1430999, _1431001, _1431003] : [class_Fields_Olinordered__field__inverse__zero(_1430997), class_Int_Onumber(_1430997), 34152 ^ _779530 : [(34179 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430997), _1430999), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))), _1431003))), 34182 ^ _779530 : [(34183 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))))], (34185 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), _1430999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430997), _1431003), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))))]], 34186 ^ _779530 : [(34187 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)))], (34189 ^ _779530) ^ [] : [34190 ^ _779530 : [(34191 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)), c_Groups_Ozero__class_Ozero(_1430997))))], (34193 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430997), _1431003), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))), _1430999))]], 34194 ^ _779530 : [(34195 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)), c_Groups_Ozero__class_Ozero(_1430997)))], (34197 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), _1431003))]]]]], (34153 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1430997), _1430999), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))), _1431003)), 34156 ^ _779530 : [(34157 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), _1430999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430997), _1431003), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)))))], (34163 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)))), 34166 ^ _779530 : [(34167 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)), c_Groups_Ozero__class_Ozero(_1430997))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430997), _1431003), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001))), _1430999)))], (34173 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430997), hAPP(c_Int_Onumber__class_Onumber__of(_1430997), _1431001)), c_Groups_Ozero__class_Ozero(_1430997)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430997), c_Groups_Ozero__class_Ozero(_1430997)), _1431003)))]]]]]]], (34201 ^ _779530) ^ [_1432111, _1432113, _1432115, _1432117] : [class_Fields_Olinordered__field__inverse__zero(_1432111), class_Int_Onumber(_1432111), 34208 ^ _779530 : [(34235 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432111), _1432113), _1432115)), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)))), 34238 ^ _779530 : [(34239 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), _1432115)))], (34241 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), _1432113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432111), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)), _1432115)))]], 34242 ^ _779530 : [(34243 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), _1432115))], (34245 ^ _779530) ^ [] : [34246 ^ _779530 : [(34247 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), _1432115), c_Groups_Ozero__class_Ozero(_1432111))))], (34249 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432111), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)), _1432115)), _1432113))]], 34250 ^ _779530 : [(34251 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), _1432115), c_Groups_Ozero__class_Ozero(_1432111)))], (34253 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)))]]]]], (34209 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432111), _1432113), _1432115)), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117))), 34212 ^ _779530 : [(34213 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), _1432115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), _1432113), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432111), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)), _1432115))))], (34219 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), _1432115))), 34222 ^ _779530 : [(34223 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), _1432115), c_Groups_Ozero__class_Ozero(_1432111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432111), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117)), _1432115)), _1432113)))], (34229 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432111), _1432115), c_Groups_Ozero__class_Ozero(_1432111)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432111), c_Groups_Ozero__class_Ozero(_1432111)), hAPP(c_Int_Onumber__class_Onumber__of(_1432111), _1432117))))]]]]]]], (34257 ^ _779530) ^ [_1433180, _1433182, _1433184, _1433186] : [class_Fields_Olinordered__field__inverse__zero(_1433180), class_Int_Onumber(_1433180), 34264 ^ _779530 : [(34291 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433180), _1433184), _1433186)))), 34294 ^ _779530 : [(34295 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), c_Groups_Ozero__class_Ozero(_1433180)), _1433186)))], (34297 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), _1433186)), _1433184))]], 34298 ^ _779530 : [(34299 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), c_Groups_Ozero__class_Ozero(_1433180)), _1433186))], (34301 ^ _779530) ^ [] : [34302 ^ _779530 : [(34303 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), _1433186), c_Groups_Ozero__class_Ozero(_1433180))))], (34305 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), _1433184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), _1433186)))]], 34306 ^ _779530 : [(34307 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), _1433186), c_Groups_Ozero__class_Ozero(_1433180)))], (34309 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), c_Groups_Ozero__class_Ozero(_1433180)))]]]]], (34265 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433180), _1433184), _1433186))), 34268 ^ _779530 : [(34269 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), c_Groups_Ozero__class_Ozero(_1433180)), _1433186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), _1433186)), _1433184)))], (34275 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), c_Groups_Ozero__class_Ozero(_1433180)), _1433186))), 34278 ^ _779530 : [(34279 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), _1433186), c_Groups_Ozero__class_Ozero(_1433180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), _1433184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), _1433186))))], (34285 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433180), _1433186), c_Groups_Ozero__class_Ozero(_1433180)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433180), hAPP(c_Int_Onumber__class_Onumber__of(_1433180), _1433182)), c_Groups_Ozero__class_Ozero(_1433180))))]]]]]]], (34313 ^ _779530) ^ [_1434249, _1434251, _1434253, _1434255] : [class_Fields_Olinordered__field__inverse__zero(_1434249), class_Int_Onumber(_1434249), 34320 ^ _779530 : [(34347 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434249), _1434253), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))))), 34350 ^ _779530 : [(34351 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), c_Groups_Ozero__class_Ozero(_1434249)), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))))], (34353 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434249), _1434251), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))), _1434253))]], 34354 ^ _779530 : [(34355 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), c_Groups_Ozero__class_Ozero(_1434249)), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)))], (34357 ^ _779530) ^ [] : [34358 ^ _779530 : [(34359 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)), c_Groups_Ozero__class_Ozero(_1434249))))], (34361 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434249), _1434251), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))))]], 34362 ^ _779530 : [(34363 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)), c_Groups_Ozero__class_Ozero(_1434249)))], (34365 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434251), c_Groups_Ozero__class_Ozero(_1434249)))]]]]], (34321 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434249), _1434253), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)))), 34324 ^ _779530 : [(34325 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), c_Groups_Ozero__class_Ozero(_1434249)), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434249), _1434251), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255))), _1434253)))], (34331 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), c_Groups_Ozero__class_Ozero(_1434249)), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)))), 34334 ^ _779530 : [(34335 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)), c_Groups_Ozero__class_Ozero(_1434249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434249), _1434251), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)))))], (34341 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434249), hAPP(c_Int_Onumber__class_Onumber__of(_1434249), _1434255)), c_Groups_Ozero__class_Ozero(_1434249)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434249), _1434251), c_Groups_Ozero__class_Ozero(_1434249))))]]]]]]], (34369 ^ _779530) ^ [_1435363, _1435365] : [class_Fields_Olinordered__field__inverse__zero(_1435363), class_Int_Onumber__ring(_1435363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435363), c_Groups_Ozero__class_Ozero(_1435363)), _1435365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435363), c_Groups_Ozero__class_Ozero(_1435363)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435363), _1435365), hAPP(c_Int_Onumber__class_Onumber__of(_1435363), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34383 ^ _779530) ^ [_1435604, _1435606] : [class_Fields_Olinordered__field__inverse__zero(_1435604), class_Int_Onumber__ring(_1435604), 34390 ^ _779530 : [(34391 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435604), c_Groups_Ozero__class_Ozero(_1435604)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435604), _1435606), hAPP(c_Int_Onumber__class_Onumber__of(_1435604), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435604), c_Groups_Ozero__class_Ozero(_1435604)), _1435606)))], (34397 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435604), c_Groups_Ozero__class_Ozero(_1435604)), _1435606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435604), c_Groups_Ozero__class_Ozero(_1435604)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435604), _1435606), hAPP(c_Int_Onumber__class_Onumber__of(_1435604), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (34403 ^ _779530) ^ [_1435954, _1435956, _1435958] : [class_Fields_Ofield(_1435954), -(_1435956 = c_Groups_Oone__class_Oone(_1435954)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1435954), hAPP(c_Power_Opower__class_Opower(_1435954), _1435956)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1435958)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1435954), hAPP(hAPP(c_Power_Opower__class_Opower(_1435954), _1435956), _1435958)), c_Groups_Oone__class_Oone(_1435954))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1435954), _1435956), c_Groups_Oone__class_Oone(_1435954))))], (34413 ^ _779530) ^ [_1436156, _1436158, _1436160, _1436162] : [class_Fields_Olinordered__field__inverse__zero(_1436156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436156), _1436158), _1436160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436156), _1436162), c_Groups_Ozero__class_Ozero(_1436156))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436156), c_Groups_Ozero__class_Ozero(_1436156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436156), _1436158), _1436160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436156), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436156), _1436162), _1436158)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436156), _1436162), _1436160))))], (34431 ^ _779530) ^ [_1436515, _1436517, _1436519, _1436521] : [class_Fields_Olinordered__field(_1436515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436515), _1436517), _1436519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436515), c_Groups_Ozero__class_Ozero(_1436515)), _1436521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436515), c_Groups_Ozero__class_Ozero(_1436515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436515), _1436519), _1436517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436515), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436515), _1436521), _1436519)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436515), _1436521), _1436517))))], (34449 ^ _779530) ^ [_1436874, _1436876, _1436878, _1436880] : [class_Fields_Olinordered__field(_1436874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436874), _1436876), c_Groups_Ozero__class_Ozero(_1436874))), 34456 ^ _779530 : [(34457 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436874), _1436878), _1436876)), _1436880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436874), _1436880), _1436876)), _1436878)))], (34463 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436874), _1436880), _1436876)), _1436878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436874), _1436878), _1436876)), _1436880)))]]], (34469 ^ _779530) ^ [_1437255, _1437257, _1437259, _1437261, _1437263] : [class_Fields_Ofield__inverse__zero(_1437255), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437255), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437255), _1437257), _1437259)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437255), _1437261), _1437263)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437255), _1437257), _1437261)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437255), _1437259), _1437263)))], (34475 ^ _779530) ^ [_1437432, _1437434, _1437436] : [class_Fields_Ofield__inverse__zero(_1437432), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1437432), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437432), _1437434), _1437436)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437432), _1437434), hAPP(c_Groups_Ouminus__class_Ouminus(_1437432), _1437436)))], (34481 ^ _779530) ^ [_1437561, _1437563, _1437565] : [class_Fields_Ofield__inverse__zero(_1437561), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437561), hAPP(c_Groups_Ouminus__class_Ouminus(_1437561), _1437563)), hAPP(c_Groups_Ouminus__class_Ouminus(_1437561), _1437565)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437561), _1437563), _1437565))], (34487 ^ _779530) ^ [_1437690, _1437692, _1437694, _1437696] : [class_Fields_Olinordered__field__inverse__zero(_1437690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437690), _1437692), _1437694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437690), _1437696), c_Groups_Ozero__class_Ozero(_1437690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437690), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437690), _1437694), _1437696)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437690), _1437692), _1437696))))], (34501 ^ _779530) ^ [_1437959, _1437961, _1437963, _1437965] : [class_Fields_Olinordered__field__inverse__zero(_1437959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437959), _1437961), _1437963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437959), c_Groups_Ozero__class_Ozero(_1437959)), _1437965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437959), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437959), _1437961), _1437965)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437959), _1437963), _1437965))))], (34515 ^ _779530) ^ [_1438228, _1438230, _1438232] : [class_Fields_Olinordered__field__inverse__zero(_1438228), 34518 ^ _779530 : [(34519 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1438228), _1438230), _1438232)), c_Groups_Ozero__class_Ozero(_1438228))), 34524 ^ _779530 : [(34525 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), c_Groups_Ozero__class_Ozero(_1438228)), _1438230)))], (34527 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), _1438232), c_Groups_Ozero__class_Ozero(_1438228))))]], 34528 ^ _779530 : [(34529 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), _1438230), c_Groups_Ozero__class_Ozero(_1438228))))], (34531 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), c_Groups_Ozero__class_Ozero(_1438228)), _1438232)))]]], (34533 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1438228), _1438230), _1438232)), c_Groups_Ozero__class_Ozero(_1438228)))), 34534 ^ _779530 : [(34535 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), c_Groups_Ozero__class_Ozero(_1438228)), _1438230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), _1438232), c_Groups_Ozero__class_Ozero(_1438228)))], (34541 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), _1438230), c_Groups_Ozero__class_Ozero(_1438228))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438228), c_Groups_Ozero__class_Ozero(_1438228)), _1438232))]]]]], (34549 ^ _779530) ^ [_1438818, _1438820, _1438822] : [class_Fields_Olinordered__field__inverse__zero(_1438818), 34552 ^ _779530 : [(34553 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1438818), _1438820), _1438822))), 34558 ^ _779530 : [(34559 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), _1438820)))], (34561 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), _1438822)))]], 34562 ^ _779530 : [(34563 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), _1438820), c_Groups_Ozero__class_Ozero(_1438818))))], (34565 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), _1438822), c_Groups_Ozero__class_Ozero(_1438818))))]]], (34567 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1438818), _1438820), _1438822)))), 34568 ^ _779530 : [(34569 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), _1438820)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), c_Groups_Ozero__class_Ozero(_1438818)), _1438822))], (34575 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), _1438820), c_Groups_Ozero__class_Ozero(_1438818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438818), _1438822), c_Groups_Ozero__class_Ozero(_1438818)))]]]]], (34583 ^ _779530) ^ [_1439408, _1439410, _1439412] : [class_Fields_Olinordered__field__inverse__zero(_1439408), 34586 ^ _779530 : [(34587 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1439408), _1439410), _1439412))), 34592 ^ _779530 : [(34593 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), _1439410)))], (34595 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), _1439412)))]], 34596 ^ _779530 : [(34597 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), _1439410), c_Groups_Ozero__class_Ozero(_1439408))))], (34599 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), _1439412), c_Groups_Ozero__class_Ozero(_1439408))))]]], (34601 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1439408), _1439410), _1439412)))), 34602 ^ _779530 : [(34603 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), _1439410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), c_Groups_Ozero__class_Ozero(_1439408)), _1439412))], (34609 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), _1439410), c_Groups_Ozero__class_Ozero(_1439408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439408), _1439412), c_Groups_Ozero__class_Ozero(_1439408)))]]]]], (34617 ^ _779530) ^ [_1439998, _1440000, _1440002] : [class_Fields_Olinordered__field__inverse__zero(_1439998), 34620 ^ _779530 : [(34621 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1439998), _1440000), _1440002)), c_Groups_Ozero__class_Ozero(_1439998))), 34626 ^ _779530 : [(34627 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), c_Groups_Ozero__class_Ozero(_1439998)), _1440000)))], (34629 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), _1440002), c_Groups_Ozero__class_Ozero(_1439998))))]], 34630 ^ _779530 : [(34631 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), _1440000), c_Groups_Ozero__class_Ozero(_1439998))))], (34633 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), c_Groups_Ozero__class_Ozero(_1439998)), _1440002)))]]], (34635 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1439998), _1440000), _1440002)), c_Groups_Ozero__class_Ozero(_1439998)))), 34636 ^ _779530 : [(34637 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), c_Groups_Ozero__class_Ozero(_1439998)), _1440000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), _1440002), c_Groups_Ozero__class_Ozero(_1439998)))], (34643 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), _1440000), c_Groups_Ozero__class_Ozero(_1439998))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439998), c_Groups_Ozero__class_Ozero(_1439998)), _1440002))]]]]], (34651 ^ _779530) ^ [_1440588, _1440590, _1440592] : [class_Fields_Olinordered__field(_1440588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440588), c_Groups_Ozero__class_Ozero(_1440588)), _1440590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440588), c_Groups_Ozero__class_Ozero(_1440588)), _1440592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440588), c_Groups_Ozero__class_Ozero(_1440588)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1440588), _1440590), _1440592))))], (34665 ^ _779530) ^ [_1440843, _1440845, _1440847] : [class_Fields_Olinordered__field(_1440843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440843), c_Groups_Ozero__class_Ozero(_1440843)), _1440845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440843), _1440847), c_Groups_Ozero__class_Ozero(_1440843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440843), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1440843), _1440845), _1440847)), c_Groups_Ozero__class_Ozero(_1440843))))], (34679 ^ _779530) ^ [_1441098, _1441100, _1441102] : [class_Fields_Olinordered__field(_1441098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441098), _1441100), c_Groups_Ozero__class_Ozero(_1441098))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441098), c_Groups_Ozero__class_Ozero(_1441098)), _1441102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441098), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441098), _1441100), _1441102)), c_Groups_Ozero__class_Ozero(_1441098))))], (34693 ^ _779530) ^ [_1441353, _1441355, _1441357] : [class_Fields_Olinordered__field(_1441353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441353), _1441355), c_Groups_Ozero__class_Ozero(_1441353))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441353), _1441357), c_Groups_Ozero__class_Ozero(_1441353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441353), c_Groups_Ozero__class_Ozero(_1441353)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441353), _1441355), _1441357))))], (34707 ^ _779530) ^ [_1441608, _1441610, _1441612, _1441614] : [class_Fields_Olinordered__field(_1441608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441608), _1441610), _1441612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441608), c_Groups_Ozero__class_Ozero(_1441608)), _1441614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441608), _1441610), _1441614)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441608), _1441612), _1441614))))], (34721 ^ _779530) ^ [_1441877, _1441879, _1441881, _1441883] : [class_Fields_Olinordered__field(_1441877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441877), _1441879), _1441881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441877), _1441883), c_Groups_Ozero__class_Ozero(_1441877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441877), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441877), _1441881), _1441883)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1441877), _1441879), _1441883))))], (34735 ^ _779530) ^ [_1442146, _1442148, _1442150, _1442152, _1442154] : [class_Fields_Ofield(_1442146), -(_1442148 = c_Groups_Ozero__class_Ozero(_1442146)), -(_1442150 = c_Groups_Ozero__class_Ozero(_1442146)), 34746 ^ _779530 : [(34747 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442146), _1442152), _1442148) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442146), _1442154), _1442150), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442146), _1442152), _1442150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442146), _1442154), _1442148))], (34753 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442146), _1442152), _1442150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442146), _1442154), _1442148), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442146), _1442152), _1442148) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442146), _1442154), _1442150))]]], (34759 ^ _779530) ^ [_1442595, _1442597, _1442599, _1442601] : [class_Fields_Ofield__inverse__zero(_1442595), -(_1442597 = c_Groups_Ozero__class_Ozero(_1442595)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442595), _1442597), _1442599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442595), _1442597), _1442601)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442595), _1442599), _1442601))], (34769 ^ _779530) ^ [_1442757, _1442759, _1442761, _1442763] : [class_Fields_Ofield__inverse__zero(_1442757), -(_1442759 = c_Groups_Ozero__class_Ozero(_1442757)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442757), _1442761), _1442759)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442757), _1442763), _1442759)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442757), _1442761), _1442763))], (34779 ^ _779530) ^ [_1442919, _1442921, _1442923, _1442925] : [class_Fields_Ofield__inverse__zero(_1442919), 34782 ^ _779530 : [(34799 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442919), _1442921), _1442923) = _1442925), 34802 ^ _779530 : [(34803 ^ _779530) ^ [] : [_1442923 = c_Groups_Ozero__class_Ozero(_1442919)], (34805 ^ _779530) ^ [] : [_1442921 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442919), _1442925), _1442923)]], 34806 ^ _779530 : [(34807 ^ _779530) ^ [] : [-(_1442923 = c_Groups_Ozero__class_Ozero(_1442919))], (34809 ^ _779530) ^ [] : [_1442925 = c_Groups_Ozero__class_Ozero(_1442919)]]], (34783 ^ _779530) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1442919), _1442921), _1442923) = _1442925, 34786 ^ _779530 : [(34787 ^ _779530) ^ [] : [-(_1442923 = c_Groups_Ozero__class_Ozero(_1442919)), -(_1442921 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442919), _1442925), _1442923))], (34793 ^ _779530) ^ [] : [_1442923 = c_Groups_Ozero__class_Ozero(_1442919), -(_1442925 = c_Groups_Ozero__class_Ozero(_1442919))]]]]], (34813 ^ _779530) ^ [_1443413, _1443415, _1443417, _1443419] : [class_Fields_Ofield__inverse__zero(_1443413), 34816 ^ _779530 : [(34833 ^ _779530) ^ [] : [-(_1443415 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1443413), _1443417), _1443419)), 34836 ^ _779530 : [(34837 ^ _779530) ^ [] : [_1443419 = c_Groups_Ozero__class_Ozero(_1443413)], (34839 ^ _779530) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443413), _1443415), _1443419) = _1443417]], 34840 ^ _779530 : [(34841 ^ _779530) ^ [] : [-(_1443419 = c_Groups_Ozero__class_Ozero(_1443413))], (34843 ^ _779530) ^ [] : [_1443415 = c_Groups_Ozero__class_Ozero(_1443413)]]], (34817 ^ _779530) ^ [] : [_1443415 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1443413), _1443417), _1443419), 34820 ^ _779530 : [(34821 ^ _779530) ^ [] : [-(_1443419 = c_Groups_Ozero__class_Ozero(_1443413)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1443413), _1443415), _1443419) = _1443417)], (34827 ^ _779530) ^ [] : [_1443419 = c_Groups_Ozero__class_Ozero(_1443413), -(_1443415 = c_Groups_Ozero__class_Ozero(_1443413))]]]]], (34847 ^ _779530) ^ [_1443907, _1443909, _1443911] : [class_Fields_Olinordered__field(_1443907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443907), c_Groups_Ozero__class_Ozero(_1443907)), _1443909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443907), c_Groups_Ozero__class_Ozero(_1443907)), _1443911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443907), c_Groups_Ozero__class_Ozero(_1443907)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1443907), _1443909), _1443911))))], (34861 ^ _779530) ^ [_1444162, _1444164, _1444166] : [class_Fields_Olinordered__field(_1444162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444162), c_Groups_Ozero__class_Ozero(_1444162)), _1444164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444162), _1444166), c_Groups_Ozero__class_Ozero(_1444162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444162), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444162), _1444164), _1444166)), c_Groups_Ozero__class_Ozero(_1444162))))], (34875 ^ _779530) ^ [_1444417, _1444419, _1444421, _1444423, _1444425] : [class_Fields_Olinordered__field(_1444417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444417), c_Groups_Ozero__class_Ozero(_1444417)), _1444419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444417), _1444419), _1444421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444417), c_Groups_Ozero__class_Ozero(_1444417)), _1444423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444417), _1444423), _1444425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444417), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444417), _1444419), _1444425)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444417), _1444421), _1444423))))], (34897 ^ _779530) ^ [_1444840, _1444842, _1444844, _1444846, _1444848] : [class_Fields_Olinordered__field(_1444840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444840), c_Groups_Ozero__class_Ozero(_1444840)), _1444842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444840), _1444842), _1444844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444840), c_Groups_Ozero__class_Ozero(_1444840)), _1444846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444840), _1444846), _1444848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1444840), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444840), _1444842), _1444848)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1444840), _1444844), _1444846))))], (34919 ^ _779530) ^ [_1445263, _1445265, _1445267, _1445269, _1445271] : [class_Fields_Olinordered__field(_1445263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445263), c_Groups_Ozero__class_Ozero(_1445263)), _1445265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445263), _1445265), _1445267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445263), c_Groups_Ozero__class_Ozero(_1445263)), _1445269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445263), _1445269), _1445271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445263), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1445263), _1445265), _1445271)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1445263), _1445267), _1445269))))], (34941 ^ _779530) ^ [_1445686, _1445688, _1445690] : [class_Fields_Olinordered__field(_1445686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445686), _1445688), c_Groups_Ozero__class_Ozero(_1445686))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445686), c_Groups_Ozero__class_Ozero(_1445686)), _1445690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445686), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1445686), _1445688), _1445690)), c_Groups_Ozero__class_Ozero(_1445686))))], (34955 ^ _779530) ^ [_1445941, _1445943, _1445945] : [class_Fields_Olinordered__field(_1445941), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445941), _1445943), c_Groups_Ozero__class_Ozero(_1445941))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445941), _1445945), c_Groups_Ozero__class_Ozero(_1445941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1445941), c_Groups_Ozero__class_Ozero(_1445941)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1445941), _1445943), _1445945))))], (34969 ^ _779530) ^ [_1446196, _1446198, _1446200, _1446202] : [class_Fields_Olinordered__field__inverse__zero(_1446196), 34972 ^ _779530 : [(34999 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446198), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1446196), _1446200), _1446202)))), 35002 ^ _779530 : [(35003 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), c_Groups_Ozero__class_Ozero(_1446196)), _1446202)))], (35005 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446196), _1446198), _1446202)), _1446200))]], 35006 ^ _779530 : [(35007 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), c_Groups_Ozero__class_Ozero(_1446196)), _1446202))], (35009 ^ _779530) ^ [] : [35010 ^ _779530 : [(35011 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446202), c_Groups_Ozero__class_Ozero(_1446196))))], (35013 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446196), _1446198), _1446202)))]], 35014 ^ _779530 : [(35015 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446202), c_Groups_Ozero__class_Ozero(_1446196)))], (35017 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446198), c_Groups_Ozero__class_Ozero(_1446196)))]]]]], (34973 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446198), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1446196), _1446200), _1446202))), 34976 ^ _779530 : [(34977 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), c_Groups_Ozero__class_Ozero(_1446196)), _1446202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446196), _1446198), _1446202)), _1446200)))], (34983 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), c_Groups_Ozero__class_Ozero(_1446196)), _1446202))), 34986 ^ _779530 : [(34987 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446202), c_Groups_Ozero__class_Ozero(_1446196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446196), _1446198), _1446202))))], (34993 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446202), c_Groups_Ozero__class_Ozero(_1446196)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446196), _1446198), c_Groups_Ozero__class_Ozero(_1446196))))]]]]]]], (35021 ^ _779530) ^ [_1447149, _1447151, _1447153, _1447155] : [class_Fields_Olinordered__field__inverse__zero(_1447149), 35024 ^ _779530 : [(35051 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1447149), _1447151), _1447153)), _1447155))), 35054 ^ _779530 : [(35055 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447153)))], (35057 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447149), _1447155), _1447153)))]], 35058 ^ _779530 : [(35059 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447153))], (35061 ^ _779530) ^ [] : [35062 ^ _779530 : [(35063 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447153), c_Groups_Ozero__class_Ozero(_1447149))))], (35065 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447149), _1447155), _1447153)), _1447151))]], 35066 ^ _779530 : [(35067 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447153), c_Groups_Ozero__class_Ozero(_1447149)))], (35069 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447155))]]]]], (35025 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1447149), _1447151), _1447153)), _1447155)), 35028 ^ _779530 : [(35029 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447149), _1447155), _1447153))))], (35035 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447153))), 35038 ^ _779530 : [(35039 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447153), c_Groups_Ozero__class_Ozero(_1447149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447149), _1447155), _1447153)), _1447151)))], (35045 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), _1447153), c_Groups_Ozero__class_Ozero(_1447149)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1447149), c_Groups_Ozero__class_Ozero(_1447149)), _1447155)))]]]]]]], (35073 ^ _779530) ^ [_1448102, _1448104, _1448106, _1448108] : [class_Fields_Olinordered__field(_1448102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448102), c_Groups_Ozero__class_Ozero(_1448102)), _1448104)), 35080 ^ _779530 : [(35081 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448102), _1448106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448102), _1448108), _1448104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1448102), _1448106), _1448104)), _1448108)))], (35087 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1448102), _1448106), _1448104)), _1448108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448102), _1448106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448102), _1448108), _1448104))))]]], (35093 ^ _779530) ^ [_1448483, _1448485, _1448487, _1448489] : [class_Fields_Olinordered__field(_1448483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448483), c_Groups_Ozero__class_Ozero(_1448483)), _1448485)), 35100 ^ _779530 : [(35101 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448483), _1448487), _1448485)), _1448489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448483), _1448487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1448483), _1448489), _1448485))))], (35107 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448483), _1448487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1448483), _1448489), _1448485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448483), _1448487), _1448485)), _1448489)))]]], (35113 ^ _779530) ^ [_1448864, _1448866, _1448868, _1448870] : [class_Fields_Olinordered__field(_1448864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448864), c_Groups_Ozero__class_Ozero(_1448864)), _1448866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448864), _1448868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1448864), _1448870), _1448866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1448864), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1448864), _1448868), _1448866)), _1448870)))], (35127 ^ _779530) ^ [_1449133, _1449135, _1449137, _1449139] : [class_Fields_Olinordered__field(_1449133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449133), c_Groups_Ozero__class_Ozero(_1449133)), _1449135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449133), _1449137), _1449135)), _1449139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449133), _1449137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449133), _1449139), _1449135))))], (35141 ^ _779530) ^ [_1449402, _1449404, _1449406, _1449408] : [class_Fields_Olinordered__field(_1449402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449402), _1449404), c_Groups_Ozero__class_Ozero(_1449402))), 35148 ^ _779530 : [(35149 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449402), _1449406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449402), _1449408), _1449404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449402), _1449408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449402), _1449406), _1449404))))], (35155 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449402), _1449408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449402), _1449406), _1449404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449402), _1449406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449402), _1449408), _1449404))))]]], (35161 ^ _779530) ^ [_1449783, _1449785, _1449787, _1449789] : [class_Fields_Olinordered__field(_1449783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449783), _1449785), c_Groups_Ozero__class_Ozero(_1449783))), 35168 ^ _779530 : [(35169 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449783), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449783), _1449787), _1449785)), _1449789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449783), _1449789), _1449785)), _1449787)))], (35175 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1449783), _1449789), _1449785)), _1449787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1449783), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449783), _1449787), _1449785)), _1449789)))]]], (35181 ^ _779530) ^ [_1450164, _1450166, _1450168, _1450170] : [class_Fields_Olinordered__field(_1450164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450164), _1450166), _1450168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450164), c_Groups_Ozero__class_Ozero(_1450164)), _1450170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450164), c_Groups_Ozero__class_Ozero(_1450164)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450164), _1450168), _1450166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450164), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450164), _1450170), _1450168)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450164), _1450170), _1450166))))], (35199 ^ _779530) ^ [_1450523, _1450525, _1450527, _1450529] : [class_Fields_Olinordered__field(_1450523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450523), _1450525), _1450527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450523), _1450529), c_Groups_Ozero__class_Ozero(_1450523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450523), c_Groups_Ozero__class_Ozero(_1450523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450523), _1450525), _1450527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1450523), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450523), _1450529), _1450525)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450523), _1450529), _1450527))))], (35217 ^ _779530) ^ [_1450882, _1450884, _1450886, _1450888, _1450890] : [class_Fields_Ofield(_1450882), -(_1450884 = c_Groups_Ozero__class_Ozero(_1450882)), -(_1450886 = c_Groups_Ozero__class_Ozero(_1450882)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450882), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450882), _1450888), _1450884)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450882), _1450890), _1450886)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1450882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450882), _1450888), _1450886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450882), _1450890), _1450884))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1450882), _1450884), _1450886)))], (35231 ^ _779530) ^ [_1451129, _1451131, _1451133, _1451135] : [class_Fields_Ofield(_1451129), -(_1451131 = c_Groups_Ozero__class_Ozero(_1451129)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451129), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451129), _1451133), _1451131)), _1451135) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451129), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451129), _1451133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451129), _1451131), _1451135))), _1451131))], (35241 ^ _779530) ^ [_1451307, _1451309, _1451311, _1451313] : [class_Fields_Ofield__inverse__zero(_1451307), -(_1451309 = c_Groups_Ozero__class_Ozero(_1451307)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451307), _1451311), _1451309)), _1451313) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451307), _1451311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451307), _1451313), _1451309))), _1451309))], (35251 ^ _779530) ^ [_1451485, _1451487, _1451489, _1451491] : [class_Fields_Ofield(_1451485), -(_1451487 = c_Groups_Ozero__class_Ozero(_1451485)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451485), _1451489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451485), _1451491), _1451487)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451485), _1451487), _1451489)), _1451491)), _1451487))], (35261 ^ _779530) ^ [_1451663, _1451665, _1451667, _1451669] : [class_Fields_Ofield__inverse__zero(_1451663), -(_1451665 = c_Groups_Ozero__class_Ozero(_1451663)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451663), _1451667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451663), _1451669), _1451665)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451663), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451663), _1451669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451663), _1451667), _1451665))), _1451665))], (35271 ^ _779530) ^ [_1451841, _1451843, _1451845, _1451847, _1451849] : [class_Fields_Ofield(_1451841), -(_1451843 = c_Groups_Ozero__class_Ozero(_1451841)), -(_1451845 = c_Groups_Ozero__class_Ozero(_1451841)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1451841), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451841), _1451847), _1451843)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451841), _1451849), _1451845)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1451841), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1451841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451841), _1451847), _1451845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451841), _1451849), _1451843))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451841), _1451843), _1451845)))], (35285 ^ _779530) ^ [_1452088, _1452090, _1452092, _1452094] : [class_Fields_Ofield(_1452088), -(_1452090 = c_Groups_Ozero__class_Ozero(_1452088)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1452088), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452088), _1452092), _1452090)), _1452094) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452088), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1452088), _1452092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452088), _1452090), _1452094))), _1452090))], (35295 ^ _779530) ^ [_1452266, _1452268, _1452270, _1452272] : [class_Fields_Ofield(_1452266), -(_1452268 = c_Groups_Ozero__class_Ozero(_1452266)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1452266), _1452270), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452266), _1452272), _1452268)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452266), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1452266), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452266), _1452268), _1452270)), _1452272)), _1452268))], (35305 ^ _779530) ^ [_1452444, _1452446, _1452448] : [class_Fields_Olinordered__field(_1452444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452444), _1452446), _1452448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452444), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452444), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452444), _1452446), _1452448)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452444), c_Groups_Oone__class_Oone(_1452444)), c_Groups_Oone__class_Oone(_1452444)))), _1452448)))], (35315 ^ _779530) ^ [_1452659, _1452661, _1452663] : [class_Fields_Olinordered__field(_1452659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452659), _1452661), _1452663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452659), _1452661), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452659), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452659), _1452661), _1452663)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452659), c_Groups_Oone__class_Oone(_1452659)), c_Groups_Oone__class_Oone(_1452659))))))], (35325 ^ _779530) ^ [_1452874, _1452876, _1452878, _1452880] : [class_Fields_Olinordered__field__inverse__zero(_1452874), 35328 ^ _779530 : [(35355 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452876), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452874), _1452878), _1452880)))), 35358 ^ _779530 : [(35359 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), c_Groups_Ozero__class_Ozero(_1452874)), _1452880)))], (35361 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452874), _1452876), _1452880)), _1452878))]], 35362 ^ _779530 : [(35363 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), c_Groups_Ozero__class_Ozero(_1452874)), _1452880))], (35365 ^ _779530) ^ [] : [35366 ^ _779530 : [(35367 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), _1452880), c_Groups_Ozero__class_Ozero(_1452874))))], (35369 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452874), _1452876), _1452880)))]], 35370 ^ _779530 : [(35371 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), _1452880), c_Groups_Ozero__class_Ozero(_1452874)))], (35373 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452876), c_Groups_Ozero__class_Ozero(_1452874)))]]]]], (35329 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452876), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1452874), _1452878), _1452880))), 35332 ^ _779530 : [(35333 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), c_Groups_Ozero__class_Ozero(_1452874)), _1452880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452874), _1452876), _1452880)), _1452878)))], (35339 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), c_Groups_Ozero__class_Ozero(_1452874)), _1452880))), 35342 ^ _779530 : [(35343 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), _1452880), c_Groups_Ozero__class_Ozero(_1452874))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452874), _1452876), _1452880))))], (35349 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1452874), _1452880), c_Groups_Ozero__class_Ozero(_1452874)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1452874), _1452876), c_Groups_Ozero__class_Ozero(_1452874))))]]]]]]], (35377 ^ _779530) ^ [_1453827, _1453829, _1453831, _1453833] : [class_Fields_Olinordered__field__inverse__zero(_1453827), 35380 ^ _779530 : [(35407 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1453827), _1453829), _1453831)), _1453833))), 35410 ^ _779530 : [(35411 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453831)))], (35413 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), _1453829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453827), _1453833), _1453831)))]], 35414 ^ _779530 : [(35415 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453831))], (35417 ^ _779530) ^ [] : [35418 ^ _779530 : [(35419 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), _1453831), c_Groups_Ozero__class_Ozero(_1453827))))], (35421 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453827), _1453833), _1453831)), _1453829))]], 35422 ^ _779530 : [(35423 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), _1453831), c_Groups_Ozero__class_Ozero(_1453827)))], (35425 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453833))]]]]], (35381 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1453827), _1453829), _1453831)), _1453833)), 35384 ^ _779530 : [(35385 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), _1453829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453827), _1453833), _1453831))))], (35391 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453831))), 35394 ^ _779530 : [(35395 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), _1453831), c_Groups_Ozero__class_Ozero(_1453827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453827), _1453833), _1453831)), _1453829)))], (35401 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453827), _1453831), c_Groups_Ozero__class_Ozero(_1453827)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453827), c_Groups_Ozero__class_Ozero(_1453827)), _1453833)))]]]]]]], (35429 ^ _779530) ^ [_1454780, _1454782, _1454784, _1454786] : [class_Fields_Olinordered__field(_1454780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454780), c_Groups_Ozero__class_Ozero(_1454780)), _1454782)), 35436 ^ _779530 : [(35437 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454780), _1454784), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454780), _1454786), _1454782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1454780), _1454784), _1454782)), _1454786)))], (35443 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1454780), _1454784), _1454782)), _1454786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454780), _1454784), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454780), _1454786), _1454782))))]]], (35449 ^ _779530) ^ [_1455161, _1455163, _1455165, _1455167] : [class_Fields_Olinordered__field(_1455161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455161), c_Groups_Ozero__class_Ozero(_1455161)), _1455163)), 35456 ^ _779530 : [(35457 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455161), _1455165), _1455163)), _1455167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455161), _1455165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455161), _1455167), _1455163))))], (35463 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455161), _1455165), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455161), _1455167), _1455163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455161), _1455165), _1455163)), _1455167)))]]], (35469 ^ _779530) ^ [_1455542, _1455544, _1455546, _1455548] : [class_Fields_Olinordered__field(_1455542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455542), c_Groups_Ozero__class_Ozero(_1455542)), _1455544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455542), _1455546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455542), _1455548), _1455544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455542), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455542), _1455546), _1455544)), _1455548)))], (35483 ^ _779530) ^ [_1455811, _1455813, _1455815, _1455817] : [class_Fields_Olinordered__field(_1455811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455811), c_Groups_Ozero__class_Ozero(_1455811)), _1455813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1455811), _1455815), _1455813)), _1455817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455811), _1455815), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455811), _1455817), _1455813))))], (35497 ^ _779530) ^ [_1456080, _1456082, _1456084, _1456086] : [class_Fields_Olinordered__field(_1456080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1456080), _1456082), c_Groups_Ozero__class_Ozero(_1456080))), 35504 ^ _779530 : [(35505 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456080), _1456084), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1456080), _1456086), _1456082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456080), _1456086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456080), _1456084), _1456082))))], (35511 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456080), _1456086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456080), _1456084), _1456082))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456080), _1456084), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1456080), _1456086), _1456082))))]]], (35517 ^ _779530) ^ [_1456461, _1456463, _1456465, _1456467, _1456469] : [class_Fields_Ofield(_1456461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456463), _1456465)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456463), _1456467)), 35531 ^ _779530 : [(35532 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456463), 35530 ^ [_1456461, _1456463, _1456465, _1456467, _1456469]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456463, tc_HOL_Obool)), _1456465), _1456467))))], (35534 ^ _779530) ^ [] : [-(hAPP(_1456469, 35530 ^ [_1456461, _1456463, _1456465, _1456467, _1456469]) = c_Groups_Ozero__class_Ozero(_1456461))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456463, _1456461), _1456469), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456463, tc_HOL_Obool)), _1456465), _1456467)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1456461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456461), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456463, _1456461), _1456469), _1456465)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456463, _1456461), _1456469), _1456467))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1456463, _1456461), _1456469), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456463, tc_HOL_Obool)), _1456465), _1456467))))], (35538 ^ _779530) ^ [_1456957] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1456957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1456957)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35540 ^ _779530) ^ [_1456992, _1456994, _1456996, _1456998, _1457000, _1457002] : [class_Groups_Oordered__ab__group__add(_1456992), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456994), _1456996)), 35550 ^ _779530 : [(35551 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456994), 35549 ^ [_1456992, _1456994, _1456996, _1456998, _1457000, _1457002]), _1456996)))], (35553 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456992), c_Groups_Ozero__class_Ozero(_1456992)), hAPP(_1456998, 35549 ^ [_1456992, _1456994, _1456996, _1456998, _1457000, _1457002])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456994, _1456992), _1456998), _1456996) = _1457000, hBOOL(hAPP(hAPP(c_member(_1456994), _1457002), _1456996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1456992), hAPP(_1456998, _1457002)), _1457000)))], (35565 ^ _779530) ^ [_1457527, _1457529] : [c_Code__Numeral_OSuc__code__numeral(_1457527) = c_Code__Numeral_OSuc__code__numeral(_1457529), -(_1457527 = _1457529)], (35571 ^ _779530) ^ [_1457608, _1457610] : [_1457608 = _1457610, -(c_Code__Numeral_OSuc__code__numeral(_1457608) = c_Code__Numeral_OSuc__code__numeral(_1457610))], (35577 ^ _779530) ^ [_1457704] : [c_Code__Numeral_OSuc__code__numeral(_1457704) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (35579 ^ _779530) ^ [_1457738] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1457738)], (35581 ^ _779530) ^ [_1457763] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1457763)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1457763)], (35583 ^ _779530) ^ [_1457794] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1457794)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1457794)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (35585 ^ _779530) ^ [_1457831, _1457833, _1457835, _1457837, _1457839] : [class_Groups_Oordered__ab__group__add(_1457831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457833), _1457835)), 35595 ^ _779530 : [(35596 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457833), 35594 ^ [_1457831, _1457833, _1457835, _1457837, _1457839]), _1457835)))], (35598 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457831), c_Groups_Ozero__class_Ozero(_1457831)), hAPP(_1457837, 35594 ^ [_1457831, _1457833, _1457835, _1457837, _1457839])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457833, _1457831), _1457837), _1457835) = c_Groups_Ozero__class_Ozero(_1457831), hBOOL(hAPP(hAPP(c_member(_1457833), _1457839), _1457835)), -(hAPP(_1457837, _1457839) = c_Groups_Ozero__class_Ozero(_1457831))], (35610 ^ _779530) ^ [] : [-(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))))], (35612 ^ _779530) ^ [_1458347, _1458349, _1458351] : [class_Orderings_Olinorder(_1458347), 35615 ^ _779530 : [(35616 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458347), _1458349) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458347), _1458351), -(_1458349 = _1458351)], (35622 ^ _779530) ^ [] : [_1458349 = _1458351, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458347), _1458349) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458347), _1458351))]]], (35628 ^ _779530) ^ [_1458588, _1458590, _1458592] : [class_Orderings_Oord(_1458588), 35631 ^ _779530 : [(35632 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1458588), _1458590), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458588), _1458592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458588), _1458592), _1458590)))], (35638 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458588), _1458592), _1458590)), -(hBOOL(hAPP(hAPP(c_member(_1458588), _1458590), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458588), _1458592))))]]], (35644 ^ _779530) ^ [_1458856, _1458858, _1458860] : [class_Orderings_Olinorder(_1458856), 35647 ^ _779530 : [(35648 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458856, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458856), _1458858)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458856), _1458860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458856), _1458860), _1458858)))], (35654 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458856), _1458860), _1458858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458856, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458856), _1458858)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1458856), _1458860))))]]], (35660 ^ _779530) ^ [_1459148, _1459150, _1459152] : [class_Orderings_Olinorder(_1459148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459148), _1459150), _1459152)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459148, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1459148, _1459150, _1459152)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1459148), _1459152)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1459148), _1459150))], (35670 ^ _779530) ^ [_1459343, _1459345] : [class_Groups_Oordered__ab__group__add(_1459343), -(hAPP(c_Set_Oimage(_1459343, _1459343, c_Groups_Ouminus__class_Ouminus(_1459343)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1459343), _1459345)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1459343), hAPP(c_Groups_Ouminus__class_Ouminus(_1459343), _1459345)))], (35676 ^ _779530) ^ [_1459466, _1459468] : [class_Groups_Oordered__ab__group__add(_1459466), -(hAPP(c_Set_Oimage(_1459466, _1459466, c_Groups_Ouminus__class_Ouminus(_1459466)), hAPP(c_SetInterval_Oord__class_OlessThan(_1459466), _1459468)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1459466), hAPP(c_Groups_Ouminus__class_Ouminus(_1459466), _1459468)))], (35682 ^ _779530) ^ [_1459589, _1459591, _1459593] : [class_Orderings_Oorder(_1459589), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459589, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1459589, _1459591, _1459593)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1459589), _1459593)) = c_Orderings_Obot__class_Obot(tc_fun(_1459589, tc_HOL_Obool)))], (35688 ^ _779530) ^ [_1459716] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1459716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1459716)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1459716)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (35690 ^ _779530) ^ [] : [-(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))], (35692 ^ _779530) ^ [_1459781, _1459783, _1459785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1459781, 35693 ^ [_1459781, _1459783, _1459785])), hAPP(_1459783, 35693 ^ [_1459781, _1459783, _1459785]))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1459783), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459785))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1459781), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459785))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1459783)), _1459781)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1459785)))], (35699 ^ _779530) ^ [_1460014, _1460016, _1460018, _1460020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460014), _1460016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1460018), _1460020)), -(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), _1460014), _1460018)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460016), _1460020))), c_FunDef_Opair__less)))], (35709 ^ _779530) ^ [_1460217, _1460219, _1460221] : [class_Orderings_Olinorder(_1460217), hAPP(_1460219, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1460217), 35714 ^ [_1460217, _1460219, _1460221]), 35715 ^ [_1460217, _1460219, _1460221])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1460217), hAPP(_1460219, 35714 ^ [_1460217, _1460219, _1460221])), hAPP(_1460219, 35715 ^ [_1460217, _1460219, _1460221])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460217), _1460221)), -(_1460221 = c_Orderings_Obot__class_Obot(tc_fun(_1460217, tc_HOL_Obool))), -(hAPP(_1460219, c_Big__Operators_Olattice_OSup__fin(_1460217, c_Orderings_Oord__class_Omax(_1460217), _1460221)) = c_Big__Operators_Olattice_OSup__fin(_1460217, c_Orderings_Oord__class_Omax(_1460217), hAPP(c_Set_Oimage(_1460217, _1460217, _1460219), _1460221)))], (35729 ^ _779530) ^ [_1460632, _1460634, _1460636, _1460638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1460632), _1460634)), -(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), _1460632), _1460636)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460634), _1460638))), c_FunDef_Opair__less)))], (35735 ^ _779530) ^ [_1460769, _1460771, _1460773, _1460775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460769), _1460771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1460773), _1460775)), -(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), _1460769), _1460773)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1460771), _1460775))), c_FunDef_Opair__leq)))], (35745 ^ _779530) ^ [_1460972, _1460974, _1460976, _1460978] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1460972), _1460974)), 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)), _1460972), _1460976)), 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)), _1460974), _1460978)), 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)), _1460974), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1460976), _1460978))), c_FunDef_Omin__strict)))], (35759 ^ _779530) ^ [_1461253, _1461255, _1461257, _1461259] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1461253), _1461255)), 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)), _1461257), _1461253)), 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)), _1461259), _1461255)), 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)), _1461257), _1461259)), _1461255)), c_FunDef_Omax__strict)))], (35773 ^ _779530) ^ [_1461534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1461534)), -(_1461534 = 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))), _1461534)), c_FunDef_Omax__strict)))], (35783 ^ _779530) ^ [_1461640] : [-(_1461640 = 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)), _1461640), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (35789 ^ _779530) ^ [_1461685, _1461687, _1461689, _1461691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1461685), _1461687)), -(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), _1461685), _1461689)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1461687), _1461691))), c_FunDef_Opair__leq)))], (35795 ^ _779530) ^ [_1461822, _1461824, _1461826, _1461828] : 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hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1461826), _1461828)), _1461824)), c_FunDef_Omax__weak)))], (35809 ^ _779530) ^ [_1462103, _1462105, _1462107, _1462109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462103), _1462105)), 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)), _1462103), _1462107)), 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)), _1462105), _1462109)), 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)), _1462105), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1462107), _1462109))), c_FunDef_Omin__weak)))], (35823 ^ _779530) ^ [_1462384] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1462384)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1462384)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1462384), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (35825 ^ _779530) ^ [_1462428, _1462430, _1462432] : [class_Orderings_Olinorder(_1462428), 35828 ^ _779530 : [(35829 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1462428), _1462430) = hAPP(c_SetInterval_Oord__class_OatLeast(_1462428), _1462432), -(_1462430 = _1462432)], (35835 ^ _779530) ^ [] : [_1462430 = _1462432, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1462428), _1462430) = hAPP(c_SetInterval_Oord__class_OatLeast(_1462428), _1462432))]]], (35841 ^ _779530) ^ [_1462669, _1462671, _1462673] : [class_Orderings_Oord(_1462669), 35844 ^ _779530 : [(35845 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1462669), _1462671), hAPP(c_SetInterval_Oord__class_OatLeast(_1462669), _1462673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1462669), _1462673), _1462671)))], (35851 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1462669), _1462673), _1462671)), -(hBOOL(hAPP(hAPP(c_member(_1462669), _1462671), hAPP(c_SetInterval_Oord__class_OatLeast(_1462669), _1462673))))]]], (35857 ^ _779530) ^ [_1462937, _1462939, _1462941] : [class_Orderings_Oorder(_1462937), 35860 ^ _779530 : [(35861 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462937, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1462937), _1462939)), hAPP(c_SetInterval_Oord__class_OatLeast(_1462937), _1462941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1462937), _1462941), _1462939)))], (35867 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1462937), _1462941), _1462939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462937, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1462937), _1462939)), hAPP(c_SetInterval_Oord__class_OatLeast(_1462937), _1462941))))]]], (35873 ^ _779530) ^ [] : [-(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)))], (35875 ^ _779530) ^ [_1463247, _1463249] : [class_Orderings_Olinorder(_1463247), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1463247, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1463247), _1463249)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1463247), _1463249))], (35881 ^ _779530) ^ [_1463358, _1463360] : 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-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463700, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1463700, _1463702), _1463704)), hAPP(c_SetInterval_Oord__class_OatLeast(_1463700), _1463704)) = c_Orderings_Obot__class_Obot(tc_fun(_1463700, tc_HOL_Obool)))], (35905 ^ _779530) ^ [] : [-(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)))], (35907 ^ _779530) ^ [_1463849, _1463851, _1463853] : [class_Orderings_Oorder(_1463849), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463849, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1463849, _1463851, _1463853)), hAPP(c_SetInterval_Oord__class_OatLeast(_1463849), _1463853)) = c_Orderings_Obot__class_Obot(tc_fun(_1463849, tc_HOL_Obool)))], 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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)))))], (35939 ^ _779530) ^ [] : [-(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)))))], (35941 ^ _779530) ^ [] : [-(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)))], (35943 ^ _779530) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (35945 ^ _779530) ^ [_1464515, _1464517, _1464519, _1464521] : [c_FunDef_Oreduction__pair(_1464515, _1464517), -(c_FunDef_Oreduction__pair(_1464519, hAPP(hAPP(c_FunDef_Orp__inv__image(_1464515, _1464519), _1464517), _1464521)))], (35951 ^ _779530) ^ [_1464614, _1464616, _1464618, _1464620, _1464622, _1464624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool)), _1464616), _1464618)), c_Wellfounded_Omax__ext(_1464614, _1464620))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool)), _1464622), _1464624)), c_Wellfounded_Omax__ext(_1464614, _1464620))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1464614, tc_HOL_Obool), tc_fun(_1464614, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464614, tc_HOL_Obool)), _1464616), _1464622)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1464614, tc_HOL_Obool)), _1464618), _1464624))), c_Wellfounded_Omax__ext(_1464614, _1464620))))], (35961 ^ _779530) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (35963 ^ _779530) ^ [] : [-(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)))], (35965 ^ _779530) ^ [_1465064, _1465066, _1465068, _1465070] : [c_Wellfounded_Omax__extp(_1465064, hAPP(hAPP(c_COMBC(_1465064, tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_fun(_1465064, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465064, tc_fun(tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_fun(_1465064, tc_HOL_Obool)), _1465064), c_COMBC(_1465064, tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465064, tc_prod(_1465064, _1465064)), tc_fun(_1465064, tc_fun(tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_HOL_Obool)), _1465064), hAPP(c_COMBB(tc_prod(_1465064, _1465064), tc_fun(tc_fun(tc_prod(_1465064, _1465064), tc_HOL_Obool), tc_HOL_Obool), _1465064), c_member(tc_prod(_1465064, _1465064)))), c_Product__Type_OPair(_1465064, _1465064)))), _1465066), _1465068, _1465070), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1465064, tc_HOL_Obool), tc_fun(_1465064, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1465064, tc_HOL_Obool), tc_fun(_1465064, tc_HOL_Obool)), _1465068), _1465070)), c_Wellfounded_Omax__ext(_1465064, _1465066))))], (35971 ^ _779530) ^ [_1465449, _1465451, _1465453, _1465455] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1465449, tc_HOL_Obool), tc_fun(_1465449, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1465449, tc_HOL_Obool), tc_fun(_1465449, tc_HOL_Obool)), _1465453), _1465455)), c_Wellfounded_Omax__ext(_1465449, _1465451))), -(c_Wellfounded_Omax__extp(_1465449, hAPP(hAPP(c_COMBC(_1465449, tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_fun(_1465449, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465449, tc_fun(tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_fun(_1465449, tc_HOL_Obool)), _1465449), c_COMBC(_1465449, tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1465449, tc_prod(_1465449, _1465449)), tc_fun(_1465449, tc_fun(tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_HOL_Obool)), _1465449), hAPP(c_COMBB(tc_prod(_1465449, _1465449), tc_fun(tc_fun(tc_prod(_1465449, _1465449), tc_HOL_Obool), tc_HOL_Obool), _1465449), c_member(tc_prod(_1465449, _1465449)))), c_Product__Type_OPair(_1465449, _1465449)))), _1465451), _1465453, _1465455))], (35977 ^ _779530) ^ [_1465855, _1465857] : [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)), _1465855), 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)), _1465857), 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)), _1465855), _1465857)), c_Int_Ointrel)))], (35983 ^ _779530) ^ [_1465986, _1465988] : [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)), _1465986), _1465988)), 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)), _1465986), 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)), _1465988), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (35989 ^ _779530) ^ [_1466138, _1466140] : [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), _1466138), _1466140)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466138), _1466140)))], (35995 ^ _779530) ^ [_1466243, _1466245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466243), _1466245)), -(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), _1466243), _1466245)), c_Wellfounded_Oless__than)))], (36001 ^ _779530) ^ [] : [-(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))], (36003 ^ _779530) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (36005 ^ _779530) ^ [_1466390] : [-(c_Wellfounded_Omeasure(_1466390) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1466390), c_Wellfounded_Oless__than))], (36007 ^ _779530) ^ [_1466421, _1466423, _1466425] : [-(c_Wellfounded_Omlex__prod(_1466421, _1466423, _1466425) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1466421), _1466421), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1466421, c_Wellfounded_Oless__than, _1466425)), hAPP(hAPP(c_COMBS(_1466421, _1466421, tc_prod(tc_Nat_Onat, _1466421)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1466421, tc_prod(tc_Nat_Onat, _1466421)), _1466421), c_Product__Type_OPair(tc_Nat_Onat, _1466421)), _1466423)), c_COMBI(_1466421))))], (36009 ^ _779530) ^ [_1466524, _1466526, _1466528, _1466530] : [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), _1466524), _1466526)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466528), _1466530))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466524), _1466530) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466528), _1466526))], (36015 ^ _779530) ^ [_1466671, _1466673, _1466675, _1466677] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466671), _1466677) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466675), _1466673), -(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), _1466671), _1466673)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466675), _1466677))), c_Int_Ointrel)))], (36021 ^ _779530) ^ [_1466824, _1466826, _1466828] : [class_Rings_Oring__1(_1466824), -(hAPP(c_Int_Oring__1__class_Oof__int(_1466824), 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), _1466826), _1466828)), 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(_1466824), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1466824), _1466826)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1466824), _1466828)))], (36027 ^ _779530) ^ [] : [-(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))))))], (36029 ^ _779530) ^ [_1467001, _1467003, _1467005, _1467007] : [-(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), _1467001), _1467003)), 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), _1467005), _1467007)), 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), _1467001), _1467005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1467003), _1467007))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1467001), _1467007)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1467003), _1467005)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36031 ^ _779530) ^ [_1467126] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1467126)) = _1467126)], (36033 ^ _779530) ^ [_1467155, _1467157] : [-(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), _1467155), _1467157)), 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), _1467157), _1467155)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36035 ^ _779530) ^ [] : [-(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))))))], (36037 ^ _779530) ^ [_1467237] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1467237) = 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), _1467237), 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))))))], (36039 ^ _779530) ^ [_1467281, _1467283, _1467285, _1467287] : [-(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), _1467281), _1467283)), 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), _1467285), _1467287)), 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), _1467281), _1467285)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467283), _1467287))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36041 ^ _779530) ^ [_1467382, _1467384] : [-(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), _1467382), _1467384)), 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), _1467382), _1467384))], (36043 ^ _779530) ^ [_1467434] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467434) = 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, _1467434)), 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))))))))], (36045 ^ _779530) ^ [_1467493, _1467495, _1467497, _1467499] : [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), _1467493), _1467495)), 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), _1467497), _1467499)), 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), _1467493), _1467499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467497), _1467495))))], (36051 ^ _779530) ^ [_1467686, _1467688, _1467690, _1467692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467686), _1467692)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467690), _1467688))), -(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), _1467686), _1467688)), 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), _1467690), _1467692)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (36057 ^ _779530) ^ [_1467906, _1467908, _1467910, _1467912] : [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), _1467906), _1467908)), 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), _1467910), _1467912)), 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), _1467906), _1467912)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467910), _1467908))))], (36063 ^ _779530) ^ [_1468099, _1468101, _1468103, _1468105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468099), _1468105)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468103), _1468101))), -(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), _1468099), _1468101)), 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), _1468103), _1468105)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (36071 ^ _779530) ^ [_1468298] : [-(_1468298 = 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), 36068 ^ [_1468298]), 36069 ^ [_1468298])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36073 ^ _779530) ^ [] : [-(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))], (36075 ^ _779530) ^ [_1468367, _1468369, _1468371] : [class_Orderings_Olinorder(_1468367), hAPP(_1468369, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1468367), 36080 ^ [_1468367, _1468369, _1468371]), 36081 ^ [_1468367, _1468369, _1468371])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1468367), hAPP(_1468369, 36080 ^ [_1468367, _1468369, _1468371])), hAPP(_1468369, 36081 ^ [_1468367, _1468369, _1468371])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468367), _1468371)), -(_1468371 = c_Orderings_Obot__class_Obot(tc_fun(_1468367, tc_HOL_Obool))), -(hAPP(_1468369, c_Big__Operators_Olattice_OInf__fin(_1468367, c_Orderings_Oord__class_Omin(_1468367), _1468371)) = c_Big__Operators_Olattice_OInf__fin(_1468367, c_Orderings_Oord__class_Omin(_1468367), hAPP(c_Set_Oimage(_1468367, _1468367, _1468369), _1468371)))], (36095 ^ _779530) ^ [_1468782] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1468782)), c_Int_OInteg)))], (36097 ^ _779530) ^ [] : [-(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))], (36099 ^ _779530) ^ [_1468831, _1468833, _1468835, _1468837] : [class_Groups_Oab__group__add(_1468831), 36102 ^ _779530 : [(36103 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1468833), _1468835)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468831), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1468831, _1468831), hAPP(hAPP(c_COMBB(_1468831, tc_fun(_1468831, _1468831), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1468831)), _1468837)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1468831, tc_Nat_Onat), _1468837), 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, _1468833, _1468835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1468831), hAPP(_1468837, _1468833)), hAPP(_1468837, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1468835), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (36109 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1468833), _1468835))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1468831), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1468831, _1468831), hAPP(hAPP(c_COMBB(_1468831, tc_fun(_1468831, _1468831), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1468831)), _1468837)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1468831, tc_Nat_Onat), _1468837), 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, _1468833, _1468835)) = c_Groups_Ozero__class_Ozero(_1468831))]]], (36115 ^ _779530) ^ [_1469269, _1469271] : [class_Rings_Ocomm__semiring__1(_1469269), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469269), c_Groups_Oone__class_Oone(_1469269)), c_Groups_Oone__class_Oone(_1469269))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469269), c_Nat_Osemiring__1__class_Oof__nat(_1469269)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1469271))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469269), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1469269), _1469271)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469269), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1469269), _1469271)), c_Groups_Oone__class_Oone(_1469269))))], (36121 ^ _779530) ^ [_1469470, _1469472] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1469470, _1469472))))], (36123 ^ _779530) ^ [_1469516, _1469518] : [36125 ^ _779530 : [(36126 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 36124 ^ [_1469516, _1469518]), _1469516)))], (36128 ^ _779530) ^ [] : [hBOOL(hAPP(_1469518, 36124 ^ [_1469516, _1469518]))]], 36129 ^ _779530 : [(36130 ^ _779530) ^ [_1469667] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1469667), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1469516))), -(hBOOL(hAPP(_1469518, _1469667)))]]], (36136 ^ _779530) ^ [_1469770, _1469772] : [36138 ^ _779530 : [(36139 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36137 ^ [_1469770, _1469772]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1469770))))], (36141 ^ _779530) ^ [] : [hBOOL(hAPP(_1469772, 36137 ^ [_1469770, _1469772]))]], 36142 ^ _779530 : [(36143 ^ _779530) ^ [_1469925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1469925), _1469770)), -(hBOOL(hAPP(_1469772, _1469925)))]]], (36149 ^ _779530) ^ [_1470041, _1470043] : [36157 ^ _779530 : [(36158 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 36156 ^ [_1470041, _1470043]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1470041))))], (36160 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1470043, 36156 ^ [_1470041, _1470043])))]], 36150 ^ _779530 : [(36151 ^ _779530) ^ [_1470110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1470110), _1470041)), hBOOL(hAPP(_1470043, _1470110))]]], (36162 ^ _779530) ^ [_1470271, _1470273] : [36170 ^ _779530 : [(36171 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 36169 ^ [_1470271, _1470273]), _1470271)))], (36173 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1470273, 36169 ^ [_1470271, _1470273])))]], 36163 ^ _779530 : [(36164 ^ _779530) ^ [_1470340] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1470340), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1470271))), hBOOL(hAPP(_1470273, _1470340))]]], (36175 ^ _779530) ^ [_1470511, _1470513] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1470511), hAPP(c_Nat_OSuc, _1470513)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1470511, _1470513))], (36177 ^ _779530) ^ [_1470549, _1470551, _1470553] : [class_Orderings_Oorder(_1470549), 36180 ^ _779530 : [(36181 ^ _779530) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1470549, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1470549, _1470551, _1470553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470549), _1470551), _1470553))], (36187 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470549), _1470551), _1470553))), -(c_Orderings_Obot__class_Obot(tc_fun(_1470549, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1470549, _1470551, _1470553))]]], (36193 ^ _779530) ^ [_1470768, _1470770, _1470772] : [class_Orderings_Oorder(_1470768), 36196 ^ _779530 : [(36197 ^ _779530) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1470768, _1470770, _1470772) = c_Orderings_Obot__class_Obot(tc_fun(_1470768, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470768), _1470770), _1470772))], (36203 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470768), _1470770), _1470772))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1470768, _1470770, _1470772) = c_Orderings_Obot__class_Obot(tc_fun(_1470768, tc_HOL_Obool)))]]], (36209 ^ _779530) ^ [_1470987, _1470989, _1470991] : 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[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471150, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1471150, _1471152, _1471154)), c_SetInterval_Oord__class_OatLeastAtMost(_1471150, _1471156, _1471158)))), 36236 ^ _779530 : [(36237 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471150), _1471152), _1471154)))], (36239 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471150), _1471156), _1471152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471150), _1471154), _1471158))]]]]], (36247 ^ _779530) ^ [_1471653, _1471655] : [class_Orderings_Oorder(_1471653), -(c_SetInterval_Oord__class_OatLeastAtMost(_1471653, _1471655, _1471655) = hAPP(hAPP(c_Set_Oinsert(_1471653), _1471655), c_Orderings_Obot__class_Obot(tc_fun(_1471653, tc_HOL_Obool))))], (36253 ^ _779530) ^ [_1471762, _1471764, _1471766, _1471768] : [class_Orderings_Oorder(_1471762), 36256 ^ _779530 : [(36257 ^ _779530) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1471762, _1471764, _1471766) = hAPP(hAPP(c_Set_Oinsert(_1471762), _1471768), c_Orderings_Obot__class_Obot(tc_fun(_1471762, tc_HOL_Obool))), 36260 ^ _779530 : [(36261 ^ _779530) ^ [] : [-(_1471764 = _1471766)], (36263 ^ _779530) ^ [] : [-(_1471766 = _1471768)]]], (36265 ^ _779530) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1471762, _1471764, _1471766) = hAPP(hAPP(c_Set_Oinsert(_1471762), _1471768), c_Orderings_Obot__class_Obot(tc_fun(_1471762, tc_HOL_Obool)))), _1471764 = _1471766, _1471766 = _1471768]]], (36275 ^ _779530) ^ [_1472106, _1472108, _1472110] : [class_Orderings_Oorder(_1472106), _1472108 = _1472110, -(c_SetInterval_Oord__class_OatLeastAtMost(_1472106, _1472108, _1472110) = hAPP(hAPP(c_Set_Oinsert(_1472106), _1472108), c_Orderings_Obot__class_Obot(tc_fun(_1472106, tc_HOL_Obool))))], (36285 ^ _779530) ^ [_1472271, _1472273, _1472275] : [class_Groups_Oordered__ab__group__add(_1472271), -(hAPP(c_Set_Oimage(_1472271, _1472271, 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hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1472444, tc_Nat_Onat), _1472446), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472448, _1472450)))], (36299 ^ _779530) ^ [_1472607, _1472609, _1472611, _1472613, _1472615] : [class_Groups_Ocomm__monoid__add(_1472607), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1472607), _1472609), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1472611), _1472613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1472615), _1472613))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1472607), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1472607, tc_Nat_Onat), _1472609), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1472613))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472611, _1472615)))], (36305 ^ _779530) ^ [_1472790, _1472792] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1472790), _1472792) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1472790, _1472792))], (36307 ^ _779530) ^ [_1472826, _1472828, _1472830] : [-(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)), _1472826)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472828, _1472830)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1472828), _1472826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1472830), _1472826)))], (36309 ^ _779530) ^ [_1472883, _1472885] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472883, _1472885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1472885)), _1472883))], (36311 ^ _779530) ^ [_1472924, _1472926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1472924), hAPP(c_Nat_OSuc, _1472926))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472924, hAPP(c_Nat_OSuc, _1472926)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1472926)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1472924, _1472926)))], (36317 ^ _779530) ^ [_1473057, _1473059] : [hAPP(_1473057, 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), _1473057), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1473059)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1473057), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1473059)))], (36323 ^ _779530) ^ [_1473180, _1473182, _1473184, _1473186] : [class_Orderings_Olinorder(_1473180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473180), _1473182), _1473184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473180), _1473184), _1473186)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473180, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1473180, _1473182), _1473184)), c_SetInterval_Oord__class_OatLeastAtMost(_1473180, _1473184, _1473186)) = c_SetInterval_Oord__class_OatLeastAtMost(_1473180, _1473182, _1473186))], (36337 ^ _779530) ^ [_1473449, _1473451, _1473453, _1473455] : [class_Orderings_Oorder(_1473449), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473449, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1473449, _1473451), _1473453)), c_SetInterval_Oord__class_OatLeastAtMost(_1473449, _1473453, _1473455)) = c_Orderings_Obot__class_Obot(tc_fun(_1473449, tc_HOL_Obool)))], (36343 ^ _779530) ^ [_1473580, _1473582, _1473584, _1473586, _1473588] : [class_Orderings_Olinorder(_1473580), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1473580, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1473580, _1473582, _1473584)), c_SetInterval_Oord__class_OatLeastAtMost(_1473580, _1473586, _1473588)) = c_SetInterval_Oord__class_OatLeastAtMost(_1473580, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1473580), _1473582), _1473586), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1473580), _1473584), _1473588)))], (36349 ^ _779530) ^ [_1473739, _1473741, _1473743, _1473745, _1473747] : [class_Orderings_Oorder(_1473739), 36352 ^ _779530 : [(36353 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1473739, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1473739, _1473741, _1473743)), c_SetInterval_Oord__class_OatLeastAtMost(_1473739, _1473745, _1473747))), 36356 ^ _779530 : [(36371 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473745), _1473747)))], (36357 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473741), _1473743)), 36360 ^ _779530 : [(36361 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473745), _1473741)))], (36363 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473743), _1473747)))], (36365 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473739), _1473745), _1473741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473739), _1473743), _1473747)))]]]]], (36373 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1473739, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1473739, _1473741, _1473743)), c_SetInterval_Oord__class_OatLeastAtMost(_1473739, _1473745, _1473747)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473745), _1473747)), 36376 ^ _779530 : [(36377 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473741), _1473743)))], (36379 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473745), _1473741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1473739), _1473743), _1473747)), 36386 ^ _779530 : [(36387 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473739), _1473745), _1473741))], (36389 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473739), _1473743), _1473747))]]]]]]], (36395 ^ _779530) ^ [_1474510, _1474512, _1474514, _1474516] : [class_Orderings_Olinorder(_1474510), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474510), _1474512), _1474514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474510), _1474514), _1474516)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474510, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1474510, _1474512, _1474514)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1474510, _1474514, _1474516)) = c_SetInterval_Oord__class_OatLeastAtMost(_1474510, _1474512, _1474516))], (36409 ^ _779530) ^ [_1474775, _1474777, _1474779] : [class_Orderings_Oorder(_1474775), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474775, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1474775), _1474777)), c_SetInterval_Oord__class_OatLeastAtMost(_1474775, _1474777, _1474779)) = c_Orderings_Obot__class_Obot(tc_fun(_1474775, tc_HOL_Obool)))], (36415 ^ _779530) ^ [_1474902, _1474904, _1474906, _1474908] : [class_Orderings_Oorder(_1474902), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474902, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1474902, _1474904, _1474906)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1474902, _1474906, _1474908)) = c_Orderings_Obot__class_Obot(tc_fun(_1474902, tc_HOL_Obool)))], (36421 ^ _779530) ^ [_1475029, _1475031, _1475033, _1475035] : [class_Orderings_Oorder(_1475029), 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hAPP(c_SetInterval_Oord__class_OatLeast(_1476767), _1476769))], (36507 ^ _779530) ^ [_1476962, _1476964, _1476966] : [class_Orderings_Olinorder(_1476962), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1476962), _1476964), _1476966)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476962, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1476962, _1476964), _1476966)), hAPP(hAPP(c_Set_Oinsert(_1476962), _1476966), c_Orderings_Obot__class_Obot(tc_fun(_1476962, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1476962, _1476964, _1476966))], (36517 ^ _779530) ^ [_1477175, _1477177, _1477179] : [class_Orderings_Olinorder(_1477175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477175), _1477177), _1477179)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477175, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1477175), _1477177), c_Orderings_Obot__class_Obot(tc_fun(_1477175, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1477175, _1477177, _1477179)) = c_SetInterval_Oord__class_OatLeastAtMost(_1477175, _1477177, _1477179))], (36527 ^ _779530) ^ [_1477384, _1477386, _1477388, _1477390] : [class_Orderings_Olinorder(_1477384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477384), _1477386), _1477388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1477384), _1477388), _1477390)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477384, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1477384, _1477386, _1477388)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1477384, _1477388, _1477390)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1477384, _1477386), _1477390))], (36541 ^ _779530) ^ [_1477653, _1477655, _1477657, _1477659] : [class_Orderings_Olinorder(_1477653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1477653), _1477655), _1477657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477653), _1477657), _1477659)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477653, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1477653, _1477655, _1477657)), c_SetInterval_Oord__class_OatLeastAtMost(_1477653, _1477657, _1477659)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1477653, _1477655, _1477659))], (36555 ^ _779530) ^ [_1477918, _1477920, _1477922, _1477924, _1477926] : [c_Typedef_Otype__definition(_1477918, _1477920, _1477922, _1477924, _1477926), -(hAPP(c_Set_Oimage(_1477918, _1477920, _1477922), c_Orderings_Otop__class_Otop(tc_fun(_1477918, tc_HOL_Obool))) = _1477926)], (36561 ^ _779530) ^ [_1478031, _1478033, _1478035, _1478037, _1478039] : [c_Typedef_Otype__definition(_1478031, _1478033, _1478035, _1478037, _1478039), -(hAPP(c_Set_Oimage(_1478033, _1478031, _1478037), _1478039) = c_Orderings_Otop__class_Otop(tc_fun(_1478031, tc_HOL_Obool)))], (36567 ^ _779530) ^ [_1478144, _1478146, _1478148, _1478150, _1478152, _1478154] : [c_Typedef_Otype__definition(_1478144, _1478146, _1478148, _1478150, _1478152), -(hBOOL(hAPP(hAPP(c_member(_1478146), hAPP(_1478148, _1478154)), _1478152)))], (36573 ^ _779530) ^ [_1478255, _1478257] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1478255, _1478257))))], (36575 ^ _779530) ^ [_1478286, _1478288] : [c_Nat__Transfer_Ois__nat(_1478286), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1478286, _1478288)))], (36581 ^ _779530) ^ [_1478367, _1478369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1478367)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1478367, _1478369)))], (36587 ^ _779530) ^ [_1478454, _1478456] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1478454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1478456), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1478454, _1478456))], (36589 ^ _779530) ^ [_1478495, _1478497] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1478495), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1478497) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1478495, _1478497))], (36591 ^ _779530) ^ [_1478534, _1478536, _1478538, _1478540, _1478542, _1478544] : [c_Typedef_Otype__definition(_1478534, _1478536, _1478538, _1478540, _1478542), -(hAPP(_1478540, hAPP(_1478538, _1478544)) = _1478544)], (36597 ^ _779530) ^ [_1478637, _1478639, _1478641, _1478643, _1478645, _1478647, _1478649] : [c_Typedef_Otype__definition(_1478637, _1478639, _1478641, _1478643, _1478645), 36600 ^ _779530 : [(36601 ^ _779530) ^ [] : [hAPP(_1478641, _1478647) = hAPP(_1478641, _1478649), -(_1478647 = _1478649)], (36607 ^ _779530) ^ [] : [_1478647 = _1478649, -(hAPP(_1478641, 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1479040), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1479038)))], (36627 ^ _779530) ^ [_1479101, _1479103] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1479101, _1479103)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1479103), _1479101)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36629 ^ _779530) ^ [_1479148, _1479150] : [c_Nat__Transfer_Ois__nat(_1479148), c_Nat__Transfer_Ois__nat(_1479150), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1479148, _1479150) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Int_Onat, _1479148), hAPP(c_Int_Onat, _1479150))))], (36639 ^ _779530) ^ [_1479307, _1479309, _1479311, _1479313, _1479315, _1479317, _1479319] : 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480381)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1480383), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1480385)), 36704 ^ _779530 : [(36705 ^ _779530) ^ [_1480589] : [36707 ^ _779530 : [(36708 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36706 ^ [_1480381, _1480383, _1480385, _1480589]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1480381))))], (36711 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36709 ^ [_1480381, _1480383, _1480385, _1480589]), _1480385)))], (36713 ^ _779530) ^ [] : [-(_1480589 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36709 ^ [_1480381, _1480383, _1480385, _1480589]), 36706 ^ [_1480381, _1480383, _1480385, _1480589]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480383), _1480589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1480589), _1480381))))]]], (36721 ^ _779530) ^ [_1480865, _1480867, _1480869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480865)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1480867), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1480869)), 36731 ^ _779530 : [(36732 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36730 ^ [_1480865, _1480867, _1480869]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1480865))))], (36735 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36733 ^ [_1480865, _1480867, _1480869]), _1480869)))], (36737 ^ _779530) ^ [] : [-(_1480867 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36733 ^ [_1480865, _1480867, _1480869]), 36730 ^ [_1480865, _1480867, _1480869]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1480867), _1480865) = _1480867)], (36741 ^ _779530) ^ [_1481204, _1481206, _1481208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481204)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1481206), _1481208)), 36748 ^ _779530 : [(36749 ^ _779530) ^ [_1481394] : [36751 ^ _779530 : [(36752 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36750 ^ [_1481204, _1481206, _1481208, _1481394]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1481204))))], (36755 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36753 ^ [_1481204, _1481206, _1481208, _1481394]), _1481208)))], (36757 ^ _779530) ^ [] : [-(_1481394 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36753 ^ [_1481204, _1481206, _1481208, _1481394]), 36750 ^ [_1481204, _1481206, _1481208, _1481394]))]], -(_1481394 = _1481206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1481394), _1481204) = _1481206]]], (36765 ^ _779530) ^ [_1481654, _1481656, _1481658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481654)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1481656), _1481658)), 36772 ^ _779530 : [(36773 ^ _779530) ^ [_1481844] : [36775 ^ _779530 : [(36776 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36774 ^ [_1481654, _1481656, _1481658, _1481844]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1481654))))], (36779 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36777 ^ [_1481654, _1481656, _1481658, _1481844]), _1481658)))], (36781 ^ _779530) ^ [] : [-(_1481844 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36777 ^ [_1481654, _1481656, _1481658, _1481844]), 36774 ^ [_1481654, _1481656, _1481658, _1481844]))]], -(_1481844 = _1481656), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1481844), _1481654) = _1481656]]], (36789 ^ _779530) ^ [_1482104, _1482106, _1482108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482104)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1482106), _1482108)), 36796 ^ _779530 : [(36797 ^ _779530) ^ [_1482300] : [36799 ^ _779530 : [(36800 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36798 ^ [_1482104, _1482106, _1482108, _1482300]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1482104))))], (36803 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36801 ^ [_1482104, _1482106, _1482108, _1482300]), _1482108)))], (36805 ^ _779530) ^ [] : [-(_1482300 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36801 ^ [_1482104, _1482106, _1482108, _1482300]), 36798 ^ [_1482104, _1482106, _1482108, _1482300]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482106), _1482300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1482300), _1482104))))]]], (36813 ^ _779530) ^ [_1482576, _1482578, _1482580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482576)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1482578), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1482580)), 36823 ^ _779530 : [(36824 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36822 ^ [_1482576, _1482578, _1482580]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1482576))))], (36827 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36825 ^ [_1482576, _1482578, _1482580]), _1482580)))], (36829 ^ _779530) ^ [] : [-(_1482578 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36825 ^ [_1482576, _1482578, _1482580]), 36822 ^ [_1482576, _1482578, _1482580]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1482578), _1482576) = _1482578)], (36833 ^ _779530) ^ [_1482915, _1482917, _1482919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482915)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1482917), _1482919)), 36840 ^ _779530 : [(36841 ^ _779530) ^ [_1483111] : [36843 ^ _779530 : [(36844 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36842 ^ [_1482915, _1482917, _1482919, _1483111]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1482915))))], (36847 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36845 ^ [_1482915, _1482917, _1482919, _1483111]), _1482919)))], (36849 ^ _779530) ^ [] : [-(_1483111 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36845 ^ [_1482915, _1482917, _1482919, _1483111]), 36842 ^ [_1482915, _1482917, _1482919, _1483111]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483111), _1482917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1483111), _1482915)), _1482917)))]]], (36857 ^ _779530) ^ [_1483387, _1483389, _1483391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483387)), 36860 ^ _779530 : [(36861 ^ _779530) ^ [_1483521] : [36863 ^ _779530 : [(36864 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36862 ^ [_1483387, _1483389, _1483391, _1483521]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1483387))))], (36867 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36865 ^ [_1483387, _1483389, _1483391, _1483521]), _1483389)))], (36869 ^ _779530) ^ [] : [-(_1483521 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36865 ^ [_1483387, _1483389, _1483391, _1483521]), 36862 ^ [_1483387, _1483389, _1483391, _1483521]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1483521), _1483391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1483521), _1483387)), _1483391)))]]], (36877 ^ _779530) ^ [_1483795, _1483797, _1483799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1483795)), 36880 ^ _779530 : [(36881 ^ _779530) ^ [_1483929] : [36883 ^ _779530 : [(36884 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36882 ^ [_1483795, _1483797, _1483799, _1483929]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1483795))))], (36887 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36885 ^ [_1483795, _1483797, _1483799, _1483929]), _1483797)))], (36889 ^ _779530) ^ [] : [-(_1483929 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36885 ^ [_1483795, _1483797, _1483799, _1483929]), 36882 ^ [_1483795, _1483797, _1483799, _1483929]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1483799), _1483929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1483799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1483929), _1483795))))]]], (36897 ^ _779530) ^ [_1484203, _1484205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484203)), 36906 ^ _779530 : [(36907 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1484205, 36902 ^ [_1484203, _1484205])))], (36909 ^ _779530) ^ [] : [hBOOL(hAPP(_1484205, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36902 ^ [_1484203, _1484205]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36903 ^ [_1484203, _1484205]), _1484203))))]], 36910 ^ _779530 : [(36911 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1484205, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36902 ^ [_1484203, _1484205]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 36903 ^ [_1484203, _1484205]), _1484203)))))], (36913 ^ _779530) ^ [] : [hBOOL(hAPP(_1484205, 36902 ^ [_1484203, _1484205]))]], 36914 ^ _779530 : [(36915 ^ _779530) ^ [] : [36916 ^ _779530 : [(36917 ^ _779530) ^ [_1484635] : [hBOOL(hAPP(_1484205, _1484635))]], 36919 ^ _779530 : [(36920 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36918 ^ [_1484203, _1484205]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1484203))))], (36922 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1484205, 36918 ^ [_1484203, _1484205])))]]], (36924 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1484205, 36931 ^ [_1484203, _1484205]))), 36925 ^ _779530 : [(36926 ^ _779530) ^ [_1484750] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1484750), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1484203))), hBOOL(hAPP(_1484205, _1484750))]]]]], (36935 ^ _779530) ^ [_1484897, _1484899, _1484901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1484897)), 36938 ^ _779530 : [(36939 ^ _779530) ^ [_1485031] : [36941 ^ _779530 : [(36942 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36940 ^ [_1484897, _1484899, _1484901, _1485031]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1484897))))], (36945 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36943 ^ [_1484897, _1484899, _1484901, _1485031]), _1484899)))], (36947 ^ _779530) ^ [] : [-(_1485031 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 36943 ^ [_1484897, _1484899, _1484901, _1485031]), 36940 ^ [_1484897, _1484899, _1484901, _1485031]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1484901), _1485031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1484901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1485031), _1484897))))]]], (36955 ^ _779530) ^ [_1485305, _1485307, _1485309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1485305)), 36958 ^ _779530 : [(36959 ^ _779530) ^ [_1485439] : [36961 ^ _779530 : [(36962 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36960 ^ [_1485305, _1485307, _1485309, _1485439]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1485305))))], (36965 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 36963 ^ [_1485305, _1485307, _1485309, _1485439]), _1485307)))], (36967 ^ _779530) ^ [] : [-(_1485439 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36963 ^ [_1485305, _1485307, _1485309, _1485439]), 36960 ^ [_1485305, _1485307, _1485309, _1485439]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1485439), _1485309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1485439), _1485305)), _1485309)))]]], (36975 ^ _779530) ^ [_1485713, _1485715, _1485717] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1485713, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1485715)), _1485717) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485713, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1485713, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1485715)), _1485717)), hAPP(_1485717, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36977 ^ _779530) ^ [_1485785] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1485785) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1485785))))], (36979 ^ _779530) ^ [_1485821] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1485821))))], (36981 ^ _779530) ^ [_1485849, _1485851, _1485853] : [class_Orderings_Olinorder(_1485849), 36984 ^ _779530 : [(36985 ^ _779530) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1485849), _1485851) = hAPP(c_SetInterval_Oord__class_OatMost(_1485849), _1485853), -(_1485851 = _1485853)], (36991 ^ _779530) ^ [] : [_1485851 = _1485853, -(hAPP(c_SetInterval_Oord__class_OatMost(_1485849), _1485851) = hAPP(c_SetInterval_Oord__class_OatMost(_1485849), _1485853))]]], (36997 ^ _779530) ^ [_1486090] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1486090) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1486090))], (36999 ^ _779530) ^ [_1486120] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1486120)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1486120))], (37001 ^ _779530) ^ [_1486152] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1486152)) = hAPP(c_Nat_OSuc, _1486152))], (37003 ^ _779530) ^ [_1486184] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1486184)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1486184)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1486184)))], (37005 ^ _779530) ^ [_1486225, _1486227, _1486229] : [class_Orderings_Oord(_1486225), 37008 ^ _779530 : [(37009 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486225), _1486227), hAPP(c_SetInterval_Oord__class_OatMost(_1486225), _1486229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486225), _1486227), _1486229)))], (37015 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486225), _1486227), _1486229)), -(hBOOL(hAPP(hAPP(c_member(_1486225), _1486227), hAPP(c_SetInterval_Oord__class_OatMost(_1486225), _1486229))))]]], (37021 ^ _779530) ^ [_1486493, _1486495, _1486497] : [class_Orderings_Oorder(_1486493), 37024 ^ _779530 : [(37025 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486493, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1486493), _1486495)), hAPP(c_SetInterval_Oord__class_OatMost(_1486493), _1486497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486493), _1486495), _1486497)))], (37031 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486493), _1486495), _1486497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486493, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1486493), _1486495)), hAPP(c_SetInterval_Oord__class_OatMost(_1486493), _1486497))))]]], (37037 ^ _779530) ^ [_1486785, _1486787] : [class_Orderings_Olinorder(_1486785), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1486785, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1486785), _1486787)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486785), _1486787))], (37043 ^ _779530) ^ [_1486896, _1486898] : [class_Orderings_Olinorder(_1486896), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1486896, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486896), _1486898)) = hAPP(c_SetInterval_Oord__class_OatMost(_1486896), _1486898))], (37049 ^ _779530) ^ [] : [-(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)))], (37051 ^ _779530) ^ [_1487025, _1487027, _1487029] : [class_Groups_Ocomm__monoid__add(_1487025), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1487025), _1487027), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1487029))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1487025), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1487025), _1487027), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1487029))), hAPP(_1487027, hAPP(c_Nat_OSuc, _1487029))))], (37057 ^ _779530) ^ [] : [-(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))))], (37059 ^ _779530) ^ [_1487202, _1487204, _1487206, _1487208] : [class_Orderings_Olinorder(_1487202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487202, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1487202, _1487204, _1487206)), hAPP(c_SetInterval_Oord__class_OatMost(_1487202), _1487208)) = c_SetInterval_Oord__class_OatLeastAtMost(_1487202, _1487204, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1487202), _1487206), _1487208)))], (37065 ^ _779530) ^ [_1487345, _1487347, _1487349, _1487351] : [class_Orderings_Olinorder(_1487345), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487345, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1487345), _1487347)), c_SetInterval_Oord__class_OatLeastAtMost(_1487345, _1487349, _1487351)) = c_SetInterval_Oord__class_OatLeastAtMost(_1487345, _1487349, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1487345), _1487347), _1487351)))], (37071 ^ _779530) ^ [_1487488, _1487490, _1487492] : [class_Orderings_Olinorder(_1487488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487488), _1487490), _1487492)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487488, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1487488), _1487490)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1487488, _1487490, _1487492)) = hAPP(c_SetInterval_Oord__class_OatMost(_1487488), _1487492))], (37081 ^ _779530) ^ [_1487683, _1487685, _1487687, _1487689] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487683, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1487685)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1487683, tc_HOL_Obool), tc_Nat_Onat), _1487687), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1487689))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1487683, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1487689, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1487685), _1487689))), _1487687))], (37083 ^ _779530) ^ [_1487765, _1487767, _1487769] : [class_Orderings_Oorder(_1487765), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487765, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1487765), _1487767)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1487765, _1487767, _1487769)) = c_Orderings_Obot__class_Obot(tc_fun(_1487765, tc_HOL_Obool)))], (37089 ^ _779530) ^ [_1487892, _1487894, _1487896] : [class_Orderings_Oorder(_1487892), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487892, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1487892), _1487894)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1487892, _1487894, _1487896)) = c_Orderings_Obot__class_Obot(tc_fun(_1487892, tc_HOL_Obool)))], (37095 ^ _779530) ^ [_1488019, _1488021] : [class_Groups_Oordered__ab__group__add(_1488019), -(hAPP(c_Set_Oimage(_1488019, _1488019, c_Groups_Ouminus__class_Ouminus(_1488019)), hAPP(c_SetInterval_Oord__class_OatMost(_1488019), _1488021)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1488019), hAPP(c_Groups_Ouminus__class_Ouminus(_1488019), _1488021)))], (37101 ^ _779530) ^ [_1488142, _1488144] : [class_Groups_Oordered__ab__group__add(_1488142), -(hAPP(c_Set_Oimage(_1488142, _1488142, c_Groups_Ouminus__class_Ouminus(_1488142)), hAPP(c_SetInterval_Oord__class_OatLeast(_1488142), _1488144)) = hAPP(c_SetInterval_Oord__class_OatMost(_1488142), hAPP(c_Groups_Ouminus__class_Ouminus(_1488142), _1488144)))], (37107 ^ _779530) ^ [_1488265, _1488267] : [class_Orderings_Olinorder(_1488265), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488265, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1488265), _1488267)), hAPP(hAPP(c_Set_Oinsert(_1488265), _1488267), c_Orderings_Obot__class_Obot(tc_fun(_1488265, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1488265), _1488267))], (37113 ^ _779530) ^ [_1488408, _1488410, _1488412] : [class_Orderings_Olinorder(_1488408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1488408), _1488410), _1488412)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488408, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1488408), _1488410)), c_SetInterval_Oord__class_OatLeastAtMost(_1488408, _1488410, _1488412)) = hAPP(c_SetInterval_Oord__class_OatMost(_1488408), _1488412))], (37123 ^ _779530) ^ [_1488603, _1488605] : [class_Orderings_Oorder(_1488603), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488603, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1488603), _1488605)), hAPP(c_SetInterval_Oord__class_OatLeast(_1488603), _1488605)) = hAPP(hAPP(c_Set_Oinsert(_1488603), _1488605), c_Orderings_Obot__class_Obot(tc_fun(_1488603, tc_HOL_Obool))))], (37129 ^ _779530) ^ [_1488746, _1488748, _1488750] : [class_Orderings_Olinorder(_1488746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1488746), _1488748), _1488750)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488746, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1488746), _1488748)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1488746, _1488748, _1488750)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1488746), _1488750))], (37139 ^ _779530) ^ [_1488941, _1488943, _1488945] : [class_Orderings_Olinorder(_1488941), hAPP(_1488943, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1488941), 37144 ^ [_1488941, _1488943, _1488945]), 37145 ^ [_1488941, _1488943, _1488945])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1488941), hAPP(_1488943, 37144 ^ [_1488941, _1488943, _1488945])), hAPP(_1488943, 37145 ^ [_1488941, _1488943, _1488945])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488941), _1488945)), -(_1488945 = c_Orderings_Obot__class_Obot(tc_fun(_1488941, tc_HOL_Obool))), -(hAPP(_1488943, c_Big__Operators_Olinorder__class_OMax(_1488941, _1488945)) = c_Big__Operators_Olinorder__class_OMax(_1488941, hAPP(c_Set_Oimage(_1488941, _1488941, _1488943), _1488945)))], (37159 ^ _779530) ^ [_1489344, _1489346, _1489348] : [class_Orderings_Olinorder(_1489344), hAPP(_1489346, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1489344), 37164 ^ [_1489344, _1489346, _1489348]), 37165 ^ [_1489344, _1489346, _1489348])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1489344), hAPP(_1489346, 37164 ^ [_1489344, _1489346, _1489348])), hAPP(_1489346, 37165 ^ [_1489344, _1489346, _1489348])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1489344), _1489348)), -(_1489348 = c_Orderings_Obot__class_Obot(tc_fun(_1489344, tc_HOL_Obool))), -(hAPP(_1489346, c_Big__Operators_Olinorder__class_OMin(_1489344, _1489348)) = c_Big__Operators_Olinorder__class_OMin(_1489344, hAPP(c_Set_Oimage(_1489344, _1489344, _1489346), _1489348)))], (37179 ^ _779530) ^ [_1489747, _1489749, _1489751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489747)), 37185 ^ _779530 : [(37186 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1489749, 37184 ^ [_1489747, _1489749, _1489751])))], (37188 ^ _779530) ^ [] : [hBOOL(hAPP(_1489749, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 37184 ^ [_1489747, _1489749, _1489751]), _1489747)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489751)), 37193 ^ _779530 : [(37194 ^ _779530) ^ [_1490036] : [hBOOL(hAPP(_1489749, _1490036)), -(hBOOL(hAPP(_1489749, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1490036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1489751), _1489747)))))]]], (37200 ^ _779530) ^ [_1490159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490159), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1490159 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 37203 ^ [_1490159]))))], (37207 ^ _779530) ^ [_1490272, _1490274, _1490276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490272)), 37213 ^ _779530 : [(37214 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1490274, 37212 ^ [_1490272, _1490274, _1490276])))], (37216 ^ _779530) ^ [] : [hBOOL(hAPP(_1490274, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 37212 ^ [_1490272, _1490274, _1490276]), _1490272)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490276)), 37221 ^ _779530 : [(37222 ^ _779530) ^ [_1490561] : [hBOOL(hAPP(_1490274, _1490561)), -(hBOOL(hAPP(_1490274, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1490561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1490276), _1490272)))))]]], (37228 ^ _779530) ^ [_1490683, _1490685] : [-(hBOOL(hAPP(_1490683, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1490683, _1490685)), 37236 ^ _779530 : [(37237 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 37235 ^ [_1490683, _1490685]), _1490685)))], (37245 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1490683, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 37235 ^ [_1490683, _1490685]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (37239 ^ _779530) ^ [_1490921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1490921), 37235 ^ [_1490683, _1490685])), hBOOL(hAPP(_1490683, _1490921))]]], (37247 ^ _779530) ^ [_1491073, _1491075, _1491077, _1491079, _1491081, _1491083, _1491085, _1491087] : [class_Groups_Ocomm__monoid__mult(_1491073), c_Fun_Oinj__on(_1491075, _1491077, _1491079, _1491081), _1491083 = hAPP(c_Set_Oimage(_1491075, _1491077, _1491079), _1491081), 37261 ^ _779530 : [(37262 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491075), 37260 ^ [_1491073, _1491075, _1491077, _1491079, _1491081, _1491083, _1491085, _1491087]), _1491081)))], (37264 ^ _779530) ^ [] : [hAPP(_1491085, 37260 ^ [_1491073, _1491075, _1491077, _1491079, _1491081, _1491083, _1491085, _1491087]) = hAPP(hAPP(c_Fun_Ocomp(_1491077, _1491073, _1491075, _1491087), _1491079), 37260 ^ [_1491073, _1491075, _1491077, _1491079, _1491081, _1491083, _1491085, _1491087])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491077, _1491073), _1491087), _1491083) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491075, _1491073), _1491085), _1491081))], (37268 ^ _779530) ^ [_1491581, _1491583, _1491585, _1491587, _1491589] : [class_Groups_Ocomm__monoid__mult(_1491581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1491583), _1491585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491583, tc_HOL_Obool)), _1491587), _1491585)), 37282 ^ _779530 : [(37283 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491583), 37281 ^ [_1491581, _1491583, _1491585, _1491587, _1491589]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1491583, tc_HOL_Obool)), _1491585), _1491587))))], (37285 ^ _779530) ^ [] : [hAPP(_1491589, 37281 ^ [_1491581, _1491583, _1491585, _1491587, _1491589]) = c_Groups_Oone__class_Oone(_1491581)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491583, _1491581), _1491589), _1491585) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1491583, _1491581), _1491589), _1491587))], (37289 ^ _779530) ^ [_1492032, _1492034, _1492036, _1492038, _1492040] : [class_Groups_Ocomm__monoid__mult(_1492032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492034), _1492036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492034, tc_HOL_Obool)), _1492038), _1492036)), 37303 ^ _779530 : [(37304 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492034), 37302 ^ [_1492032, _1492034, _1492036, _1492038, _1492040]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492034, tc_HOL_Obool)), _1492036), _1492038))))], (37306 ^ _779530) ^ [] : [hAPP(_1492040, 37302 ^ [_1492032, _1492034, _1492036, _1492038, _1492040]) = c_Groups_Oone__class_Oone(_1492032)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492034, _1492032), _1492040), _1492038) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1492034, _1492032), _1492040), _1492036))], (37310 ^ _779530) ^ [_1492483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1492483)), 37314 ^ _779530 : [(37315 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37313 ^ [_1492483])))], (37317 ^ _779530) ^ [] : [-(_1492483 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 37313 ^ [_1492483]))]]], (37319 ^ _779530) ^ [_1492613, _1492615, _1492617, _1492619, _1492621] : [class_Groups_Ocomm__monoid__add(_1492613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492615), _1492617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492615, tc_HOL_Obool)), _1492619), _1492617)), 37333 ^ _779530 : [(37334 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492615), 37332 ^ [_1492613, _1492615, _1492617, _1492619, _1492621]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492615, tc_HOL_Obool)), _1492617), _1492619))))], (37336 ^ _779530) ^ [] : [hAPP(_1492621, 37332 ^ [_1492613, _1492615, _1492617, _1492619, _1492621]) = c_Groups_Ozero__class_Ozero(_1492613)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492615, _1492613), _1492621), _1492617) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1492615, _1492613), _1492621), _1492619))], (37340 ^ _779530) ^ [_1493064, _1493066, _1493068, _1493070, _1493072] : [class_Groups_Ocomm__monoid__add(_1493064), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493066), _1493068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493066, tc_HOL_Obool)), _1493070), _1493068)), 37354 ^ _779530 : [(37355 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493066), 37353 ^ [_1493064, _1493066, _1493068, _1493070, _1493072]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493066, tc_HOL_Obool)), _1493068), _1493070))))], (37357 ^ _779530) ^ [] : [hAPP(_1493072, 37353 ^ [_1493064, _1493066, _1493068, _1493070, _1493072]) = c_Groups_Ozero__class_Ozero(_1493064)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493066, _1493064), _1493072), _1493070) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493066, _1493064), _1493072), _1493068))], (37361 ^ _779530) ^ [_1493515, _1493517, _1493519] : [class_Fields_Olinordered__field__inverse__zero(_1493515), 37367 ^ _779530 : [(37368 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493515), c_Groups_Ozero__class_Ozero(_1493515)), 37366 ^ [_1493515, _1493517, _1493519])))], (37370 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493515), 37366 ^ [_1493515, _1493517, _1493519]), c_Groups_Oone__class_Oone(_1493515))))], (37372 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1493515), 37366 ^ [_1493515, _1493517, _1493519]), _1493517)), _1493519))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493515), _1493517), _1493519)))], (37376 ^ _779530) ^ [_1493864, _1493866, _1493868, _1493870, _1493872] : [class_Groups_Ocomm__monoid__add(_1493864), class_Groups_Ocomm__monoid__mult(_1493864), _1493866 = _1493868, c_Nat__Transfer_Onat__set(_1493868), 37394 ^ _779530 : [(37395 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37393 ^ [_1493864, _1493866, _1493868, _1493870, _1493872])))], (37397 ^ _779530) ^ [] : [hAPP(_1493870, 37393 ^ [_1493864, _1493866, _1493868, _1493870, _1493872]) = hAPP(_1493872, 37393 ^ [_1493864, _1493866, _1493868, _1493870, _1493872])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1493864), _1493870), _1493866) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1493864), _1493872), _1493868))], (37401 ^ _779530) ^ [_1494327, _1494329] : [class_Rings_Olinordered__idom(_1494327), 37404 ^ _779530 : [(37405 ^ _779530) ^ [] : [c_Groups_Osgn__class_Osgn(_1494327, _1494329) = hAPP(c_Groups_Ouminus__class_Ouminus(_1494327), c_Groups_Oone__class_Oone(_1494327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1494327), _1494329), c_Groups_Ozero__class_Ozero(_1494327))))], (37411 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1494327), _1494329), c_Groups_Ozero__class_Ozero(_1494327))), -(c_Groups_Osgn__class_Osgn(_1494327, _1494329) = hAPP(c_Groups_Ouminus__class_Ouminus(_1494327), c_Groups_Oone__class_Oone(_1494327)))]]], (37417 ^ _779530) ^ [_1494589, _1494591, _1494593] : [class_Rings_Olinordered__idom(_1494589), -(c_Groups_Osgn__class_Osgn(_1494589, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1494589), _1494591), _1494593)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1494589), c_Groups_Osgn__class_Osgn(_1494589, _1494591)), c_Groups_Osgn__class_Osgn(_1494589, _1494593)))], (37423 ^ _779530) ^ [_1494716, _1494718] : [class_Rings_Olinordered__idom(_1494716), -(c_Groups_Osgn__class_Osgn(_1494716, c_Groups_Osgn__class_Osgn(_1494716, _1494718)) = c_Groups_Osgn__class_Osgn(_1494716, _1494718))], (37429 ^ _779530) ^ [_1494809] : [class_Groups_Osgn__if(_1494809), -(c_Groups_Osgn__class_Osgn(_1494809, c_Groups_Ozero__class_Ozero(_1494809)) = c_Groups_Ozero__class_Ozero(_1494809))], (37435 ^ _779530) ^ [_1494896, _1494898] : [class_Rings_Olinordered__idom(_1494896), 37438 ^ _779530 : [(37439 ^ _779530) ^ [] : [c_Groups_Osgn__class_Osgn(_1494896, _1494898) = c_Groups_Ozero__class_Ozero(_1494896), -(_1494898 = c_Groups_Ozero__class_Ozero(_1494896))], (37445 ^ _779530) ^ [] : [_1494898 = c_Groups_Ozero__class_Ozero(_1494896), -(c_Groups_Osgn__class_Osgn(_1494896, _1494898) = c_Groups_Ozero__class_Ozero(_1494896))]]], (37451 ^ _779530) ^ [_1495122, _1495124] : [class_Rings_Olinordered__idom(_1495122), 37454 ^ _779530 : [(37455 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495122), c_Groups_Ozero__class_Ozero(_1495122)), c_Groups_Osgn__class_Osgn(_1495122, _1495124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495122), c_Groups_Ozero__class_Ozero(_1495122)), _1495124)))], (37461 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495122), c_Groups_Ozero__class_Ozero(_1495122)), _1495124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495122), c_Groups_Ozero__class_Ozero(_1495122)), c_Groups_Osgn__class_Osgn(_1495122, _1495124))))]]], (37467 ^ _779530) ^ [_1495390, _1495392] : [class_Rings_Olinordered__idom(_1495390), 37470 ^ _779530 : [(37471 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495390), c_Groups_Osgn__class_Osgn(_1495390, _1495392)), c_Groups_Ozero__class_Ozero(_1495390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495390), _1495392), c_Groups_Ozero__class_Ozero(_1495390))))], (37477 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495390), _1495392), c_Groups_Ozero__class_Ozero(_1495390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495390), c_Groups_Osgn__class_Osgn(_1495390, _1495392)), c_Groups_Ozero__class_Ozero(_1495390))))]]], (37483 ^ _779530) ^ [_1495658, _1495660] : [class_Rings_Olinordered__idom(_1495658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495658), c_Groups_Ozero__class_Ozero(_1495658)), _1495660)), -(c_Groups_Osgn__class_Osgn(_1495658, _1495660) = c_Groups_Oone__class_Oone(_1495658))], (37493 ^ _779530) ^ [_1495813, _1495815] : [class_Rings_Olinordered__idom(_1495813), 37496 ^ _779530 : [(37497 ^ _779530) ^ [] : [c_Groups_Osgn__class_Osgn(_1495813, _1495815) = c_Groups_Oone__class_Oone(_1495813), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495813), c_Groups_Ozero__class_Ozero(_1495813)), _1495815)))], (37503 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1495813), c_Groups_Ozero__class_Ozero(_1495813)), _1495815)), -(c_Groups_Osgn__class_Osgn(_1495813, _1495815) = c_Groups_Oone__class_Oone(_1495813))]]], (37509 ^ _779530) ^ [_1496066] : [_1496066 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1496066) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37515 ^ _779530) ^ [_1496142] : [-(_1496142 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37518 ^ _779530 : [(37519 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1496142)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1496142) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37525 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1496142))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1496142) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (37531 ^ _779530) ^ [_1496334, _1496336] : [class_Groups_Osgn__if(_1496334), 37534 ^ _779530 : [(37535 ^ _779530) ^ [] : [_1496336 = c_Groups_Ozero__class_Ozero(_1496334), -(c_Groups_Osgn__class_Osgn(_1496334, _1496336) = c_Groups_Ozero__class_Ozero(_1496334))], (37541 ^ _779530) ^ [] : [-(_1496336 = c_Groups_Ozero__class_Ozero(_1496334)), 37544 ^ _779530 : [(37545 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496334), c_Groups_Ozero__class_Ozero(_1496334)), _1496336)), -(c_Groups_Osgn__class_Osgn(_1496334, _1496336) = c_Groups_Oone__class_Oone(_1496334))], (37551 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496334), c_Groups_Ozero__class_Ozero(_1496334)), _1496336))), -(c_Groups_Osgn__class_Osgn(_1496334, _1496336) = hAPP(c_Groups_Ouminus__class_Ouminus(_1496334), c_Groups_Oone__class_Oone(_1496334)))]]]]], (37557 ^ _779530) ^ [_1496731, _1496733] : [class_Rings_Olinordered__idom(_1496731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496731), _1496733), c_Groups_Ozero__class_Ozero(_1496731))), -(c_Groups_Osgn__class_Osgn(_1496731, _1496733) = hAPP(c_Groups_Ouminus__class_Ouminus(_1496731), c_Groups_Oone__class_Oone(_1496731)))], (37567 ^ _779530) ^ [_1496896, _1496898, _1496900, _1496902] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1496896, _1496898, _1496900, c_Code__Numeral_OSuc__code__numeral(_1496902)) = hAPP(_1496900, _1496902))], (37569 ^ _779530) ^ [_1496935, _1496937, _1496939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1496935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1496937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1496939), 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), _1496939), _1496937))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1496935)))))], (37575 ^ _779530) ^ [_1497082, _1497084, _1497086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1497084), 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), _1497084), _1497086))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1497082))), _1497086)))], (37581 ^ _779530) ^ [_1497229, _1497231, _1497233, _1497235] : [class_Groups_Oordered__ab__group__add__abs(_1497229), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497229), hAPP(c_Groups_Oabs__class_Oabs(_1497229), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497231, _1497229), _1497233), _1497235))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497231, _1497229), hAPP(hAPP(c_COMBB(_1497229, _1497229, _1497231), c_Groups_Oabs__class_Oabs(_1497229)), _1497233)), _1497235))))], (37587 ^ _779530) ^ [_1497392, _1497394, _1497396, _1497398] : [class_Groups_Oordered__ab__group__add__abs(_1497392), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497392), c_Groups_Ozero__class_Ozero(_1497392)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497394, _1497392), hAPP(hAPP(c_COMBB(_1497392, _1497392, _1497394), c_Groups_Oabs__class_Oabs(_1497392)), _1497396)), _1497398))))], (37593 ^ _779530) ^ [_1497531, _1497533, _1497535] : [class_Rings_Olinordered__idom(_1497531), -(hAPP(c_Groups_Oabs__class_Oabs(_1497531), hAPP(hAPP(c_Power_Opower__class_Opower(_1497531), hAPP(c_Groups_Ouminus__class_Ouminus(_1497531), _1497533)), _1497535)) = hAPP(c_Groups_Oabs__class_Oabs(_1497531), hAPP(hAPP(c_Power_Opower__class_Opower(_1497531), _1497533), _1497535)))], (37599 ^ _779530) ^ [_1497670, _1497672, _1497674] : [class_Fields_Olinordered__field(_1497670), -(_1497672 = c_Groups_Ozero__class_Ozero(_1497670)), -(hAPP(c_Groups_Oabs__class_Oabs(_1497670), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1497670), _1497674), _1497672)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1497670), hAPP(c_Groups_Oabs__class_Oabs(_1497670), _1497674)), hAPP(c_Groups_Oabs__class_Oabs(_1497670), _1497672)))], (37609 ^ _779530) ^ [_1497828, _1497830, _1497832] : [class_Groups_Oordered__ab__group__add__abs(_1497828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497828), hAPP(c_Groups_Oabs__class_Oabs(_1497828), _1497830)), _1497832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497828), hAPP(c_Groups_Ouminus__class_Ouminus(_1497828), _1497830)), _1497832)))], (37619 ^ _779530) ^ [_1498007, _1498009, _1498011] : [class_Groups_Oordered__ab__group__add__abs(_1498007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498007), _1498009), _1498011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498007), hAPP(c_Groups_Ouminus__class_Ouminus(_1498007), _1498009)), _1498011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498007), hAPP(c_Groups_Oabs__class_Oabs(_1498007), _1498009)), _1498011)))], (37633 ^ _779530) ^ [_1498254, _1498256, _1498258] : [class_Groups_Oordered__ab__group__add__abs(_1498254), 37636 ^ _779530 : [(37637 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), hAPP(c_Groups_Oabs__class_Oabs(_1498254), _1498256)), _1498258)), 37640 ^ _779530 : [(37641 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), _1498256), _1498258)))], (37643 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), hAPP(c_Groups_Ouminus__class_Ouminus(_1498254), _1498256)), _1498258)))]]], (37645 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), hAPP(c_Groups_Oabs__class_Oabs(_1498254), _1498256)), _1498258))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), _1498256), _1498258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498254), hAPP(c_Groups_Ouminus__class_Ouminus(_1498254), _1498256)), _1498258))]]], (37655 ^ _779530) ^ [_1498632, _1498634] : [class_Groups_Oordered__ab__group__add__abs(_1498632), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498632), hAPP(c_Groups_Ouminus__class_Ouminus(_1498632), _1498634)), hAPP(c_Groups_Oabs__class_Oabs(_1498632), _1498634))))], (37661 ^ _779530) ^ [_1498741, _1498743, _1498745] : [class_Rings_Olinordered__idom(_1498741), 37664 ^ _779530 : [(37665 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), hAPP(c_Groups_Oabs__class_Oabs(_1498741), _1498743)), _1498745)), 37668 ^ _779530 : [(37669 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), _1498743), _1498745)))], (37671 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), hAPP(c_Groups_Ouminus__class_Ouminus(_1498741), _1498743)), _1498745)))]]], (37673 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), hAPP(c_Groups_Oabs__class_Oabs(_1498741), _1498743)), _1498745))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), _1498743), _1498745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498741), hAPP(c_Groups_Ouminus__class_Ouminus(_1498741), _1498743)), _1498745))]]], (37683 ^ _779530) ^ [_1499119, _1499121, _1499123, _1499125, _1499127] : [class_Rings_Olinordered__idom(_1499119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1499119), hAPP(c_Groups_Oabs__class_Oabs(_1499119), _1499121)), _1499123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1499119), hAPP(c_Groups_Oabs__class_Oabs(_1499119), _1499125)), _1499127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1499119), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499119), hAPP(c_Groups_Oabs__class_Oabs(_1499119), _1499121)), hAPP(c_Groups_Oabs__class_Oabs(_1499119), _1499125))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499119), _1499123), _1499127))))], (37697 ^ _779530) ^ [_1499430, _1499432, _1499434] : [class_Groups_Oordered__ab__group__add__abs(_1499430), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499430), hAPP(c_Groups_Oabs__class_Oabs(_1499430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499430), hAPP(c_Groups_Oabs__class_Oabs(_1499430), _1499432)), hAPP(c_Groups_Oabs__class_Oabs(_1499430), _1499434)))), hAPP(c_Groups_Oabs__class_Oabs(_1499430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499430), _1499432), _1499434)))))], (37703 ^ _779530) ^ [_1499593, _1499595, _1499597] : [class_Groups_Oordered__ab__group__add__abs(_1499593), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499593), hAPP(c_Groups_Oabs__class_Oabs(_1499593), _1499595)), hAPP(c_Groups_Oabs__class_Oabs(_1499593), _1499597))), hAPP(c_Groups_Oabs__class_Oabs(_1499593), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499593), _1499595), _1499597)))))], (37709 ^ _779530) ^ [_1499746, _1499748, _1499750] : [class_Groups_Oordered__ab__group__add__abs(_1499746), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499746), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499746), hAPP(c_Groups_Oabs__class_Oabs(_1499746), _1499748)), hAPP(c_Groups_Oabs__class_Oabs(_1499746), _1499750))), hAPP(c_Groups_Oabs__class_Oabs(_1499746), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499746), _1499750), _1499748)))))], (37715 ^ _779530) ^ [_1499899, _1499901, _1499903] : [class_Groups_Oordered__ab__group__add__abs(_1499899), -(hAPP(c_Groups_Oabs__class_Oabs(_1499899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499899), _1499901), _1499903)) = hAPP(c_Groups_Oabs__class_Oabs(_1499899), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499899), _1499903), _1499901)))], (37721 ^ _779530) ^ [_1500028, _1500030] : [class_Groups_Oordered__ab__group__add__abs(_1500028), 37724 ^ _779530 : [(37725 ^ _779530) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1500028), _1500030) = c_Groups_Ozero__class_Ozero(_1500028), -(_1500030 = c_Groups_Ozero__class_Ozero(_1500028))], (37731 ^ _779530) ^ [] : [_1500030 = c_Groups_Ozero__class_Ozero(_1500028), -(hAPP(c_Groups_Oabs__class_Oabs(_1500028), _1500030) = c_Groups_Ozero__class_Ozero(_1500028))]]], (37737 ^ _779530) ^ [_1500260] : [class_Groups_Oordered__ab__group__add__abs(_1500260), -(hAPP(c_Groups_Oabs__class_Oabs(_1500260), c_Groups_Ozero__class_Ozero(_1500260)) = c_Groups_Ozero__class_Ozero(_1500260))], (37743 ^ _779530) ^ [_1500351, _1500353, _1500355, _1500357] : [class_Groups_Oordered__ab__group__add__abs(_1500351), -(hAPP(c_Groups_Oabs__class_Oabs(_1500351), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500353, _1500351), hAPP(hAPP(c_COMBB(_1500351, _1500351, _1500353), c_Groups_Oabs__class_Oabs(_1500351)), _1500355)), _1500357)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500353, _1500351), hAPP(hAPP(c_COMBB(_1500351, _1500351, _1500353), c_Groups_Oabs__class_Oabs(_1500351)), _1500355)), _1500357))], (37749 ^ _779530) ^ [_1500524, _1500526, _1500528] : [class_Rings_Olinordered__idom(_1500524), -(hAPP(c_Groups_Oabs__class_Oabs(_1500524), hAPP(hAPP(c_Power_Opower__class_Opower(_1500524), _1500526), _1500528)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1500524), hAPP(c_Groups_Oabs__class_Oabs(_1500524), _1500526)), _1500528))], (37755 ^ _779530) ^ [_1500653, _1500655] : [class_Groups_Oordered__ab__group__add__abs(_1500653), -(hAPP(c_Groups_Oabs__class_Oabs(_1500653), hAPP(c_Groups_Ouminus__class_Ouminus(_1500653), _1500655)) = hAPP(c_Groups_Oabs__class_Oabs(_1500653), _1500655))], (37761 ^ _779530) ^ [_1500758, _1500760] : [class_Rings_Olinordered__idom(_1500758), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1500758), hAPP(c_Groups_Oabs__class_Oabs(_1500758), _1500760)), hAPP(c_Groups_Oabs__class_Oabs(_1500758), _1500760)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1500758), _1500760), _1500760))], (37767 ^ _779530) ^ [_1500885, _1500887, _1500889] : [class_Rings_Olinordered__idom(_1500885), -(hAPP(c_Groups_Oabs__class_Oabs(_1500885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1500885), _1500887), _1500889)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1500885), hAPP(c_Groups_Oabs__class_Oabs(_1500885), _1500887)), hAPP(c_Groups_Oabs__class_Oabs(_1500885), _1500889)))], (37773 ^ _779530) ^ [_1501024, _1501026, _1501028] : [class_Groups_Oordered__ab__group__add__abs(_1501024), -(hAPP(c_Groups_Oabs__class_Oabs(_1501024), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1501024), hAPP(c_Groups_Oabs__class_Oabs(_1501024), _1501026)), hAPP(c_Groups_Oabs__class_Oabs(_1501024), _1501028))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1501024), hAPP(c_Groups_Oabs__class_Oabs(_1501024), _1501026)), hAPP(c_Groups_Oabs__class_Oabs(_1501024), _1501028)))], (37779 ^ _779530) ^ [_1501183, _1501185] : [class_Rings_Olinordered__idom(_1501183), -(hAPP(c_Groups_Oabs__class_Oabs(_1501183), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1501183), _1501185)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1501183), _1501185))], (37785 ^ _779530) ^ [_1501288, _1501290] : [class_Groups_Oordered__ab__group__add__abs(_1501288), -(hAPP(c_Groups_Oabs__class_Oabs(_1501288), hAPP(c_Groups_Oabs__class_Oabs(_1501288), _1501290)) = hAPP(c_Groups_Oabs__class_Oabs(_1501288), _1501290))], (37791 ^ _779530) ^ [_1501393] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1501393)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1501393))], (37793 ^ _779530) ^ [_1501425, _1501427, _1501429] : [class_Groups_Oordered__ab__group__add__abs(_1501425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501425), hAPP(c_Groups_Oabs__class_Oabs(_1501425), _1501427)), _1501429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501425), _1501427), _1501429)))], (37803 ^ _779530) ^ [_1501594, _1501596] : [class_Groups_Oordered__ab__group__add__abs(_1501594), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1501594), _1501596), hAPP(c_Groups_Oabs__class_Oabs(_1501594), _1501596))))], (37809 ^ _779530) ^ [_1501693, _1501695, _1501697, _1501699] : [class_Fields_Olinordered__field(_1501693), -(hAPP(c_Groups_Oabs__class_Oabs(_1501693), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1501695, _1501693), _1501697), _1501699)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1501695, _1501693), hAPP(hAPP(c_COMBB(_1501693, _1501693, _1501695), c_Groups_Oabs__class_Oabs(_1501693)), _1501697)), _1501699))], (37815 ^ _779530) ^ [_1501842] : [class_Rings_Olinordered__idom(_1501842), -(hAPP(c_Groups_Oabs__class_Oabs(_1501842), c_Groups_Oone__class_Oone(_1501842)) = c_Groups_Oone__class_Oone(_1501842))], (37821 ^ _779530) ^ [_1501933, _1501935, _1501937] : [class_Fields_Olinordered__field__inverse__zero(_1501933), -(hAPP(c_Groups_Oabs__class_Oabs(_1501933), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1501933), _1501935), _1501937)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1501933), hAPP(c_Groups_Oabs__class_Oabs(_1501933), _1501935)), hAPP(c_Groups_Oabs__class_Oabs(_1501933), _1501937)))], (37827 ^ _779530) ^ [_1502072, _1502074] : [class_Groups_Oordered__ab__group__add__abs(_1502072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1502072), c_Groups_Ozero__class_Ozero(_1502072)), _1502074)), -(hAPP(c_Groups_Oabs__class_Oabs(_1502072), _1502074) = _1502074)], (37837 ^ _779530) ^ [_1502227, _1502229] : [class_Groups_Oordered__ab__group__add__abs(_1502227), 37840 ^ _779530 : [(37841 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1502227), c_Groups_Ozero__class_Ozero(_1502227)), hAPP(c_Groups_Oabs__class_Oabs(_1502227), _1502229))), _1502229 = c_Groups_Ozero__class_Ozero(_1502227)], (37847 ^ _779530) ^ [] : [-(_1502229 = c_Groups_Ozero__class_Ozero(_1502227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1502227), c_Groups_Ozero__class_Ozero(_1502227)), hAPP(c_Groups_Oabs__class_Oabs(_1502227), _1502229))))]]], (37853 ^ _779530) ^ [_1502442, _1502444] : [class_Groups_Oordered__ab__group__add__abs(_1502442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1502442), hAPP(c_Groups_Oabs__class_Oabs(_1502442), _1502444)), c_Groups_Ozero__class_Ozero(_1502442)))], (37859 ^ _779530) ^ [_1502546, _1502548] : [class_Groups_Oordered__ab__group__add__abs(_1502546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502546), c_Groups_Ozero__class_Ozero(_1502546)), _1502548)), -(hAPP(c_Groups_Oabs__class_Oabs(_1502546), _1502548) = _1502548)], (37869 ^ _779530) ^ [_1502701, _1502703] : [class_Groups_Oordered__ab__group__add__abs(_1502701), 37872 ^ _779530 : [(37873 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502701), hAPP(c_Groups_Oabs__class_Oabs(_1502701), _1502703)), c_Groups_Ozero__class_Ozero(_1502701))), -(_1502703 = c_Groups_Ozero__class_Ozero(_1502701))], (37879 ^ _779530) ^ [] : [_1502703 = c_Groups_Ozero__class_Ozero(_1502701), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502701), hAPP(c_Groups_Oabs__class_Oabs(_1502701), _1502703)), c_Groups_Ozero__class_Ozero(_1502701))))]]], (37885 ^ _779530) ^ [_1502954, _1502956] : [class_Groups_Oordered__ab__group__add__abs(_1502954), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1502954), c_Groups_Ozero__class_Ozero(_1502954)), hAPP(c_Groups_Oabs__class_Oabs(_1502954), _1502956))))], (37891 ^ _779530) ^ [_1503057, _1503059, _1503061] : [class_Groups_Oordered__ab__group__add__abs(_1503057), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503057), hAPP(c_Groups_Oabs__class_Oabs(_1503057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1503057), _1503059), _1503061))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1503057), hAPP(c_Groups_Oabs__class_Oabs(_1503057), _1503059)), hAPP(c_Groups_Oabs__class_Oabs(_1503057), _1503061)))))], (37897 ^ _779530) ^ [_1503210, _1503212] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1503210), _1503212)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1503210) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37903 ^ _779530) ^ [_1503311, _1503313] : [class_Rings_Olinordered__idom(_1503311), -(hAPP(c_Groups_Oabs__class_Oabs(_1503311), _1503313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503311), _1503313), c_Groups_Osgn__class_Osgn(_1503311, _1503313)))], (37909 ^ _779530) ^ [_1503418, _1503420] : [class_Rings_Olinordered__idom(_1503418), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503418), c_Groups_Osgn__class_Osgn(_1503418, _1503420)), hAPP(c_Groups_Oabs__class_Oabs(_1503418), _1503420)) = _1503420)], (37915 ^ _779530) ^ [_1503525, _1503527, _1503529] : [class_Rings_Oordered__ring__abs(_1503525), -(hAPP(c_Groups_Oabs__class_Oabs(_1503525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503525), _1503527), _1503529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503525), hAPP(c_Groups_Oabs__class_Oabs(_1503525), _1503527)), hAPP(c_Groups_Oabs__class_Oabs(_1503525), _1503529))), 37922 ^ _779530 : [(37923 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503525), c_Groups_Ozero__class_Ozero(_1503525)), _1503527))], (37925 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503525), _1503527), c_Groups_Ozero__class_Ozero(_1503525)))]], 37926 ^ _779530 : [(37927 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503525), c_Groups_Ozero__class_Ozero(_1503525)), _1503529))], (37929 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503525), _1503529), c_Groups_Ozero__class_Ozero(_1503525)))]]], (37933 ^ _779530) ^ [_1503920, _1503922, _1503924] : [class_Rings_Olinordered__idom(_1503920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1503920), c_Groups_Ozero__class_Ozero(_1503920)), _1503922)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503920), hAPP(c_Groups_Oabs__class_Oabs(_1503920), _1503924)), _1503922) = hAPP(c_Groups_Oabs__class_Oabs(_1503920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1503920), _1503924), _1503922)))], (37943 ^ _779530) ^ [_1504121, _1504123, _1504125, _1504127, _1504129] : [class_Groups_Oordered__ab__group__add__abs(_1504121), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504121), hAPP(c_Groups_Oabs__class_Oabs(_1504121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1504121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1504121), _1504123), _1504125)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1504121), _1504127), _1504129)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1504121), hAPP(c_Groups_Oabs__class_Oabs(_1504121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1504121), _1504123), _1504127))), hAPP(c_Groups_Oabs__class_Oabs(_1504121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1504121), _1504125), _1504129))))))], (37949 ^ _779530) ^ [_1504342, _1504344, _1504346] : [class_Groups_Oordered__ab__group__add__abs(_1504342), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504342), hAPP(c_Groups_Oabs__class_Oabs(_1504342), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1504342), _1504344), _1504346))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1504342), hAPP(c_Groups_Oabs__class_Oabs(_1504342), _1504344)), hAPP(c_Groups_Oabs__class_Oabs(_1504342), _1504346)))))], (37955 ^ _779530) ^ [_1504495, _1504497] : [class_Groups_Oordered__ab__group__add__abs(_1504495), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504495), hAPP(c_Groups_Ouminus__class_Ouminus(_1504495), hAPP(c_Groups_Oabs__class_Oabs(_1504495), _1504497))), c_Groups_Ozero__class_Ozero(_1504495))))], (37961 ^ _779530) ^ [_1504608, _1504610] : [class_Groups_Oordered__ab__group__add__abs(_1504608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504608), _1504610), c_Groups_Ozero__class_Ozero(_1504608))), -(hAPP(c_Groups_Oabs__class_Oabs(_1504608), _1504610) = hAPP(c_Groups_Ouminus__class_Ouminus(_1504608), _1504610))], (37971 ^ _779530) ^ [_1504773, _1504775] : [class_Groups_Oabs__if(_1504773), 37974 ^ _779530 : [(37975 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1504773), _1504775), c_Groups_Ozero__class_Ozero(_1504773))), -(hAPP(c_Groups_Oabs__class_Oabs(_1504773), _1504775) = hAPP(c_Groups_Ouminus__class_Ouminus(_1504773), _1504775))], (37981 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1504773), _1504775), c_Groups_Ozero__class_Ozero(_1504773)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1504773), _1504775) = _1504775)]]], (37987 ^ _779530) ^ [_1505013, _1505015] : [class_Groups_Oordered__ab__group__add__abs(_1505013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1505013), _1505015), c_Groups_Ozero__class_Ozero(_1505013))), -(hAPP(c_Groups_Oabs__class_Oabs(_1505013), _1505015) = hAPP(c_Groups_Ouminus__class_Ouminus(_1505013), _1505015))], (37997 ^ _779530) ^ [_1505178, _1505180, _1505182] : [class_Rings_Olinordered__idom(_1505178), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505178), c_Groups_Ozero__class_Ozero(_1505178)), hAPP(hAPP(c_Power_Opower__class_Opower(_1505178), hAPP(c_Groups_Oabs__class_Oabs(_1505178), _1505180)), _1505182))))], (38003 ^ _779530) ^ [_1505299, _1505301, _1505303] : [class_Fields_Olinordered__field__inverse__zero(_1505299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1505299), c_Groups_Ozero__class_Ozero(_1505299)), _1505301)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1505299), hAPP(c_Groups_Oabs__class_Oabs(_1505299), _1505303)), _1505301) = hAPP(c_Groups_Oabs__class_Oabs(_1505299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1505299), _1505303), _1505301)))], (38013 ^ _779530) ^ [_1505500] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1505500), hAPP(c_Int_Onumber__class_Onumber__of(_1505500), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1505500)), class_Int_Onumber__ring(_1505500), class_Rings_Olinordered__idom(_1505500)], (38023 ^ _779530) ^ [_1505657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505657)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1505657 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38029 ^ _779530) ^ [_1505744] : [_1505744 = 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), _1505744)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38035 ^ _779530) ^ [_1505843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1505843), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505843) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1505843))], (38041 ^ _779530) ^ [_1505934] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1505934), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505934) = _1505934)], (38047 ^ _779530) ^ [_1505978, _1505980] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1505978), _1505980))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505978))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505980))))], (38049 ^ _779530) ^ [_1506033, _1506035] : [-(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), _1506033)), _1506035))))], (38051 ^ _779530) ^ [_1506069, _1506071] : [class_Int_Onumber__ring(_1506069), class_Rings_Olinordered__idom(_1506069), 38058 ^ _779530 : [(38059 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1506069), hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071)), c_Groups_Ozero__class_Ozero(_1506069))), -(hAPP(c_Groups_Oabs__class_Oabs(_1506069), hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1506069), hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071)))], (38065 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1506069), hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071)), c_Groups_Ozero__class_Ozero(_1506069)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1506069), hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071)) = hAPP(c_Int_Onumber__class_Onumber__of(_1506069), _1506071))]]], (38071 ^ _779530) ^ [_1506421, _1506423] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1506421), hAPP(hAPP(c_Power_Opower__class_Opower(_1506421), hAPP(c_Int_Onumber__class_Onumber__of(_1506421), c_Int_OMin)), _1506423)) = c_Groups_Oone__class_Oone(_1506421)), class_Int_Onumber__ring(_1506421), class_Rings_Olinordered__idom(_1506421)], (38091 ^ _779530) ^ [_1506750, _1506752] : [38092 ^ _779530 : [(38093 ^ _779530) ^ [] : [-(_1506750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (38095 ^ _779530) ^ [] : [_1506752 = 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), _1506750)), _1506752))))], (38081 ^ _779530) ^ [_1506601, _1506603] : [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), _1506601)), _1506603))), _1506601 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1506603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38099 ^ _779530) ^ [_1506886, _1506888] : [class_Rings_Olinordered__idom(_1506886), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1506886), hAPP(c_Groups_Oabs__class_Oabs(_1506886), _1506888)), 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(_1506886), _1506888), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (38105 ^ _779530) ^ [_1507003, _1507005] : [class_Rings_Olinordered__idom(_1507003), -(hAPP(c_Groups_Oabs__class_Oabs(_1507003), hAPP(hAPP(c_Power_Opower__class_Opower(_1507003), _1507005), 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(_1507003), _1507005), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (38111 ^ _779530) ^ [_1507120, _1507122, _1507124] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1507120, _1507122, _1507124, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1507122)], (38113 ^ _779530) ^ [_1507161, _1507163] : [_1507161 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1507161, _1507163) = 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)))], (38119 ^ _779530) ^ [_1507239, _1507241] : [-(_1507239 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38122 ^ _779530 : [(38123 ^ _779530) ^ [] : [_1507241 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1507239, _1507241) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1507239))], (38129 ^ _779530) ^ [] : [-(_1507241 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1507239, _1507241) = 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, _1507241))), 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)), _1507241)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1507239))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1507241), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1507239), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1507239, _1507241)), 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), _1507241))))), c_Divides_Opdivmod(_1507239, _1507241)))))]]], (38135 ^ _779530) ^ [_1507599, _1507601] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1507599), _1507601) = 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), _1507599)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1507601)))))], (38137 ^ _779530) ^ [_1507657, _1507659] : [_1507657 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1507657, _1507659) = 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)))], (38143 ^ _779530) ^ [_1507735, _1507737] : [-(_1507735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38146 ^ _779530 : [(38147 ^ _779530) ^ [] : [_1507737 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1507735, _1507737) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1507735))], (38153 ^ _779530) ^ [] : [-(_1507737 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1507735, _1507737) = 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, _1507737))), 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, _1507735)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1507737))), c_Divides_Opdivmod(_1507735, _1507737)), 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), _1507737))))), c_Divides_Opdivmod(_1507735, _1507737)))))]]], (38159 ^ _779530) ^ [_1508047, _1508049, _1508051, _1508053, _1508055, _1508057] : [-(hAPP(c_Product__Type_Oapsnd(_1508047, _1508049, _1508051, _1508053), hAPP(hAPP(c_Product__Type_OPair(_1508051, _1508047), _1508055), _1508057)) = hAPP(hAPP(c_Product__Type_OPair(_1508051, _1508049), _1508055), hAPP(_1508053, _1508057)))], (38161 ^ _779530) ^ [_1508109, _1508111, _1508113, _1508115, _1508117, _1508119, _1508121] : [-(hAPP(c_Product__Type_Oapsnd(_1508109, _1508111, _1508113, _1508115), hAPP(c_Product__Type_Oapsnd(_1508117, _1508109, _1508113, _1508119), _1508121)) = hAPP(c_Product__Type_Oapsnd(_1508117, _1508111, _1508113, hAPP(c_Fun_Ocomp(_1508109, _1508111, _1508117, _1508115), _1508119)), _1508121))], (38163 ^ _779530) ^ [_1508176, _1508178, _1508180, _1508182, _1508184] : [-(hAPP(c_Product__Type_Ofst(_1508176, _1508178), hAPP(c_Product__Type_Oapsnd(_1508180, _1508178, _1508176, _1508182), _1508184)) = hAPP(c_Product__Type_Ofst(_1508176, _1508180), _1508184))], (38165 ^ _779530) ^ [_1508227, _1508229, _1508231, _1508233, _1508235] : [-(hAPP(c_Product__Type_Osnd(_1508227, _1508229), hAPP(c_Product__Type_Oapsnd(_1508231, _1508229, _1508227, _1508233), _1508235)) = hAPP(_1508233, hAPP(c_Product__Type_Osnd(_1508227, _1508231), _1508235)))], (38167 ^ _779530) ^ [_1508308, _1508310, _1508312, _1508314, _1508316, _1508318] : [hAPP(c_Product__Type_Oapsnd(_1508308, _1508310, _1508312, _1508314), _1508316) = hAPP(c_Product__Type_Oapsnd(_1508308, _1508310, _1508312, _1508318), _1508316), -(hAPP(_1508314, hAPP(c_Product__Type_Osnd(_1508312, _1508308), _1508316)) = hAPP(_1508318, hAPP(c_Product__Type_Osnd(_1508312, _1508308), _1508316)))], (38173 ^ _779530) ^ [_1508457, _1508459, _1508461, _1508463, _1508465, _1508467] : [hAPP(_1508463, hAPP(c_Product__Type_Osnd(_1508461, _1508457), _1508465)) = hAPP(_1508467, hAPP(c_Product__Type_Osnd(_1508461, _1508457), _1508465)), -(hAPP(c_Product__Type_Oapsnd(_1508457, _1508459, _1508461, _1508463), _1508465) = hAPP(c_Product__Type_Oapsnd(_1508457, _1508459, _1508461, _1508467), _1508465))], (38179 ^ _779530) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (38181 ^ _779530) ^ [_1508639, _1508641] : [_1508639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1508641, _1508639) = _1508641)], (38187 ^ _779530) ^ [_1508716, _1508718] : [-(_1508716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1508718, _1508716) = c_Nitpick_Onat__gcd(_1508716, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1508718, _1508716)))], (38193 ^ _779530) ^ [_1508764, _1508766] : [-(c_Divides_Opdivmod(_1508764, _1508766) = 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), _1508764)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1508766))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1508764), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1508766))))], (38195 ^ _779530) ^ [_1508829, _1508831] : [_1508829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1508831, _1508829) = 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), _1508831)))], (38201 ^ _779530) ^ [_1508918, _1508920] : [-(_1508918 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1508920, _1508918) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1508920), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1508918)))], (38207 ^ _779530) ^ [_1508968, _1508970] : [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), _1508968), _1508970))), 38210 ^ _779530 : [(38211 ^ _779530) ^ [] : [_1508970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1508968, _1508970) = _1508968)], (38217 ^ _779530) ^ [] : [-(_1508970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1508968, _1508970) = c_Nitpick_Onat__gcd(_1508970, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1508968, _1508970)))]]], (38223 ^ _779530) ^ [_1509186, _1509188] : [-(c_Nitpick_Onat__lcm(_1509186, _1509188) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1509186), _1509188)), c_Nitpick_Onat__gcd(_1509186, _1509188)))], (38225 ^ _779530) ^ [_1509229, _1509231] : [-(c_Nitpick_Oint__lcm(_1509229, _1509231) = 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), _1509229)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1509231)))))], (38227 ^ _779530) ^ [_1509275, _1509277, _1509279] : [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), _1509275), _1509277))), -(hBOOL(hAPP(hAPP(_1509279, _1509275), _1509277))), 38234 ^ _779530 : [(38235 ^ _779530) ^ [] : [-(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), 38232 ^ [_1509275, _1509277, _1509279]), 38233 ^ [_1509275, _1509277, _1509279]))))], (38243 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1509279, 38232 ^ [_1509275, _1509277, _1509279]), 38233 ^ [_1509275, _1509277, _1509279]))], (38237 ^ _779530) ^ [] : [-(38233 ^ [_1509275, _1509277, _1509279] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1509279, 38233 ^ [_1509275, _1509277, _1509279]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 38232 ^ [_1509275, _1509277, _1509279], 38233 ^ [_1509275, _1509277, _1509279]))))]]], (38247 ^ _779530) ^ [_1509697, _1509699, _1509701, _1509703, _1509705, _1509707, _1509709] : [-(hAPP(c_Product__Type_Oapfst(_1509697, _1509699, _1509701, _1509703), hAPP(c_Product__Type_Oapsnd(_1509705, _1509701, _1509697, _1509707), _1509709)) = hAPP(hAPP(c_Product__Type_OPair(_1509699, _1509701), hAPP(_1509703, hAPP(c_Product__Type_Ofst(_1509697, _1509705), _1509709))), hAPP(_1509707, hAPP(c_Product__Type_Osnd(_1509697, _1509705), _1509709))))], (38249 ^ _779530) ^ [_1509775, _1509777, _1509779, _1509781, _1509783, _1509785, _1509787] : [-(hAPP(c_Product__Type_Oapsnd(_1509775, _1509777, _1509779, _1509781), hAPP(c_Product__Type_Oapfst(_1509783, _1509779, _1509775, _1509785), _1509787)) = hAPP(hAPP(c_Product__Type_OPair(_1509779, _1509777), hAPP(_1509785, hAPP(c_Product__Type_Ofst(_1509783, _1509775), _1509787))), hAPP(_1509781, hAPP(c_Product__Type_Osnd(_1509783, _1509775), _1509787))))], (38251 ^ _779530) ^ [_1509853, _1509855, _1509857, _1509859, _1509861, _1509863] : [-(hAPP(c_Product__Type_Oapfst(_1509853, _1509855, _1509857, _1509859), hAPP(hAPP(c_Product__Type_OPair(_1509853, _1509857), _1509861), _1509863)) = hAPP(hAPP(c_Product__Type_OPair(_1509855, _1509857), hAPP(_1509859, _1509861)), _1509863))], (38253 ^ _779530) ^ [_1509915, _1509917, _1509919, _1509921, _1509923] : [-(hAPP(c_Product__Type_Osnd(_1509915, _1509917), hAPP(c_Product__Type_Oapfst(_1509919, _1509915, _1509917, _1509921), _1509923)) = hAPP(c_Product__Type_Osnd(_1509919, _1509917), _1509923))], (38255 ^ _779530) ^ [_1509966, _1509968, _1509970, _1509972, _1509974] : [-(hAPP(c_Product__Type_Ofst(_1509966, _1509968), hAPP(c_Product__Type_Oapfst(_1509970, _1509966, _1509968, _1509972), _1509974)) = hAPP(_1509972, hAPP(c_Product__Type_Ofst(_1509970, _1509968), _1509974)))], (38257 ^ _779530) ^ [_1510047, _1510049, _1510051, _1510053, _1510055, _1510057] : [hAPP(c_Product__Type_Oapfst(_1510047, _1510049, _1510051, _1510053), _1510055) = hAPP(c_Product__Type_Oapfst(_1510047, _1510049, _1510051, _1510057), _1510055), -(hAPP(_1510053, hAPP(c_Product__Type_Ofst(_1510047, _1510051), _1510055)) = hAPP(_1510057, hAPP(c_Product__Type_Ofst(_1510047, _1510051), _1510055)))], (38263 ^ _779530) ^ [_1510196, _1510198, _1510200, _1510202, _1510204, _1510206] : [hAPP(_1510202, hAPP(c_Product__Type_Ofst(_1510196, _1510200), _1510204)) = hAPP(_1510206, hAPP(c_Product__Type_Ofst(_1510196, _1510200), _1510204)), -(hAPP(c_Product__Type_Oapfst(_1510196, _1510198, _1510200, _1510202), _1510204) = hAPP(c_Product__Type_Oapfst(_1510196, _1510198, _1510200, _1510206), _1510204))], (38269 ^ _779530) ^ [_1510351, _1510353, _1510355, _1510357, _1510359, _1510361, _1510363] : [-(hAPP(c_Product__Type_Oapfst(_1510351, _1510353, _1510355, _1510357), hAPP(c_Product__Type_Oapfst(_1510359, _1510351, _1510355, _1510361), _1510363)) = hAPP(c_Product__Type_Oapfst(_1510359, _1510353, _1510355, hAPP(c_Fun_Ocomp(_1510351, _1510353, _1510359, _1510357), _1510361)), _1510363))], (38271 ^ _779530) ^ [_1510418, _1510420, _1510422, _1510424, _1510426, _1510428, _1510430] : [-(hAPP(c_Product__Type_Oapsnd(_1510418, _1510420, _1510422, _1510424), hAPP(c_Product__Type_Oapfst(_1510426, _1510422, _1510418, _1510428), _1510430)) = hAPP(c_Product__Type_Oapfst(_1510426, _1510422, _1510420, _1510428), hAPP(c_Product__Type_Oapsnd(_1510418, _1510420, _1510426, _1510424), _1510430)))], (38273 ^ _779530) ^ [_1510485, _1510487, _1510489, _1510491, _1510493] : [class_Groups_Ocomm__monoid__add(_1510485), class_Groups_Ocomm__monoid__mult(_1510485), _1510487 = _1510489, c_Nat__Transfer_Onat__set(_1510489), 38291 ^ _779530 : [(38292 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 38290 ^ [_1510485, _1510487, _1510489, _1510491, _1510493])))], (38294 ^ _779530) ^ [] : [hAPP(_1510491, 38290 ^ [_1510485, _1510487, _1510489, _1510491, _1510493]) = hAPP(_1510493, 38290 ^ [_1510485, _1510487, _1510489, _1510491, _1510493])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1510485), _1510491), _1510487) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1510485), _1510493), _1510489))], (38298 ^ _779530) ^ [_1510966, _1510968, _1510970] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1510966, hAPP(hAPP(c_COMBC(_1510966, tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_fun(_1510966, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510966, tc_fun(tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_fun(_1510966, tc_HOL_Obool)), _1510966), c_COMBC(_1510966, tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510966, tc_prod(_1510966, _1510966)), tc_fun(_1510966, tc_fun(tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_HOL_Obool)), _1510966), hAPP(c_COMBB(tc_prod(_1510966, _1510966), tc_fun(tc_fun(tc_prod(_1510966, _1510966), tc_HOL_Obool), tc_HOL_Obool), _1510966), c_member(tc_prod(_1510966, _1510966)))), c_Product__Type_OPair(_1510966, _1510966)))), _1510968)), _1510970)), -(hBOOL(hAPP(hAPP(c_member(_1510966), _1510970), c_Wellfounded_Oacc(_1510966, _1510968))))], (38304 ^ _779530) ^ [_1511307, _1511309, _1511311] : [hBOOL(hAPP(hAPP(c_member(_1511307), _1511311), c_Wellfounded_Oacc(_1511307, _1511309))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1511307, hAPP(hAPP(c_COMBC(_1511307, tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_fun(_1511307, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511307, tc_fun(tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_fun(_1511307, tc_HOL_Obool)), _1511307), c_COMBC(_1511307, tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511307, tc_prod(_1511307, _1511307)), tc_fun(_1511307, tc_fun(tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_HOL_Obool)), _1511307), hAPP(c_COMBB(tc_prod(_1511307, _1511307), tc_fun(tc_fun(tc_prod(_1511307, _1511307), tc_HOL_Obool), tc_HOL_Obool), _1511307), c_member(tc_prod(_1511307, _1511307)))), c_Product__Type_OPair(_1511307, _1511307)))), _1511309)), _1511311)))], (38310 ^ _779530) ^ [_1511654, _1511656, _1511658, _1511660, _1511662] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1511654, _1511656, _1511658), _1511660), _1511662) = hAPP(c_Set_OCollect(tc_prod(_1511654, _1511658)), hAPP(c_Product__Type_Oprod_Oprod__case(_1511654, _1511658, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1511658, tc_fun(_1511656, tc_HOL_Obool)), tc_fun(_1511658, tc_HOL_Obool), _1511654), hAPP(c_COMBB(tc_fun(_1511656, tc_HOL_Obool), tc_HOL_Obool, _1511658), c_HOL_OEx(_1511656))), hAPP(hAPP(c_COMBC(_1511654, tc_fun(_1511658, tc_fun(_1511656, tc_HOL_Obool)), tc_fun(_1511658, tc_fun(_1511656, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1511656, tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), tc_fun(tc_fun(_1511658, tc_fun(_1511656, tc_HOL_Obool)), tc_fun(_1511658, tc_fun(_1511656, tc_HOL_Obool))), _1511654), c_COMBB(tc_fun(_1511656, tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool), _1511658)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511656, tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), _1511654), c_COMBS(_1511656, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_HOL_Obool), tc_fun(_1511656, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511654), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511656), c_fconj)), hAPP(hAPP(c_COMBC(_1511654, tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_fun(tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), _1511654), c_COMBC(_1511656, tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_prod(_1511654, _1511656)), tc_fun(_1511656, tc_fun(tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_HOL_Obool)), _1511654), hAPP(c_COMBB(tc_prod(_1511654, _1511656), tc_fun(tc_fun(tc_prod(_1511654, _1511656), tc_HOL_Obool), tc_HOL_Obool), _1511656), c_member(tc_prod(_1511654, _1511656)))), c_Product__Type_OPair(_1511654, _1511656)))), _1511660))))), hAPP(hAPP(c_COMBC(_1511658, tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_fun(tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_fun(_1511656, tc_HOL_Obool)), _1511658), c_COMBC(_1511656, tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511656, tc_prod(_1511656, _1511658)), tc_fun(_1511656, tc_fun(tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_HOL_Obool)), _1511658), hAPP(c_COMBB(tc_prod(_1511656, _1511658), tc_fun(tc_fun(tc_prod(_1511656, _1511658), tc_HOL_Obool), tc_HOL_Obool), _1511656), c_member(tc_prod(_1511656, _1511658)))), hAPP(c_COMBC(_1511656, _1511658, tc_prod(_1511656, _1511658)), c_Product__Type_OPair(_1511656, _1511658))))), _1511662))))))], (38312 ^ _779530) ^ [_1512102, _1512104, _1512106, _1512108, _1512110, _1512112, _1512114, _1512116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1512102, _1512104)), hAPP(hAPP(c_Product__Type_OPair(_1512102, _1512104), _1512106), _1512108)), _1512110)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512104, _1512112)), hAPP(hAPP(c_Product__Type_OPair(_1512104, _1512112), _1512108), _1512114)), _1512116)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1512102, _1512112)), hAPP(hAPP(c_Product__Type_OPair(_1512102, _1512112), _1512106), _1512114)), hAPP(hAPP(c_Relation_Orel__comp(_1512102, _1512104, _1512112), _1512110), _1512116))))], (38322 ^ _779530) ^ [_1512389, _1512391, _1512393, _1512395, _1512397, _1512399, _1512401] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1512389, _1512391, _1512393), _1512395), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512397, tc_fun(tc_prod(_1512391, _1512393), tc_HOL_Obool)), _1512399), _1512401)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512397, tc_fun(tc_prod(_1512389, _1512393), tc_HOL_Obool)), _1512399), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1512391, _1512393), tc_HOL_Obool), tc_fun(tc_prod(_1512389, _1512393), tc_HOL_Obool), _1512397), hAPP(c_Relation_Orel__comp(_1512389, _1512391, _1512393), _1512395)), _1512401)))], (38324 ^ _779530) ^ [_1512493, _1512495, _1512497, _1512499, _1512501, _1512503, _1512505] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1512493, _1512495, _1512497), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512499, tc_fun(tc_prod(_1512493, _1512495), tc_HOL_Obool)), _1512501), _1512503)), _1512505) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512499, tc_fun(tc_prod(_1512493, _1512497), tc_HOL_Obool)), _1512501), hAPP(hAPP(c_COMBC(_1512499, tc_fun(tc_prod(_1512495, _1512497), tc_HOL_Obool), tc_fun(tc_prod(_1512493, _1512497), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1512493, _1512495), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1512495, _1512497), tc_HOL_Obool), tc_fun(tc_prod(_1512493, _1512497), tc_HOL_Obool)), _1512499), c_Relation_Orel__comp(_1512493, _1512495, _1512497)), _1512503)), _1512505)))], (38326 ^ _779530) ^ [_1512625, _1512627, _1512629, _1512631, _1512633, _1512635, _1512637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512625, _1512627), tc_HOL_Obool)), _1512629), _1512631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512627, _1512633), tc_HOL_Obool)), _1512635), _1512637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512625, _1512633), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1512625, _1512627, _1512633), _1512629), _1512635)), hAPP(hAPP(c_Relation_Orel__comp(_1512625, _1512627, _1512633), _1512631), _1512637))))], (38336 ^ _779530) ^ [_1512892, _1512894, _1512896, _1512898, _1512900, _1512902, _1512904] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1512892, _1512894, _1512896), hAPP(hAPP(c_Relation_Orel__comp(_1512892, _1512898, _1512894), _1512900), _1512902)), _1512904) = hAPP(hAPP(c_Relation_Orel__comp(_1512892, _1512898, _1512896), _1512900), hAPP(hAPP(c_Relation_Orel__comp(_1512898, _1512894, _1512896), _1512902), _1512904)))], (38338 ^ _779530) ^ [_1512967, _1512969, _1512971, _1512973, _1512975, _1512977] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1512967, _1512969, _1512971), _1512973), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512969, _1512971), tc_HOL_Obool)), _1512975), _1512977)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1512967, _1512971), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1512967, _1512969, _1512971), _1512973), _1512975)), hAPP(hAPP(c_Relation_Orel__comp(_1512967, _1512969, _1512971), _1512973), _1512977)))], (38340 ^ _779530) ^ [_1513058, _1513060, _1513062, _1513064, _1513066, _1513068] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1513058, _1513060, _1513062), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1513058, _1513060), tc_HOL_Obool)), _1513064), _1513066)), _1513068) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1513058, _1513062), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1513058, _1513060, _1513062), _1513064), _1513068)), hAPP(hAPP(c_Relation_Orel__comp(_1513058, _1513060, _1513062), _1513066), _1513068)))], (38342 ^ _779530) ^ [_1513149, _1513151, _1513153, _1513155] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1513149, _1513151, _1513153), _1513155), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513151, _1513153), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513149, _1513153), tc_HOL_Obool)))], (38344 ^ _779530) ^ [_1513204, _1513206, _1513208, _1513210] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1513204, _1513206, _1513208), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513204, _1513206), tc_HOL_Obool))), _1513210) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513204, _1513208), tc_HOL_Obool)))], (38346 ^ _779530) ^ [_1513259, _1513261, _1513263, _1513265] : [hAPP(hAPP(c_Relation_Orel__comp(_1513259, _1513259, _1513259), _1513261), _1513263) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513259, _1513259), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1513259, _1513259, _1513259), _1513265), _1513263) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513259, _1513259), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1513259, _1513259, _1513259), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1513259, _1513259), tc_HOL_Obool)), _1513261), _1513265)), _1513263) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513259, _1513259), tc_HOL_Obool)))], (38356 ^ _779530) ^ [_1513532, _1513534, _1513536, _1513538] : [hAPP(hAPP(c_Relation_Orel__comp(_1513532, _1513532, _1513532), _1513534), _1513536) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513532, _1513532), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1513532, _1513532, _1513532), _1513534), _1513538) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513532, _1513532), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1513532, _1513532, _1513532), _1513534), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1513532, _1513532), tc_HOL_Obool)), _1513536), _1513538)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513532, _1513532), tc_HOL_Obool)))], (38366 ^ _779530) ^ [_1513805, _1513807, _1513809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1513805, _1513805), tc_HOL_Obool)), _1513807), _1513809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513805, tc_HOL_Obool)), c_Wellfounded_Oacc(_1513805, _1513809)), c_Wellfounded_Oacc(_1513805, _1513807))))], (38382 ^ _779530) ^ [_1514213, _1514215, _1514217] : [38384 ^ _779530 : [(38385 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514213, _1514213)), hAPP(hAPP(c_Product__Type_OPair(_1514213, _1514213), 38383 ^ [_1514213, _1514215, _1514217]), _1514215)), _1514217)))], (38387 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1514213), 38383 ^ [_1514213, _1514215, _1514217]), c_Wellfounded_Oacc(_1514213, _1514217)))]], -(hBOOL(hAPP(hAPP(c_member(_1514213), _1514215), c_Wellfounded_Oacc(_1514213, _1514217))))], (38372 ^ _779530) ^ [_1513960, _1513962, _1513964] : [hBOOL(hAPP(hAPP(c_member(_1513960), _1513962), c_Wellfounded_Oacc(_1513960, _1513964))), 38375 ^ _779530 : [(38376 ^ _779530) ^ [_1514074] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513960, _1513960)), hAPP(hAPP(c_Product__Type_OPair(_1513960, _1513960), _1514074), _1513962)), _1513964)), -(hBOOL(hAPP(hAPP(c_member(_1513960), _1514074), c_Wellfounded_Oacc(_1513960, _1513964))))]]], (38391 ^ _779530) ^ [_1514453, _1514455, _1514457, _1514459] : [hBOOL(hAPP(hAPP(c_member(_1514453), _1514455), c_Wellfounded_Oacc(_1514453, _1514457))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1514453, _1514453)), hAPP(hAPP(c_Product__Type_OPair(_1514453, _1514453), _1514459), _1514455)), _1514457)), -(hBOOL(hAPP(hAPP(c_member(_1514453), _1514459), c_Wellfounded_Oacc(_1514453, _1514457))))], (38401 ^ _779530) ^ [_1514668, _1514670, _1514672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514668, _1514668), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1514668, _1514668, _1514668), _1514670), _1514672)), _1514670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1514668, _1514670)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1514668, _1514672)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1514668, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1514668, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1514668, tc_HOL_Obool), tc_fun(_1514668, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1514668, _1514670))))], (38407 ^ _779530) ^ [_1515039, _1515041, _1515043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515039, _1515039), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1515039, _1515039, _1515039), _1515041), _1515043)), _1515041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1515039, _1515041)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1515039, _1515043)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1515039, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1515039, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1515039, tc_HOL_Obool), tc_fun(_1515039, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1515039, _1515041))))], (38413 ^ _779530) ^ [_1515440, _1515442, _1515444, _1515446, _1515448, _1515450, _1515452] : [c_Predicate_Opred__comp(_1515440, _1515442, _1515444, hAPP(hAPP(c_COMBC(_1515440, tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_fun(_1515442, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515442, tc_fun(tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_fun(_1515442, tc_HOL_Obool)), _1515440), c_COMBC(_1515442, tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515442, tc_prod(_1515440, _1515442)), tc_fun(_1515442, tc_fun(tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_HOL_Obool)), _1515440), hAPP(c_COMBB(tc_prod(_1515440, _1515442), tc_fun(tc_fun(tc_prod(_1515440, _1515442), tc_HOL_Obool), tc_HOL_Obool), _1515442), c_member(tc_prod(_1515440, _1515442)))), c_Product__Type_OPair(_1515440, _1515442)))), _1515446), hAPP(hAPP(c_COMBC(_1515442, tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_fun(_1515444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515444, tc_fun(tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_fun(_1515444, tc_HOL_Obool)), _1515442), c_COMBC(_1515444, tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515444, tc_prod(_1515442, _1515444)), tc_fun(_1515444, tc_fun(tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_HOL_Obool)), _1515442), hAPP(c_COMBB(tc_prod(_1515442, _1515444), tc_fun(tc_fun(tc_prod(_1515442, _1515444), tc_HOL_Obool), tc_HOL_Obool), _1515444), c_member(tc_prod(_1515442, _1515444)))), c_Product__Type_OPair(_1515442, _1515444)))), _1515448), _1515450, _1515452), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515440, _1515444)), hAPP(hAPP(c_Product__Type_OPair(_1515440, _1515444), _1515450), _1515452)), hAPP(hAPP(c_Relation_Orel__comp(_1515440, _1515442, _1515444), _1515446), _1515448))))], (38419 ^ _779530) ^ [_1516063, _1516065, _1516067, _1516069, _1516071, _1516073, _1516075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516063, _1516067)), hAPP(hAPP(c_Product__Type_OPair(_1516063, _1516067), _1516073), _1516075)), hAPP(hAPP(c_Relation_Orel__comp(_1516063, _1516065, _1516067), _1516069), _1516071))), -(c_Predicate_Opred__comp(_1516063, _1516065, _1516067, hAPP(hAPP(c_COMBC(_1516063, tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_fun(_1516065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516065, tc_fun(tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_fun(_1516065, tc_HOL_Obool)), _1516063), c_COMBC(_1516065, tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516065, tc_prod(_1516063, _1516065)), tc_fun(_1516065, tc_fun(tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_HOL_Obool)), _1516063), hAPP(c_COMBB(tc_prod(_1516063, _1516065), tc_fun(tc_fun(tc_prod(_1516063, _1516065), tc_HOL_Obool), tc_HOL_Obool), _1516065), c_member(tc_prod(_1516063, _1516065)))), c_Product__Type_OPair(_1516063, _1516065)))), _1516069), hAPP(hAPP(c_COMBC(_1516065, tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_fun(_1516067, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516067, tc_fun(tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_fun(_1516067, tc_HOL_Obool)), _1516065), c_COMBC(_1516067, tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516067, tc_prod(_1516065, _1516067)), tc_fun(_1516067, tc_fun(tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_HOL_Obool)), _1516065), hAPP(c_COMBB(tc_prod(_1516065, _1516067), tc_fun(tc_fun(tc_prod(_1516065, _1516067), tc_HOL_Obool), tc_HOL_Obool), _1516067), c_member(tc_prod(_1516065, _1516067)))), c_Product__Type_OPair(_1516065, _1516067)))), _1516071), _1516073, _1516075))], (38425 ^ _779530) ^ [_1516692, _1516694, _1516696] : [c_Wellfounded_Owf(_1516692, _1516694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516692, _1516692), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1516692, _1516692, _1516692), _1516694), _1516696)), _1516694)), -(c_FunDef_Oreduction__pair(_1516692, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1516692, _1516692), tc_HOL_Obool), tc_fun(tc_prod(_1516692, _1516692), tc_HOL_Obool)), _1516694), _1516696)))], (38435 ^ _779530) ^ [_1516934, _1516936, _1516938, _1516940] : [c_Wellfounded_Omax__extp(_1516934, _1516936, _1516938, _1516940), 38438 ^ _779530 : [(38439 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516934), _1516938)))], (38441 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516934), _1516940)))], (38443 ^ _779530) ^ [] : [_1516940 = c_Orderings_Obot__class_Obot(tc_fun(_1516934, tc_HOL_Obool))], (38445 ^ _779530) ^ [_1517150] : [hBOOL(hAPP(hAPP(c_member(_1516934), _1517150), _1516938)), 38449 ^ _779530 : [(38450 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516934), 38448 ^ [_1516934, _1516936, _1516938, _1516940, _1517150]), _1516940)))], (38452 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1516936, _1517150), 38448 ^ [_1516934, _1516936, _1516938, _1516940, _1517150])))]]]]], (38454 ^ _779530) ^ [_1517334, _1517336, _1517338, _1517340] : [-(c_Wellfounded_Omax__extp(_1517334, _1517336, _1517338, _1517340)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517334), _1517338)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517334), _1517340)), -(_1517340 = c_Orderings_Obot__class_Obot(tc_fun(_1517334, tc_HOL_Obool))), 38468 ^ _779530 : [(38469 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517334), 38467 ^ [_1517334, _1517336, _1517338, _1517340]), _1517338)))], (38471 ^ _779530) ^ [_1517679] : [hBOOL(hAPP(hAPP(c_member(_1517334), _1517679), _1517340)), hBOOL(hAPP(hAPP(_1517336, 38467 ^ [_1517334, _1517336, _1517338, _1517340]), _1517679))]]], (38479 ^ _779530) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (38481 ^ _779530) ^ [_1517865, _1517867, _1517869, _1517871, _1517873, _1517875, _1517877, _1517879] : [hBOOL(hAPP(hAPP(_1517865, _1517867), _1517869)), hBOOL(hAPP(hAPP(_1517871, _1517869), _1517873)), -(c_Predicate_Opred__comp(_1517875, _1517877, _1517879, _1517865, _1517871, _1517867, _1517873))], (38491 ^ _779530) ^ [_1518048] : [-(c_Wellfounded_Owf(_1518048, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518048, _1518048), tc_HOL_Obool))))], (38493 ^ _779530) ^ [_1518079, _1518081, _1518083, _1518085] : [c_Wellfounded_Owf(_1518079, _1518081), -(c_Wellfounded_Owf(_1518083, hAPP(hAPP(c_Relation_Oinv__image(_1518079, _1518083), _1518081), _1518085)))], (38499 ^ _779530) ^ [_1518178, _1518180, _1518182, _1518184] : [c_Wellfounded_Owf(_1518178, _1518180), c_Wellfounded_Owf(_1518182, _1518184), -(c_Wellfounded_Owf(tc_prod(_1518178, _1518182), c_Wellfounded_Olex__prod(_1518178, _1518182, _1518180, _1518184)))], (38509 ^ _779530) ^ [_1518331, _1518333] : [-(c_Wellfounded_Owf(_1518331, hAPP(c_Wellfounded_Omeasure(_1518331), _1518333)))], (38511 ^ _779530) ^ [_1518376, _1518378] : [c_Wellfounded_Owf(_1518376, _1518378), -(c_Wellfounded_Owf(_1518376, hAPP(hAPP(c_Relation_Orel__comp(_1518376, _1518376, _1518376), _1518378), _1518378)))], (38517 ^ _779530) ^ [_1518469, _1518471] : [c_Wellfounded_Owf(_1518469, hAPP(hAPP(c_Relation_Orel__comp(_1518469, _1518469, _1518469), _1518471), _1518471)), -(c_Wellfounded_Owf(_1518469, _1518471))], (38523 ^ _779530) ^ [_1518568, _1518570] : [c_Wellfounded_Owf(_1518568, _1518570), -(c_Wellfounded_Owf(tc_fun(_1518568, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1518568, _1518570)))], (38529 ^ _779530) ^ [_1518657] : [-(c_Wellfounded_Owf(tc_fun(_1518657, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1518657)))], (38531 ^ _779530) ^ [_1518685, _1518687, _1518689] : [c_Wellfounded_Owf(_1518685, _1518687), -(c_Wellfounded_Owf(_1518685, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518685, _1518685), tc_HOL_Obool)), _1518687), _1518689)))], (38537 ^ _779530) ^ [_1518792, _1518794, _1518796] : [c_Wellfounded_Owf(_1518792, _1518794), -(c_Wellfounded_Owf(_1518792, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1518792, _1518792), tc_HOL_Obool)), _1518796), _1518794)))], (38543 ^ _779530) ^ [_1518899, _1518901, _1518903] : [c_Wellfounded_Owf(_1518899, _1518901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518899, _1518899), tc_HOL_Obool)), _1518903), _1518901)), -(c_Wellfounded_Owf(_1518899, _1518903))], (38553 ^ _779530) ^ [_1519088, _1519090, _1519092, _1519094, _1519096, _1519098, _1519100] : [c_Predicate_Opred__comp(_1519088, _1519090, _1519092, _1519094, _1519096, _1519098, _1519100), 38557 ^ _779530 : [(38558 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1519094, _1519098), 38556 ^ [_1519088, _1519090, _1519092, _1519094, _1519096, _1519098, _1519100])))], (38560 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1519096, 38556 ^ [_1519088, _1519090, _1519092, _1519094, _1519096, _1519098, _1519100]), _1519100)))]]], (38562 ^ _779530) ^ [_1519266, _1519268, _1519270, _1519272, _1519274, _1519276, _1519278] : [-(c_Predicate_Opred__comp(_1519266, _1519268, _1519270, _1519272, _1519274, _1519276, _1519278)), 38563 ^ _779530 : [(38564 ^ _779530) ^ [_1519331] : [hBOOL(hAPP(hAPP(_1519272, _1519276), _1519331)), hBOOL(hAPP(hAPP(_1519274, _1519331), _1519278))]]], (38572 ^ _779530) ^ [_1519474, _1519476, _1519478] : [c_Wellfounded_Owf(_1519474, _1519476), -(c_Wellfounded_Owf(_1519474, c_Wellfounded_Omlex__prod(_1519474, _1519478, _1519476)))], (38578 ^ _779530) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38580 ^ _779530) ^ [_1519579, _1519581] : [c_Wellfounded_Owf(_1519579, _1519581), -(c_Wellfounded_Owf(tc_fun(_1519579, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1519579, _1519581)))], (38586 ^ _779530) ^ [] : [-(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)))))], (38588 ^ _779530) ^ [_1519686, _1519688, _1519690] : [c_Wellfounded_Owf(_1519686, _1519688), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519686, _1519686)), hAPP(hAPP(c_Product__Type_OPair(_1519686, _1519686), _1519690), _1519690)), _1519688))], (38594 ^ _779530) ^ [_1519804, _1519806, _1519808, _1519810] : [c_Wellfounded_Owf(_1519804, _1519806), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519804, _1519804)), hAPP(hAPP(c_Product__Type_OPair(_1519804, _1519804), _1519808), _1519810)), _1519806)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519804, _1519804)), hAPP(hAPP(c_Product__Type_OPair(_1519804, _1519804), _1519810), _1519808)), _1519806))], (38604 ^ _779530) ^ [_1520018, _1520020, _1520022, _1520024] : [c_Wellfounded_Owf(_1520018, _1520020), hBOOL(hAPP(hAPP(c_member(tc_prod(_1520018, _1520018)), hAPP(hAPP(c_Product__Type_OPair(_1520018, _1520018), _1520022), _1520024)), _1520020)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1520018, _1520018)), hAPP(hAPP(c_Product__Type_OPair(_1520018, _1520018), _1520024), _1520022)), _1520020))], (38614 ^ _779530) ^ [_1520232, _1520234, _1520236] : [c_Wellfounded_Owf(_1520232, _1520234), hBOOL(hAPP(hAPP(c_member(tc_prod(_1520232, _1520232)), hAPP(hAPP(c_Product__Type_OPair(_1520232, _1520232), _1520236), _1520236)), _1520234))], (38620 ^ _779530) ^ [_1520350] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1520350)))], (38622 ^ _779530) ^ [_1520375] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1520375)))], (38624 ^ _779530) ^ [_1520415, _1520417] : [c_Wellfounded_Owf(_1520415, _1520417), 38627 ^ _779530 : [(38628 ^ _779530) ^ [_1520484] : [-(hBOOL(hAPP(hAPP(c_member(_1520415), _1520484), c_Wellfounded_Oacc(_1520415, _1520417))))]]], (38630 ^ _779530) ^ [_1520517, _1520519] : [hBOOL(hAPP(hAPP(c_member(_1520517), 38631 ^ [_1520517, _1520519]), c_Wellfounded_Oacc(_1520517, _1520519))), -(c_Wellfounded_Owf(_1520517, _1520519))], (38637 ^ _779530) ^ [_1520650, _1520652, _1520654] : [c_Wellfounded_Owf(_1520650, _1520652), -(hBOOL(hAPP(hAPP(c_member(_1520650), _1520654), c_Wellfounded_Oacc(_1520650, _1520652))))], (38643 ^ _779530) ^ [_1520749, _1520751] : [hAPP(hAPP(c_Relation_Orel__comp(_1520749, _1520749, _1520749), _1520751), _1520751) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520749, _1520749), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1520749, _1520751))], (38649 ^ _779530) ^ [_1520880, _1520882, _1520884] : [c_Wellfounded_Owf(_1520880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520880, _1520880), tc_HOL_Obool)), _1520882), _1520884)), -(c_Wellfounded_Owf(_1520880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520880, _1520880), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520880, _1520880), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520880, _1520880, _1520880), _1520882), _1520882)), hAPP(hAPP(c_Relation_Orel__comp(_1520880, _1520880, _1520880), _1520884), _1520882))), _1520884)))], (38655 ^ _779530) ^ [_1521079, _1521081, _1521083] : [c_Wellfounded_Owf(_1521079, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521079, _1521079), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521079, _1521079), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521079, _1521079, _1521079), _1521081), _1521081)), hAPP(hAPP(c_Relation_Orel__comp(_1521079, _1521079, _1521079), _1521083), _1521081))), _1521083)), -(c_Wellfounded_Owf(_1521079, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521079, _1521079), tc_HOL_Obool)), _1521081), _1521083)))], (38661 ^ _779530) ^ [_1521299, _1521301] : [c_Wellfounded_Owf(_1521299, _1521301), 38665 ^ _779530 : [(38666 ^ _779530) ^ [_1521435] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521299, _1521299)), hAPP(hAPP(c_Product__Type_OPair(_1521299, _1521299), hAPP(_1521435, hAPP(c_Nat_OSuc, 38664 ^ [_1521299, _1521301, _1521435]))), hAPP(_1521435, 38664 ^ [_1521299, _1521301, _1521435]))), _1521301))]]], (38668 ^ _779530) ^ [_1521502, _1521504] : [38670 ^ _779530 : [(38671 ^ _779530) ^ [_1521527] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521502, _1521502)), hAPP(hAPP(c_Product__Type_OPair(_1521502, _1521502), hAPP(38669 ^ [_1521502, _1521504], hAPP(c_Nat_OSuc, _1521527))), hAPP(38669 ^ [_1521502, _1521504], _1521527))), _1521504)))]], -(c_Wellfounded_Owf(_1521502, _1521504))], (38675 ^ _779530) ^ [_1521603, _1521605, _1521607] : [c_Wellfounded_Owf(_1521603, _1521605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521603, tc_HOL_Obool)), _1521607), hAPP(c_Relation_OImage(_1521603, _1521603, _1521605), _1521607))), -(_1521607 = c_Orderings_Obot__class_Obot(tc_fun(_1521603, tc_HOL_Obool)))], (38685 ^ _779530) ^ [_1521780, _1521782, _1521784] : [c_Wellfounded_Owf(_1521780, _1521782), c_Wellfounded_Owf(_1521780, _1521784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521780, _1521780), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521780, _1521780, _1521780), _1521782), _1521784)), _1521782)), -(c_Wellfounded_Owf(_1521780, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521780, _1521780), tc_HOL_Obool)), _1521782), _1521784)))], (38699 ^ _779530) ^ [_1522041] : [class_Orderings_Owellorder(_1522041), -(c_Wellfounded_Owf(_1522041, hAPP(c_Set_OCollect(tc_prod(_1522041, _1522041)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522041, _1522041, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1522041)))))], (38705 ^ _779530) ^ [_1522163, _1522165] : [c_FunDef_Oreduction__pair(_1522163, _1522165), 38708 ^ _779530 : [(38709 ^ _779530) ^ [] : [-(c_Wellfounded_Owf(_1522163, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool), tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool)), _1522165)))], (38711 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522163, _1522163, _1522163), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool), tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool)), _1522165)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool), tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool)), _1522165))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool), tc_fun(tc_prod(_1522163, _1522163), tc_HOL_Obool)), _1522165))))]]], (38713 ^ _779530) ^ [_1522452, _1522454] : [-(c_FunDef_Oreduction__pair(_1522452, _1522454)), c_Wellfounded_Owf(_1522452, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool), tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool)), _1522454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522452, _1522452, _1522452), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool), tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool)), _1522454)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool), tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool)), _1522454))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool), tc_fun(tc_prod(_1522452, _1522452), tc_HOL_Obool)), _1522454)))], (38723 ^ _779530) ^ [_1522773, _1522775, _1522777, _1522779] : [c_FunDef_Oreduction__pair(_1522773, _1522775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool)), _1522777), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool), tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool)), _1522775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool)), _1522779), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool), tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool)), _1522775))), c_Wellfounded_Owf(_1522773, _1522779), -(c_Wellfounded_Owf(_1522773, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1522773, _1522773), tc_HOL_Obool)), _1522777), _1522779)))], (38741 ^ _779530) ^ [_1523174, _1523176] : [c_Wellfounded_Owf(_1523174, _1523176), -(c_Wellfounded_Owf(tc_List_Olist(_1523174), c_List_Olenlex(_1523174, _1523176)))], (38747 ^ _779530) ^ [_1523261, _1523263, _1523265, _1523267] : [38749 ^ _779530 : [(38750 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1523261, 38748 ^ [_1523261, _1523263, _1523265, _1523267])))], (38752 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1523263, hAPP(_1523265, 38748 ^ [_1523261, _1523263, _1523265, _1523267]))), hAPP(_1523263, 38748 ^ [_1523261, _1523263, _1523265, _1523267])))]], -(c_Wellfounded_Owf(_1523267, hAPP(c_Set_OCollect(tc_prod(_1523267, _1523267)), hAPP(c_Product__Type_Oprod_Oprod__case(_1523267, _1523267, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1523267, tc_HOL_Obool), tc_fun(_1523267, tc_HOL_Obool), _1523267), hAPP(c_COMBS(_1523267, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523267), c_fconj), _1523261))), hAPP(hAPP(c_COMBC(_1523267, tc_fun(_1523267, _1523267), tc_fun(_1523267, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523267, tc_HOL_Obool), tc_fun(tc_fun(_1523267, _1523267), tc_fun(_1523267, tc_HOL_Obool)), _1523267), c_COMBB(_1523267, tc_HOL_Obool, _1523267)), c_fequal)), _1523265))))))], (38756 ^ _779530) ^ [_1523654, _1523656, _1523658, _1523660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523654), _1523656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523654), _1523658)), -(_1523658 = c_Orderings_Obot__class_Obot(tc_fun(_1523654, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1523654, tc_HOL_Obool), tc_fun(_1523654, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1523654, tc_HOL_Obool), tc_fun(_1523654, tc_HOL_Obool)), _1523656), _1523658)), c_Wellfounded_Omax__ext(_1523654, _1523660)))), 38770 ^ _779530 : [(38771 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523654), 38769 ^ [_1523654, _1523656, _1523658, _1523660]), _1523656)))], (38773 ^ _779530) ^ [_1524059] : [hBOOL(hAPP(hAPP(c_member(_1523654), _1524059), _1523658)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523654, _1523654)), hAPP(hAPP(c_Product__Type_OPair(_1523654, _1523654), 38769 ^ [_1523654, _1523656, _1523658, _1523660]), _1524059)), _1523660))]]], (38781 ^ _779530) ^ [] : [-(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))))], (38783 ^ _779530) ^ [_1524303, _1524305] : [c_Wellfounded_Owf(_1524303, _1524305), -(c_Wellfounded_Owf(tc_List_Olist(_1524303), c_List_Olex(_1524303, _1524305)))], (38789 ^ _779530) ^ [_1524390, _1524392, _1524394] : [c_Wellfounded_Owf(_1524390, _1524392), -(c_Wellfounded_Owf(tc_List_Olist(_1524390), hAPP(c_List_Olexn(_1524390, _1524392), _1524394)))], (38795 ^ _779530) ^ [_1524485, _1524487] : [-(c_List_Olex(_1524485, _1524487) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1524485), tc_List_Olist(_1524485)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1524485, _1524487)))], (38797 ^ _779530) ^ [_1524535, _1524537] : [-(hAPP(c_List_Olexn(_1524535, _1524537), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1524535), tc_List_Olist(_1524535)), tc_HOL_Obool)))], (38799 ^ _779530) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38801 ^ _779530) ^ [_1524596, _1524598, _1524600, _1524602] : [38803 ^ _779530 : [(38804 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1524596, 38802 ^ [_1524596, _1524598, _1524600, _1524602])))], (38806 ^ _779530) ^ [] : [c_Wellfounded_Owf(_1524598, hAPP(_1524600, 38802 ^ [_1524596, _1524598, _1524600, _1524602]))]], -(c_Wellfounded_Owf(tc_prod(_1524602, _1524598), c_Recdef_Osame__fst(_1524602, _1524598, _1524596, _1524600)))], (38810 ^ _779530) ^ [_1524781] : [-(c_Nitpick_Ozero__frac(_1524781) = c_Nitpick_OAbs__Frac(_1524781, 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))))], (38812 ^ _779530) ^ [_1524809, _1524811, _1524813] : [-(hAPP(c_Relation_ORange(_1524809, _1524811), hAPP(c_Set_OCollect(tc_prod(_1524809, _1524811)), hAPP(c_Product__Type_Oprod_Oprod__case(_1524809, _1524811, tc_HOL_Obool), _1524813))) = hAPP(c_Set_OCollect(_1524811), hAPP(hAPP(c_COMBB(tc_fun(_1524809, tc_HOL_Obool), tc_HOL_Obool, _1524811), c_HOL_OEx(_1524809)), hAPP(c_COMBC(_1524809, _1524811, tc_HOL_Obool), _1524813))))], (38814 ^ _779530) ^ [_1524884, _1524886, _1524888, _1524890, _1524892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524884, _1524886)), hAPP(hAPP(c_Product__Type_OPair(_1524884, _1524886), _1524888), _1524890)), _1524892)), -(hBOOL(hAPP(hAPP(c_member(_1524886), _1524890), hAPP(c_Relation_ORange(_1524884, _1524886), _1524892))))], (38820 ^ _779530) ^ [_1525031, _1525033] : [-(hAPP(c_Relation_ORange(_1525031, _1525031), c_Relation_OId__on(_1525031, _1525033)) = _1525033)], (38822 ^ _779530) ^ [_1525065, _1525067, _1525069, _1525071] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525065, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1525065, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1525067, _1525065), _1525069)), hAPP(c_Relation_ORange(_1525067, _1525065), _1525071))), hAPP(c_Relation_ORange(_1525067, _1525065), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1525067, _1525065), tc_HOL_Obool)), _1525069), _1525071)))))], (38824 ^ _779530) ^ [_1525147, _1525149] : [-(hAPP(c_Relation_ORange(_1525147, _1525149), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1525147, _1525149), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1525149, tc_HOL_Obool)))], (38826 ^ _779530) ^ [_1525209, _1525211, _1525213] : [hAPP(c_Relation_ORange(_1525209, _1525211), _1525213) = c_Orderings_Obot__class_Obot(tc_fun(_1525211, tc_HOL_Obool)), -(_1525213 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1525209, _1525211), tc_HOL_Obool)))], (38832 ^ _779530) ^ [_1525322, _1525324, _1525326] : [_1525326 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1525322, _1525324), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1525322, _1525324), _1525326) = c_Orderings_Obot__class_Obot(tc_fun(_1525324, tc_HOL_Obool)))], (38838 ^ _779530) ^ [_1525441, _1525443, _1525445, _1525447] : [-(hAPP(c_Relation_ORange(_1525441, _1525443), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525441, _1525443), tc_HOL_Obool)), _1525445), _1525447)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525443, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1525441, _1525443), _1525445)), hAPP(c_Relation_ORange(_1525441, _1525443), _1525447)))], (38840 ^ _779530) ^ [_1525513, _1525515, _1525517] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1525513, _1525515)), _1525517)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525515), hAPP(c_Relation_ORange(_1525513, _1525515), _1525517))))], (38846 ^ _779530) ^ [_1525626, _1525628, _1525630] : [-(hAPP(c_Set_Oimage(tc_prod(_1525626, _1525628), _1525628, c_Product__Type_Osnd(_1525626, _1525628)), _1525630) = hAPP(c_Relation_ORange(_1525626, _1525628), _1525630))], (38848 ^ _779530) ^ [_1525693, _1525695, _1525697, _1525699] : [hBOOL(hAPP(hAPP(c_member(_1525693), _1525695), hAPP(c_Relation_ORange(_1525697, _1525693), _1525699))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525697, _1525693)), hAPP(hAPP(c_Product__Type_OPair(_1525697, _1525693), 38851 ^ [_1525693, _1525695, _1525697, _1525699]), _1525695)), _1525699)))], (38855 ^ _779530) ^ [_1525850, _1525852, _1525854, _1525856] : [38856 ^ _779530 : [(38857 ^ _779530) ^ [_1525925] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525854, _1525850)), hAPP(hAPP(c_Product__Type_OPair(_1525854, _1525850), _1525925), _1525852)), _1525856))]], -(hBOOL(hAPP(hAPP(c_member(_1525850), _1525852), hAPP(c_Relation_ORange(_1525854, _1525850), _1525856))))], (38861 ^ _779530) ^ [_1526010, _1526012, _1526014, _1526016, _1526018] : [-(hAPP(c_Relation_ORange(_1526010, _1526012), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1526010, _1526012)), hAPP(hAPP(c_Product__Type_OPair(_1526010, _1526012), _1526014), _1526016)), _1526018)) = hAPP(hAPP(c_Set_Oinsert(_1526012), _1526016), hAPP(c_Relation_ORange(_1526010, _1526012), _1526018)))], (38863 ^ _779530) ^ [_1526081, _1526083, _1526085, _1526087] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1526081, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1526083, _1526081), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1526083, _1526081), tc_HOL_Obool)), _1526085), _1526087))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526081, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1526083, _1526081), _1526085)), hAPP(c_Relation_ORange(_1526083, _1526081), _1526087)))))], (38865 ^ _779530) ^ [_1526163] : [-(c_Nitpick_Oone__frac(_1526163) = c_Nitpick_OAbs__Frac(_1526163, 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))))], (38867 ^ _779530) ^ [_1526191, _1526193] : [-(c_Nitpick_Onumber__of__frac(_1526191, _1526193) = c_Nitpick_OAbs__Frac(_1526191, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1526193), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38869 ^ _779530) ^ [_1526249, _1526251, _1526253, _1526255] : [hBOOL(hAPP(c_Predicate_ORangeP(_1526249, _1526251, hAPP(hAPP(c_COMBC(_1526249, tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_fun(_1526251, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526251, tc_fun(tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_fun(_1526251, tc_HOL_Obool)), _1526249), c_COMBC(_1526251, tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526251, tc_prod(_1526249, _1526251)), tc_fun(_1526251, tc_fun(tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_HOL_Obool)), _1526249), hAPP(c_COMBB(tc_prod(_1526249, _1526251), tc_fun(tc_fun(tc_prod(_1526249, _1526251), tc_HOL_Obool), tc_HOL_Obool), _1526251), c_member(tc_prod(_1526249, _1526251)))), c_Product__Type_OPair(_1526249, _1526251)))), _1526253)), _1526255)), -(hBOOL(hAPP(hAPP(c_member(_1526251), _1526255), hAPP(c_Relation_ORange(_1526249, _1526251), _1526253))))], (38875 ^ _779530) ^ [_1526600, _1526602, _1526604, _1526606] : [hBOOL(hAPP(hAPP(c_member(_1526602), _1526606), hAPP(c_Relation_ORange(_1526600, _1526602), _1526604))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1526600, _1526602, hAPP(hAPP(c_COMBC(_1526600, tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_fun(_1526602, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526602, tc_fun(tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_fun(_1526602, tc_HOL_Obool)), _1526600), c_COMBC(_1526602, tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526602, tc_prod(_1526600, _1526602)), tc_fun(_1526602, tc_fun(tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_HOL_Obool)), _1526600), hAPP(c_COMBB(tc_prod(_1526600, _1526602), tc_fun(tc_fun(tc_prod(_1526600, _1526602), tc_HOL_Obool), tc_HOL_Obool), _1526602), c_member(tc_prod(_1526600, _1526602)))), c_Product__Type_OPair(_1526600, _1526602)))), _1526604)), _1526606)))], (38881 ^ _779530) ^ [_1526957, _1526959, _1526961, _1526963, _1526965] : [hBOOL(hAPP(hAPP(_1526957, _1526959), _1526961)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1526963, _1526965, _1526957), _1526961)))], (38887 ^ _779530) ^ [_1527083, _1527085, _1527087, _1527089] : [hBOOL(hAPP(c_Predicate_ORangeP(_1527083, _1527085, _1527087), _1527089)), -(hBOOL(hAPP(hAPP(_1527087, 38890 ^ [_1527083, _1527085, _1527087, _1527089]), _1527089)))], (38894 ^ _779530) ^ [_1527198, _1527200, _1527202, _1527204] : [38895 ^ _779530 : [(38896 ^ _779530) ^ [_1527252] : [hBOOL(hAPP(hAPP(_1527202, _1527252), _1527204))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1527198, _1527200, _1527202), _1527204)))], (38900 ^ _779530) ^ [_1527316, _1527318, _1527320] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1527316), _1527318), _1527320) = c_Nitpick_OAbs__Frac(_1527316, c_Nitpick_Onorm__frac(_1527318, _1527320)))], (38902 ^ _779530) ^ [_1527357, _1527359, _1527361, _1527363] : [hBOOL(hAPP(hAPP(c_member(_1527357), _1527359), hAPP(c_Relation_ORange(_1527361, _1527357), _1527363))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527361, _1527357)), hAPP(hAPP(c_Product__Type_OPair(_1527361, _1527357), 38905 ^ [_1527357, _1527359, _1527361, _1527363]), _1527359)), _1527363)))], (38909 ^ _779530) ^ [_1527522, _1527524, _1527526] : [c_Wellfounded_Owf(_1527522, _1527524), c_Wellfounded_Owf(_1527522, _1527526), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1527522, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1527522, _1527522), _1527524)), hAPP(c_Relation_ORange(_1527522, _1527522), _1527526)) = c_Orderings_Obot__class_Obot(tc_fun(_1527522, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1527522, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527522, _1527522), tc_HOL_Obool)), _1527524), _1527526)))], (38923 ^ _779530) ^ [_1527793, _1527795, _1527797, _1527799, _1527801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527793, _1527795)), hAPP(hAPP(c_Product__Type_OPair(_1527793, _1527795), _1527797), _1527799)), _1527801)), -(hBOOL(hAPP(hAPP(c_member(_1527793), _1527797), hAPP(c_Relation_ODomain(_1527793, _1527795), _1527801))))], (38929 ^ _779530) ^ [_1527940, _1527942] : [-(hAPP(c_Relation_ODomain(_1527940, _1527940), c_Relation_OId__on(_1527940, _1527942)) = _1527942)], (38931 ^ _779530) ^ [_1527974, _1527976] : [-(hAPP(c_Relation_ODomain(_1527974, _1527976), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527974, _1527976), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1527974, tc_HOL_Obool)))], (38933 ^ _779530) ^ [_1528036, _1528038, _1528040] : [hAPP(c_Relation_ODomain(_1528036, _1528038), _1528040) = c_Orderings_Obot__class_Obot(tc_fun(_1528036, tc_HOL_Obool)), -(_1528040 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528036, _1528038), tc_HOL_Obool)))], (38939 ^ _779530) ^ [_1528149, _1528151, _1528153] : [_1528153 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528149, _1528151), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1528149, _1528151), _1528153) = c_Orderings_Obot__class_Obot(tc_fun(_1528149, tc_HOL_Obool)))], (38945 ^ _779530) ^ [_1528268, _1528270, _1528272, _1528274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528268, _1528270), tc_HOL_Obool)), _1528272), _1528274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1528268, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1528268, _1528270), _1528272)), hAPP(c_Relation_ODomain(_1528268, _1528270), _1528274))))], (38951 ^ _779530) ^ [_1528419, _1528421, _1528423, _1528425] : [-(hAPP(c_Relation_ODomain(_1528419, _1528421), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528419, _1528421), tc_HOL_Obool)), _1528423), _1528425)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528419, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1528419, _1528421), _1528423)), hAPP(c_Relation_ODomain(_1528419, _1528421), _1528425)))], (38953 ^ _779530) ^ [_1528491, _1528493, _1528495] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1528491, _1528493)), _1528495)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1528491), hAPP(c_Relation_ODomain(_1528491, _1528493), _1528495))))], (38959 ^ _779530) ^ [_1528604, _1528606, _1528608] : [-(hAPP(c_Set_Oimage(tc_prod(_1528604, _1528606), _1528604, c_Product__Type_Ofst(_1528604, _1528606)), _1528608) = hAPP(c_Relation_ODomain(_1528604, _1528606), _1528608))], (38961 ^ _779530) ^ [_1528671, _1528673, _1528675, _1528677] : [hBOOL(hAPP(hAPP(c_member(_1528671), _1528673), hAPP(c_Relation_ODomain(_1528671, _1528675), _1528677))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528671, _1528675)), hAPP(hAPP(c_Product__Type_OPair(_1528671, _1528675), _1528673), 38964 ^ [_1528671, _1528673, _1528675, _1528677])), _1528677)))], (38968 ^ _779530) ^ [_1528828, _1528830, _1528832, _1528834] : [38969 ^ _779530 : [(38970 ^ _779530) ^ [_1528903] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528828, _1528832)), hAPP(hAPP(c_Product__Type_OPair(_1528828, _1528832), _1528830), _1528903)), _1528834))]], -(hBOOL(hAPP(hAPP(c_member(_1528828), _1528830), hAPP(c_Relation_ODomain(_1528828, _1528832), _1528834))))], (38974 ^ _779530) ^ [_1528988, _1528990, _1528992, _1528994, _1528996] : [-(hAPP(c_Relation_ODomain(_1528988, _1528990), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1528988, _1528990)), hAPP(hAPP(c_Product__Type_OPair(_1528988, _1528990), _1528992), _1528994)), _1528996)) = hAPP(hAPP(c_Set_Oinsert(_1528988), _1528992), hAPP(c_Relation_ODomain(_1528988, _1528990), _1528996)))], (38976 ^ _779530) ^ [_1529059, _1529061, _1529063, _1529065] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1529059, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1529059, _1529061), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529059, _1529061), tc_HOL_Obool)), _1529063), _1529065))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529059, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1529059, _1529061), _1529063)), hAPP(c_Relation_ODomain(_1529059, _1529061), _1529065)))))], (38978 ^ _779530) ^ [_1529141, _1529143, _1529145, _1529147] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1529141, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529141, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1529141, _1529143), _1529145)), hAPP(c_Relation_ODomain(_1529141, _1529143), _1529147))), hAPP(c_Relation_ODomain(_1529141, _1529143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529141, _1529143), tc_HOL_Obool)), _1529145), _1529147)))))], (38980 ^ _779530) ^ [_1529223, _1529225] : [-(hAPP(c_Relation_OField(_1529223), _1529225) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1529223, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1529223, _1529223), _1529225)), hAPP(c_Relation_ORange(_1529223, _1529223), _1529225)))], (38982 ^ _779530) ^ [_1529276, _1529278, _1529280] : [-(hAPP(c_Relation_ODomain(_1529276, _1529278), hAPP(c_Set_OCollect(tc_prod(_1529276, _1529278)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529276, _1529278, tc_HOL_Obool), _1529280))) = hAPP(c_Set_OCollect(_1529276), hAPP(hAPP(c_COMBB(tc_fun(_1529278, tc_HOL_Obool), tc_HOL_Obool, _1529276), c_HOL_OEx(_1529278)), _1529280)))], (38984 ^ _779530) ^ [_1529365, _1529367, _1529369, _1529371] : [hBOOL(hAPP(c_Predicate_ODomainP(_1529365, _1529367, hAPP(hAPP(c_COMBC(_1529365, tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_fun(_1529367, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529367, tc_fun(tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_fun(_1529367, tc_HOL_Obool)), _1529365), c_COMBC(_1529367, tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529367, tc_prod(_1529365, _1529367)), tc_fun(_1529367, tc_fun(tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_HOL_Obool)), _1529365), hAPP(c_COMBB(tc_prod(_1529365, _1529367), tc_fun(tc_fun(tc_prod(_1529365, _1529367), tc_HOL_Obool), tc_HOL_Obool), _1529367), c_member(tc_prod(_1529365, _1529367)))), c_Product__Type_OPair(_1529365, _1529367)))), _1529369)), _1529371)), -(hBOOL(hAPP(hAPP(c_member(_1529365), _1529371), hAPP(c_Relation_ODomain(_1529365, _1529367), _1529369))))], (38990 ^ _779530) ^ [_1529716, _1529718, _1529720, _1529722] : [hBOOL(hAPP(hAPP(c_member(_1529716), _1529722), hAPP(c_Relation_ODomain(_1529716, _1529718), _1529720))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1529716, _1529718, hAPP(hAPP(c_COMBC(_1529716, tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_fun(_1529718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529718, tc_fun(tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_fun(_1529718, tc_HOL_Obool)), _1529716), c_COMBC(_1529718, tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529718, tc_prod(_1529716, _1529718)), tc_fun(_1529718, tc_fun(tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_HOL_Obool)), _1529716), hAPP(c_COMBB(tc_prod(_1529716, _1529718), tc_fun(tc_fun(tc_prod(_1529716, _1529718), tc_HOL_Obool), tc_HOL_Obool), _1529718), c_member(tc_prod(_1529716, _1529718)))), c_Product__Type_OPair(_1529716, _1529718)))), _1529720)), _1529722)))], (38996 ^ _779530) ^ [_1530073, _1530075, _1530077, _1530079] : [hBOOL(hAPP(hAPP(c_member(_1530073), _1530075), hAPP(c_Relation_ODomain(_1530073, _1530077), _1530079))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530073, _1530077)), hAPP(hAPP(c_Product__Type_OPair(_1530073, _1530077), _1530075), 38999 ^ [_1530073, _1530075, _1530077, _1530079])), _1530079)))], (39003 ^ _779530) ^ [_1530262, _1530264, _1530266, _1530268, _1530270] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1530262, _1530264, hAPP(hAPP(c_Set_Oinsert(_1530262), _1530266), _1530268)), _1530270)), 39008 ^ _779530 : [(39009 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1530262), _1530266), _1530268) = hAPP(hAPP(c_Set_Oinsert(_1530262), 39006 ^ [_1530262, _1530264, _1530266, _1530268, _1530270]), 39007 ^ [_1530262, _1530264, _1530266, _1530268, _1530270]))], (39011 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530262, _1530262, _1530264, 39006 ^ [_1530262, _1530264, _1530266, _1530268, _1530270], 39007 ^ [_1530262, _1530264, _1530266, _1530268, _1530270]), _1530270)))], (39013 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1530262), 39006 ^ [_1530262, _1530264, _1530266, _1530268, _1530270]), 39007 ^ [_1530262, _1530264, _1530266, _1530268, _1530270]))]]], (39015 ^ _779530) ^ [_1530653, _1530655, _1530657, _1530659, _1530661] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1530653, _1530655, hAPP(hAPP(c_Set_Oinsert(_1530653), _1530657), _1530659)), _1530661))), 39016 ^ _779530 : [(39017 ^ _779530) ^ [_1530757, _1530759] : [hAPP(hAPP(c_Set_Oinsert(_1530653), _1530657), _1530659) = hAPP(hAPP(c_Set_Oinsert(_1530653), _1530759), _1530757), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1530653, _1530653, _1530655, _1530759, _1530757), _1530661)), -(hBOOL(hAPP(hAPP(c_member(_1530653), _1530759), _1530757)))]]], (39029 ^ _779530) ^ [_1531014, _1531016, _1531018, _1531020, _1531022] : [hBOOL(hAPP(hAPP(_1531014, _1531016), _1531018)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1531020, _1531022, _1531014), _1531016)))], (39035 ^ _779530) ^ [_1531140, _1531142, _1531144, _1531146] : [hBOOL(hAPP(c_Predicate_ODomainP(_1531140, _1531142, _1531144), _1531146)), -(hBOOL(hAPP(hAPP(_1531144, _1531146), 39038 ^ [_1531140, _1531142, _1531144, _1531146])))], (39042 ^ _779530) ^ [_1531255, _1531257, _1531259, _1531261] : [39043 ^ _779530 : [(39044 ^ _779530) ^ [_1531309] : [hBOOL(hAPP(hAPP(_1531259, _1531261), _1531309))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1531255, _1531257, _1531259), _1531261)))], (39048 ^ _779530) ^ [_1531373, _1531375, _1531377, _1531379, _1531381] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1531373, _1531375, hAPP(hAPP(c_Set_Oinsert(_1531373), _1531377), _1531379)), _1531381)), 39053 ^ _779530 : [(39054 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1531373), _1531377), _1531379) = hAPP(hAPP(c_Set_Oinsert(_1531373), 39051 ^ [_1531373, _1531375, _1531377, _1531379, _1531381]), 39052 ^ [_1531373, _1531375, _1531377, _1531379, _1531381]))], (39056 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1531373, _1531373, _1531375, 39051 ^ [_1531373, _1531375, _1531377, _1531379, _1531381], 39052 ^ [_1531373, _1531375, _1531377, _1531379, _1531381]), _1531381)))], (39058 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1531373), 39051 ^ [_1531373, _1531375, _1531377, _1531379, _1531381]), 39052 ^ [_1531373, _1531375, _1531377, _1531379, _1531381]))]]], (39060 ^ _779530) ^ [_1531766, _1531768, _1531770, _1531772, _1531774, _1531776] : [-(hAPP(c_Set_Oimage(_1531766, tc_prod(_1531768, _1531770), hAPP(hAPP(c_COMBS(_1531766, _1531770, tc_prod(_1531768, _1531770)), hAPP(hAPP(c_COMBB(_1531768, tc_fun(_1531770, tc_prod(_1531768, _1531770)), _1531766), c_Product__Type_OPair(_1531768, _1531770)), _1531772)), _1531774)), _1531776) = hAPP(hAPP(c_Product__Type_OSigma(_1531768, _1531770), hAPP(c_Set_Oimage(_1531766, _1531768, _1531772), _1531776)), hAPP(hAPP(c_COMBB(tc_fun(_1531766, tc_HOL_Obool), tc_fun(_1531770, tc_HOL_Obool), _1531768), c_Set_Oimage(_1531766, _1531770, _1531774)), hAPP(hAPP(c_COMBC(_1531768, tc_fun(_1531766, tc_HOL_Obool), tc_fun(_1531766, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531766, tc_HOL_Obool), tc_fun(tc_fun(_1531766, tc_HOL_Obool), tc_fun(_1531766, tc_HOL_Obool)), _1531768), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1531766, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1531768, tc_HOL_Obool), tc_fun(_1531766, tc_HOL_Obool), _1531768), c_Set_Ovimage(_1531766, _1531768, _1531772)), hAPP(hAPP(c_COMBC(_1531768, tc_fun(_1531768, tc_HOL_Obool), tc_fun(_1531768, tc_HOL_Obool)), c_Set_Oinsert(_1531768)), c_Orderings_Obot__class_Obot(tc_fun(_1531768, tc_HOL_Obool)))))), _1531776))))], (39062 ^ _779530) ^ [_1531963, _1531965, _1531967] : [39064 ^ _779530 : [(39065 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39063 ^ [_1531963, _1531965, _1531967]), _1531963)))], (39067 ^ _779530) ^ [] : [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(_1531965, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 39063 ^ [_1531963, _1531965, _1531967]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1531965, 39063 ^ [_1531963, _1531965, _1531967])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1531965, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1531967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1531967), hAPP(_1531965, _1531963))), 39077 ^ _779530 : [(39078 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 39076 ^ [_1531963, _1531965, _1531967]), _1531963)))], (39080 ^ _779530) ^ [] : [-(hAPP(_1531965, 39076 ^ [_1531963, _1531965, _1531967]) = _1531967)]]], (39082 ^ _779530) ^ [_1532413, _1532415, _1532417, _1532419, _1532421, _1532423] : [hBOOL(hAPP(hAPP(c_member(_1532413), _1532415), _1532417)), hBOOL(hAPP(hAPP(c_member(_1532419), _1532421), hAPP(_1532423, _1532415))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532413, _1532419)), hAPP(hAPP(c_Product__Type_OPair(_1532413, _1532419), _1532415), _1532421)), hAPP(hAPP(c_Product__Type_OSigma(_1532413, _1532419), _1532417), _1532423))))], (39092 ^ _779530) ^ [_1532648, _1532650, _1532652, _1532654, _1532656, _1532658] : [hBOOL(hAPP(hAPP(c_member(_1532648), _1532650), _1532652)), 39095 ^ _779530 : [(39096 ^ _779530) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1532654, _1532648), _1532656), hAPP(c_COMBK(tc_fun(_1532648, tc_HOL_Obool), _1532654), _1532652)) = hAPP(hAPP(c_Product__Type_OSigma(_1532654, _1532648), _1532658), hAPP(c_COMBK(tc_fun(_1532648, tc_HOL_Obool), _1532654), _1532652)), -(_1532656 = _1532658)], (39102 ^ _779530) ^ [] : [_1532656 = _1532658, -(hAPP(hAPP(c_Product__Type_OSigma(_1532654, _1532648), _1532656), hAPP(c_COMBK(tc_fun(_1532648, tc_HOL_Obool), _1532654), _1532652)) = hAPP(hAPP(c_Product__Type_OSigma(_1532654, _1532648), _1532658), hAPP(c_COMBK(tc_fun(_1532648, tc_HOL_Obool), _1532654), _1532652)))]]], (39108 ^ _779530) ^ [_1533001, _1533003, _1533005] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533001, _1533003), c_Orderings_Obot__class_Obot(tc_fun(_1533001, tc_HOL_Obool))), _1533005) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533001, _1533003), tc_HOL_Obool)))], (39110 ^ _779530) ^ [_1533050, _1533052, _1533054, _1533056] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1533050, _1533052)), hAPP(hAPP(c_Product__Type_OSigma(_1533050, _1533052), _1533054), hAPP(c_COMBK(tc_fun(_1533052, tc_HOL_Obool), _1533050), _1533056))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1533050), _1533054)), hAPP(c_Finite__Set_Ocard(_1533052), _1533056)))], (39112 ^ _779530) ^ [_1533121, _1533123, _1533125, _1533127, _1533129, _1533131] : [class_Groups_Ocomm__monoid__add(_1533121), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1533123, _1533121), hAPP(hAPP(c_COMBC(_1533123, tc_fun(_1533125, tc_HOL_Obool), _1533121), hAPP(hAPP(c_COMBB(tc_fun(_1533125, _1533121), tc_fun(tc_fun(_1533125, tc_HOL_Obool), _1533121), _1533123), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1533125, _1533121)), _1533127)), _1533129)), _1533131) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1533123, _1533125), _1533121), hAPP(c_Product__Type_Oprod_Oprod__case(_1533123, _1533125, _1533121), _1533127)), hAPP(hAPP(c_Product__Type_OSigma(_1533123, _1533125), _1533131), hAPP(c_COMBK(tc_fun(_1533125, tc_HOL_Obool), _1533123), _1533129))))], (39118 ^ _779530) ^ [_1533366, _1533368, _1533370] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533366, _1533368), _1533370), hAPP(c_COMBK(tc_fun(_1533368, tc_HOL_Obool), _1533366), c_Orderings_Obot__class_Obot(tc_fun(_1533368, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533366, _1533368), tc_HOL_Obool)))], (39130 ^ _779530) ^ [_1533607, _1533609, _1533611, _1533613] : [39131 ^ _779530 : [(39132 ^ _779530) ^ [] : [_1533611 = c_Orderings_Obot__class_Obot(tc_fun(_1533607, tc_HOL_Obool))], (39134 ^ _779530) ^ [] : [_1533613 = c_Orderings_Obot__class_Obot(tc_fun(_1533609, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1533607, _1533609), _1533611), hAPP(c_COMBK(tc_fun(_1533609, tc_HOL_Obool), _1533607), _1533613)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533607, _1533609), tc_HOL_Obool)))], (39120 ^ _779530) ^ [_1533445, _1533447, _1533449, _1533451] : [hAPP(hAPP(c_Product__Type_OSigma(_1533445, _1533447), _1533449), hAPP(c_COMBK(tc_fun(_1533447, tc_HOL_Obool), _1533445), _1533451)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533445, _1533447), tc_HOL_Obool)), -(_1533449 = c_Orderings_Obot__class_Obot(tc_fun(_1533445, tc_HOL_Obool))), -(_1533451 = c_Orderings_Obot__class_Obot(tc_fun(_1533447, tc_HOL_Obool)))], (39138 ^ _779530) ^ [_1533800, _1533802, _1533804] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1533800, _1533802), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533800, _1533802), _1533804), hAPP(c_COMBK(tc_fun(_1533802, tc_HOL_Obool), _1533800), c_Orderings_Otop__class_Otop(tc_fun(_1533802, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1533800, _1533802), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1533800, tc_HOL_Obool)), _1533804)), hAPP(c_COMBK(tc_fun(_1533802, tc_HOL_Obool), _1533800), c_Orderings_Otop__class_Otop(tc_fun(_1533802, tc_HOL_Obool)))))], (39140 ^ _779530) ^ [_1533892, _1533894, _1533896] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1533892, _1533894), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533892, _1533894), c_Orderings_Otop__class_Otop(tc_fun(_1533892, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1533894, tc_HOL_Obool), _1533892), _1533896))) = hAPP(hAPP(c_Product__Type_OSigma(_1533892, _1533894), c_Orderings_Otop__class_Otop(tc_fun(_1533892, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1533894, tc_HOL_Obool), _1533892), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1533894, tc_HOL_Obool)), _1533896))))], (39142 ^ _779530) ^ [_1533984, _1533986, _1533988, _1533990, _1533992, _1533994] : [class_Groups_Ocomm__monoid__mult(_1533984), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533986, _1533984), hAPP(hAPP(c_COMBC(_1533986, tc_fun(_1533988, tc_HOL_Obool), _1533984), hAPP(hAPP(c_COMBB(tc_fun(_1533988, _1533984), tc_fun(tc_fun(_1533988, tc_HOL_Obool), _1533984), _1533986), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533988, _1533984)), _1533990)), _1533992)), _1533994) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1533986, _1533988), _1533984), hAPP(c_Product__Type_Oprod_Oprod__case(_1533986, _1533988, _1533984), _1533990)), hAPP(hAPP(c_Product__Type_OSigma(_1533986, _1533988), _1533994), hAPP(c_COMBK(tc_fun(_1533988, tc_HOL_Obool), _1533986), _1533992))))], (39148 ^ _779530) ^ [_1534229, _1534231, _1534233, _1534235, _1534237] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534229, _1534231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534229, tc_HOL_Obool)), _1534233), _1534235)), _1534237) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1534229, _1534231), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534229, _1534231), _1534233), _1534237)), hAPP(hAPP(c_Product__Type_OSigma(_1534229, _1534231), _1534235), _1534237)))], (39150 ^ _779530) ^ [_1534312, _1534314, _1534316, _1534318, _1534320] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534312, _1534314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534312, tc_HOL_Obool)), _1534316), _1534318)), hAPP(c_COMBK(tc_fun(_1534314, tc_HOL_Obool), _1534312), _1534320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1534312, _1534314), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534312, _1534314), _1534316), hAPP(c_COMBK(tc_fun(_1534314, tc_HOL_Obool), _1534312), _1534320))), hAPP(hAPP(c_Product__Type_OSigma(_1534312, _1534314), _1534318), hAPP(c_COMBK(tc_fun(_1534314, tc_HOL_Obool), _1534312), _1534320))))], (39152 ^ _779530) ^ [_1534422, _1534424, _1534426, _1534428, _1534430] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534422, _1534424), _1534426), hAPP(hAPP(c_COMBS(_1534422, tc_fun(_1534424, tc_HOL_Obool), tc_fun(_1534424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534424, tc_HOL_Obool), tc_fun(tc_fun(_1534424, tc_HOL_Obool), tc_fun(_1534424, tc_HOL_Obool)), _1534422), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534424, tc_HOL_Obool))), _1534428)), _1534430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1534422, _1534424), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534422, _1534424), _1534426), _1534428)), hAPP(hAPP(c_Product__Type_OSigma(_1534422, _1534424), _1534426), _1534430)))], (39154 ^ _779530) ^ [_1534537, _1534539, _1534541, _1534543, _1534545, _1534547, _1534549, _1534551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534537, _1534539), tc_HOL_Obool)), _1534541), hAPP(hAPP(c_Product__Type_OSigma(_1534537, _1534539), _1534543), hAPP(c_COMBK(tc_fun(_1534539, tc_HOL_Obool), _1534537), _1534545)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534539, _1534547), tc_HOL_Obool)), _1534549), hAPP(hAPP(c_Product__Type_OSigma(_1534539, _1534547), _1534545), hAPP(c_COMBK(tc_fun(_1534547, tc_HOL_Obool), _1534539), _1534551)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534537, _1534547), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1534537, _1534539, _1534547), _1534541), _1534549)), hAPP(hAPP(c_Product__Type_OSigma(_1534537, _1534547), _1534543), hAPP(c_COMBK(tc_fun(_1534547, tc_HOL_Obool), _1534537), _1534551)))))], (39164 ^ _779530) ^ [_1534896, _1534898, _1534900, _1534902] : [-(hAPP(c_Set_Oimage(tc_prod(_1534896, _1534898), tc_prod(_1534898, _1534896), hAPP(c_Product__Type_Oprod_Oprod__case(_1534896, _1534898, tc_prod(_1534898, _1534896)), hAPP(c_COMBC(_1534898, _1534896, tc_prod(_1534898, _1534896)), c_Product__Type_OPair(_1534898, _1534896)))), hAPP(hAPP(c_Product__Type_OSigma(_1534896, _1534898), _1534900), hAPP(c_COMBK(tc_fun(_1534898, tc_HOL_Obool), _1534896), _1534902))) = hAPP(hAPP(c_Product__Type_OSigma(_1534898, _1534896), _1534902), hAPP(c_COMBK(tc_fun(_1534896, tc_HOL_Obool), _1534898), _1534900)))], (39166 ^ _779530) ^ [_1534997, _1534999, _1535001, _1535003] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534997), _1534999)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535001), _1535003)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1534997, _1535001)), hAPP(hAPP(c_Product__Type_OSigma(_1534997, _1535001), _1534999), hAPP(c_COMBK(tc_fun(_1535001, tc_HOL_Obool), _1534997), _1535003)))))], (39176 ^ _779530) ^ [_1535200, _1535202, _1535204] : [c_Equiv__Relations_Oequiv(_1535200, _1535202, _1535204), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535200, _1535200), tc_HOL_Obool)), _1535204), hAPP(hAPP(c_Product__Type_OSigma(_1535200, _1535200), _1535202), hAPP(c_COMBK(tc_fun(_1535200, tc_HOL_Obool), _1535200), _1535202)))))], (39182 ^ _779530) ^ [_1535343, _1535345, _1535347, _1535349, _1535351] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535343, _1535345), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535343, tc_HOL_Obool)), _1535347), _1535349)), _1535351) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535343, _1535345), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535343, _1535345), _1535347), _1535351)), hAPP(hAPP(c_Product__Type_OSigma(_1535343, _1535345), _1535349), _1535351)))], (39184 ^ _779530) ^ [_1535426, _1535428, _1535430, _1535432, _1535434] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535426, _1535428), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535426, tc_HOL_Obool)), _1535430), _1535432)), hAPP(c_COMBK(tc_fun(_1535428, tc_HOL_Obool), _1535426), _1535434)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535426, _1535428), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535426, _1535428), _1535430), hAPP(c_COMBK(tc_fun(_1535428, tc_HOL_Obool), _1535426), _1535434))), hAPP(hAPP(c_Product__Type_OSigma(_1535426, _1535428), _1535432), hAPP(c_COMBK(tc_fun(_1535428, tc_HOL_Obool), _1535426), _1535434))))], (39186 ^ _779530) ^ [_1535536, _1535538, _1535540, _1535542, _1535544] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535536, _1535538), _1535540), hAPP(hAPP(c_COMBS(_1535536, tc_fun(_1535538, tc_HOL_Obool), tc_fun(_1535538, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535538, tc_HOL_Obool), tc_fun(tc_fun(_1535538, tc_HOL_Obool), tc_fun(_1535538, tc_HOL_Obool)), _1535536), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1535538, tc_HOL_Obool))), _1535542)), _1535544)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535536, _1535538), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535536, _1535538), _1535540), _1535542)), hAPP(hAPP(c_Product__Type_OSigma(_1535536, _1535538), _1535540), _1535544)))], (39188 ^ _779530) ^ [_1535651, _1535653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535651, _1535651), tc_HOL_Obool)), c_Relation_OId__on(_1535651, _1535653)), hAPP(hAPP(c_Product__Type_OSigma(_1535651, _1535651), _1535653), hAPP(c_COMBK(tc_fun(_1535651, tc_HOL_Obool), _1535651), _1535653)))))], (39190 ^ _779530) ^ [_1535710, _1535712, _1535714, _1535716, _1535718] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535710, _1535712), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1535710, tc_HOL_Obool)), _1535714), _1535716)), _1535718) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535710, _1535712), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535710, _1535712), _1535714), _1535718)), hAPP(hAPP(c_Product__Type_OSigma(_1535710, _1535712), _1535716), _1535718)))], (39192 ^ _779530) ^ [_1535793, _1535795, _1535797, _1535799, _1535801] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535793, _1535795), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1535793, tc_HOL_Obool)), _1535797), _1535799)), hAPP(c_COMBK(tc_fun(_1535795, tc_HOL_Obool), _1535793), _1535801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535793, _1535795), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535793, _1535795), _1535797), hAPP(c_COMBK(tc_fun(_1535795, tc_HOL_Obool), _1535793), _1535801))), hAPP(hAPP(c_Product__Type_OSigma(_1535793, _1535795), _1535799), hAPP(c_COMBK(tc_fun(_1535795, tc_HOL_Obool), _1535793), _1535801))))], (39194 ^ _779530) ^ [_1535903, _1535905, _1535907, _1535909, _1535911] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1535903, _1535905), _1535907), hAPP(hAPP(c_COMBS(_1535903, tc_fun(_1535905, tc_HOL_Obool), tc_fun(_1535905, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535905, tc_HOL_Obool), tc_fun(tc_fun(_1535905, tc_HOL_Obool), tc_fun(_1535905, tc_HOL_Obool)), _1535903), c_Groups_Ominus__class_Ominus(tc_fun(_1535905, tc_HOL_Obool))), _1535909)), _1535911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535903, _1535905), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1535903, _1535905), _1535907), _1535909)), hAPP(hAPP(c_Product__Type_OSigma(_1535903, _1535905), _1535907), _1535911)))], (39196 ^ _779530) ^ [_1536018, _1536020] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1536018, _1536020), c_Orderings_Otop__class_Otop(tc_fun(_1536018, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1536020, tc_HOL_Obool), _1536018), c_Orderings_Otop__class_Otop(tc_fun(_1536020, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1536018, _1536020), tc_HOL_Obool)))], (39198 ^ _779530) ^ [_1536106, _1536108, _1536110, _1536112, _1536114, _1536116] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536106, _1536108)), hAPP(hAPP(c_Product__Type_OPair(_1536106, _1536108), _1536110), _1536112)), hAPP(hAPP(c_Product__Type_OSigma(_1536106, _1536108), _1536114), _1536116))), 39201 ^ _779530 : [(39202 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536106), _1536110), _1536114)))], (39204 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536108), _1536112), hAPP(_1536116, _1536110))))]]], (39206 ^ _779530) ^ [_1536303, _1536305, _1536307, _1536309, _1536311, _1536313] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536303, _1536305)), hAPP(hAPP(c_Product__Type_OPair(_1536303, _1536305), _1536307), _1536309)), hAPP(hAPP(c_Product__Type_OSigma(_1536303, _1536305), _1536311), _1536313)))), hBOOL(hAPP(hAPP(c_member(_1536303), _1536307), _1536311)), hBOOL(hAPP(hAPP(c_member(_1536305), _1536309), hAPP(_1536313, _1536307)))], (39216 ^ _779530) ^ [_1536540, _1536542, _1536544, _1536546, _1536548, _1536550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536540, _1536542)), hAPP(hAPP(c_Product__Type_OPair(_1536540, _1536542), _1536544), _1536546)), hAPP(hAPP(c_Product__Type_OSigma(_1536540, _1536542), _1536548), _1536550))), -(hBOOL(hAPP(hAPP(c_member(_1536540), _1536544), _1536548)))], (39222 ^ _779530) ^ [_1536695, _1536697, _1536699, _1536701, _1536703, _1536705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536695, _1536697)), hAPP(hAPP(c_Product__Type_OPair(_1536695, _1536697), _1536699), _1536701)), hAPP(hAPP(c_Product__Type_OSigma(_1536695, _1536697), _1536703), _1536705))), -(hBOOL(hAPP(hAPP(c_member(_1536697), _1536701), hAPP(_1536705, _1536699))))], (39228 ^ _779530) ^ [_1536856, _1536858, _1536860, _1536862, _1536864, _1536866] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536856, _1536858)), hAPP(hAPP(c_Product__Type_OPair(_1536856, _1536858), _1536860), _1536862)), hAPP(hAPP(c_Product__Type_OSigma(_1536856, _1536858), _1536864), _1536866))), 39231 ^ _779530 : [(39232 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536856), _1536860), _1536864)))], (39234 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536858), _1536862), hAPP(_1536866, _1536860))))]]], (39236 ^ _779530) ^ [_1537061, _1537063, _1537065, _1537067] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1537061, _1537063)), hAPP(hAPP(c_Product__Type_OSigma(_1537061, _1537063), hAPP(hAPP(c_Set_Oinsert(_1537061), _1537065), c_Orderings_Obot__class_Obot(tc_fun(_1537061, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1537063, tc_HOL_Obool), _1537061), _1537067))) = hAPP(c_Finite__Set_Ocard(_1537063), _1537067))], (39238 ^ _779530) ^ [_1537134, _1537136, _1537138, _1537140, _1537142, _1537144] : [hBOOL(hAPP(hAPP(c_member(_1537134), _1537136), _1537138)), 39241 ^ _779530 : [(39242 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537140, _1537134), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537140, _1537134), _1537142), hAPP(c_COMBK(tc_fun(_1537134, tc_HOL_Obool), _1537140), _1537138))), hAPP(hAPP(c_Product__Type_OSigma(_1537140, _1537134), _1537144), hAPP(c_COMBK(tc_fun(_1537134, tc_HOL_Obool), _1537140), _1537138)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537140, tc_HOL_Obool)), _1537142), _1537144)))], (39248 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537140, tc_HOL_Obool)), _1537142), _1537144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537140, _1537134), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1537140, _1537134), _1537142), hAPP(c_COMBK(tc_fun(_1537134, tc_HOL_Obool), _1537140), _1537138))), hAPP(hAPP(c_Product__Type_OSigma(_1537140, _1537134), _1537144), hAPP(c_COMBK(tc_fun(_1537134, tc_HOL_Obool), _1537140), _1537138)))))]]], (39254 ^ _779530) ^ [_1537556, _1537558, _1537560, _1537562, _1537564, _1537566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537556, _1537558), tc_HOL_Obool)), _1537560), hAPP(hAPP(c_Product__Type_OSigma(_1537556, _1537558), _1537562), hAPP(c_COMBK(tc_fun(_1537558, tc_HOL_Obool), _1537556), _1537564)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537558, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1537556, _1537558, _1537560), _1537566)), _1537564)))], (39260 ^ _779530) ^ [_1537737, _1537739, _1537741, _1537743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1537737, _1537739)), hAPP(hAPP(c_Product__Type_OSigma(_1537737, _1537739), _1537741), hAPP(c_COMBK(tc_fun(_1537739, tc_HOL_Obool), _1537737), _1537743)))), -(_1537741 = c_Orderings_Obot__class_Obot(tc_fun(_1537737, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1537739), _1537743)))], (39270 ^ _779530) ^ [_1537901, _1537903, _1537905, _1537907] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1537901, _1537903)), hAPP(hAPP(c_Product__Type_OSigma(_1537901, _1537903), _1537905), hAPP(c_COMBK(tc_fun(_1537903, tc_HOL_Obool), _1537901), _1537907)))), -(_1537907 = c_Orderings_Obot__class_Obot(tc_fun(_1537903, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1537901), _1537905)))], (39280 ^ _779530) ^ [_1538065, _1538067, _1538069, _1538071] : [-(hAPP(c_Set_OCollect(tc_prod(_1538065, _1538067)), hAPP(c_Product__Type_Oprod_Oprod__case(_1538065, _1538067, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1538065, tc_fun(_1538067, tc_HOL_Obool), tc_fun(_1538067, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1538067, tc_HOL_Obool), tc_fun(_1538067, tc_HOL_Obool)), _1538065), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1538067)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538065), c_fconj), _1538069))), _1538071))) = hAPP(hAPP(c_Product__Type_OSigma(_1538065, _1538067), hAPP(c_Set_OCollect(_1538065), _1538069)), hAPP(hAPP(c_COMBB(tc_fun(_1538067, tc_HOL_Obool), tc_fun(_1538067, tc_HOL_Obool), _1538065), c_Set_OCollect(_1538067)), _1538071)))], (39282 ^ _779530) ^ [_1538190, _1538192, _1538194, _1538196] : [-(hAPP(c_Set_OCollect(tc_prod(_1538190, _1538192)), hAPP(c_Product__Type_Oprod_Oprod__case(_1538190, _1538192, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1538190, tc_fun(_1538192, tc_HOL_Obool), tc_fun(_1538192, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1538192, tc_HOL_Obool), tc_fun(_1538192, tc_HOL_Obool)), _1538190), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1538192)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538190), c_fconj), _1538194))), _1538196))) = hAPP(hAPP(c_Product__Type_OSigma(_1538190, _1538192), hAPP(c_Set_OCollect(_1538190), _1538194)), hAPP(c_COMBK(tc_fun(_1538192, tc_HOL_Obool), _1538190), hAPP(c_Set_OCollect(_1538192), _1538196))))], (39284 ^ _779530) ^ [_1538326, _1538328, _1538330, _1538332] : [_1538326 = c_Orderings_Obot__class_Obot(tc_fun(_1538328, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1538330, _1538328), _1538330, c_Product__Type_Ofst(_1538330, _1538328)), hAPP(hAPP(c_Product__Type_OSigma(_1538330, _1538328), _1538332), hAPP(c_COMBK(tc_fun(_1538328, tc_HOL_Obool), _1538330), _1538326))) = c_Orderings_Obot__class_Obot(tc_fun(_1538330, tc_HOL_Obool)))], (39290 ^ _779530) ^ [_1538483, _1538485, _1538487, _1538489] : [-(_1538483 = c_Orderings_Obot__class_Obot(tc_fun(_1538485, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1538487, _1538485), _1538487, c_Product__Type_Ofst(_1538487, _1538485)), hAPP(hAPP(c_Product__Type_OSigma(_1538487, _1538485), _1538489), hAPP(c_COMBK(tc_fun(_1538485, tc_HOL_Obool), _1538487), _1538483))) = _1538489)], (39296 ^ _779530) ^ [_1538576, _1538578, _1538580, _1538582] : [_1538576 = c_Orderings_Obot__class_Obot(tc_fun(_1538578, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1538578, _1538580), _1538580, c_Product__Type_Osnd(_1538578, _1538580)), hAPP(hAPP(c_Product__Type_OSigma(_1538578, _1538580), _1538576), hAPP(c_COMBK(tc_fun(_1538580, tc_HOL_Obool), _1538578), _1538582))) = c_Orderings_Obot__class_Obot(tc_fun(_1538580, tc_HOL_Obool)))], (39302 ^ _779530) ^ [_1538733, _1538735, _1538737, _1538739] : [-(_1538733 = c_Orderings_Obot__class_Obot(tc_fun(_1538735, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1538735, _1538737), _1538737, c_Product__Type_Osnd(_1538735, _1538737)), hAPP(hAPP(c_Product__Type_OSigma(_1538735, _1538737), _1538733), hAPP(c_COMBK(tc_fun(_1538737, tc_HOL_Obool), _1538735), _1538739))) = _1538739)], (39308 ^ _779530) ^ [_1538811, _1538813, _1538815, _1538817, _1538819, _1538821] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1538811, _1538813), hAPP(hAPP(c_Set_Oinsert(_1538811), _1538815), _1538817)), hAPP(c_COMBK(tc_fun(_1538813, tc_HOL_Obool), _1538811), hAPP(hAPP(c_Set_Oinsert(_1538813), _1538819), _1538821))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1538811, _1538813)), hAPP(hAPP(c_Product__Type_OPair(_1538811, _1538813), _1538815), _1538819)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538811, _1538813), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1538811, _1538813), _1538817), hAPP(c_COMBK(tc_fun(_1538813, tc_HOL_Obool), _1538811), hAPP(hAPP(c_Set_Oinsert(_1538813), _1538819), _1538821)))), hAPP(hAPP(c_Product__Type_OSigma(_1538811, _1538813), hAPP(hAPP(c_Set_Oinsert(_1538811), _1538815), _1538817)), hAPP(c_COMBK(tc_fun(_1538813, tc_HOL_Obool), _1538811), _1538821)))))], (39310 ^ _779530) ^ [_1538964, _1538966, _1538968, _1538970] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538964), _1538966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538964, _1538964), tc_HOL_Obool)), _1538968), hAPP(hAPP(c_Product__Type_OSigma(_1538964, _1538964), _1538966), hAPP(c_COMBK(tc_fun(_1538964, tc_HOL_Obool), _1538964), _1538966)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1538964, tc_HOL_Obool)), _1538970), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1538964), _1538966), _1538968))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1538964), _1538970)))], (39324 ^ _779530) ^ [_1539271, _1539273, _1539275, _1539277, _1539279, _1539281] : [-(hAPP(c_Set_Ovimage(_1539271, tc_prod(_1539273, _1539275), _1539277), hAPP(hAPP(c_Product__Type_OSigma(_1539273, _1539275), _1539279), hAPP(c_COMBK(tc_fun(_1539275, tc_HOL_Obool), _1539273), _1539281))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539271, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1539271, _1539273, hAPP(c_Fun_Ocomp(tc_prod(_1539273, _1539275), _1539273, _1539271, c_Product__Type_Ofst(_1539273, _1539275)), _1539277)), _1539279)), hAPP(c_Set_Ovimage(_1539271, _1539275, hAPP(c_Fun_Ocomp(tc_prod(_1539273, _1539275), _1539275, _1539271, c_Product__Type_Osnd(_1539273, _1539275)), _1539277)), _1539281)))], (39326 ^ _779530) ^ [_1539385, _1539387, _1539389, _1539391, _1539393, _1539395, _1539397, _1539399] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1539385, _1539387), tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1539385, _1539387), _1539393), hAPP(c_COMBK(tc_fun(_1539387, tc_HOL_Obool), _1539385), _1539395))), hAPP(c_Product__Type_Oprod_Oprod__case(_1539385, _1539387, tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1539385, tc_fun(_1539387, tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool))), tc_fun(_1539387, tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool)), tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool)), tc_fun(tc_fun(_1539387, tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool))), tc_fun(_1539387, tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool))), _1539385), c_COMBB(tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool)), tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool), _1539387)), hAPP(hAPP(c_COMBB(tc_fun(_1539389, tc_HOL_Obool), tc_fun(tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool)), tc_fun(tc_prod(_1539389, _1539391), tc_HOL_Obool)), _1539385), c_Product__Type_OSigma(_1539389, _1539391)), _1539397))), hAPP(hAPP(c_COMBB(tc_fun(_1539391, tc_HOL_Obool), tc_fun(_1539389, tc_fun(_1539391, tc_HOL_Obool)), _1539387), c_COMBK(tc_fun(_1539391, tc_HOL_Obool), _1539389)), _1539399)))) = hAPP(hAPP(c_Product__Type_OSigma(_1539389, _1539391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539385, tc_fun(_1539389, tc_HOL_Obool)), _1539393), _1539397)), hAPP(c_COMBK(tc_fun(_1539391, tc_HOL_Obool), _1539389), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539387, tc_fun(_1539391, tc_HOL_Obool)), _1539395), _1539399))))], (39328 ^ _779530) ^ [_1539659, _1539661, _1539663, _1539665] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1539659, _1539661), _1539663), _1539665) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539659, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), _1539663), hAPP(hAPP(c_COMBS(_1539659, tc_fun(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1539661, tc_HOL_Obool), tc_fun(tc_fun(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), _1539659), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), _1539665)), hAPP(hAPP(c_COMBC(_1539659, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539661, tc_fun(tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), _1539659), c_COMBC(_1539661, tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1539661, tc_prod(_1539659, _1539661)), tc_fun(_1539661, tc_fun(tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))), _1539659), hAPP(c_COMBB(tc_prod(_1539659, _1539661), tc_fun(tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool), tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool)), _1539661), c_Set_Oinsert(tc_prod(_1539659, _1539661)))), c_Product__Type_OPair(_1539659, _1539661)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1539659, _1539661), tc_HOL_Obool))))))], (39330 ^ _779530) ^ [_1539939, _1539941, _1539943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539939), _1539941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539939, _1539939), tc_HOL_Obool)), _1539943), hAPP(hAPP(c_Product__Type_OSigma(_1539939, _1539939), _1539941), hAPP(c_COMBK(tc_fun(_1539939, tc_HOL_Obool), _1539939), _1539941)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1539939, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1539939), _1539941), _1539943))))], (39340 ^ _779530) ^ [_1540172, _1540174, _1540176, _1540178, _1540180, _1540182, _1540184] : [class_Rings_Osemiring__0(_1540172), c_Fun_Oinj__on(tc_prod(_1540174, _1540176), _1540172, hAPP(c_Product__Type_Oprod_Oprod__case(_1540174, _1540176, _1540172), hAPP(hAPP(c_COMBC(_1540174, tc_fun(_1540176, _1540172), tc_fun(_1540176, _1540172)), hAPP(hAPP(c_COMBB(tc_fun(_1540172, _1540172), tc_fun(tc_fun(_1540176, _1540172), tc_fun(_1540176, _1540172)), _1540174), c_COMBB(_1540172, _1540172, _1540176)), hAPP(hAPP(c_COMBB(_1540172, tc_fun(_1540172, _1540172), _1540174), c_Groups_Otimes__class_Otimes(_1540172)), _1540178))), _1540180)), hAPP(hAPP(c_Product__Type_OSigma(_1540174, _1540176), _1540182), hAPP(c_COMBK(tc_fun(_1540176, tc_HOL_Obool), _1540174), _1540184))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1540172), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540174, _1540172), _1540178), _1540182)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540176, _1540172), _1540180), _1540184)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540172, _1540172), c_Fun_Oid(_1540172)), hAPP(c_Set_OCollect(_1540172), hAPP(hAPP(c_COMBB(tc_fun(_1540174, tc_HOL_Obool), tc_HOL_Obool, _1540172), c_HOL_OEx(_1540174)), hAPP(hAPP(c_COMBB(tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool)), tc_fun(_1540174, tc_HOL_Obool), _1540172), hAPP(c_COMBB(tc_fun(_1540176, tc_HOL_Obool), tc_HOL_Obool, _1540174), c_HOL_OEx(_1540176))), hAPP(hAPP(c_COMBC(_1540172, tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool)), tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540174, tc_fun(tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool))), tc_fun(tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool)), tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool))), _1540172), c_COMBS(_1540174, tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540174, tc_fun(_1540176, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1540174, tc_fun(tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool))), _1540172), hAPP(c_COMBB(tc_fun(_1540176, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool)), _1540174), c_COMBS(_1540176, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool)), tc_fun(_1540174, tc_fun(_1540176, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1540172), hAPP(c_COMBB(tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1540174), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540176), c_fconj))), hAPP(hAPP(c_COMBC(_1540172, tc_fun(_1540174, tc_fun(_1540176, _1540172)), tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1540176, _1540172), tc_fun(_1540176, tc_HOL_Obool)), tc_fun(tc_fun(_1540174, tc_fun(_1540176, _1540172)), tc_fun(_1540174, tc_fun(_1540176, tc_HOL_Obool))), _1540172), c_COMBB(tc_fun(_1540176, _1540172), tc_fun(_1540176, tc_HOL_Obool), _1540174)), hAPP(hAPP(c_COMBB(tc_fun(_1540172, tc_HOL_Obool), tc_fun(tc_fun(_1540176, _1540172), tc_fun(_1540176, tc_HOL_Obool)), _1540172), c_COMBB(_1540172, tc_HOL_Obool, _1540176)), c_fequal))), hAPP(hAPP(c_COMBC(_1540174, tc_fun(_1540176, _1540172), tc_fun(_1540176, _1540172)), hAPP(hAPP(c_COMBB(tc_fun(_1540172, _1540172), tc_fun(tc_fun(_1540176, _1540172), tc_fun(_1540176, _1540172)), _1540174), c_COMBB(_1540172, _1540172, _1540176)), hAPP(hAPP(c_COMBB(_1540172, tc_fun(_1540172, _1540172), _1540174), c_Groups_Otimes__class_Otimes(_1540172)), _1540178))), _1540180)))))), hAPP(hAPP(c_COMBC(_1540174, tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540176, tc_HOL_Obool), tc_fun(_1540176, tc_HOL_Obool)), _1540174), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540176)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540174), c_fconj), hAPP(hAPP(c_COMBC(_1540174, tc_fun(_1540174, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540174)), _1540182)))), hAPP(hAPP(c_COMBC(_1540176, tc_fun(_1540176, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540176)), _1540184))))))))], (39351 ^ _779530) ^ [_1541447, _1541449, _1541451, _1541453] : [-(c_Fun_Oinj__on(_1541447, tc_prod(_1541449, _1541447), 39349 ^ [_1541447, _1541449, _1541451, _1541453], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541449, tc_fun(_1541447, tc_HOL_Obool)), _1541451), _1541453)))], (39353 ^ _779530) ^ [_1541501, _1541503, _1541505, _1541507] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541503, _1541501), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1541501, tc_prod(_1541503, _1541501), 39349 ^ [_1541501, _1541503, _1541505, _1541507]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1541503, tc_fun(_1541501, tc_HOL_Obool)), _1541505), _1541507))), hAPP(hAPP(c_Product__Type_OSigma(_1541503, _1541501), _1541505), _1541507))))], (39355 ^ _779530) ^ [_1541587, _1541589, _1541591, _1541593, _1541595, _1541597] : [class_Groups_Ocomm__monoid__mult(_1541587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1541589), _1541591)), 39365 ^ _779530 : [(39366 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541589), 39364 ^ [_1541587, _1541589, _1541591, _1541593, _1541595, _1541597]), _1541591)))], (39368 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541593), hAPP(_1541595, 39364 ^ [_1541587, _1541589, _1541591, _1541593, _1541595, _1541597])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1541587, _1541589, c_Groups_Otimes__class_Otimes(_1541587)), hAPP(hAPP(c_COMBS(_1541589, tc_fun(_1541593, tc_HOL_Obool), _1541587), hAPP(hAPP(c_COMBC(_1541589, _1541587, tc_fun(tc_fun(_1541593, tc_HOL_Obool), _1541587)), hAPP(hAPP(c_COMBB(tc_fun(_1541593, _1541587), tc_fun(_1541587, tc_fun(tc_fun(_1541593, tc_HOL_Obool), _1541587)), _1541589), c_Finite__Set_Ofold__image(_1541587, _1541593, c_Groups_Otimes__class_Otimes(_1541587))), _1541597)), c_Groups_Oone__class_Oone(_1541587))), _1541595)), c_Groups_Oone__class_Oone(_1541587)), _1541591) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1541587, tc_prod(_1541589, _1541593), c_Groups_Otimes__class_Otimes(_1541587)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541589, _1541593, _1541587), _1541597)), c_Groups_Oone__class_Oone(_1541587)), hAPP(hAPP(c_Product__Type_OSigma(_1541589, _1541593), _1541591), _1541595)))], (39372 ^ _779530) ^ [_1542144, _1542146] : [-(hAPP(c_Set_Oimage(_1542144, _1542144, c_Fun_Oid(_1542144)), _1542146) = _1542146)], (39374 ^ _779530) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (39376 ^ _779530) ^ [_1542196, _1542198] : [-(c_Product__Type_Oapsnd(_1542196, _1542196, _1542198, c_Fun_Oid(_1542196)) = c_Fun_Oid(tc_prod(_1542198, _1542196)))], (39378 ^ _779530) ^ [_1542233, _1542235, _1542237] : [-(hAPP(c_Fun_Ocomp(_1542233, _1542233, _1542235, c_Fun_Oid(_1542233)), _1542237) = _1542237)], (39380 ^ _779530) ^ [_1542270, _1542272, _1542274] : [-(hAPP(c_Fun_Ocomp(_1542270, _1542272, _1542270, _1542274), c_Fun_Oid(_1542270)) = _1542274)], (39382 ^ _779530) ^ [_1542307, _1542309, _1542311, _1542313, _1542315, _1542317, _1542319] : [hAPP(c_Fun_Ocomp(_1542307, _1542309, _1542311, _1542313), _1542315) = hAPP(c_Fun_Ocomp(_1542309, _1542309, _1542311, c_Fun_Oid(_1542309)), _1542317), -(hAPP(_1542313, hAPP(_1542315, _1542319)) = hAPP(_1542317, _1542319))], (39388 ^ _779530) ^ [_1542448, _1542450] : [-(hAPP(c_Set_Ovimage(_1542448, _1542448, c_Fun_Oid(_1542448)), _1542450) = _1542450)], (39390 ^ _779530) ^ [_1542482, _1542484] : [-(hAPP(c_Fun_Oid(_1542482), _1542484) = _1542484)], (39392 ^ _779530) ^ [_1542512, _1542514] : [-(hAPP(c_Fun_Oid(_1542512), _1542514) = _1542514)], (39394 ^ _779530) ^ [_1542542, _1542544] : [-(c_Fun_Oinj__on(_1542542, _1542542, c_Fun_Oid(_1542542), _1542544))], (39396 ^ _779530) ^ [_1542571, _1542573] : [-(c_Product__Type_Oapfst(_1542571, _1542571, _1542573, c_Fun_Oid(_1542571)) = c_Fun_Oid(tc_prod(_1542571, _1542573)))], (39398 ^ _779530) ^ [_1542608] : [-(hAPP(c_Set_Oimage(_1542608, _1542608, c_Fun_Oid(_1542608)), c_Orderings_Otop__class_Otop(tc_fun(_1542608, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1542608, tc_HOL_Obool)))], (39400 ^ _779530) ^ [_1542650, _1542652, _1542654, _1542656] : [c_Finite__Set_Ofolding(_1542650, _1542652, _1542654, _1542656), -(hAPP(_1542656, c_Orderings_Obot__class_Obot(tc_fun(_1542650, tc_HOL_Obool))) = c_Fun_Oid(_1542652))], (39406 ^ _779530) ^ [_1542755, _1542757] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1542755, _1542757, tc_prod(_1542755, _1542757)), c_Product__Type_OPair(_1542755, _1542757)) = c_Fun_Oid(tc_prod(_1542755, _1542757)))], (39408 ^ _779530) ^ [_1542798, _1542800, _1542802, _1542804] : [class_Groups_Ocomm__monoid__add(_1542798), c_Fun_Oinj__on(_1542800, _1542798, _1542802, _1542804), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1542800, _1542798), _1542802), _1542804) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1542798, _1542798), c_Fun_Oid(_1542798)), hAPP(c_Set_Oimage(_1542800, _1542798, _1542802), _1542804)))], (39418 ^ _779530) ^ [_1542991, _1542993, _1542995, _1542997] : [class_Groups_Ocomm__monoid__mult(_1542991), c_Fun_Oinj__on(_1542993, _1542991, _1542995, _1542997), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1542993, _1542991), _1542995), _1542997) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1542991, _1542991), c_Fun_Oid(_1542991)), hAPP(c_Set_Oimage(_1542993, _1542991, _1542995), _1542997)))], (39428 ^ _779530) ^ [_1543184, _1543186, _1543188, _1543190, _1543192, _1543194] : [class_Groups_Ocomm__monoid__mult(_1543184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543186), _1543188)), 39438 ^ _779530 : [(39439 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543186), 39437 ^ [_1543184, _1543186, _1543188, _1543190, _1543192, _1543194]), _1543188)))], (39441 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543190), hAPP(_1543192, 39437 ^ [_1543184, _1543186, _1543188, _1543190, _1543192, _1543194])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1543186, _1543184), hAPP(hAPP(c_COMBS(_1543186, tc_fun(_1543190, tc_HOL_Obool), _1543184), hAPP(hAPP(c_COMBB(tc_fun(_1543190, _1543184), tc_fun(tc_fun(_1543190, tc_HOL_Obool), _1543184), _1543186), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1543190, _1543184)), _1543194)), _1543192)), _1543188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1543186, _1543190), _1543184), hAPP(c_Product__Type_Oprod_Oprod__case(_1543186, _1543190, _1543184), _1543194)), hAPP(hAPP(c_Product__Type_OSigma(_1543186, _1543190), _1543188), _1543192)))], (39445 ^ _779530) ^ [_1543661, _1543663, _1543665, _1543667, _1543669, _1543671] : [class_Groups_Ocomm__monoid__add(_1543661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543663), _1543665)), 39455 ^ _779530 : [(39456 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543663), 39454 ^ [_1543661, _1543663, _1543665, _1543667, _1543669, _1543671]), _1543665)))], (39458 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543667), hAPP(_1543669, 39454 ^ [_1543661, _1543663, _1543665, _1543667, _1543669, _1543671])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543663, _1543661), hAPP(hAPP(c_COMBS(_1543663, tc_fun(_1543667, tc_HOL_Obool), _1543661), hAPP(hAPP(c_COMBB(tc_fun(_1543667, _1543661), tc_fun(tc_fun(_1543667, tc_HOL_Obool), _1543661), _1543663), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543667, _1543661)), _1543671)), _1543669)), _1543665) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1543663, _1543667), _1543661), hAPP(c_Product__Type_Oprod_Oprod__case(_1543663, _1543667, _1543661), _1543671)), hAPP(hAPP(c_Product__Type_OSigma(_1543663, _1543667), _1543665), _1543669)))], (39462 ^ _779530) ^ [_1544138, _1544140, _1544142, _1544144] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544138), _1544140)), 39468 ^ _779530 : [(39469 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544138), 39467 ^ [_1544138, _1544140, _1544142, _1544144]), _1544140)))], (39471 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544142), hAPP(_1544144, 39467 ^ [_1544138, _1544140, _1544142, _1544144])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1544138, _1544142)), hAPP(hAPP(c_Product__Type_OSigma(_1544138, _1544142), _1544140), _1544144)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1544138, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1544142, tc_HOL_Obool), tc_Nat_Onat, _1544138), c_Finite__Set_Ocard(_1544142)), _1544144)), _1544140))], (39475 ^ _779530) ^ [_1544475, _1544477, _1544479, _1544481] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544475), _1544477)), 39481 ^ _779530 : [(39482 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544475), 39480 ^ [_1544475, _1544477, _1544479, _1544481]), _1544477)))], (39484 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1544479), hAPP(_1544481, 39480 ^ [_1544475, _1544477, _1544479, _1544481])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544475, _1544479)), hAPP(hAPP(c_Product__Type_OSigma(_1544475, _1544479), _1544477), _1544481))))], (39488 ^ _779530) ^ [_1544762, _1544764, _1544766, _1544768, _1544770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544762, _1544764)), _1544766), hAPP(hAPP(c_Product__Type_OSigma(_1544762, _1544764), _1544768), _1544770))), 39492 ^ _779530 : [(39493 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544762), 39491 ^ [_1544762, _1544764, _1544766, _1544768, _1544770]), _1544768)))], (39496 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544764), 39494 ^ [_1544762, _1544764, _1544766, _1544768, _1544770]), hAPP(_1544770, 39491 ^ [_1544762, _1544764, _1544766, _1544768, _1544770]))))], (39498 ^ _779530) ^ [] : [-(_1544766 = hAPP(hAPP(c_Product__Type_OPair(_1544762, _1544764), 39491 ^ [_1544762, _1544764, _1544766, _1544768, _1544770]), 39494 ^ [_1544762, _1544764, _1544766, _1544768, _1544770]))]]], (39500 ^ _779530) ^ [_1545064, _1545066, _1545068, _1545070, _1545072, _1545074] : [hAPP(c_Set_Oimage(_1545064, _1545066, _1545068), c_Orderings_Otop__class_Otop(tc_fun(_1545064, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545066, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1545070, _1545072, _1545074), c_Orderings_Otop__class_Otop(tc_fun(_1545070, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1545072, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1545064, _1545070), tc_prod(_1545066, _1545072), c_Product__Type_Omap__pair(_1545064, _1545066, _1545070, _1545072, _1545068, _1545074)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1545064, _1545070), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1545066, _1545072), tc_HOL_Obool)))], (39510 ^ _779530) ^ [_1545349, _1545351, _1545353, _1545355, _1545357, _1545359, _1545361, _1545363, _1545365] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545349, _1545351)), hAPP(hAPP(c_Product__Type_OPair(_1545349, _1545351), _1545353), _1545355)), _1545357)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545359, _1545361)), hAPP(hAPP(c_Product__Type_OPair(_1545359, _1545361), hAPP(_1545363, _1545353)), hAPP(_1545365, _1545355))), hAPP(c_Set_Oimage(tc_prod(_1545349, _1545351), tc_prod(_1545359, _1545361), c_Product__Type_Omap__pair(_1545349, _1545359, _1545351, _1545361, _1545363, _1545365)), _1545357))))], (39516 ^ _779530) ^ [_1545568, _1545570, _1545572, _1545574, _1545576, _1545578, _1545580] : [-(hAPP(c_Product__Type_Osnd(_1545568, _1545570), hAPP(c_Product__Type_Omap__pair(_1545572, _1545568, _1545574, _1545570, _1545576, _1545578), _1545580)) = hAPP(_1545578, hAPP(c_Product__Type_Osnd(_1545572, _1545574), _1545580)))], (39518 ^ _779530) ^ [_1545628, _1545630, _1545632, _1545634, _1545636, _1545638, _1545640] : [-(hAPP(c_Product__Type_Ofst(_1545628, _1545630), hAPP(c_Product__Type_Omap__pair(_1545632, _1545628, _1545634, _1545630, _1545636, _1545638), _1545640)) = hAPP(_1545636, hAPP(c_Product__Type_Ofst(_1545632, _1545634), _1545640)))], (39520 ^ _779530) ^ [_1545688, _1545690, _1545692, _1545694, _1545696, _1545698, _1545700, _1545702] : [-(hAPP(c_Product__Type_Omap__pair(_1545688, _1545690, _1545692, _1545694, _1545696, _1545698), hAPP(hAPP(c_Product__Type_OPair(_1545688, _1545692), _1545700), _1545702)) = hAPP(hAPP(c_Product__Type_OPair(_1545690, _1545694), hAPP(_1545696, _1545700)), hAPP(_1545698, _1545702)))], (39522 ^ _779530) ^ [_1545759, _1545761, _1545763] : [-(hAPP(c_Product__Type_Omap__pair(_1545759, _1545759, _1545761, _1545761, c_COMBI(_1545759), c_COMBI(_1545761)), _1545763) = _1545763)], (39524 ^ _779530) ^ [_1545800, _1545802, _1545804, _1545806, _1545808, _1545810, _1545812, _1545814, _1545816, _1545818, _1545820] : [-(hAPP(c_Product__Type_Omap__pair(_1545800, _1545802, _1545804, _1545806, _1545808, _1545810), hAPP(c_Product__Type_Omap__pair(_1545812, _1545800, _1545814, _1545804, _1545816, _1545818), _1545820)) = hAPP(c_Product__Type_Omap__pair(_1545812, _1545802, _1545814, _1545806, hAPP(c_Fun_Ocomp(_1545800, _1545802, _1545812, _1545808), _1545816), hAPP(c_Fun_Ocomp(_1545804, _1545806, _1545814, _1545810), _1545818)), _1545820))], (39526 ^ _779530) ^ [_1545889, _1545891, _1545893, _1545895, _1545897, _1545899, _1545901, _1545903, _1545905, _1545907] : [-(c_Product__Type_Omap__pair(_1545889, _1545891, _1545893, _1545895, hAPP(c_Fun_Ocomp(_1545897, _1545891, _1545889, _1545899), _1545901), hAPP(c_Fun_Ocomp(_1545903, _1545895, _1545893, _1545905), _1545907)) = hAPP(c_Fun_Ocomp(tc_prod(_1545897, _1545903), tc_prod(_1545891, _1545895), tc_prod(_1545889, _1545893), c_Product__Type_Omap__pair(_1545897, _1545891, _1545903, _1545895, _1545899, _1545905)), c_Product__Type_Omap__pair(_1545889, _1545897, _1545893, _1545903, _1545901, _1545907)))], (39528 ^ _779530) ^ [_1545984, _1545986, _1545988, _1545990, _1545992, _1545994, _1545996, _1545998, _1546000, _1546002] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1545984, _1545986), tc_prod(_1545988, _1545990), tc_prod(_1545992, _1545994), c_Product__Type_Omap__pair(_1545984, _1545988, _1545986, _1545990, _1545996, _1545998)), c_Product__Type_Omap__pair(_1545992, _1545984, _1545994, _1545986, _1546000, _1546002)) = c_Product__Type_Omap__pair(_1545992, _1545988, _1545994, _1545990, hAPP(c_Fun_Ocomp(_1545984, _1545988, _1545992, _1545996), _1546000), hAPP(c_Fun_Ocomp(_1545986, _1545990, _1545994, _1545998), _1546002)))], (39530 ^ _779530) ^ [_1546079, _1546081, _1546083, _1546085, _1546087, _1546089] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1546079, _1546081), _1546079, tc_prod(_1546083, _1546085), c_Product__Type_Ofst(_1546079, _1546081)), c_Product__Type_Omap__pair(_1546083, _1546079, _1546085, _1546081, _1546087, _1546089)) = hAPP(c_Fun_Ocomp(_1546083, _1546079, tc_prod(_1546083, _1546085), _1546087), c_Product__Type_Ofst(_1546083, _1546085)))], (39532 ^ _779530) ^ [_1546150, _1546152, _1546154, _1546156, _1546158, _1546160] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1546150, _1546152), _1546152, tc_prod(_1546154, _1546156), c_Product__Type_Osnd(_1546150, _1546152)), c_Product__Type_Omap__pair(_1546154, _1546150, _1546156, _1546152, _1546158, _1546160)) = hAPP(c_Fun_Ocomp(_1546156, _1546152, tc_prod(_1546154, _1546156), _1546160), c_Product__Type_Osnd(_1546154, _1546156)))], (39534 ^ _779530) ^ [_1546221, _1546223] : [-(c_Product__Type_Omap__pair(_1546221, _1546221, _1546223, _1546223, c_COMBI(_1546221), c_COMBI(_1546223)) = c_Fun_Oid(tc_prod(_1546221, _1546223)))], (39536 ^ _779530) ^ [_1546262, _1546264, _1546266, _1546268] : [-(c_Product__Type_Oapsnd(_1546262, _1546264, _1546266, _1546268) = c_Product__Type_Omap__pair(_1546266, _1546266, _1546262, _1546264, c_Fun_Oid(_1546266), _1546268))], (39538 ^ _779530) ^ [_1546305, _1546307, _1546309, _1546311] : [-(c_Product__Type_Oapfst(_1546305, _1546307, _1546309, _1546311) = c_Product__Type_Omap__pair(_1546305, _1546307, _1546309, _1546309, _1546311, c_Fun_Oid(_1546309)))], (39540 ^ _779530) ^ [_1546348, _1546350] : [-(c_Product__Type_Omap__pair(_1546348, _1546348, _1546350, _1546350, c_Fun_Oid(_1546348), c_Fun_Oid(_1546350)) = c_Fun_Oid(tc_prod(_1546348, _1546350)))], (39542 ^ _779530) ^ [_1546389, _1546391, _1546393, _1546395, _1546397, _1546399] : [-(c_Product__Type_Omap__pair(_1546389, _1546391, _1546393, _1546395, _1546397, _1546399) = hAPP(c_Product__Type_Oprod_Oprod__case(_1546389, _1546393, tc_prod(_1546391, _1546395)), hAPP(hAPP(c_COMBC(_1546389, tc_fun(_1546393, _1546395), tc_fun(_1546393, tc_prod(_1546391, _1546395))), hAPP(hAPP(c_COMBB(tc_fun(_1546395, tc_prod(_1546391, _1546395)), tc_fun(tc_fun(_1546393, _1546395), tc_fun(_1546393, tc_prod(_1546391, _1546395))), _1546389), c_COMBB(_1546395, tc_prod(_1546391, _1546395), _1546393)), hAPP(hAPP(c_COMBB(_1546391, tc_fun(_1546395, tc_prod(_1546391, _1546395)), _1546389), c_Product__Type_OPair(_1546391, _1546395)), _1546397))), _1546399)))], (39544 ^ _779530) ^ [_1546512, _1546514, _1546516, _1546518, _1546520, _1546522, _1546524, _1546526, _1546528, _1546530] : [hAPP(c_Set_Oimage(_1546512, _1546514, _1546516), _1546518) = _1546520, hAPP(c_Set_Oimage(_1546522, _1546524, _1546526), _1546528) = _1546530, -(hAPP(c_Set_Oimage(tc_prod(_1546512, _1546522), tc_prod(_1546514, _1546524), c_Product__Type_Omap__pair(_1546512, _1546514, _1546522, _1546524, _1546516, _1546526)), hAPP(hAPP(c_Product__Type_OSigma(_1546512, _1546522), _1546518), hAPP(c_COMBK(tc_fun(_1546522, tc_HOL_Obool), _1546512), _1546528))) = hAPP(hAPP(c_Product__Type_OSigma(_1546514, _1546524), _1546520), hAPP(c_COMBK(tc_fun(_1546524, tc_HOL_Obool), _1546514), _1546530)))], (39554 ^ _779530) ^ [_1546813, _1546815, _1546817, _1546819] : [c_Wellfounded_Owf(_1546813, _1546815), c_Fun_Oinj__on(_1546813, _1546817, _1546819, c_Orderings_Otop__class_Otop(tc_fun(_1546813, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1546817, hAPP(c_Set_Oimage(tc_prod(_1546813, _1546813), tc_prod(_1546817, _1546817), c_Product__Type_Omap__pair(_1546813, _1546817, _1546813, _1546817, _1546819, _1546819)), _1546815)))], (39564 ^ _779530) ^ [_1547004, _1547006, _1547008, _1547010, _1547012, _1547014, _1547016, _1547018] : [c_Fun_Oinj__on(_1547004, _1547006, _1547008, _1547010), c_Fun_Oinj__on(_1547012, _1547014, _1547016, _1547018), -(c_Fun_Oinj__on(tc_prod(_1547004, _1547012), tc_prod(_1547006, _1547014), c_Product__Type_Omap__pair(_1547004, _1547006, _1547012, _1547014, _1547008, _1547016), hAPP(hAPP(c_Product__Type_OSigma(_1547004, _1547012), _1547010), hAPP(c_COMBK(tc_fun(_1547012, tc_HOL_Obool), _1547004), _1547018))))], (39574 ^ _779530) ^ [_1547231, _1547233, _1547235, _1547237, _1547239, _1547241, _1547243, _1547245] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547231, _1547233)), _1547235), hAPP(c_Set_Oimage(tc_prod(_1547237, _1547239), tc_prod(_1547231, _1547233), c_Product__Type_Omap__pair(_1547237, _1547231, _1547239, _1547233, _1547241, _1547243)), _1547245))), 39579 ^ _779530 : [(39580 ^ _779530) ^ [] : [-(_1547235 = hAPP(hAPP(c_Product__Type_OPair(_1547231, _1547233), hAPP(_1547241, 39577 ^ [_1547231, _1547233, _1547235, _1547237, _1547239, _1547241, _1547243, _1547245])), hAPP(_1547243, 39578 ^ [_1547231, _1547233, _1547235, _1547237, _1547239, _1547241, _1547243, _1547245])))], (39582 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547237, _1547239)), hAPP(hAPP(c_Product__Type_OPair(_1547237, _1547239), 39577 ^ [_1547231, _1547233, _1547235, _1547237, _1547239, _1547241, _1547243, _1547245]), 39578 ^ [_1547231, _1547233, _1547235, _1547237, _1547239, _1547241, _1547243, _1547245])), _1547245)))]]], (39584 ^ _779530) ^ [_1547582, _1547584, _1547586] : [c_Relation_Orefl__on(_1547582, _1547584, _1547586), 39587 ^ _779530 : [(39588 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547582, _1547582), tc_HOL_Obool)), _1547586), hAPP(hAPP(c_Product__Type_OSigma(_1547582, _1547582), _1547584), hAPP(c_COMBK(tc_fun(_1547582, tc_HOL_Obool), _1547582), _1547584)))))], (39590 ^ _779530) ^ [_1547764] : [hBOOL(hAPP(hAPP(c_member(_1547582), _1547764), _1547584)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547582, _1547582)), hAPP(hAPP(c_Product__Type_OPair(_1547582, _1547582), _1547764), _1547764)), _1547586)))]]], (39596 ^ _779530) ^ [_1547899, _1547901, _1547903] : [-(c_Relation_Orefl__on(_1547899, _1547901, _1547903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547899, _1547899), tc_HOL_Obool)), _1547903), hAPP(hAPP(c_Product__Type_OSigma(_1547899, _1547899), _1547901), hAPP(c_COMBK(tc_fun(_1547899, tc_HOL_Obool), _1547899), _1547901)))), 39602 ^ _779530 : [(39603 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547899), 39601 ^ [_1547899, _1547901, _1547903]), _1547901)))], (39605 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547899, _1547899)), hAPP(hAPP(c_Product__Type_OPair(_1547899, _1547899), 39601 ^ [_1547899, _1547901, _1547903]), 39601 ^ [_1547899, _1547901, _1547903])), _1547903))]]], (39609 ^ _779530) ^ [_1548248, _1548250, _1548252] : [39611 ^ _779530 : [(39612 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39610 ^ [_1548248, _1548250, _1548252]), _1548248)))], (39614 ^ _779530) ^ [] : [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(_1548250, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 39610 ^ [_1548248, _1548250, _1548252]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1548250, 39610 ^ [_1548248, _1548250, _1548252])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1548250, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1548252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1548252), hAPP(_1548250, _1548248))), 39624 ^ _779530 : [(39625 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 39623 ^ [_1548248, _1548250, _1548252]), _1548248)))], (39627 ^ _779530) ^ [] : [-(hAPP(_1548250, 39623 ^ [_1548248, _1548250, _1548252]) = _1548252)]]], (39629 ^ _779530) ^ [_1548698, _1548700] : [-(c_Relation_Orefl__on(_1548698, _1548700, c_Relation_OId__on(_1548698, _1548700)))], (39631 ^ _779530) ^ [_1548727] : [-(c_Relation_Orefl__on(_1548727, c_Orderings_Obot__class_Obot(tc_fun(_1548727, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1548727, _1548727), tc_HOL_Obool))))], (39633 ^ _779530) ^ [_1548764, _1548766, _1548768, _1548770, _1548772] : [c_Relation_Orefl__on(_1548764, _1548766, _1548768), c_Relation_Orefl__on(_1548764, _1548770, _1548772), -(c_Relation_Orefl__on(_1548764, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1548764, tc_HOL_Obool)), _1548766), _1548770), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1548764, _1548764), tc_HOL_Obool)), _1548768), _1548772)))], (39643 ^ _779530) ^ [_1548961, _1548963, _1548965, _1548967, _1548969] : [c_Relation_Orefl__on(_1548961, _1548963, _1548965), c_Relation_Orefl__on(_1548961, _1548967, _1548969), -(c_Relation_Orefl__on(_1548961, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1548961, tc_HOL_Obool)), _1548963), _1548967), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1548961, _1548961), tc_HOL_Obool)), _1548965), _1548969)))], (39653 ^ _779530) ^ [_1549158, _1549160, _1549162, _1549164, _1549166] : [c_Relation_Orefl__on(_1549158, _1549160, _1549162), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549158, _1549158)), hAPP(hAPP(c_Product__Type_OPair(_1549158, _1549158), _1549164), _1549166)), _1549162)), -(hBOOL(hAPP(hAPP(c_member(_1549158), _1549166), _1549160)))], (39663 ^ _779530) ^ [_1549353, _1549355, _1549357, _1549359, _1549361] : [c_Relation_Orefl__on(_1549353, _1549355, _1549357), hBOOL(hAPP(hAPP(c_member(tc_prod(_1549353, _1549353)), hAPP(hAPP(c_Product__Type_OPair(_1549353, _1549353), _1549359), _1549361)), _1549357)), -(hBOOL(hAPP(hAPP(c_member(_1549353), _1549359), _1549355)))], (39673 ^ _779530) ^ [_1549548, _1549550, _1549552, _1549554] : [c_Relation_Orefl__on(_1549548, _1549550, _1549552), hBOOL(hAPP(hAPP(c_member(_1549548), _1549554), _1549550)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549548, _1549548)), hAPP(hAPP(c_Product__Type_OPair(_1549548, _1549548), _1549554), _1549554)), _1549552)))], (39683 ^ _779530) ^ [_1549754, _1549756] : [c_Predicate_Oreflp(_1549754, _1549756), -(c_Relation_Orefl__on(_1549754, c_Orderings_Otop__class_Otop(tc_fun(_1549754, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1549754, _1549754)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549754, _1549754, tc_HOL_Obool), _1549756))))], (39689 ^ _779530) ^ [_1549869, _1549871] : [c_Relation_Orefl__on(_1549869, c_Orderings_Otop__class_Otop(tc_fun(_1549869, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1549869, _1549869)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549869, _1549869, tc_HOL_Obool), _1549871))), -(c_Predicate_Oreflp(_1549869, _1549871))], (39695 ^ _779530) ^ [_1549990, _1549992, _1549994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549990, _1549990), tc_HOL_Obool)), _1549992), hAPP(hAPP(c_Product__Type_OSigma(_1549990, _1549990), _1549994), hAPP(c_COMBK(tc_fun(_1549990, tc_HOL_Obool), _1549990), _1549994)))), 39701 ^ _779530 : [(39702 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549990), 39700 ^ [_1549990, _1549992, _1549994]), _1549994)))], (39704 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549990, _1549990)), hAPP(hAPP(c_Product__Type_OPair(_1549990, _1549990), 39700 ^ [_1549990, _1549992, _1549994]), 39700 ^ [_1549990, _1549992, _1549994])), _1549992))]], -(c_Relation_Orefl__on(_1549990, _1549994, _1549992))], (39708 ^ _779530) ^ [_1550337, _1550339, _1550341] : [class_Groups_Oab__semigroup__mult(_1550337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550337), _1550339)), -(_1550339 = c_Orderings_Obot__class_Obot(tc_fun(_1550337, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550337), _1550341)), -(_1550341 = c_Orderings_Obot__class_Obot(tc_fun(_1550337, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1550337, tc_HOL_Obool)), _1550339), _1550341) = c_Orderings_Obot__class_Obot(tc_fun(_1550337, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1550337, c_Groups_Otimes__class_Otimes(_1550337)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1550337, tc_HOL_Obool)), _1550339), _1550341)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1550337), hAPP(c_Finite__Set_Ofold1(_1550337, c_Groups_Otimes__class_Otimes(_1550337)), _1550339)), hAPP(c_Finite__Set_Ofold1(_1550337, c_Groups_Otimes__class_Otimes(_1550337)), _1550341)))], (39734 ^ _779530) ^ [_1550844, _1550846, _1550848] : [c_Predicate_Oreflp(_1550844, _1550846), -(hBOOL(hAPP(hAPP(_1550846, _1550848), _1550848)))], (39740 ^ _779530) ^ [_1550933, _1550935, _1550937, _1550939] : [_1550933 = c_Finite__Set_Ofold1(_1550935, _1550937), -(hAPP(_1550933, hAPP(hAPP(c_Set_Oinsert(_1550935), _1550939), c_Orderings_Obot__class_Obot(tc_fun(_1550935, tc_HOL_Obool)))) = _1550939)], (39746 ^ _779530) ^ [_1551052, _1551054, _1551056] : [-(hAPP(c_Finite__Set_Ofold1(_1551052, _1551054), hAPP(hAPP(c_Set_Oinsert(_1551052), _1551056), c_Orderings_Obot__class_Obot(tc_fun(_1551052, tc_HOL_Obool)))) = _1551056)], (39748 ^ _779530) ^ [_1551098, _1551100, _1551102, _1551104] : [c_Finite__Set_Ofolding__one(_1551098, _1551100, _1551102), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551098), _1551104)), -(hAPP(_1551102, _1551104) = hAPP(c_Finite__Set_Ofold1(_1551098, _1551100), _1551104))], (39758 ^ _779530) ^ [_1551263, _1551265, _1551267] : [-(hAPP(c_Finite__Set_Ofold1(_1551263, _1551265), _1551267) = c_HOL_OThe(_1551263, c_Finite__Set_Ofold1Set(_1551263, _1551265, _1551267)))], (39760 ^ _779530) ^ [_1551303, _1551305] : [class_Lattices_Olattice(_1551303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551303), _1551305)), -(c_Big__Operators_Olattice__class_OSup__fin(_1551303, _1551305) = hAPP(c_Finite__Set_Ofold1(_1551303, c_Lattices_Osemilattice__sup__class_Osup(_1551303)), _1551305))], (39770 ^ _779530) ^ [_1551460, _1551462] : [class_Lattices_Olattice(_1551460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551460), _1551462)), -(c_Big__Operators_Olattice__class_OInf__fin(_1551460, _1551462) = hAPP(c_Finite__Set_Ofold1(_1551460, c_Lattices_Osemilattice__inf__class_Oinf(_1551460)), _1551462))], (39780 ^ _779530) ^ [_1551617, _1551619] : [class_Orderings_Olinorder(_1551617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551617), _1551619)), -(c_Big__Operators_Olinorder__class_OMin(_1551617, _1551619) = hAPP(c_Finite__Set_Ofold1(_1551617, c_Orderings_Oord__class_Omin(_1551617)), _1551619))], (39790 ^ _779530) ^ [_1551774, _1551776] : [class_Orderings_Olinorder(_1551774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551774), _1551776)), -(c_Big__Operators_Olinorder__class_OMax(_1551774, _1551776) = hAPP(c_Finite__Set_Ofold1(_1551774, c_Orderings_Oord__class_Omax(_1551774)), _1551776))], (39800 ^ _779530) ^ [_1551931, _1551933] : [class_Orderings_Olinorder(_1551931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551931), _1551933)), -(c_Big__Operators_Olattice_OInf__fin(_1551931, c_Orderings_Oord__class_Omin(_1551931), _1551933) = hAPP(c_Finite__Set_Ofold1(_1551931, c_Orderings_Oord__class_Omin(_1551931)), _1551933))], (39810 ^ _779530) ^ [_1552094, _1552096] : [class_Orderings_Olinorder(_1552094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552094), _1552096)), -(c_Big__Operators_Olattice_OSup__fin(_1552094, c_Orderings_Oord__class_Omax(_1552094), _1552096) = hAPP(c_Finite__Set_Ofold1(_1552094, c_Orderings_Oord__class_Omax(_1552094)), _1552096))], (39820 ^ _779530) ^ [_1552257, _1552259, _1552261] : [class_Lattices_Osemilattice__inf(_1552257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552257), _1552259)), hBOOL(hAPP(hAPP(c_member(_1552257), _1552261), _1552259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552257), hAPP(c_Finite__Set_Ofold1(_1552257, c_Lattices_Osemilattice__inf__class_Oinf(_1552257)), _1552259)), _1552261)))], (39834 ^ _779530) ^ [_1552494, _1552496, _1552498] : [class_Lattices_Osemilattice__inf(_1552494), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552494), _1552496)), -(_1552496 = c_Orderings_Obot__class_Obot(tc_fun(_1552494, tc_HOL_Obool))), 39845 ^ _779530 : [(39856 ^ _779530) ^ [] : [39858 ^ _779530 : [(39859 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552494), 39857 ^ [_1552494, _1552496, _1552498]), _1552496)))], (39861 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552494), _1552498), 39857 ^ [_1552494, _1552496, _1552498]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552494), _1552498), hAPP(c_Finite__Set_Ofold1(_1552494, c_Lattices_Osemilattice__inf__class_Oinf(_1552494)), _1552496))))], (39846 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552494), _1552498), hAPP(c_Finite__Set_Ofold1(_1552494, c_Lattices_Osemilattice__inf__class_Oinf(_1552494)), _1552496))), 39849 ^ _779530 : [(39850 ^ _779530) ^ [_1552787] : [hBOOL(hAPP(hAPP(c_member(_1552494), _1552787), _1552496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552494), _1552498), _1552787)))]]]]], (39865 ^ _779530) ^ [_1553072, _1553074, _1553076] : [class_Orderings_Olinorder(_1553072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553072), _1553074)), hBOOL(hAPP(hAPP(c_member(_1553072), _1553076), _1553074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553072), hAPP(c_Finite__Set_Ofold1(_1553072, c_Orderings_Oord__class_Omin(_1553072)), _1553074)), _1553076)))], (39879 ^ _779530) ^ [_1553309, _1553311, _1553313] : [class_Lattices_Oab__semigroup__idem__mult(_1553309), -(_1553311 = c_Orderings_Obot__class_Obot(tc_fun(_1553309, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553309), _1553311)), -(hAPP(c_Finite__Set_Ofold1(_1553309, c_Groups_Otimes__class_Otimes(_1553309)), hAPP(hAPP(c_Set_Oinsert(_1553309), _1553313), _1553311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1553309), _1553313), hAPP(c_Finite__Set_Ofold1(_1553309, c_Groups_Otimes__class_Otimes(_1553309)), _1553311)))], (39893 ^ _779530) ^ [_1553579, _1553581, _1553583] : [class_Orderings_Olinorder(_1553579), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553579), _1553581)), -(_1553581 = c_Orderings_Obot__class_Obot(tc_fun(_1553579, tc_HOL_Obool))), 39904 ^ _779530 : [(39915 ^ _779530) ^ [] : [39917 ^ _779530 : [(39918 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553579), 39916 ^ [_1553579, _1553581, _1553583]), _1553581)))], (39920 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553579), _1553583), 39916 ^ [_1553579, _1553581, _1553583]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553579), _1553583), hAPP(c_Finite__Set_Ofold1(_1553579, c_Orderings_Oord__class_Omin(_1553579)), _1553581))))], (39905 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553579), _1553583), hAPP(c_Finite__Set_Ofold1(_1553579, c_Orderings_Oord__class_Omin(_1553579)), _1553581))), 39908 ^ _779530 : [(39909 ^ _779530) ^ [_1553872] : [hBOOL(hAPP(hAPP(c_member(_1553579), _1553872), _1553581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1553579), _1553583), _1553872)))]]]]], (39924 ^ _779530) ^ [_1554157, _1554159, _1554161] : [class_Orderings_Olinorder(_1554157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554157), _1554159)), -(_1554159 = c_Orderings_Obot__class_Obot(tc_fun(_1554157, tc_HOL_Obool))), 39935 ^ _779530 : [(39936 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554157), hAPP(c_Finite__Set_Ofold1(_1554157, c_Orderings_Oord__class_Omin(_1554157)), _1554159)), _1554161)), 39940 ^ _779530 : [(39941 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554157), 39939 ^ [_1554157, _1554159, _1554161]), _1554159)))], (39943 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554157), 39939 ^ [_1554157, _1554159, _1554161]), _1554161)))]]], (39945 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554157), hAPP(c_Finite__Set_Ofold1(_1554157, c_Orderings_Oord__class_Omin(_1554157)), _1554159)), _1554161))), 39946 ^ _779530 : [(39947 ^ _779530) ^ [_1554546] : [hBOOL(hAPP(hAPP(c_member(_1554157), _1554546), _1554159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554157), _1554546), _1554161))]]]]], (39955 ^ _779530) ^ [_1554707, _1554709, _1554711] : [class_Lattices_Oab__semigroup__idem__mult(_1554707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554707), _1554709)), -(_1554709 = c_Orderings_Obot__class_Obot(tc_fun(_1554707, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554707), _1554711)), -(_1554711 = c_Orderings_Obot__class_Obot(tc_fun(_1554707, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1554707, c_Groups_Otimes__class_Otimes(_1554707)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1554707, tc_HOL_Obool)), _1554709), _1554711)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1554707), hAPP(c_Finite__Set_Ofold1(_1554707, c_Groups_Otimes__class_Otimes(_1554707)), _1554709)), hAPP(c_Finite__Set_Ofold1(_1554707, c_Groups_Otimes__class_Otimes(_1554707)), _1554711)))], (39977 ^ _779530) ^ [_1555086, _1555088, _1555090] : [class_Orderings_Olinorder(_1555086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555086), _1555088)), -(_1555088 = c_Orderings_Obot__class_Obot(tc_fun(_1555086, tc_HOL_Obool))), 39988 ^ _779530 : [(39989 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555086), hAPP(c_Finite__Set_Ofold1(_1555086, c_Orderings_Oord__class_Omin(_1555086)), _1555088)), _1555090)), 39993 ^ _779530 : [(39994 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555086), 39992 ^ [_1555086, _1555088, _1555090]), _1555088)))], (39996 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555086), 39992 ^ [_1555086, _1555088, _1555090]), _1555090)))]]], (39998 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555086), hAPP(c_Finite__Set_Ofold1(_1555086, c_Orderings_Oord__class_Omin(_1555086)), _1555088)), _1555090))), 39999 ^ _779530 : [(40000 ^ _779530) ^ [_1555475] : [hBOOL(hAPP(hAPP(c_member(_1555086), _1555475), _1555088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555086), _1555475), _1555090))]]]]], (40008 ^ _779530) ^ [_1555636, _1555638, _1555640] : [class_Orderings_Olinorder(_1555636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555636), _1555638)), -(_1555638 = c_Orderings_Obot__class_Obot(tc_fun(_1555636, tc_HOL_Obool))), 40019 ^ _779530 : [(40030 ^ _779530) ^ [] : [40032 ^ _779530 : [(40033 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555636), 40031 ^ [_1555636, _1555638, _1555640]), _1555638)))], (40035 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555636), _1555640), 40031 ^ [_1555636, _1555638, _1555640]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555636), _1555640), hAPP(c_Finite__Set_Ofold1(_1555636, c_Orderings_Oord__class_Omin(_1555636)), _1555638))))], (40020 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555636), _1555640), hAPP(c_Finite__Set_Ofold1(_1555636, c_Orderings_Oord__class_Omin(_1555636)), _1555638))), 40023 ^ _779530 : [(40024 ^ _779530) ^ [_1555929] : [hBOOL(hAPP(hAPP(c_member(_1555636), _1555929), _1555638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1555636), _1555640), _1555929)))]]]]], (40039 ^ _779530) ^ [_1556214, _1556216, _1556218] : [class_Groups_Oab__semigroup__mult(_1556214), -(_1556216 = c_Orderings_Obot__class_Obot(tc_fun(_1556214, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556214), _1556216)), -(hBOOL(hAPP(hAPP(c_member(_1556214), _1556218), _1556216))), -(hAPP(c_Finite__Set_Ofold1(_1556214, c_Groups_Otimes__class_Otimes(_1556214)), hAPP(hAPP(c_Set_Oinsert(_1556214), _1556218), _1556216)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1556214), _1556218), hAPP(c_Finite__Set_Ofold1(_1556214, c_Groups_Otimes__class_Otimes(_1556214)), _1556216)))], (40057 ^ _779530) ^ [_1556513, _1556515, _1556517] : [class_Orderings_Olinorder(_1556513), -(_1556515 = c_Orderings_Obot__class_Obot(tc_fun(_1556513, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556513, tc_HOL_Obool)), _1556515), _1556517)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556513), _1556517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556513), hAPP(c_Finite__Set_Ofold1(_1556513, c_Orderings_Oord__class_Omin(_1556513)), _1556517)), hAPP(c_Finite__Set_Ofold1(_1556513, c_Orderings_Oord__class_Omin(_1556513)), _1556515))))], (40075 ^ _779530) ^ [_1556839, _1556841, _1556843, _1556845] : [c_Big__Operators_Osemilattice__big(_1556839, _1556841, _1556843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556839), _1556845)), -(hAPP(_1556843, _1556845) = hAPP(c_Finite__Set_Ofold1(_1556839, _1556841), _1556845))], (40085 ^ _779530) ^ [_1557004, _1557006] : [class_Groups_Oab__semigroup__mult(_1557004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557004), _1557006)), -(_1557006 = c_Orderings_Obot__class_Obot(tc_fun(_1557004, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1557004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1557004), 40098 ^ [_1557004, _1557006]), 40099 ^ [_1557004, _1557006])), hAPP(hAPP(c_Set_Oinsert(_1557004), 40098 ^ [_1557004, _1557006]), hAPP(hAPP(c_Set_Oinsert(_1557004), 40099 ^ [_1557004, _1557006]), c_Orderings_Obot__class_Obot(tc_fun(_1557004, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1557004), hAPP(c_Finite__Set_Ofold1(_1557004, c_Groups_Otimes__class_Otimes(_1557004)), _1557006)), _1557006)))], (40105 ^ _779530) ^ [_1557458, _1557460, _1557462] : [class_Lattices_Oab__semigroup__idem__mult(_1557458), hAPP(_1557460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1557458), 40110 ^ [_1557458, _1557460, _1557462]), 40111 ^ [_1557458, _1557460, _1557462])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1557458), hAPP(_1557460, 40110 ^ [_1557458, _1557460, _1557462])), hAPP(_1557460, 40111 ^ [_1557458, _1557460, _1557462])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557458), _1557462)), -(_1557462 = c_Orderings_Obot__class_Obot(tc_fun(_1557458, tc_HOL_Obool))), -(hAPP(_1557460, hAPP(c_Finite__Set_Ofold1(_1557458, c_Groups_Otimes__class_Otimes(_1557458)), _1557462)) = hAPP(c_Finite__Set_Ofold1(_1557458, c_Groups_Otimes__class_Otimes(_1557458)), hAPP(c_Set_Oimage(_1557458, _1557458, _1557460), _1557462)))], (40125 ^ _779530) ^ [_1557896, _1557898] : [c_Wellfounded_OwfP(_1557896, _1557898), -(c_Wellfounded_Owf(_1557896, hAPP(c_Set_OCollect(tc_prod(_1557896, _1557896)), hAPP(c_Product__Type_Oprod_Oprod__case(_1557896, _1557896, tc_HOL_Obool), _1557898))))], (40131 ^ _779530) ^ [_1557999, _1558001] : [c_Wellfounded_Owf(_1557999, hAPP(c_Set_OCollect(tc_prod(_1557999, _1557999)), hAPP(c_Product__Type_Oprod_Oprod__case(_1557999, _1557999, tc_HOL_Obool), _1558001))), -(c_Wellfounded_OwfP(_1557999, _1558001))], (40137 ^ _779530) ^ [_1558108, _1558110, _1558112] : [-(hAPP(c_Option_Omap(_1558108, _1558110), _1558112) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1558110), _1558108, c_Option_Ooption_ONone(_1558110), hAPP(hAPP(c_COMBB(_1558110, tc_Option_Ooption(_1558110), _1558108), c_Option_Ooption_OSome(_1558110)), _1558112)))], (40139 ^ _779530) ^ [_1558164, _1558166, _1558168] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1558164), _1558166)), 40145 ^ _779530 : [(40146 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558164), 40144 ^ [_1558164, _1558166, _1558168]), _1558166)))], (40148 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1558168, 40144 ^ [_1558164, _1558166, _1558168])))]], -(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(_1558164, tc_Nat_Onat), _1558168), _1558166))))], (40152 ^ _779530) ^ [_1558425] : [-(c_Wellfounded_OwfP(_1558425, hAPP(c_COMBK(tc_fun(_1558425, tc_HOL_Obool), _1558425), hAPP(c_COMBK(tc_HOL_Obool, _1558425), c_fFalse))))], (40154 ^ _779530) ^ [_1558463, _1558465, _1558467, _1558469, _1558471] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1558463), tc_Option_Ooption(_1558465), tc_Option_Ooption(_1558467), hAPP(c_Option_Omap(_1558463, _1558465), _1558469)), hAPP(c_Option_Omap(_1558467, _1558463), _1558471)) = hAPP(c_Option_Omap(_1558467, _1558465), hAPP(c_Fun_Ocomp(_1558463, _1558465, _1558467, _1558469), _1558471)))], (40156 ^ _779530) ^ [_1558534, _1558536, _1558538, _1558540, _1558542, _1558544] : [-(hAPP(hAPP(c_Option_Omap(_1558534, _1558536), _1558538), hAPP(hAPP(c_Option_Omap(_1558540, _1558534), _1558542), _1558544)) = hAPP(hAPP(c_Option_Omap(_1558540, _1558536), hAPP(c_Fun_Ocomp(_1558534, _1558536, _1558540, _1558538), _1558542)), _1558544))], (40158 ^ _779530) ^ [_1558602, _1558604, _1558606, _1558608, _1558610, _1558612] : [-(hAPP(hAPP(c_Option_Omap(_1558602, _1558604), _1558606), hAPP(hAPP(c_Option_Omap(_1558608, _1558602), _1558610), _1558612)) = hAPP(hAPP(c_Option_Omap(_1558608, _1558604), hAPP(c_Fun_Ocomp(_1558602, _1558604, _1558608, _1558606), _1558610)), _1558612))], (40160 ^ _779530) ^ [_1558670, _1558672, _1558674, _1558676, _1558678] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1558670), tc_Option_Ooption(_1558672), _1558674, hAPP(c_Option_Omap(_1558670, _1558672), _1558676)), hAPP(c_COMBK(tc_Option_Ooption(_1558670), _1558674), c_Option_Ooption_ONone(_1558670))), _1558678) = c_Option_Ooption_ONone(_1558672))], (40162 ^ _779530) ^ [_1558734] : [-(hAPP(c_Option_Omap(_1558734, _1558734), c_Fun_Oid(_1558734)) = c_Fun_Oid(tc_Option_Ooption(_1558734)))], (40164 ^ _779530) ^ [_1558769] : [-(hAPP(c_Option_Omap(_1558769, _1558769), c_COMBI(_1558769)) = c_Fun_Oid(tc_Option_Ooption(_1558769)))], (40166 ^ _779530) ^ [_1558804, _1558806, _1558808, _1558810, _1558812] : [-(c_Map_Odom(_1558804, _1558806, hAPP(hAPP(c_COMBS(_1558804, tc_Option_Ooption(_1558808), tc_Option_Ooption(_1558806)), hAPP(hAPP(c_COMBB(tc_fun(_1558808, _1558806), tc_fun(tc_Option_Ooption(_1558808), tc_Option_Ooption(_1558806)), _1558804), c_Option_Omap(_1558808, _1558806)), _1558810)), _1558812)) = c_Map_Odom(_1558804, _1558808, _1558812))], (40168 ^ _779530) ^ [_1558880, _1558882, _1558884] : [c_Wellfounded_OwfP(_1558880, _1558882), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1558880, _1558882), _1558884)))], (40174 ^ _779530) ^ [_1558984, _1558986] : [c_Wellfounded_OwfP(_1558984, _1558986), 40177 ^ _779530 : [(40178 ^ _779530) ^ [_1559048] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1558984, _1558986), _1559048)))]]], (40180 ^ _779530) ^ [_1559076, _1559078] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1559076, _1559078), 40181 ^ [_1559076, _1559078])), -(c_Wellfounded_OwfP(_1559076, _1559078))], (40187 ^ _779530) ^ [_1559215, _1559217, _1559219, _1559221] : [hAPP(hAPP(c_Option_Omap(_1559215, _1559217), _1559219), _1559221) = c_Option_Ooption_ONone(_1559217), -(_1559221 = c_Option_Ooption_ONone(_1559215))], (40193 ^ _779530) ^ [_1559318, _1559320, _1559322, _1559324] : [_1559324 = c_Option_Ooption_ONone(_1559318), -(hAPP(hAPP(c_Option_Omap(_1559318, _1559320), _1559322), _1559324) = c_Option_Ooption_ONone(_1559320))], (40199 ^ _779530) ^ [_1559427, _1559429, _1559431] : [-(hAPP(hAPP(c_Option_Omap(_1559427, _1559429), _1559431), c_Option_Ooption_ONone(_1559427)) = c_Option_Ooption_ONone(_1559429))], (40201 ^ _779530) ^ [_1559491, _1559493, _1559495, _1559497, _1559499] : [hAPP(hAPP(c_Option_Omap(_1559491, _1559493), _1559495), _1559497) = hAPP(c_Option_Ooption_OSome(_1559493), _1559499), 40205 ^ _779530 : [(40206 ^ _779530) ^ [] : [-(_1559497 = hAPP(c_Option_Ooption_OSome(_1559491), 40204 ^ [_1559491, _1559493, _1559495, _1559497, _1559499]))], (40208 ^ _779530) ^ [] : [-(hAPP(_1559495, 40204 ^ [_1559491, _1559493, _1559495, _1559497, _1559499]) = _1559499)]]], (40210 ^ _779530) ^ [_1559671, _1559673, _1559675, _1559677, _1559679] : [-(hAPP(hAPP(c_Option_Omap(_1559671, _1559673), _1559675), _1559677) = hAPP(c_Option_Ooption_OSome(_1559673), _1559679)), 40211 ^ _779530 : [(40212 ^ _779530) ^ [_1559739] : [_1559677 = hAPP(c_Option_Ooption_OSome(_1559671), _1559739), hAPP(_1559675, _1559739) = _1559679]]], (40220 ^ _779530) ^ [_1559883, _1559885, _1559887, _1559889] : [-(hAPP(hAPP(c_Option_Omap(_1559883, _1559885), _1559887), hAPP(c_Option_Ooption_OSome(_1559883), _1559889)) = hAPP(c_Option_Ooption_OSome(_1559885), hAPP(_1559887, _1559889)))], (40222 ^ _779530) ^ [_1559934, _1559936, _1559938] : [c_Wellfounded_OwfP(_1559934, _1559936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559934, tc_fun(_1559934, tc_HOL_Obool))), _1559938), _1559936)), -(c_Wellfounded_OwfP(_1559934, _1559938))], (40232 ^ _779530) ^ [_1560093, _1560095, _1560097, _1560099, _1560101, _1560103, _1560105] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1560093), tc_Option_Ooption(_1560095), _1560097, hAPP(c_Option_Omap(_1560093, _1560095), _1560099)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1560097, tc_Option_Ooption(_1560093)), _1560101), _1560103), hAPP(c_Option_Ooption_OSome(_1560093), _1560105))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1560097, tc_Option_Ooption(_1560095)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1560093), tc_Option_Ooption(_1560095), _1560097, hAPP(c_Option_Omap(_1560093, _1560095), _1560099)), _1560101)), _1560103), hAPP(c_Option_Ooption_OSome(_1560095), hAPP(_1560099, _1560105))))], (40234 ^ _779530) ^ [_1560205, _1560207] : [c_Wellfounded_Owf(_1560205, _1560207), -(c_Wellfounded_OwfP(_1560205, c_FunDef_Oin__rel(_1560205, _1560205, _1560207)))], (40240 ^ _779530) ^ [_1560305, _1560307] : [c_Wellfounded_OwfP(_1560305, hAPP(hAPP(c_COMBC(_1560305, tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_fun(_1560305, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560305, tc_fun(tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_fun(_1560305, tc_HOL_Obool)), _1560305), c_COMBC(_1560305, tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560305, tc_prod(_1560305, _1560305)), tc_fun(_1560305, tc_fun(tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_HOL_Obool)), _1560305), hAPP(c_COMBB(tc_prod(_1560305, _1560305), tc_fun(tc_fun(tc_prod(_1560305, _1560305), tc_HOL_Obool), tc_HOL_Obool), _1560305), c_member(tc_prod(_1560305, _1560305)))), c_Product__Type_OPair(_1560305, _1560305)))), _1560307)), -(c_Wellfounded_Owf(_1560305, _1560307))], (40246 ^ _779530) ^ [_1560614, _1560616] : [c_Wellfounded_Owf(_1560614, _1560616), -(c_Wellfounded_OwfP(_1560614, hAPP(hAPP(c_COMBC(_1560614, tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_fun(_1560614, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560614, tc_fun(tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_fun(_1560614, tc_HOL_Obool)), _1560614), c_COMBC(_1560614, tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560614, tc_prod(_1560614, _1560614)), tc_fun(_1560614, tc_fun(tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_HOL_Obool)), _1560614), hAPP(c_COMBB(tc_prod(_1560614, _1560614), tc_fun(tc_fun(tc_prod(_1560614, _1560614), tc_HOL_Obool), tc_HOL_Obool), _1560614), c_member(tc_prod(_1560614, _1560614)))), c_Product__Type_OPair(_1560614, _1560614)))), _1560616)))], (40252 ^ _779530) ^ [_1560929, _1560931] : [c_Wellfounded_OwfP(_1560929, _1560931), -(c_Wellfounded_Oacyclic(_1560929, hAPP(c_Set_OCollect(tc_prod(_1560929, _1560929)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560929, _1560929, tc_HOL_Obool), _1560931))))], (40258 ^ _779530) ^ [_1561036, _1561038, _1561040, _1561042, _1561044] : [c_Finite__Set_Ofolding__one__idem(_1561036, _1561038, _1561040), hAPP(_1561042, hAPP(hAPP(_1561038, 40263 ^ [_1561036, _1561038, _1561040, _1561042, _1561044]), 40264 ^ [_1561036, _1561038, _1561040, _1561042, _1561044])) = hAPP(hAPP(_1561038, hAPP(_1561042, 40263 ^ [_1561036, _1561038, _1561040, _1561042, _1561044])), hAPP(_1561042, 40264 ^ [_1561036, _1561038, _1561040, _1561042, _1561044])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561036), _1561044)), -(_1561044 = c_Orderings_Obot__class_Obot(tc_fun(_1561036, tc_HOL_Obool))), -(hAPP(_1561042, hAPP(_1561040, _1561044)) = hAPP(_1561040, hAPP(c_Set_Oimage(_1561036, _1561036, _1561042), _1561044)))], (40278 ^ _779530) ^ [_1561471] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1561471), c_Int_OInteg)), -(_1561471 = hAPP(c_Int_ORep__Integ, 40281 ^ [_1561471]))], (40285 ^ _779530) ^ [_1561576, _1561578, _1561580] : [c_Wellfounded_Oacyclic(_1561576, _1561578), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561576, _1561576), tc_HOL_Obool)), _1561580), _1561578)), -(c_Wellfounded_Oacyclic(_1561576, _1561580))], (40295 ^ _779530) ^ [_1561735, _1561737] : [c_Wellfounded_Owf(_1561735, _1561737), -(c_Wellfounded_Oacyclic(_1561735, _1561737))], (40301 ^ _779530) ^ [_1561812, _1561814] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1561812, _1561812)), _1561814)), 40304 ^ _779530 : [(40305 ^ _779530) ^ [] : [c_Wellfounded_Owf(_1561812, _1561814), -(c_Wellfounded_Oacyclic(_1561812, _1561814))], (40311 ^ _779530) ^ [] : [c_Wellfounded_Oacyclic(_1561812, _1561814), -(c_Wellfounded_Owf(_1561812, _1561814))]]], (40317 ^ _779530) ^ [_1562033, _1562035] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562033, _1562033)), _1562035)), c_Wellfounded_Oacyclic(_1562033, _1562035), -(c_Wellfounded_Owf(_1562033, _1562035))], (40327 ^ _779530) ^ [_1562191, _1562193] : [c_Nitpick_Owf_H(_1562191, _1562193), 40330 ^ _779530 : [(40331 ^ _779530) ^ [] : [-(c_Wellfounded_Oacyclic(_1562191, _1562193))], (40333 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562191, _1562191)), _1562193))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (40339 ^ _779530) ^ [_1562311, _1562313] : [-(c_Nitpick_Owf_H(_1562311, _1562313)), c_Wellfounded_Oacyclic(_1562311, _1562313), 40344 ^ _779530 : [(40345 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562311, _1562311)), _1562313))], (40347 ^ _779530) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (40351 ^ _779530) ^ [_1562488, _1562490] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1562488), c_Int_OInteg)), hBOOL(hAPP(_1562490, hAPP(c_Int_ORep__Integ, 40356 ^ [_1562488, _1562490]))), -(hBOOL(hAPP(_1562490, _1562488)))], (40362 ^ _779530) ^ [_1562670, _1562672, _1562674, _1562676, _1562678, _1562680, _1562682, _1562684] : [c_Finite__Set_Ofolding__image__simple(_1562670, _1562672, _1562674, _1562676, _1562678, _1562680), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562672), _1562682)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562672), _1562684)), 40376 ^ _779530 : [(40377 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562672), 40375 ^ [_1562670, _1562672, _1562674, _1562676, _1562678, _1562680, _1562682, _1562684]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562672, tc_HOL_Obool)), _1562682), _1562684))))], (40379 ^ _779530) ^ [] : [hAPP(_1562678, 40375 ^ [_1562670, _1562672, _1562674, _1562676, _1562678, _1562680, _1562682, _1562684]) = _1562676]], -(hAPP(_1562680, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562672, tc_HOL_Obool)), _1562682), _1562684)) = hAPP(hAPP(_1562674, hAPP(_1562680, _1562682)), hAPP(_1562680, _1562684)))], (40383 ^ _779530) ^ [_1563170, _1563172, _1563174, _1563176] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1563170), _1563172))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563174), hAPP(c_Set_Oimage(_1563170, _1563174, _1563176), _1563172))), 40391 ^ _779530 : [(40392 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1563170), 40390 ^ [_1563170, _1563172, _1563174, _1563176]), _1563172)))], (40394 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1563170), hAPP(c_Set_OCollect(_1563170), hAPP(hAPP(c_COMBS(_1563170, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563170), c_fconj), hAPP(hAPP(c_COMBC(_1563170, tc_fun(_1563170, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563170)), _1563172))), hAPP(hAPP(c_COMBC(_1563170, _1563174, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1563174, tc_fun(_1563174, tc_HOL_Obool), _1563170), c_fequal), _1563176)), hAPP(_1563176, 40390 ^ [_1563170, _1563172, _1563174, _1563176]))))))]]], (40412 ^ _779530) ^ [_1564272, _1564274, _1564276] : [-(c_Relation_Orefl__on(_1564272, _1564274, _1564276)), 40416 ^ _779530 : [(40417 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564272, _1564272)), 40415 ^ [_1564272, _1564274, _1564276]), _1564276)))], (40419 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1564272, _1564272, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1564272, tc_fun(_1564272, tc_HOL_Obool), tc_fun(_1564272, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1564272, tc_HOL_Obool), tc_fun(_1564272, tc_HOL_Obool)), _1564272), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1564272)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1564272), c_fconj), hAPP(hAPP(c_COMBC(_1564272, tc_fun(_1564272, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564272)), _1564274)))), hAPP(hAPP(c_COMBC(_1564272, tc_fun(_1564272, tc_HOL_Obool), tc_HOL_Obool), c_member(_1564272)), _1564274))), 40415 ^ [_1564272, _1564274, _1564276]))]], 40421 ^ _779530 : [(40422 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564272), 40420 ^ [_1564272, _1564274, _1564276]), _1564274)))], (40424 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564272, _1564272)), hAPP(hAPP(c_Product__Type_OPair(_1564272, _1564272), 40420 ^ [_1564272, _1564274, _1564276]), 40420 ^ [_1564272, _1564274, _1564276])), _1564276))]]], (40396 ^ _779530) ^ [_1563653, _1563655, _1563657] : [c_Relation_Orefl__on(_1563653, _1563655, _1563657), 40399 ^ _779530 : [(40400 ^ _779530) ^ [_1563864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563653, _1563653)), _1563864), _1563657)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1563653, _1563653, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1563653, tc_fun(_1563653, tc_HOL_Obool), tc_fun(_1563653, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1563653, tc_HOL_Obool), tc_fun(_1563653, tc_HOL_Obool)), _1563653), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1563653)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1563653), c_fconj), hAPP(hAPP(c_COMBC(_1563653, tc_fun(_1563653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563653)), _1563655)))), hAPP(hAPP(c_COMBC(_1563653, tc_fun(_1563653, tc_HOL_Obool), tc_HOL_Obool), c_member(_1563653)), _1563655))), _1563864)))], (40406 ^ _779530) ^ [_1564137] : [hBOOL(hAPP(hAPP(c_member(_1563653), _1564137), _1563655)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563653, _1563653)), hAPP(hAPP(c_Product__Type_OPair(_1563653, _1563653), _1564137), _1564137)), _1563657)))]]], (40429 ^ _779530) ^ [_1564911] : [-(_1564911 = hAPP(c_Int_OAbs__Integ, 40427 ^ [_1564911]))], (40431 ^ _779530) ^ [_1564939] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40427 ^ [_1564939]), c_Int_OInteg)))], (40433 ^ _779530) ^ [_1564974, _1564976, _1564978] : [hBOOL(hAPP(hAPP(c_member(_1564976), _1564974), c_Orderings_Obot__class_Obot(tc_fun(_1564976, tc_HOL_Obool)))), -(hBOOL(hAPP(_1564978, _1564974)))], (40449 ^ _779530) ^ [_1565282, _1565284, _1565286] : [40451 ^ _779530 : [(40452 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565282), 40450 ^ [_1565282, _1565284, _1565286]), _1565286)))], (40454 ^ _779530) ^ [] : [hBOOL(hAPP(_1565284, 40450 ^ [_1565282, _1565284, _1565286]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1565282, _1565284), _1565286)))], (40439 ^ _779530) ^ [_1565099, _1565101, _1565103] : [hBOOL(hAPP(c_Predicate_OPowp(_1565099, _1565101), _1565103)), 40442 ^ _779530 : [(40443 ^ _779530) ^ [_1565183] : [hBOOL(hAPP(hAPP(c_member(_1565099), _1565183), _1565103)), -(hBOOL(hAPP(_1565101, _1565183)))]]], (40468 ^ _779530) ^ [_1565859, _1565861, _1565863, _1565865] : [40470 ^ _779530 : [(40471 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565859, _1565859)), 40469 ^ [_1565859, _1565861, _1565863, _1565865]), _1565863)))], (40473 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565859, _1565859, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1565859, tc_fun(_1565859, _1565861), tc_fun(_1565859, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565861, tc_HOL_Obool), tc_fun(tc_fun(_1565859, _1565861), tc_fun(_1565859, tc_HOL_Obool)), _1565859), c_COMBB(_1565861, tc_HOL_Obool, _1565859)), hAPP(hAPP(c_COMBB(_1565861, tc_fun(_1565861, tc_HOL_Obool), _1565859), c_fequal), _1565865))), _1565865)), 40469 ^ [_1565859, _1565861, _1565863, _1565865]))]], -(c_Equiv__Relations_Ocongruent(_1565859, _1565861, _1565863, _1565865))], (40458 ^ _779530) ^ [_1565483, _1565485, _1565487, _1565489] : [c_Equiv__Relations_Ocongruent(_1565483, _1565485, _1565487, _1565489), 40461 ^ _779530 : [(40462 ^ _779530) ^ [_1565628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565483, _1565483)), _1565628), _1565487)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1565483, _1565483, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1565483, tc_fun(_1565483, _1565485), tc_fun(_1565483, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565485, tc_HOL_Obool), tc_fun(tc_fun(_1565483, _1565485), tc_fun(_1565483, tc_HOL_Obool)), _1565483), c_COMBB(_1565485, tc_HOL_Obool, _1565483)), hAPP(hAPP(c_COMBB(_1565485, tc_fun(_1565485, tc_HOL_Obool), _1565483), c_fequal), _1565489))), _1565489)), _1565628)))]]], (40477 ^ _779530) ^ [_1566234, _1566236] : [40479 ^ _779530 : [(40480 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40478 ^ [_1566234, _1566236]), c_Int_OInteg)))], (40482 ^ _779530) ^ [] : [hBOOL(hAPP(_1566234, hAPP(c_Int_OAbs__Integ, 40478 ^ [_1566234, _1566236])))]], -(hBOOL(hAPP(_1566234, _1566236)))], (40486 ^ _779530) ^ [_1566403, _1566405, _1566407, _1566409] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1566403)), hAPP(c_Set_Oimage(_1566405, tc_Option_Ooption(_1566403), _1566407), c_Orderings_Otop__class_Otop(tc_fun(_1566405, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1566403)), hAPP(c_Set_Oimage(_1566405, tc_Option_Ooption(_1566403), c_Map_Omap__add(_1566405, _1566403, _1566407, hAPP(c_Map_Omap__of(_1566405, _1566403), _1566409))), c_Orderings_Otop__class_Otop(tc_fun(_1566405, tc_HOL_Obool))))))], (40492 ^ _779530) ^ [_1566586, _1566588, _1566590] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566586), c_Map_Odom(_1566586, _1566588, hAPP(c_Map_Omap__of(_1566586, _1566588), _1566590)))))], (40494 ^ _779530) ^ [_1566627, _1566629, _1566631] : [40496 ^ _779530 : [(40497 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566627)), 40495 ^ [_1566627, _1566629, _1566631]), _1566629)))], (40499 ^ _779530) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1566627, hAPP(c_Nat_OSuc, _1566631), 40495 ^ [_1566627, _1566629, _1566631])]], 40500 ^ _779530 : [(40501 ^ _779530) ^ [_1566800] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566627)), _1566800), _1566629)), -(c_Hoare__Mirabelle_Otriple__valid(_1566627, _1566631, _1566800))]]], (40507 ^ _779530) ^ [_1566907, _1566909, _1566911] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1566907)), hAPP(c_Set_Oimage(_1566909, tc_Option_Ooption(_1566907), hAPP(c_Map_Omap__of(_1566909, _1566907), _1566911)), c_Orderings_Otop__class_Otop(tc_fun(_1566909, tc_HOL_Obool))))))], (40526 ^ _779530) ^ [_1567368, _1567370, _1567372] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1567368, _1567370, _1567372)), 40528 ^ _779530 : [(40536 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1567368)), 40534 ^ [_1567368, _1567370, _1567372]), _1567372)))], (40538 ^ _779530) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1567368, 40527 ^ [_1567368, _1567370, _1567372], 40534 ^ [_1567368, _1567370, _1567372])], (40529 ^ _779530) ^ [_1567514] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1567368)), _1567514), _1567370)), -(c_Hoare__Mirabelle_Otriple__valid(_1567368, 40527 ^ [_1567368, _1567370, _1567372], _1567514))]]], (40509 ^ _779530) ^ [_1566978, _1566980, _1566982] : [c_Hoare__Mirabelle_Ohoare__valids(_1566978, _1566980, _1566982), 40512 ^ _779530 : [(40513 ^ _779530) ^ [_1567087] : [40515 ^ _779530 : [(40516 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566978)), 40514 ^ [_1566978, _1566980, _1566982, _1567087]), _1566980)))], (40518 ^ _779530) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1566978, _1567087, 40514 ^ [_1566978, _1566980, _1566982, _1567087])]], 40519 ^ _779530 : [(40520 ^ _779530) ^ [_1567259] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1566978)), _1567259), _1566982)), -(c_Hoare__Mirabelle_Otriple__valid(_1566978, _1567087, _1567259))]]]]], (40542 ^ _779530) ^ [_1567769, _1567771, _1567773, _1567775] : [-(c_Map_Omap__add(_1567769, _1567771, _1567773, hAPP(c_Map_Omap__of(_1567769, _1567771), _1567775)) = c_List_Ofoldr(tc_prod(_1567769, _1567771), tc_fun(_1567769, tc_Option_Ooption(_1567771)), hAPP(c_Product__Type_Oprod_Oprod__case(_1567769, _1567771, tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), hAPP(hAPP(c_COMBC(_1567769, tc_fun(_1567771, tc_Option_Ooption(_1567771)), tc_fun(_1567771, tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1567771), tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), tc_fun(tc_fun(_1567771, tc_Option_Ooption(_1567771)), tc_fun(_1567771, tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771))))), _1567769), c_COMBB(tc_Option_Ooption(_1567771), tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771))), _1567771)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(tc_Option_Ooption(_1567771), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), tc_fun(tc_Option_Ooption(_1567771), tc_fun(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), _1567769), c_COMBC(tc_fun(_1567769, tc_Option_Ooption(_1567771)), tc_Option_Ooption(_1567771), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), hAPP(c_COMBC(tc_fun(_1567769, tc_Option_Ooption(_1567771)), _1567769, tc_fun(tc_Option_Ooption(_1567771), tc_fun(_1567769, tc_Option_Ooption(_1567771)))), c_Fun_Ofun__upd(_1567769, tc_Option_Ooption(_1567771)))))), c_Option_Ooption_OSome(_1567771))), _1567775, _1567773))], (40544 ^ _779530) ^ [_1568036, _1568038, _1568040, _1568042, _1568044, _1568046, _1568048] : [c_Fun_Oinj__on(_1568036, _1568038, _1568040, c_Orderings_Otop__class_Otop(tc_fun(_1568036, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1568036, _1568042), _1568044), _1568046) = hAPP(c_Option_Ooption_OSome(_1568042), _1568048), -(hAPP(hAPP(c_Map_Omap__of(_1568038, _1568042), hAPP(hAPP(c_List_Omap(tc_prod(_1568036, _1568042), tc_prod(_1568038, _1568042)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568036, _1568042, tc_prod(_1568038, _1568042)), hAPP(hAPP(c_COMBB(_1568038, tc_fun(_1568042, tc_prod(_1568038, _1568042)), _1568036), c_Product__Type_OPair(_1568038, _1568042)), _1568040))), _1568044)), hAPP(_1568040, _1568046)) = hAPP(c_Option_Ooption_OSome(_1568042), _1568048))], (40554 ^ _779530) ^ [_1568349, _1568351, _1568353, _1568355, _1568357] : [-(hAPP(c_Map_Omap__of(_1568349, _1568351), hAPP(hAPP(c_List_Omap(tc_prod(_1568349, _1568353), tc_prod(_1568349, _1568351)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568349, _1568353, tc_prod(_1568349, _1568351)), hAPP(hAPP(c_COMBC(_1568349, tc_fun(_1568353, _1568351), tc_fun(_1568353, tc_prod(_1568349, _1568351))), hAPP(hAPP(c_COMBB(tc_fun(_1568351, tc_prod(_1568349, _1568351)), tc_fun(tc_fun(_1568353, _1568351), tc_fun(_1568353, tc_prod(_1568349, _1568351))), _1568349), c_COMBB(_1568351, tc_prod(_1568349, _1568351), _1568353)), c_Product__Type_OPair(_1568349, _1568351))), _1568355))), _1568357)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1568353), tc_Option_Ooption(_1568351), _1568349, hAPP(c_Option_Omap(_1568353, _1568351), _1568355)), hAPP(c_Map_Omap__of(_1568349, _1568353), _1568357)))], (40556 ^ _779530) ^ [_1568492, _1568494, _1568496] : [c_Fun_Oinj__on(_1568492, _1568494, _1568496, c_Orderings_Otop__class_Otop(tc_fun(_1568492, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1568492), tc_List_Olist(_1568494), hAPP(c_List_Omap(_1568492, _1568494), _1568496), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1568492), tc_HOL_Obool))))], (40562 ^ _779530) ^ [_1568623, _1568625, _1568627, _1568629, _1568631, _1568633, _1568635] : [-(c_List_Ofoldr(_1568623, _1568625, _1568627, hAPP(hAPP(c_List_Omap(_1568629, _1568623), _1568631), _1568633), _1568635) = c_List_Ofoldr(_1568629, _1568625, hAPP(c_Fun_Ocomp(_1568623, tc_fun(_1568625, _1568625), _1568629, _1568627), _1568631), _1568633, _1568635))], (40564 ^ _779530) ^ [_1568690, _1568692, _1568694, _1568696, _1568698] : [hAPP(hAPP(c_List_Omap(_1568690, _1568692), _1568694), _1568696) = hAPP(hAPP(c_List_Omap(_1568690, _1568692), _1568694), _1568698), c_Fun_Oinj__on(_1568690, _1568692, _1568694, c_Orderings_Otop__class_Otop(tc_fun(_1568690, tc_HOL_Obool))), -(_1568696 = _1568698)], (40574 ^ _779530) ^ [_1568881, _1568883, _1568885] : [c_Fun_Oinj__on(tc_List_Olist(_1568881), tc_List_Olist(_1568883), hAPP(c_List_Omap(_1568881, _1568883), _1568885), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1568881), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1568881, _1568883, _1568885, c_Orderings_Otop__class_Otop(tc_fun(_1568881, tc_HOL_Obool))))], (40580 ^ _779530) ^ [_1569012, _1569014, _1569016, _1569018, _1569020] : [c_Fun_Oinj__on(_1569012, _1569014, _1569016, c_Orderings_Otop__class_Otop(tc_fun(_1569012, tc_HOL_Obool))), 40583 ^ _779530 : [(40584 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Omap(_1569012, _1569014), _1569016), _1569018) = hAPP(hAPP(c_List_Omap(_1569012, _1569014), _1569016), _1569020), -(_1569018 = _1569020)], (40590 ^ _779530) ^ [] : [_1569018 = _1569020, -(hAPP(hAPP(c_List_Omap(_1569012, _1569014), _1569016), _1569018) = hAPP(hAPP(c_List_Omap(_1569012, _1569014), _1569016), _1569020))]]], (40596 ^ _779530) ^ [_1569323, _1569325, _1569327] : [c_Fun_Oinj__on(tc_List_Olist(_1569323), tc_List_Olist(_1569325), hAPP(c_List_Omap(_1569323, _1569325), _1569327), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1569323), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1569323, _1569325, _1569327, c_Orderings_Otop__class_Otop(tc_fun(_1569323, tc_HOL_Obool))))], (40602 ^ _779530) ^ [_1569450, _1569452, _1569454] : [c_Fun_Oinj__on(_1569450, _1569452, _1569454, c_Orderings_Otop__class_Otop(tc_fun(_1569450, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1569450), tc_List_Olist(_1569452), hAPP(c_List_Omap(_1569450, _1569452), _1569454), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1569450), tc_HOL_Obool))))], (40608 ^ _779530) ^ [_1569583, _1569585] : [-(hAPP(hAPP(c_List_Omap(_1569583, _1569583), c_COMBI(_1569583)), _1569585) = _1569585)], (40610 ^ _779530) ^ [_1569619, _1569621, _1569623, _1569625, _1569627, _1569629] : [-(hAPP(hAPP(c_List_Omap(_1569619, _1569621), _1569623), hAPP(hAPP(c_List_Omap(_1569625, _1569619), _1569627), _1569629)) = hAPP(hAPP(c_List_Omap(_1569625, _1569621), hAPP(c_Fun_Ocomp(_1569619, _1569621, _1569625, _1569623), _1569627)), _1569629))], (40612 ^ _779530) ^ [_1569687, _1569689, _1569691, _1569693, _1569695, _1569697] : [-(hAPP(hAPP(c_List_Omap(_1569687, _1569689), _1569691), hAPP(hAPP(c_List_Omap(_1569693, _1569687), _1569695), _1569697)) = hAPP(hAPP(c_List_Omap(_1569693, _1569689), hAPP(c_Fun_Ocomp(_1569687, _1569689, _1569693, _1569691), _1569695)), _1569697))], (40614 ^ _779530) ^ [_1569755, _1569757, _1569759, _1569761, _1569763] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1569755), tc_List_Olist(_1569757), tc_List_Olist(_1569759), hAPP(c_List_Omap(_1569755, _1569757), _1569761)), hAPP(c_List_Omap(_1569759, _1569755), _1569763)) = hAPP(c_List_Omap(_1569759, _1569757), hAPP(c_Fun_Ocomp(_1569755, _1569757, _1569759, _1569761), _1569763)))], (40616 ^ _779530) ^ [_1569826, _1569828, _1569830, _1569832, _1569834] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1569826), tc_List_Olist(_1569828), tc_List_Olist(_1569830), hAPP(c_List_Omap(_1569826, _1569828), _1569832)), hAPP(c_List_Omap(_1569830, _1569826), _1569834)) = hAPP(c_List_Omap(_1569830, _1569828), hAPP(c_Fun_Ocomp(_1569826, _1569828, _1569830, _1569832), _1569834)))], (40618 ^ _779530) ^ [_1569897] : [-(hAPP(c_List_Omap(_1569897, _1569897), c_Fun_Oid(_1569897)) = c_Fun_Oid(tc_List_Olist(_1569897)))], (40620 ^ _779530) ^ [_1569932] : [-(hAPP(c_List_Omap(_1569932, _1569932), c_COMBI(_1569932)) = c_Fun_Oid(tc_List_Olist(_1569932)))], (40622 ^ _779530) ^ [_1569967, _1569969, _1569971, _1569973] : [-(hAPP(c_Map_Omap__of(_1569967, _1569969), hAPP(hAPP(c_List_Omap(_1569967, tc_prod(_1569967, _1569969)), hAPP(hAPP(c_COMBS(_1569967, _1569969, tc_prod(_1569967, _1569969)), c_Product__Type_OPair(_1569967, _1569969)), _1569971)), _1569973)) = c_Map_Orestrict__map(_1569967, _1569969, hAPP(c_Fun_Ocomp(_1569969, tc_Option_Ooption(_1569969), _1569967, c_Option_Ooption_OSome(_1569969)), _1569971), hAPP(c_List_Oset(_1569967), _1569973)))], (40624 ^ _779530) ^ [_1570052, _1570054, _1570056, _1570058] : [-(hAPP(c_Map_Omap__of(_1570052, _1570054), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1570052, _1570054)), _1570056), _1570058)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570052, tc_Option_Ooption(_1570054)), hAPP(c_Map_Omap__of(_1570052, _1570054), _1570058)), hAPP(c_Product__Type_Ofst(_1570052, _1570054), _1570056)), hAPP(c_Option_Ooption_OSome(_1570054), hAPP(c_Product__Type_Osnd(_1570052, _1570054), _1570056))))], (40626 ^ _779530) ^ [_1570135, _1570137] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1570135), hAPP(c_List_Oset(_1570135), _1570137))))], (40628 ^ _779530) ^ [_1570169, _1570171, _1570173, _1570175] : [-(hAPP(c_List_Oset(_1570169), hAPP(hAPP(c_List_Omap(_1570171, _1570169), _1570173), _1570175)) = hAPP(c_Set_Oimage(_1570171, _1570169, _1570173), hAPP(c_List_Oset(_1570171), _1570175)))], (40630 ^ _779530) ^ [_1570224, _1570226, _1570228, _1570230, _1570232] : [-(hAPP(hAPP(c_List_Omap(_1570224, _1570226), _1570228), hAPP(hAPP(c_List_Olist_OCons(_1570224), _1570230), _1570232)) = hAPP(hAPP(c_List_Olist_OCons(_1570226), hAPP(_1570228, _1570230)), hAPP(hAPP(c_List_Omap(_1570224, _1570226), _1570228), _1570232)))], (40642 ^ _779530) ^ [_1570560, _1570562, _1570564, _1570566, _1570568] : [40644 ^ _779530 : [(40645 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1570560), 40643 ^ [_1570560, _1570562, _1570564, _1570566, _1570568]), hAPP(c_List_Oset(_1570560), _1570566))))], (40647 ^ _779530) ^ [] : [hAPP(_1570564, 40643 ^ [_1570560, _1570562, _1570564, _1570566, _1570568]) = hAPP(_1570568, 40643 ^ [_1570560, _1570562, _1570564, _1570566, _1570568])]], -(hAPP(hAPP(c_List_Omap(_1570560, _1570562), _1570564), _1570566) = hAPP(hAPP(c_List_Omap(_1570560, _1570562), _1570568), _1570566))], (40632 ^ _779530) ^ [_1570316, _1570318, _1570320, _1570322, _1570324] : [hAPP(hAPP(c_List_Omap(_1570316, _1570318), _1570320), _1570322) = hAPP(hAPP(c_List_Omap(_1570316, _1570318), _1570324), _1570322), 40635 ^ _779530 : [(40636 ^ _779530) ^ [_1570439] : [hBOOL(hAPP(hAPP(c_member(_1570316), _1570439), hAPP(c_List_Oset(_1570316), _1570322))), -(hAPP(_1570320, _1570439) = hAPP(_1570324, _1570439))]]], (40651 ^ _779530) ^ [_1570817, _1570819, _1570821, _1570823] : [hBOOL(hAPP(hAPP(c_member(_1570817), _1570819), hAPP(c_List_Oset(_1570817), hAPP(hAPP(c_List_Olist_OCons(_1570817), _1570821), _1570823)))), -(_1570819 = _1570821), -(hBOOL(hAPP(hAPP(c_member(_1570817), _1570819), hAPP(c_List_Oset(_1570817), _1570823))))], (40661 ^ _779530) ^ [_1570984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1570984)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1570984), tc_HOL_Obool))))], (40663 ^ _779530) ^ [_1571044, _1571046, _1571048, _1571050, _1571052] : [hAPP(hAPP(c_List_Olist_OCons(_1571044), _1571046), _1571048) = hAPP(hAPP(c_List_Olist_OCons(_1571044), _1571050), _1571052), 40666 ^ _779530 : [(40667 ^ _779530) ^ [] : [-(_1571046 = _1571050)], (40669 ^ _779530) ^ [] : [-(_1571048 = _1571052)]]], (40671 ^ _779530) ^ [_1571181, _1571183, _1571185, _1571187, _1571189] : [-(hAPP(hAPP(c_List_Olist_OCons(_1571181), _1571183), _1571185) = hAPP(hAPP(c_List_Olist_OCons(_1571181), _1571187), _1571189)), _1571183 = _1571187, _1571185 = _1571189], (40681 ^ _779530) ^ [_1571371, _1571373, _1571375] : [hAPP(hAPP(c_List_Olist_OCons(_1571371), _1571373), _1571375) = _1571375], (40683 ^ _779530) ^ [_1571421, _1571423, _1571425] : [_1571421 = hAPP(hAPP(c_List_Olist_OCons(_1571423), _1571425), _1571421)], (40685 ^ _779530) ^ [_1571456, _1571458, _1571460] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571456, tc_HOL_Obool)), hAPP(c_List_Oset(_1571456), _1571458)), hAPP(c_List_Oset(_1571456), hAPP(hAPP(c_List_Olist_OCons(_1571456), _1571460), _1571458)))))], (40687 ^ _779530) ^ [_1571511, _1571513, _1571515] : [-(hAPP(c_List_Oset(_1571511), hAPP(hAPP(c_List_Olist_OCons(_1571511), _1571513), _1571515)) = hAPP(hAPP(c_Set_Oinsert(_1571511), _1571513), hAPP(c_List_Oset(_1571511), _1571515)))], (40689 ^ _779530) ^ [_1571564, _1571566, _1571568, _1571570, _1571572, _1571574] : [-(c_List_Ofoldr(_1571564, _1571566, _1571568, hAPP(hAPP(c_List_Olist_OCons(_1571564), _1571570), _1571572), _1571574) = hAPP(hAPP(_1571568, _1571570), c_List_Ofoldr(_1571564, _1571566, _1571568, _1571572, _1571574)))], (40691 ^ _779530) ^ [_1571623, _1571625, _1571627, _1571629, _1571631] : [hAPP(hAPP(c_List_Omap(_1571623, _1571625), _1571627), _1571629) = hAPP(hAPP(c_List_Omap(_1571623, _1571625), _1571627), _1571631), c_Fun_Oinj__on(_1571623, _1571625, _1571627, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571623, tc_HOL_Obool)), hAPP(c_List_Oset(_1571623), _1571629)), hAPP(c_List_Oset(_1571623), _1571631))), -(_1571629 = _1571631)], (40701 ^ _779530) ^ [_1571846, _1571848, _1571850, _1571852, _1571854] : [c_Fun_Oinj__on(_1571846, _1571848, _1571850, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571846, tc_HOL_Obool)), hAPP(c_List_Oset(_1571846), _1571852)), hAPP(c_List_Oset(_1571846), _1571854))), 40704 ^ _779530 : [(40705 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Omap(_1571846, _1571848), _1571850), _1571852) = hAPP(hAPP(c_List_Omap(_1571846, _1571848), _1571850), _1571854), -(_1571852 = _1571854)], (40711 ^ _779530) ^ [] : [_1571852 = _1571854, -(hAPP(hAPP(c_List_Omap(_1571846, _1571848), _1571850), _1571852) = hAPP(hAPP(c_List_Omap(_1571846, _1571848), _1571850), _1571854))]]], (40717 ^ _779530) ^ [_1572167, _1572169, _1572171, _1572173, _1572175, _1572177] : [-(hBOOL(hAPP(hAPP(c_member(_1572167), _1572169), hAPP(c_List_Oset(_1572167), _1572171)))), -(hAPP(hAPP(c_List_Omap(_1572167, _1572173), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1572167, _1572173), _1572175), _1572169), _1572177)), _1572171) = hAPP(hAPP(c_List_Omap(_1572167, _1572173), _1572175), _1572171))], (40723 ^ _779530) ^ [_1572274, _1572276, _1572278, _1572280, _1572282, _1572284] : [_1572274 = _1572276, -(hAPP(hAPP(c_Map_Omap__of(_1572278, _1572280), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1572278, _1572280)), hAPP(hAPP(c_Product__Type_OPair(_1572278, _1572280), _1572274), _1572282)), _1572284)), _1572276) = hAPP(c_Option_Ooption_OSome(_1572280), _1572282))], (40729 ^ _779530) ^ [_1572421, _1572423, _1572425, _1572427, _1572429, _1572431] : [-(_1572421 = _1572423), -(hAPP(hAPP(c_Map_Omap__of(_1572425, _1572427), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1572425, _1572427)), hAPP(hAPP(c_Product__Type_OPair(_1572425, _1572427), _1572421), _1572429)), _1572431)), _1572423) = hAPP(hAPP(c_Map_Omap__of(_1572425, _1572427), _1572431), _1572423))], (40735 ^ _779530) ^ [_1572505, _1572507, _1572509, _1572511] : [hAPP(c_Map_Omap__of(_1572505, _1572507), _1572509) = hAPP(c_Map_Omap__of(_1572505, _1572507), _1572511), -(hAPP(c_Set_Oimage(tc_prod(_1572505, _1572507), _1572505, c_Product__Type_Ofst(_1572505, _1572507)), hAPP(c_List_Oset(tc_prod(_1572505, _1572507)), _1572509)) = hAPP(c_Set_Oimage(tc_prod(_1572505, _1572507), _1572505, c_Product__Type_Ofst(_1572505, _1572507)), hAPP(c_List_Oset(tc_prod(_1572505, _1572507)), _1572511)))], (40741 ^ _779530) ^ [_1572694, _1572696, _1572698, _1572700, _1572702] : [hAPP(hAPP(c_Map_Omap__of(_1572694, _1572696), _1572698), _1572700) = hAPP(c_Option_Ooption_OSome(_1572696), _1572702), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572694, _1572696)), hAPP(hAPP(c_Product__Type_OPair(_1572694, _1572696), _1572700), _1572702)), hAPP(c_List_Oset(tc_prod(_1572694, _1572696)), _1572698))))], (40747 ^ _779530) ^ [_1572859, _1572861, _1572863, _1572865, _1572867] : [hAPP(hAPP(c_Map_Omap__of(_1572859, _1572861), _1572863), _1572865) = hAPP(c_Option_Ooption_OSome(_1572861), _1572867), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572859, _1572861)), hAPP(hAPP(c_Product__Type_OPair(_1572859, _1572861), _1572865), _1572867)), hAPP(c_List_Oset(tc_prod(_1572859, _1572861)), _1572863))))], (40753 ^ _779530) ^ [_1573024, _1573026, _1573028] : [-(c_Map_Odom(_1573024, _1573026, hAPP(c_Map_Omap__of(_1573024, _1573026), _1573028)) = hAPP(c_Set_Oimage(tc_prod(_1573024, _1573026), _1573024, c_Product__Type_Ofst(_1573024, _1573026)), hAPP(c_List_Oset(tc_prod(_1573024, _1573026)), _1573028)))], (40755 ^ _779530) ^ [_1573103, _1573105, _1573107, _1573109] : [hAPP(hAPP(c_Map_Omap__of(_1573103, _1573105), _1573107), _1573109) = c_Option_Ooption_ONone(_1573105), hBOOL(hAPP(hAPP(c_member(_1573103), _1573109), hAPP(c_Set_Oimage(tc_prod(_1573103, _1573105), _1573103, c_Product__Type_Ofst(_1573103, _1573105)), hAPP(c_List_Oset(tc_prod(_1573103, _1573105)), _1573107))))], (40761 ^ _779530) ^ [_1573257, _1573259, _1573261, _1573263] : [-(hBOOL(hAPP(hAPP(c_member(_1573257), _1573263), hAPP(c_Set_Oimage(tc_prod(_1573257, _1573259), _1573257, c_Product__Type_Ofst(_1573257, _1573259)), hAPP(c_List_Oset(tc_prod(_1573257, _1573259)), _1573261))))), -(hAPP(hAPP(c_Map_Omap__of(_1573257, _1573259), _1573261), _1573263) = c_Option_Ooption_ONone(_1573259))], (40767 ^ _779530) ^ [_1573338, _1573340, _1573342, _1573344] : [hAPP(c_List_Oset(_1573338), _1573340) = c_Map_Odom(_1573338, _1573342, _1573344), -(hAPP(c_Map_Omap__of(_1573338, _1573342), hAPP(hAPP(c_List_Omap(_1573338, tc_prod(_1573338, _1573342)), hAPP(hAPP(c_COMBS(_1573338, _1573342, tc_prod(_1573338, _1573342)), c_Product__Type_OPair(_1573338, _1573342)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1573342), _1573342, _1573338), c_Option_Othe(_1573342)), _1573344))), _1573340)) = _1573344)], (40773 ^ _779530) ^ [_1573533, _1573535, _1573537] : [-(c_List_Oset__Cons(_1573533, _1573535, _1573537) = hAPP(c_Set_OCollect(tc_List_Olist(_1573533)), hAPP(hAPP(c_COMBB(tc_fun(_1573533, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1573533)), c_HOL_OEx(_1573533)), hAPP(hAPP(c_COMBB(tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_fun(_1573533, tc_HOL_Obool), tc_List_Olist(_1573533)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_HOL_Obool, _1573533), c_HOL_OEx(tc_List_Olist(_1573533)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1573533), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1573533, tc_fun(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), tc_fun(tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), tc_List_Olist(_1573533)), c_COMBS(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1573533, tc_fun(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), tc_List_Olist(_1573533)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1573533), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), _1573533), c_COMBS(tc_List_Olist(_1573533), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1573533)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1573533), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1573533)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1573533), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_List_Olist(_1573533))), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1573533), tc_List_Olist(_1573533)), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_fun(tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_List_Olist(_1573533))), tc_fun(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool))), tc_List_Olist(_1573533)), c_COMBB(tc_fun(tc_List_Olist(_1573533), tc_List_Olist(_1573533)), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), _1573533)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1573533), tc_List_Olist(_1573533)), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), tc_List_Olist(_1573533)), c_COMBB(tc_List_Olist(_1573533), tc_HOL_Obool, tc_List_Olist(_1573533))), c_fequal))), c_List_Olist_OCons(_1573533)))))), hAPP(hAPP(c_COMBC(_1573533, tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool)), _1573533), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1573533))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573533), c_fconj), hAPP(hAPP(c_COMBC(_1573533, tc_fun(_1573533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573533)), _1573535)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1573533), tc_fun(tc_List_Olist(_1573533), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1573533))), _1573537)))))))], (40775 ^ _779530) ^ [_1574068, _1574070] : [-(hAPP(c_Option_Othe(_1574068), hAPP(c_Option_Ooption_OSome(_1574068), _1574070)) = _1574070)], (40777 ^ _779530) ^ [_1574103, _1574105, _1574107, _1574109] : [-(hAPP(c_List_Oset(tc_prod(_1574103, _1574105)), c_Enum_Oproduct(_1574103, _1574105, _1574107, _1574109)) = hAPP(hAPP(c_Product__Type_OSigma(_1574103, _1574105), hAPP(c_List_Oset(_1574103), _1574107)), hAPP(c_COMBK(tc_fun(_1574105, tc_HOL_Obool), _1574103), hAPP(c_List_Oset(_1574105), _1574109))))], (40779 ^ _779530) ^ [_1574173, _1574175, _1574177] : [hBOOL(hAPP(c_List_Odistinct(_1574173), hAPP(hAPP(c_List_Omap(tc_prod(_1574173, _1574175), _1574173), c_Product__Type_Ofst(_1574173, _1574175)), _1574177))), -(c_Map_Oran(_1574173, _1574175, hAPP(c_Map_Omap__of(_1574173, _1574175), _1574177)) = hAPP(c_Set_Oimage(tc_prod(_1574173, _1574175), _1574175, c_Product__Type_Osnd(_1574173, _1574175)), hAPP(c_List_Oset(tc_prod(_1574173, _1574175)), _1574177)))], (40785 ^ _779530) ^ [_1574352, _1574354, _1574356, _1574358] : [hBOOL(hAPP(c_List_Odistinct(_1574352), _1574354)), hBOOL(hAPP(c_List_Odistinct(_1574356), _1574358)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1574352, _1574356)), c_Enum_Oproduct(_1574352, _1574356, _1574354, _1574358))))], (40795 ^ _779530) ^ [_1574547, _1574549, _1574551] : [hBOOL(hAPP(c_List_Odistinct(_1574547), hAPP(hAPP(c_List_Olist_OCons(_1574547), _1574549), _1574551))), 40798 ^ _779530 : [(40799 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1574547), _1574549), hAPP(c_List_Oset(_1574547), _1574551)))], (40801 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1574547), _1574551)))]]], (40803 ^ _779530) ^ [_1574714, _1574716, _1574718] : [-(hBOOL(hAPP(c_List_Odistinct(_1574714), hAPP(hAPP(c_List_Olist_OCons(_1574714), _1574716), _1574718)))), -(hBOOL(hAPP(hAPP(c_member(_1574714), _1574716), hAPP(c_List_Oset(_1574714), _1574718)))), hBOOL(hAPP(c_List_Odistinct(_1574714), _1574718))], (40813 ^ _779530) ^ [_1574929, _1574931, _1574933, _1574935] : [hBOOL(hAPP(c_List_Odistinct(_1574929), hAPP(hAPP(c_List_Omap(_1574931, _1574929), _1574933), _1574935))), 40816 ^ _779530 : [(40817 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1574931), _1574935)))], (40819 ^ _779530) ^ [] : [-(c_Fun_Oinj__on(_1574931, _1574929, _1574933, hAPP(c_List_Oset(_1574931), _1574935)))]]], (40821 ^ _779530) ^ [_1575080, _1575082, _1575084, _1575086] : [-(hBOOL(hAPP(c_List_Odistinct(_1575080), hAPP(hAPP(c_List_Omap(_1575082, _1575080), _1575084), _1575086)))), hBOOL(hAPP(c_List_Odistinct(_1575082), _1575086)), c_Fun_Oinj__on(_1575082, _1575080, _1575084, hAPP(c_List_Oset(_1575082), _1575086))], (40831 ^ _779530) ^ [_1575267, _1575269, _1575271, _1575273] : [hBOOL(hAPP(c_List_Odistinct(_1575267), hAPP(hAPP(c_List_Omap(tc_prod(_1575267, _1575269), _1575267), c_Product__Type_Ofst(_1575267, _1575269)), _1575271))), hBOOL(hAPP(c_List_Odistinct(_1575267), hAPP(hAPP(c_List_Omap(tc_prod(_1575267, _1575269), _1575267), c_Product__Type_Ofst(_1575267, _1575269)), _1575273))), 40838 ^ _779530 : [(40839 ^ _779530) ^ [] : [hAPP(c_Map_Omap__of(_1575267, _1575269), _1575271) = hAPP(c_Map_Omap__of(_1575267, _1575269), _1575273), -(hAPP(c_List_Oset(tc_prod(_1575267, _1575269)), _1575271) = hAPP(c_List_Oset(tc_prod(_1575267, _1575269)), _1575273))], (40845 ^ _779530) ^ [] : [hAPP(c_List_Oset(tc_prod(_1575267, _1575269)), _1575271) = hAPP(c_List_Oset(tc_prod(_1575267, _1575269)), _1575273), -(hAPP(c_Map_Omap__of(_1575267, _1575269), _1575271) = hAPP(c_Map_Omap__of(_1575267, _1575269), _1575273))]]], (40851 ^ _779530) ^ [_1575702, _1575704, _1575706, _1575708, _1575710] : [hBOOL(hAPP(c_List_Odistinct(_1575702), hAPP(hAPP(c_List_Omap(tc_prod(_1575702, _1575704), _1575702), c_Product__Type_Ofst(_1575702, _1575704)), _1575706))), 40854 ^ _779530 : [(40855 ^ _779530) ^ [] : [hAPP(c_Option_Ooption_OSome(_1575704), _1575708) = hAPP(hAPP(c_Map_Omap__of(_1575702, _1575704), _1575706), _1575710), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575702, _1575704)), hAPP(hAPP(c_Product__Type_OPair(_1575702, _1575704), _1575710), _1575708)), hAPP(c_List_Oset(tc_prod(_1575702, _1575704)), _1575706))))], (40861 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575702, _1575704)), hAPP(hAPP(c_Product__Type_OPair(_1575702, _1575704), _1575710), _1575708)), hAPP(c_List_Oset(tc_prod(_1575702, _1575704)), _1575706))), -(hAPP(c_Option_Ooption_OSome(_1575704), _1575708) = hAPP(hAPP(c_Map_Omap__of(_1575702, _1575704), _1575706), _1575710))]]], (40867 ^ _779530) ^ [_1576088, _1576090, _1576092, _1576094, _1576096] : [hBOOL(hAPP(c_List_Odistinct(_1576088), hAPP(hAPP(c_List_Omap(tc_prod(_1576088, _1576090), _1576088), c_Product__Type_Ofst(_1576088, _1576090)), _1576092))), 40870 ^ _779530 : [(40871 ^ _779530) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1576088, _1576090), _1576092), _1576094) = hAPP(c_Option_Ooption_OSome(_1576090), _1576096), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576088, _1576090)), hAPP(hAPP(c_Product__Type_OPair(_1576088, _1576090), _1576094), _1576096)), hAPP(c_List_Oset(tc_prod(_1576088, _1576090)), _1576092))))], (40877 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576088, _1576090)), hAPP(hAPP(c_Product__Type_OPair(_1576088, _1576090), _1576094), _1576096)), hAPP(c_List_Oset(tc_prod(_1576088, _1576090)), _1576092))), -(hAPP(hAPP(c_Map_Omap__of(_1576088, _1576090), _1576092), _1576094) = hAPP(c_Option_Ooption_OSome(_1576090), _1576096))]]], (40883 ^ _779530) ^ [_1576474, _1576476, _1576478, _1576480, _1576482] : [hBOOL(hAPP(c_List_Odistinct(_1576474), hAPP(hAPP(c_List_Omap(tc_prod(_1576474, _1576476), _1576474), c_Product__Type_Ofst(_1576474, _1576476)), _1576478))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576474, _1576476)), hAPP(hAPP(c_Product__Type_OPair(_1576474, _1576476), _1576480), _1576482)), hAPP(c_List_Oset(tc_prod(_1576474, _1576476)), _1576478))), -(hAPP(hAPP(c_Map_Omap__of(_1576474, _1576476), _1576478), _1576480) = hAPP(c_Option_Ooption_OSome(_1576476), _1576482))], (40893 ^ _779530) ^ [_1576735, _1576737, _1576739] : [hBOOL(hAPP(c_List_Odistinct(_1576735), hAPP(hAPP(c_List_Omap(tc_prod(_1576735, _1576737), _1576735), c_Product__Type_Ofst(_1576735, _1576737)), _1576739))), -(hAPP(c_List_Oset(tc_prod(_1576735, _1576737)), _1576739) = hAPP(c_Set_OCollect(tc_prod(_1576735, _1576737)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576735, _1576737, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1576735, tc_fun(_1576737, tc_Option_Ooption(_1576737)), tc_fun(_1576737, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1576737), tc_HOL_Obool), tc_fun(tc_fun(_1576737, tc_Option_Ooption(_1576737)), tc_fun(_1576737, tc_HOL_Obool)), _1576735), c_COMBB(tc_Option_Ooption(_1576737), tc_HOL_Obool, _1576737)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1576737), tc_fun(tc_Option_Ooption(_1576737), tc_HOL_Obool), _1576735), c_fequal), hAPP(c_Map_Omap__of(_1576735, _1576737), _1576739)))), c_Option_Ooption_OSome(_1576737)))))], (40899 ^ _779530) ^ [_1577048, _1577050, _1577052] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1577048), _1577050)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1577048)), hAPP(c_Set_OCollect(tc_List_Olist(_1577048)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1577048), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1577048)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1577048), tc_fun(_1577048, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1577048, tc_HOL_Obool), tc_fun(tc_fun(_1577048, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1577048)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1577048, tc_HOL_Obool))), c_List_Oset(_1577048))), _1577050))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1577048), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1577048)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1577048)))), _1577052))))))], (40905 ^ _779530) ^ [_1577351, _1577353, _1577355, _1577357] : [-(c_List_Olist_Olist__size(_1577351, _1577353, hAPP(hAPP(c_List_Olist_OCons(_1577351), _1577355), _1577357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1577353, _1577355)), c_List_Olist_Olist__size(_1577351, _1577353, _1577357))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40907 ^ _779530) ^ [_1577411, _1577413, _1577415, _1577417, _1577419] : [-(c_List_Olist_Olist__size(_1577411, _1577413, hAPP(hAPP(c_List_Omap(_1577415, _1577411), _1577417), _1577419)) = c_List_Olist_Olist__size(_1577415, hAPP(c_Fun_Ocomp(_1577411, tc_Nat_Onat, _1577415, _1577413), _1577417), _1577419))], (40909 ^ _779530) ^ [_1577467, _1577469, _1577471, _1577473] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577467)), hAPP(hAPP(c_List_Omap(_1577469, _1577467), _1577471), _1577473)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577469)), _1577473))], (40911 ^ _779530) ^ [_1577519, _1577521, _1577523, _1577525, _1577527, _1577529, _1577531] : [hAPP(hAPP(c_List_Omap(_1577519, _1577521), _1577523), _1577525) = hAPP(hAPP(c_List_Omap(_1577527, _1577521), _1577529), _1577531), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577519)), _1577525) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577527)), _1577531))], (40917 ^ _779530) ^ [_1577669, _1577671, _1577673] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577669)), _1577671) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577669)), _1577673)), _1577671 = _1577673], (40923 ^ _779530) ^ [_1577761, _1577763, _1577765, _1577767, _1577769] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1577761), tc_List_Olist(_1577761))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1577761), tc_List_Olist(_1577761)), _1577763), _1577765)), hAPP(c_List_Olexn(_1577761, _1577767), _1577769))), 40926 ^ _779530 : [(40927 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577761)), _1577763) = _1577769)], (40929 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577761)), _1577765) = _1577769)]]], (40931 ^ _779530) ^ [_1577964, _1577966, _1577968, _1577970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577964)), _1577966)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577964)), _1577968))), _1577966 = hAPP(hAPP(c_List_Olist_OCons(_1577964), _1577970), _1577968)], (40937 ^ _779530) ^ [_1578100, _1578102] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1578100), hAPP(c_List_Oset(_1578100), _1578102))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578100)), _1578102))))], (40939 ^ _779530) ^ [_1578147, _1578149] : [hAPP(c_Finite__Set_Ocard(_1578147), hAPP(c_List_Oset(_1578147), _1578149)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578147)), _1578149), -(hBOOL(hAPP(c_List_Odistinct(_1578147), _1578149)))], (40945 ^ _779530) ^ [_1578266, _1578268] : [hBOOL(hAPP(c_List_Odistinct(_1578266), _1578268)), -(hAPP(c_Finite__Set_Ocard(_1578266), hAPP(c_List_Oset(_1578266), _1578268)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578266)), _1578268))], (40951 ^ _779530) ^ [_1578385, _1578387, _1578389] : [-(hAPP(c_List_Olexn(_1578385, _1578387), hAPP(c_Nat_OSuc, _1578389)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1578385), tc_List_Olist(_1578385)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1578385, tc_List_Olist(_1578385)), tc_prod(_1578385, tc_List_Olist(_1578385))), tc_prod(tc_List_Olist(_1578385), tc_List_Olist(_1578385)), c_Product__Type_Omap__pair(tc_prod(_1578385, tc_List_Olist(_1578385)), tc_List_Olist(_1578385), tc_prod(_1578385, tc_List_Olist(_1578385)), tc_List_Olist(_1578385), hAPP(c_Product__Type_Oprod_Oprod__case(_1578385, tc_List_Olist(_1578385), tc_List_Olist(_1578385)), c_List_Olist_OCons(_1578385)), hAPP(c_Product__Type_Oprod_Oprod__case(_1578385, tc_List_Olist(_1578385), tc_List_Olist(_1578385)), c_List_Olist_OCons(_1578385)))), c_Wellfounded_Olex__prod(_1578385, tc_List_Olist(_1578385), _1578387, hAPP(c_List_Olexn(_1578385, _1578387), _1578389)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1578385), tc_List_Olist(_1578385))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1578385), tc_List_Olist(_1578385), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1578385), tc_fun(tc_List_Olist(_1578385), tc_HOL_Obool), tc_fun(tc_List_Olist(_1578385), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1578385), tc_HOL_Obool), tc_fun(tc_List_Olist(_1578385), tc_HOL_Obool)), tc_List_Olist(_1578385)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1578385))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1578385)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1578385), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1578385)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1578385)))), hAPP(c_Nat_OSuc, _1578389))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1578385), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1578385)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1578385)))), hAPP(c_Nat_OSuc, _1578389)))))))], (40953 ^ _779530) ^ [_1578676, _1578678, _1578680] : [hBOOL(hAPP(hAPP(c_member(_1578676), _1578678), hAPP(c_List_Oset(_1578676), _1578680))), -(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(_1578676)), _1578680))))], (40959 ^ _779530) ^ [_1578797, _1578799, _1578801] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578797)), hAPP(hAPP(c_List_Olist_OCons(_1578797), _1578799), _1578801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578797)), _1578801)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40961 ^ _779530) ^ [_1578879, _1578881, _1578883, _1578885, _1578887, _1578889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1578879), tc_List_Olist(_1578879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1578879), tc_List_Olist(_1578879)), hAPP(hAPP(c_List_Olist_OCons(_1578879), _1578881), _1578883)), hAPP(hAPP(c_List_Olist_OCons(_1578879), _1578885), _1578887))), c_List_Olex(_1578879, _1578889))), 40966 ^ _779530 : [(40967 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578879, _1578879)), hAPP(hAPP(c_Product__Type_OPair(_1578879, _1578879), _1578881), _1578885)), _1578889)))], (40969 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578879)), _1578883) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578879)), _1578887))]], 40970 ^ _779530 : [(40971 ^ _779530) ^ [] : [-(_1578881 = _1578885)], (40973 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1578879), tc_List_Olist(_1578879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1578879), tc_List_Olist(_1578879)), _1578883), _1578887)), c_List_Olex(_1578879, _1578889))))]]], (40975 ^ _779530) ^ [_1579277, _1579279, _1579281, _1579283, _1579285, _1579287] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1579277), tc_List_Olist(_1579277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1579277), tc_List_Olist(_1579277)), hAPP(hAPP(c_List_Olist_OCons(_1579277), _1579279), _1579281)), hAPP(hAPP(c_List_Olist_OCons(_1579277), _1579283), _1579285))), c_List_Olex(_1579277, _1579287)))), 40976 ^ _779530 : [(40977 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579277, _1579277)), hAPP(hAPP(c_Product__Type_OPair(_1579277, _1579277), _1579279), _1579283)), _1579287)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579277)), _1579281) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579277)), _1579285)], (40983 ^ _779530) ^ [] : [_1579279 = _1579283, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1579277), tc_List_Olist(_1579277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1579277), tc_List_Olist(_1579277)), _1579281), _1579285)), c_List_Olex(_1579277, _1579287)))]]], (40991 ^ _779530) ^ [_1579733, _1579735] : [-(c_List_Olenlex(_1579733, _1579735) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1579733), tc_List_Olist(_1579733), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1579733), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), tc_List_Olist(_1579733)), c_COMBS(tc_List_Olist(_1579733), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1579733)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1579733)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1579733), tc_fun(tc_List_Olist(_1579733), tc_Nat_Onat), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1579733), tc_Nat_Onat), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), tc_List_Olist(_1579733)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1579733))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1579733)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1579733))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1579733)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1579733), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), tc_List_Olist(_1579733)), c_COMBS(tc_List_Olist(_1579733), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1579733)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1579733)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1579733), tc_fun(tc_List_Olist(_1579733), tc_Nat_Onat), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1579733), tc_Nat_Onat), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), tc_List_Olist(_1579733)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1579733))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1579733)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1579733))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1579733)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1579733), tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1579733), tc_HOL_Obool)), tc_List_Olist(_1579733)), c_COMBC(tc_List_Olist(_1579733), tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1579733), tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733))), tc_fun(tc_List_Olist(_1579733), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1579733)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1579733)), c_member(tc_prod(tc_List_Olist(_1579733), tc_List_Olist(_1579733))))), c_Product__Type_OPair(tc_List_Olist(_1579733), tc_List_Olist(_1579733))))), c_List_Olex(_1579733, _1579735)))))))], (40993 ^ _779530) ^ [_1580289, _1580291] : [-(c_List_Olenlex(_1580289, _1580291) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1580289)), tc_List_Olist(_1580289)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1580289), c_Wellfounded_Oless__than, c_List_Olex(_1580289, _1580291))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1580289), tc_List_Olist(_1580289), tc_prod(tc_Nat_Onat, tc_List_Olist(_1580289))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1580289), tc_prod(tc_Nat_Onat, tc_List_Olist(_1580289))), tc_List_Olist(_1580289)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1580289))), c_Nat_Osize__class_Osize(tc_List_Olist(_1580289)))), c_COMBI(tc_List_Olist(_1580289)))))], (40995 ^ _779530) ^ [_1580397, _1580399, _1580401, _1580403, _1580405] : [hBOOL(hAPP(hAPP(c_member(_1580397), _1580399), hAPP(c_List_Oset(_1580397), _1580401))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1580403), hAPP(_1580405, _1580399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1580403), c_List_Olist_Olist__size(_1580397, _1580405, _1580401))))], (41005 ^ _779530) ^ [_1580596, _1580598, _1580600, _1580602, _1580604] : [hBOOL(hAPP(hAPP(c_member(_1580596), _1580598), hAPP(c_List_Oset(_1580596), _1580600))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580602), hAPP(_1580604, _1580598))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1580602), c_List_Olist_Olist__size(_1580596, _1580604, _1580600))))], (41015 ^ _779530) ^ [_1580795, _1580797, _1580799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1580795), _1580797)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1580795)), hAPP(c_Set_OCollect(tc_List_Olist(_1580795)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1580795), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1580795)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1580795), tc_fun(_1580795, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1580795, tc_HOL_Obool), tc_fun(tc_fun(_1580795, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1580795)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1580795, tc_HOL_Obool))), c_List_Oset(_1580795))), _1580797))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1580795), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1580795)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1580795)))), _1580799))))))], (41021 ^ _779530) ^ [_1581098, _1581100] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1581098))), c_Enum_Osublists(_1581098, _1581100)) = 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(_1581098)), _1581100)))], (41023 ^ _779530) ^ [_1581145, _1581147, _1581149] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581145)), c_List_Osublist(_1581145, _1581147, _1581149)) = 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(_1581145)), _1581147)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1581149)))))], (41025 ^ _779530) ^ [_1581211, _1581213, _1581215] : [hBOOL(hAPP(c_List_Odistinct(_1581211), _1581213)), -(hBOOL(hAPP(c_List_Odistinct(_1581211), c_List_Osublist(_1581211, _1581213, _1581215))))], (41031 ^ _779530) ^ [_1581313, _1581315, _1581317, _1581319] : [-(hBOOL(hAPP(hAPP(c_member(_1581313), _1581315), hAPP(c_List_Oset(_1581313), _1581317)))), hBOOL(hAPP(hAPP(c_member(_1581313), _1581315), hAPP(c_List_Oset(_1581313), c_List_Osublist(_1581313, _1581317, _1581319))))], (41037 ^ _779530) ^ [_1581437, _1581439, _1581441, _1581443] : [hBOOL(hAPP(hAPP(c_member(_1581437), _1581439), hAPP(c_List_Oset(_1581437), c_List_Osublist(_1581437, _1581441, _1581443)))), -(hBOOL(hAPP(hAPP(c_member(_1581437), _1581439), hAPP(c_List_Oset(_1581437), _1581441))))], (41043 ^ _779530) ^ [_1581574, _1581576, _1581578] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581574, tc_HOL_Obool)), hAPP(c_List_Oset(_1581574), c_List_Osublist(_1581574, _1581576, _1581578))), hAPP(c_List_Oset(_1581574), _1581576))))], (41045 ^ _779530) ^ [_1581625, _1581627] : [hBOOL(hAPP(c_List_Odistinct(_1581625), _1581627)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1581625, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1581625), tc_fun(_1581625, tc_HOL_Obool)), c_List_Oset(_1581625)), c_Enum_Osublists(_1581625, _1581627)))))], (41051 ^ _779530) ^ [_1581762, _1581764] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1581762), tc_fun(_1581762, tc_HOL_Obool), c_List_Oset(_1581762)), hAPP(c_List_Oset(tc_List_Olist(_1581762)), c_Enum_Osublists(_1581762, _1581764))) = hAPP(c_Set_OPow(_1581762), hAPP(c_List_Oset(_1581762), _1581764)))], (41053 ^ _779530) ^ [_1581821, _1581823, _1581825] : [-(hAPP(c_List_Oset(tc_List_Olist(_1581821)), c_Enum_On__lists(_1581821, _1581823, _1581825)) = hAPP(c_Set_OCollect(tc_List_Olist(_1581821)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1581821), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1581821)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1581821), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1581821)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1581821)))), _1581823))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1581821), tc_fun(_1581821, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1581821, tc_HOL_Obool), tc_fun(tc_fun(_1581821, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1581821)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1581821, tc_HOL_Obool))), c_List_Oset(_1581821))), hAPP(c_List_Oset(_1581821), _1581825)))))], (41055 ^ _779530) ^ [_1581993, _1581995, _1581997, _1581999, _1582001, _1582003] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1581993), tc_List_Olist(_1581993))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1581993), tc_List_Olist(_1581993)), hAPP(hAPP(c_List_Olist_OCons(_1581993), _1581995), _1581997)), hAPP(hAPP(c_List_Olist_OCons(_1581993), _1581999), _1582001))), c_List_Olexord(_1581993, _1582003))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581993, _1581993)), hAPP(hAPP(c_Product__Type_OPair(_1581993, _1581993), _1581995), _1581999)), _1582003))), 41062 ^ _779530 : [(41063 ^ _779530) ^ [] : [-(_1581995 = _1581999)], (41065 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1581993), tc_List_Olist(_1581993))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1581993), tc_List_Olist(_1581993)), _1581997), _1582001)), c_List_Olexord(_1581993, _1582003))))]]], (41067 ^ _779530) ^ [_1582320, _1582322, _1582324, _1582326, _1582328, _1582330] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1582320), tc_List_Olist(_1582320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1582320), tc_List_Olist(_1582320)), hAPP(hAPP(c_List_Olist_OCons(_1582320), _1582322), _1582324)), hAPP(hAPP(c_List_Olist_OCons(_1582320), _1582326), _1582328))), c_List_Olexord(_1582320, _1582330)))), 41068 ^ _779530 : [(41069 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582320, _1582320)), hAPP(hAPP(c_Product__Type_OPair(_1582320, _1582320), _1582322), _1582326)), _1582330))], (41071 ^ _779530) ^ [] : [_1582322 = _1582326, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1582320), tc_List_Olist(_1582320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1582320), tc_List_Olist(_1582320)), _1582324), _1582328)), c_List_Olexord(_1582320, _1582330)))]]], (41079 ^ _779530) ^ [_1582693, _1582695, _1582697] : [hBOOL(hAPP(c_List_Odistinct(_1582693), _1582695)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1582693)), c_Enum_On__lists(_1582693, _1582697, _1582695))))], (41085 ^ _779530) ^ [_1582800, _1582802, _1582804, _1582806] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1582800)), _1582802), hAPP(c_List_Oset(tc_List_Olist(_1582800)), c_Enum_On__lists(_1582800, _1582804, _1582806)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582800)), _1582802) = _1582804)], (41091 ^ _779530) ^ [_1582935, _1582937, _1582939] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1582935))), c_Enum_On__lists(_1582935, _1582937, _1582939)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582935)), _1582939)), _1582937))], (41093 ^ _779530) ^ [_1583009, _1583011, _1583013, _1583015] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583009), tc_List_Olist(_1583009))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583009), tc_List_Olist(_1583009)), _1583011), _1583013)), c_List_Olex(_1583009, _1583015))), 41096 ^ _779530 : [(41097 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583009), tc_List_Olist(_1583009))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583009), tc_List_Olist(_1583009)), _1583011), _1583013)), c_List_Olexord(_1583009, _1583015))))], (41099 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583009)), _1583011) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583009)), _1583013))]]], (41101 ^ _779530) ^ [_1583260, _1583262, _1583264, _1583266] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583260), tc_List_Olist(_1583260))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583260), tc_List_Olist(_1583260)), _1583262), _1583264)), c_List_Olex(_1583260, _1583266)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583260), tc_List_Olist(_1583260))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583260), tc_List_Olist(_1583260)), _1583262), _1583264)), c_List_Olexord(_1583260, _1583266))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583260)), _1583262) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583260)), _1583264)], (41111 ^ _779530) ^ [_1583547, _1583549, _1583551, _1583553] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1583547), tc_List_Olist(_1583547), c_List_Olistrel(_1583547, _1583549)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1583547)), hAPP(hAPP(c_List_Olist_OCons(_1583547), _1583551), _1583553)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1583547), tc_HOL_Obool)))) = c_List_Oset__Cons(_1583547, hAPP(c_Relation_OImage(_1583547, _1583547, _1583549), hAPP(hAPP(c_Set_Oinsert(_1583547), _1583551), c_Orderings_Obot__class_Obot(tc_fun(_1583547, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1583547), tc_List_Olist(_1583547), c_List_Olistrel(_1583547, _1583549)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1583547)), _1583553), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1583547), tc_HOL_Obool))))))], (41113 ^ _779530) ^ [_1583670, _1583672] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1583670, _1583672) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1583670), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1583672), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (41115 ^ _779530) ^ [_1583717, _1583719] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1583717, _1583719) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1583717, _1583719)))], (41117 ^ _779530) ^ [_1583752, _1583754] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1583752, _1583754)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1583752, _1583754))], (41119 ^ _779530) ^ [_1583787, _1583789] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1583787, _1583789))))], (41121 ^ _779530) ^ [_1583817, _1583819, _1583821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583817, _1583817), tc_HOL_Obool)), _1583819), _1583821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1583817), tc_List_Olist(_1583817)), tc_HOL_Obool)), c_List_Olistrel(_1583817, _1583819)), c_List_Olistrel(_1583817, _1583821))))], (41127 ^ _779530) ^ [_1583968, _1583970, _1583972, _1583974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1583968), tc_List_Olist(_1583968))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1583968), tc_List_Olist(_1583968)), _1583970), _1583972)), c_List_Olistrel(_1583968, _1583974))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583968)), _1583970) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583968)), _1583972))], (41133 ^ _779530) ^ [_1584137, _1584139] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1584137), _1584139) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1584137, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1584139), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (41135 ^ _779530) ^ [_1584180, _1584182] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1584180, _1584182) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1584180), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1584182)))], (41137 ^ _779530) ^ [_1584221, _1584223, _1584225, _1584227, _1584229, _1584231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584221, _1584221)), hAPP(hAPP(c_Product__Type_OPair(_1584221, _1584221), _1584223), _1584225)), _1584227)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584221), tc_List_Olist(_1584221))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584221), tc_List_Olist(_1584221)), _1584229), _1584231)), c_List_Olistrel(_1584221, _1584227))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584221), tc_List_Olist(_1584221))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584221), tc_List_Olist(_1584221)), hAPP(hAPP(c_List_Olist_OCons(_1584221), _1584223), _1584229)), hAPP(hAPP(c_List_Olist_OCons(_1584221), _1584225), _1584231))), c_List_Olistrel(_1584221, _1584227))))], (41147 ^ _779530) ^ [_1584568] : [c_List_Onat__list(_1584568), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1584568)))], (41153 ^ _779530) ^ [_1584641] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1584641)), -(c_List_Onat__list(_1584641))], (41159 ^ _779530) ^ [_1584741, _1584743, _1584745, _1584747] : [c_List_Olistrelp(_1584741, hAPP(hAPP(c_COMBC(_1584741, tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_fun(_1584741, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584741, tc_fun(tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_fun(_1584741, tc_HOL_Obool)), _1584741), c_COMBC(_1584741, tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584741, tc_prod(_1584741, _1584741)), tc_fun(_1584741, tc_fun(tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_HOL_Obool)), _1584741), hAPP(c_COMBB(tc_prod(_1584741, _1584741), tc_fun(tc_fun(tc_prod(_1584741, _1584741), tc_HOL_Obool), tc_HOL_Obool), _1584741), c_member(tc_prod(_1584741, _1584741)))), c_Product__Type_OPair(_1584741, _1584741)))), _1584743), _1584745, _1584747), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584741), tc_List_Olist(_1584741))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584741), tc_List_Olist(_1584741)), _1584745), _1584747)), c_List_Olistrel(_1584741, _1584743))))], (41165 ^ _779530) ^ [_1585118, _1585120, _1585122, _1585124] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1585118), tc_List_Olist(_1585118))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1585118), tc_List_Olist(_1585118)), _1585122), _1585124)), c_List_Olistrel(_1585118, _1585120))), -(c_List_Olistrelp(_1585118, hAPP(hAPP(c_COMBC(_1585118, tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_fun(_1585118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585118, tc_fun(tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_fun(_1585118, tc_HOL_Obool)), _1585118), c_COMBC(_1585118, tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585118, tc_prod(_1585118, _1585118)), tc_fun(_1585118, tc_fun(tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_HOL_Obool)), _1585118), hAPP(c_COMBB(tc_prod(_1585118, _1585118), tc_fun(tc_fun(tc_prod(_1585118, _1585118), tc_HOL_Obool), tc_HOL_Obool), _1585118), c_member(tc_prod(_1585118, _1585118)))), c_Product__Type_OPair(_1585118, _1585118)))), _1585120), _1585122, _1585124))], (41171 ^ _779530) ^ [_1585528, _1585530, _1585532, _1585534, _1585536, _1585538] : [c_List_Olistrelp(_1585528, _1585530, hAPP(hAPP(c_List_Olist_OCons(_1585528), _1585532), _1585534), hAPP(hAPP(c_List_Olist_OCons(_1585528), _1585536), _1585538)), 41174 ^ _779530 : [(41175 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1585530, _1585532), _1585536)))], (41177 ^ _779530) ^ [] : [-(c_List_Olistrelp(_1585528, _1585530, _1585534, _1585538))]]], (41179 ^ _779530) ^ [_1585685, _1585687, _1585689, _1585691, _1585693, _1585695] : [-(c_List_Olistrelp(_1585685, _1585687, hAPP(hAPP(c_List_Olist_OCons(_1585685), _1585689), _1585691), hAPP(hAPP(c_List_Olist_OCons(_1585685), _1585693), _1585695))), hBOOL(hAPP(hAPP(_1585687, _1585689), _1585693)), c_List_Olistrelp(_1585685, _1585687, _1585691, _1585695)], (41189 ^ _779530) ^ [_1585882, _1585884, _1585886, _1585888, _1585890, _1585892] : [hBOOL(hAPP(hAPP(_1585882, _1585884), _1585886)), c_List_Olistrelp(_1585888, _1585882, _1585890, _1585892), -(c_List_Olistrelp(_1585888, _1585882, hAPP(hAPP(c_List_Olist_OCons(_1585888), _1585884), _1585890), hAPP(hAPP(c_List_Olist_OCons(_1585888), _1585886), _1585892)))], (41199 ^ _779530) ^ [_1586098, _1586100, _1586102, _1586104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586098), tc_List_Olist(_1586098))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586098), tc_List_Olist(_1586098)), _1586100), _1586102)), c_List_Olistrel(_1586098, _1586104))), 41202 ^ _779530 : [(41203 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586098)), _1586100) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586098)), _1586102))], (41205 ^ _779530) ^ [_1586434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586098, _1586098)), _1586434), hAPP(c_List_Oset(tc_prod(_1586098, _1586098)), hAPP(hAPP(c_List_Ozip(_1586098, _1586098), _1586100), _1586102)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1586098, _1586098, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1586098, tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_fun(_1586098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586098, tc_fun(tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_fun(_1586098, tc_HOL_Obool)), _1586098), c_COMBC(_1586098, tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586098, tc_prod(_1586098, _1586098)), tc_fun(_1586098, tc_fun(tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_HOL_Obool)), _1586098), hAPP(c_COMBB(tc_prod(_1586098, _1586098), tc_fun(tc_fun(tc_prod(_1586098, _1586098), tc_HOL_Obool), tc_HOL_Obool), _1586098), c_member(tc_prod(_1586098, _1586098)))), c_Product__Type_OPair(_1586098, _1586098)))), _1586104)), _1586434)))]]], (41211 ^ _779530) ^ [_1586827, _1586829, _1586831, _1586833] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586827), tc_List_Olist(_1586827))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586827), tc_List_Olist(_1586827)), _1586829), _1586831)), c_List_Olistrel(_1586827, _1586833)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586827)), _1586829) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586827)), _1586831), 41217 ^ _779530 : [(41218 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586827, _1586827)), 41216 ^ [_1586827, _1586829, _1586831, _1586833]), hAPP(c_List_Oset(tc_prod(_1586827, _1586827)), hAPP(hAPP(c_List_Ozip(_1586827, _1586827), _1586829), _1586831)))))], (41220 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1586827, _1586827, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1586827, tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_fun(_1586827, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586827, tc_fun(tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_fun(_1586827, tc_HOL_Obool)), _1586827), c_COMBC(_1586827, tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1586827, tc_prod(_1586827, _1586827)), tc_fun(_1586827, tc_fun(tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_HOL_Obool)), _1586827), hAPP(c_COMBB(tc_prod(_1586827, _1586827), tc_fun(tc_fun(tc_prod(_1586827, _1586827), tc_HOL_Obool), tc_HOL_Obool), _1586827), c_member(tc_prod(_1586827, _1586827)))), c_Product__Type_OPair(_1586827, _1586827)))), _1586833)), 41216 ^ [_1586827, _1586829, _1586831, _1586833]))]]], (41224 ^ _779530) ^ [_1587565, _1587567, _1587569, _1587571, _1587573] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1587565), tc_List_Olist(_1587565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1587565), tc_List_Olist(_1587565)), _1587567), hAPP(hAPP(c_List_Olist_OCons(_1587565), _1587569), _1587571))), c_List_Olistrel(_1587565, _1587573))), 41229 ^ _779530 : [(41230 ^ _779530) ^ [] : [-(_1587567 = hAPP(hAPP(c_List_Olist_OCons(_1587565), 41227 ^ [_1587565, _1587567, _1587569, _1587571, _1587573]), 41228 ^ [_1587565, _1587567, _1587569, _1587571, _1587573]))], (41232 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587565, _1587565)), hAPP(hAPP(c_Product__Type_OPair(_1587565, _1587565), 41227 ^ [_1587565, _1587567, _1587569, _1587571, _1587573]), _1587569)), _1587573)))], (41234 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1587565), tc_List_Olist(_1587565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1587565), tc_List_Olist(_1587565)), 41228 ^ [_1587565, _1587567, _1587569, _1587571, _1587573]), _1587571)), c_List_Olistrel(_1587565, _1587573))))]]], (41236 ^ _779530) ^ [_1587954, _1587956, _1587958, _1587960] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1587954, _1587956))), hAPP(hAPP(c_List_Ozip(_1587954, _1587956), _1587958), _1587960)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587954)), _1587958)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587956)), _1587960)))], (41238 ^ _779530) ^ [_1588022, _1588024] : [-(hAPP(hAPP(c_List_Ozip(_1588022, _1588022), _1588024), _1588024) = hAPP(hAPP(c_List_Omap(_1588022, tc_prod(_1588022, _1588022)), hAPP(hAPP(c_COMBS(_1588022, _1588022, tc_prod(_1588022, _1588022)), c_Product__Type_OPair(_1588022, _1588022)), c_COMBI(_1588022))), _1588024))], (41240 ^ _779530) ^ [_1588086, _1588088, _1588090, _1588092] : [hBOOL(hAPP(c_List_Odistinct(_1588086), _1588088)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1588086, _1588090)), hAPP(hAPP(c_List_Ozip(_1588086, _1588090), _1588088), _1588092))))], (41246 ^ _779530) ^ [_1588207, _1588209, _1588211, _1588213] : [hBOOL(hAPP(c_List_Odistinct(_1588207), _1588209)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1588211, _1588207)), hAPP(hAPP(c_List_Ozip(_1588211, _1588207), _1588213), _1588209))))], (41252 ^ _779530) ^ [_1588328, _1588330, _1588332, _1588334, _1588336] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588328)), _1588330) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588332)), _1588334), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588328)), _1588336) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588332)), _1588334), hBOOL(hAPP(c_List_Odistinct(_1588332), _1588334)), hAPP(c_Map_Omap__of(_1588332, _1588328), hAPP(hAPP(c_List_Ozip(_1588332, _1588328), _1588334), _1588330)) = hAPP(c_Map_Omap__of(_1588332, _1588328), hAPP(hAPP(c_List_Ozip(_1588332, _1588328), _1588334), _1588336)), -(_1588330 = _1588336)], (41270 ^ _779530) ^ [_1588709, _1588711, _1588713, _1588715] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588709)), _1588711) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588713)), _1588715), -(hAPP(hAPP(c_List_Omap(tc_prod(_1588709, _1588713), _1588709), c_Product__Type_Ofst(_1588709, _1588713)), hAPP(hAPP(c_List_Ozip(_1588709, _1588713), _1588711), _1588715)) = _1588711)], (41276 ^ _779530) ^ [_1588866, _1588868, _1588870, _1588872] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588866)), _1588868) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588870)), _1588872), -(hAPP(hAPP(c_List_Omap(tc_prod(_1588866, _1588870), _1588870), c_Product__Type_Osnd(_1588866, _1588870)), hAPP(hAPP(c_List_Ozip(_1588866, _1588870), _1588868), _1588872)) = _1588872)], (41282 ^ _779530) ^ [_1589023, _1589025, _1589027] : [-(hAPP(hAPP(c_List_Ozip(_1589023, _1589025), hAPP(hAPP(c_List_Omap(tc_prod(_1589023, _1589025), _1589023), c_Product__Type_Ofst(_1589023, _1589025)), _1589027)), hAPP(hAPP(c_List_Omap(tc_prod(_1589023, _1589025), _1589025), c_Product__Type_Osnd(_1589023, _1589025)), _1589027)) = _1589027)], (41284 ^ _779530) ^ [_1589089, _1589091, _1589093, _1589095, _1589097, _1589099] : [-(hAPP(hAPP(c_List_Ozip(_1589089, _1589091), hAPP(hAPP(c_List_Olist_OCons(_1589089), _1589093), _1589095)), hAPP(hAPP(c_List_Olist_OCons(_1589091), _1589097), _1589099)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1589089, _1589091)), hAPP(hAPP(c_Product__Type_OPair(_1589089, _1589091), _1589093), _1589097)), hAPP(hAPP(c_List_Ozip(_1589089, _1589091), _1589095), _1589099)))], (41286 ^ _779530) ^ [_1589176, _1589178, _1589180, _1589182, _1589184] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589176)), _1589178) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589180)), _1589182), 41289 ^ _779530 : [(41290 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Ozip(_1589176, _1589180), _1589178), _1589182) = _1589184, 41293 ^ _779530 : [(41294 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1589176, _1589180), _1589176), c_Product__Type_Ofst(_1589176, _1589180)), _1589184) = _1589178)], (41296 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1589176, _1589180), _1589180), c_Product__Type_Osnd(_1589176, _1589180)), _1589184) = _1589182)]]], (41298 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1589176, _1589180), _1589178), _1589182) = _1589184), hAPP(hAPP(c_List_Omap(tc_prod(_1589176, _1589180), _1589176), c_Product__Type_Ofst(_1589176, _1589180)), _1589184) = _1589178, hAPP(hAPP(c_List_Omap(tc_prod(_1589176, _1589180), _1589180), c_Product__Type_Osnd(_1589176, _1589180)), _1589184) = _1589182]]], (41308 ^ _779530) ^ [_1589624, _1589626, _1589628, _1589630, _1589632, _1589634, _1589636, _1589638] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1589624, _1589626), _1589628), _1589630), hAPP(hAPP(c_List_Ozip(_1589624, _1589626), hAPP(hAPP(c_List_Omap(_1589632, _1589624), _1589634), _1589636)), _1589638)) = hAPP(hAPP(c_List_Omap(tc_prod(_1589632, _1589626), _1589628), hAPP(c_Product__Type_Oprod_Oprod__case(_1589632, _1589626, _1589628), hAPP(hAPP(c_COMBB(tc_fun(_1589626, tc_prod(_1589624, _1589626)), tc_fun(_1589626, _1589628), _1589632), hAPP(c_COMBB(tc_prod(_1589624, _1589626), _1589628, _1589626), _1589630)), hAPP(hAPP(c_COMBB(_1589624, tc_fun(_1589626, tc_prod(_1589624, _1589626)), _1589632), c_Product__Type_OPair(_1589624, _1589626)), _1589634)))), hAPP(hAPP(c_List_Ozip(_1589632, _1589626), _1589636), _1589638)))], (41310 ^ _779530) ^ [_1589767, _1589769, _1589771, _1589773, _1589775, _1589777, _1589779, _1589781] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1589767, _1589769), _1589771), _1589773), hAPP(hAPP(c_List_Ozip(_1589767, _1589769), _1589775), hAPP(hAPP(c_List_Omap(_1589777, _1589769), _1589779), _1589781))) = hAPP(hAPP(c_List_Omap(tc_prod(_1589767, _1589777), _1589771), hAPP(c_Product__Type_Oprod_Oprod__case(_1589767, _1589777, _1589771), hAPP(hAPP(c_COMBB(tc_fun(_1589777, tc_prod(_1589767, _1589769)), tc_fun(_1589777, _1589771), _1589767), hAPP(c_COMBB(tc_prod(_1589767, _1589769), _1589771, _1589777), _1589773)), hAPP(hAPP(c_COMBC(_1589767, tc_fun(_1589777, _1589769), tc_fun(_1589777, tc_prod(_1589767, _1589769))), hAPP(hAPP(c_COMBB(tc_fun(_1589769, tc_prod(_1589767, _1589769)), tc_fun(tc_fun(_1589777, _1589769), tc_fun(_1589777, tc_prod(_1589767, _1589769))), _1589767), c_COMBB(_1589769, tc_prod(_1589767, _1589769), _1589777)), c_Product__Type_OPair(_1589767, _1589769))), _1589779)))), hAPP(hAPP(c_List_Ozip(_1589767, _1589777), _1589775), _1589781)))], (41312 ^ _779530) ^ [_1589966, _1589968, _1589970] : [_1589966 = _1589968, 41315 ^ _779530 : [(41316 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589970)), _1589966) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589970)), _1589968))], (41318 ^ _779530) ^ [_1590122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589970, _1589970)), _1590122), hAPP(c_List_Oset(tc_prod(_1589970, _1589970)), hAPP(hAPP(c_List_Ozip(_1589970, _1589970), _1589966), _1589968)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1589970, _1589970, tc_HOL_Obool), c_fequal), _1590122)))]]], (41324 ^ _779530) ^ [_1590277, _1590279, _1590281] : [-(_1590277 = _1590279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1590281)), _1590277) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1590281)), _1590279), 41330 ^ _779530 : [(41331 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590281, _1590281)), 41329 ^ [_1590277, _1590279, _1590281]), hAPP(c_List_Oset(tc_prod(_1590281, _1590281)), hAPP(hAPP(c_List_Ozip(_1590281, _1590281), _1590277), _1590279)))))], (41333 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1590281, _1590281, tc_HOL_Obool), c_fequal), 41329 ^ [_1590277, _1590279, _1590281]))]]], (41337 ^ _779530) ^ [_1590591, _1590593, _1590595, _1590597, _1590599, _1590601] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590591, _1590593)), hAPP(hAPP(c_Product__Type_OPair(_1590591, _1590593), _1590595), _1590597)), hAPP(c_List_Oset(tc_prod(_1590591, _1590593)), hAPP(hAPP(c_List_Ozip(_1590591, _1590593), _1590599), _1590601)))), 41340 ^ _779530 : [(41341 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590591), _1590595), hAPP(c_List_Oset(_1590591), _1590599))))], (41343 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590593), _1590597), hAPP(c_List_Oset(_1590593), _1590601))))]]], (41345 ^ _779530) ^ [_1590826, _1590828, _1590830, _1590832, _1590834, _1590836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590826, _1590828)), hAPP(hAPP(c_Product__Type_OPair(_1590826, _1590828), _1590830), _1590832)), hAPP(c_List_Oset(tc_prod(_1590826, _1590828)), hAPP(hAPP(c_List_Ozip(_1590826, _1590828), _1590834), _1590836)))), -(hBOOL(hAPP(hAPP(c_member(_1590828), _1590832), hAPP(c_List_Oset(_1590828), _1590836))))], (41351 ^ _779530) ^ [_1591007, _1591009, _1591011, _1591013, _1591015, _1591017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591007, _1591009)), hAPP(hAPP(c_Product__Type_OPair(_1591007, _1591009), _1591011), _1591013)), hAPP(c_List_Oset(tc_prod(_1591007, _1591009)), hAPP(hAPP(c_List_Ozip(_1591007, _1591009), _1591015), _1591017)))), -(hBOOL(hAPP(hAPP(c_member(_1591007), _1591011), hAPP(c_List_Oset(_1591007), _1591015))))], (41357 ^ _779530) ^ [_1591209, _1591211, _1591213, _1591215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591209, _1591209)), hAPP(hAPP(c_Product__Type_OPair(_1591209, _1591209), _1591211), _1591213)), hAPP(c_List_Oset(tc_prod(_1591209, _1591209)), hAPP(hAPP(c_List_Ozip(_1591209, _1591209), _1591215), _1591215)))), 41360 ^ _779530 : [(41361 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591209), _1591211), hAPP(c_List_Oset(_1591209), _1591215))))], (41363 ^ _779530) ^ [] : [-(_1591211 = _1591213)]]], (41365 ^ _779530) ^ [_1591408, _1591410, _1591412, _1591414] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591408, _1591408)), hAPP(hAPP(c_Product__Type_OPair(_1591408, _1591408), _1591410), _1591412)), hAPP(c_List_Oset(tc_prod(_1591408, _1591408)), hAPP(hAPP(c_List_Ozip(_1591408, _1591408), _1591414), _1591414))))), hBOOL(hAPP(hAPP(c_member(_1591408), _1591410), hAPP(c_List_Oset(_1591408), _1591414))), _1591410 = _1591412], (41375 ^ _779530) ^ [_1591643, _1591645, _1591647, _1591649, _1591651] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591643)), _1591645) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591647)), _1591649), 41378 ^ _779530 : [(41379 ^ _779530) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1591643, _1591647), hAPP(hAPP(c_List_Ozip(_1591643, _1591647), _1591645), _1591649)), _1591651) = c_Option_Ooption_ONone(_1591647), hBOOL(hAPP(hAPP(c_member(_1591643), _1591651), hAPP(c_List_Oset(_1591643), _1591645)))], (41385 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591643), _1591651), hAPP(c_List_Oset(_1591643), _1591645)))), -(hAPP(hAPP(c_Map_Omap__of(_1591643, _1591647), hAPP(hAPP(c_List_Ozip(_1591643, _1591647), _1591645), _1591649)), _1591651) = c_Option_Ooption_ONone(_1591647))]]], (41391 ^ _779530) ^ [_1591948, _1591950, _1591952, _1591954, _1591956] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591948)), _1591950) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591952)), _1591954), 41394 ^ _779530 : [(41395 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1591948), _1591956), hAPP(c_List_Oset(_1591948), _1591950))), -(hAPP(hAPP(c_Map_Omap__of(_1591948, _1591952), hAPP(hAPP(c_List_Ozip(_1591948, _1591952), _1591950), _1591954)), _1591956) = hAPP(c_Option_Ooption_OSome(_1591952), 41398 ^ [_1591948, _1591950, _1591952, _1591954, _1591956]))], (41402 ^ _779530) ^ [] : [41403 ^ _779530 : [(41404 ^ _779530) ^ [_1592240] : [hAPP(hAPP(c_Map_Omap__of(_1591948, _1591952), hAPP(hAPP(c_List_Ozip(_1591948, _1591952), _1591950), _1591954)), _1591956) = hAPP(c_Option_Ooption_OSome(_1591952), _1592240)]], -(hBOOL(hAPP(hAPP(c_member(_1591948), _1591956), hAPP(c_List_Oset(_1591948), _1591950))))]]], (41408 ^ _779530) ^ [_1592332, _1592334, _1592336, _1592338, _1592340, _1592342, _1592344, _1592346] : [-(hAPP(hAPP(c_List_Ozip(_1592332, _1592334), hAPP(hAPP(c_List_Omap(_1592336, _1592332), _1592338), _1592340)), hAPP(hAPP(c_List_Omap(_1592342, _1592334), _1592344), _1592346)) = hAPP(hAPP(c_List_Omap(tc_prod(_1592336, _1592342), tc_prod(_1592332, _1592334)), hAPP(c_Product__Type_Oprod_Oprod__case(_1592336, _1592342, tc_prod(_1592332, _1592334)), hAPP(hAPP(c_COMBC(_1592336, tc_fun(_1592342, _1592334), tc_fun(_1592342, tc_prod(_1592332, _1592334))), hAPP(hAPP(c_COMBB(tc_fun(_1592334, tc_prod(_1592332, _1592334)), tc_fun(tc_fun(_1592342, _1592334), tc_fun(_1592342, tc_prod(_1592332, _1592334))), _1592336), c_COMBB(_1592334, tc_prod(_1592332, _1592334), _1592342)), hAPP(hAPP(c_COMBB(_1592332, tc_fun(_1592334, tc_prod(_1592332, _1592334)), _1592336), c_Product__Type_OPair(_1592332, _1592334)), _1592338))), _1592344))), hAPP(hAPP(c_List_Ozip(_1592336, _1592342), _1592340), _1592346)))], (41410 ^ _779530) ^ [_1592503, _1592505, _1592507, _1592509, _1592511, _1592513] : [-(hAPP(hAPP(c_List_Ozip(_1592503, _1592505), hAPP(hAPP(c_List_Omap(_1592507, _1592503), _1592509), _1592511)), _1592513) = hAPP(hAPP(c_List_Omap(tc_prod(_1592507, _1592505), tc_prod(_1592503, _1592505)), hAPP(c_Product__Type_Oprod_Oprod__case(_1592507, _1592505, tc_prod(_1592503, _1592505)), hAPP(hAPP(c_COMBB(_1592503, tc_fun(_1592505, tc_prod(_1592503, _1592505)), _1592507), c_Product__Type_OPair(_1592503, _1592505)), _1592509))), hAPP(hAPP(c_List_Ozip(_1592507, _1592505), _1592511), _1592513)))], (41412 ^ _779530) ^ [_1592607, _1592609, _1592611, _1592613, _1592615, _1592617] : [-(hAPP(hAPP(c_List_Ozip(_1592607, _1592609), _1592611), hAPP(hAPP(c_List_Omap(_1592613, _1592609), _1592615), _1592617)) = hAPP(hAPP(c_List_Omap(tc_prod(_1592607, _1592613), tc_prod(_1592607, _1592609)), hAPP(c_Product__Type_Oprod_Oprod__case(_1592607, _1592613, tc_prod(_1592607, _1592609)), hAPP(hAPP(c_COMBC(_1592607, tc_fun(_1592613, _1592609), tc_fun(_1592613, tc_prod(_1592607, _1592609))), hAPP(hAPP(c_COMBB(tc_fun(_1592609, tc_prod(_1592607, _1592609)), tc_fun(tc_fun(_1592613, _1592609), tc_fun(_1592613, tc_prod(_1592607, _1592609))), _1592607), c_COMBB(_1592609, tc_prod(_1592607, _1592609), _1592613)), c_Product__Type_OPair(_1592607, _1592609))), _1592615))), hAPP(hAPP(c_List_Ozip(_1592607, _1592613), _1592611), _1592617)))], (41414 ^ _779530) ^ [_1592749, _1592751, _1592753, _1592755] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592749)), _1592751) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592753)), _1592755), hBOOL(hAPP(c_List_Odistinct(_1592749), _1592751)), -(c_Map_Odom(_1592749, _1592753, hAPP(c_Map_Omap__of(_1592749, _1592753), hAPP(hAPP(c_List_Ozip(_1592749, _1592753), _1592751), _1592755))) = hAPP(c_List_Oset(_1592749), _1592751))], (41424 ^ _779530) ^ [_1592970, _1592972, _1592974, _1592976, _1592978, _1592980, _1592982, _1592984] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592970)), _1592972) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592974)), _1592976), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592970)), _1592978) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592974)), _1592976), -(hBOOL(hAPP(hAPP(c_member(_1592974), _1592980), hAPP(c_List_Oset(_1592974), _1592976)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1592974, tc_Option_Ooption(_1592970)), hAPP(c_Map_Omap__of(_1592974, _1592970), hAPP(hAPP(c_List_Ozip(_1592974, _1592970), _1592976), _1592972))), _1592980), hAPP(c_Option_Ooption_OSome(_1592970), _1592982)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1592974, tc_Option_Ooption(_1592970)), hAPP(c_Map_Omap__of(_1592974, _1592970), hAPP(hAPP(c_List_Ozip(_1592974, _1592970), _1592976), _1592978))), _1592980), hAPP(c_Option_Ooption_OSome(_1592970), _1592984)), -(hAPP(c_Map_Omap__of(_1592974, _1592970), hAPP(hAPP(c_List_Ozip(_1592974, _1592970), _1592976), _1592972)) = hAPP(c_Map_Omap__of(_1592974, _1592970), hAPP(hAPP(c_List_Ozip(_1592974, _1592970), _1592976), _1592978)))], (41442 ^ _779530) ^ [_1593548, _1593550, _1593552, _1593554, _1593556] : [hBOOL(hAPP(hAPP(c_member(_1593548), _1593550), hAPP(c_List_Oset(_1593548), _1593552))), -(hAPP(hAPP(c_Map_Omap__of(_1593548, _1593554), hAPP(hAPP(c_List_Ozip(_1593548, _1593554), _1593552), hAPP(hAPP(c_List_Omap(_1593548, _1593554), _1593556), _1593552))), _1593550) = hAPP(c_Option_Ooption_OSome(_1593554), hAPP(_1593556, _1593550)))], (41448 ^ _779530) ^ [_1593719, _1593721, _1593723, _1593725, _1593727] : [-(hBOOL(hAPP(hAPP(c_member(_1593719), _1593721), hAPP(c_List_Oset(_1593719), _1593723)))), -(hAPP(hAPP(c_Map_Omap__of(_1593719, _1593725), hAPP(hAPP(c_List_Ozip(_1593719, _1593725), _1593723), hAPP(hAPP(c_List_Omap(_1593719, _1593725), _1593727), _1593723))), _1593721) = c_Option_Ooption_ONone(_1593725))], (41454 ^ _779530) ^ [_1593804, _1593806, _1593808, _1593810, _1593812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593804), tc_List_Olist(_1593804))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593804), tc_List_Olist(_1593804)), hAPP(hAPP(c_List_Olist_OCons(_1593804), _1593806), _1593808)), _1593810)), c_List_Olistrel(_1593804, _1593812))), 41459 ^ _779530 : [(41460 ^ _779530) ^ [] : [-(_1593810 = hAPP(hAPP(c_List_Olist_OCons(_1593804), 41457 ^ [_1593804, _1593806, _1593808, _1593810, _1593812]), 41458 ^ [_1593804, _1593806, _1593808, _1593810, _1593812]))], (41462 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593804, _1593804)), hAPP(hAPP(c_Product__Type_OPair(_1593804, _1593804), _1593806), 41457 ^ [_1593804, _1593806, _1593808, _1593810, _1593812])), _1593812)))], (41464 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593804), tc_List_Olist(_1593804))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593804), tc_List_Olist(_1593804)), _1593808), 41458 ^ [_1593804, _1593806, _1593808, _1593810, _1593812])), c_List_Olistrel(_1593804, _1593812))))]]], (41466 ^ _779530) ^ [_1594193, _1594195, _1594197, _1594199] : [class_Enum_Oenum(_1594193), class_Enum_Oenum(_1594195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594195)), _1594197) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594193)), c_Enum_Oenum__class_Oenum(_1594193)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594195)), _1594199) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594193)), c_Enum_Oenum__class_Oenum(_1594193)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1594195), _1594195, _1594193, c_Option_Othe(_1594195)), hAPP(c_Map_Omap__of(_1594193, _1594195), hAPP(hAPP(c_List_Ozip(_1594193, _1594195), c_Enum_Oenum__class_Oenum(_1594193)), _1594197))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1594195), _1594195, _1594193, c_Option_Othe(_1594195)), hAPP(c_Map_Omap__of(_1594193, _1594195), hAPP(hAPP(c_List_Ozip(_1594193, _1594195), c_Enum_Oenum__class_Oenum(_1594193)), _1594199))), -(_1594197 = _1594199)], (41488 ^ _779530) ^ [_1594676, _1594678] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1594676, _1594678)) = c_Enum_Oproduct(_1594676, _1594678, c_Enum_Oenum__class_Oenum(_1594676), c_Enum_Oenum__class_Oenum(_1594678))), class_Enum_Oenum(_1594676), class_Enum_Oenum(_1594678)], (41498 ^ _779530) ^ [_1594829] : [class_Enum_Oenum(_1594829), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1594829)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1594829)), c_Option_Ooption_ONone(_1594829)), hAPP(hAPP(c_List_Omap(_1594829, tc_Option_Ooption(_1594829)), c_Option_Ooption_OSome(_1594829)), c_Enum_Oenum__class_Oenum(_1594829))))], (41504 ^ _779530) ^ [_1594964] : [class_Enum_Oenum(_1594964), -(hBOOL(hAPP(c_List_Odistinct(_1594964), c_Enum_Oenum__class_Oenum(_1594964))))], (41510 ^ _779530) ^ [_1595049, _1595051] : [class_Enum_Oenum(_1595049), -(hBOOL(hAPP(hAPP(c_member(_1595049), _1595051), hAPP(c_List_Oset(_1595049), c_Enum_Oenum__class_Oenum(_1595049)))))], (41516 ^ _779530) ^ [_1595152] : [class_Enum_Oenum(_1595152), -(c_Orderings_Otop__class_Otop(tc_fun(_1595152, tc_HOL_Obool)) = hAPP(c_List_Oset(_1595152), c_Enum_Oenum__class_Oenum(_1595152)))], (41522 ^ _779530) ^ [_1595249] : [class_Enum_Oenum(_1595249), -(hAPP(c_List_Oset(_1595249), c_Enum_Oenum__class_Oenum(_1595249)) = c_Orderings_Otop__class_Otop(tc_fun(_1595249, tc_HOL_Obool)))], (41528 ^ _779530) ^ [_1595346, _1595348] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1595346, _1595348)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1595348), tc_fun(_1595346, _1595348)), hAPP(hAPP(c_COMBB(tc_fun(_1595346, tc_Option_Ooption(_1595348)), tc_fun(_1595346, _1595348), tc_List_Olist(_1595348)), c_Fun_Ocomp(tc_Option_Ooption(_1595348), _1595348, _1595346, 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599658)), _1599660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599662)), _1599664))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1599658, _1599662)), hAPP(hAPP(c_List_Ozip(_1599658, _1599662), _1599660), _1599664)), _1599656) = hAPP(hAPP(c_Product__Type_OPair(_1599658, _1599662), hAPP(hAPP(c_List_Onth(_1599658), _1599660), _1599656)), hAPP(hAPP(c_List_Onth(_1599662), _1599664), _1599656)))], (41704 ^ _779530) ^ [_1599953, _1599955, _1599957] : [_1599953 = _1599955, 41707 ^ _779530 : [(41708 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599957)), _1599953) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599957)), _1599955))], (41710 ^ _779530) ^ [_1600101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1600101), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599957)), _1599953))), -(hAPP(hAPP(c_List_Onth(_1599957), _1599953), _1600101) = hAPP(hAPP(c_List_Onth(_1599957), _1599955), _1600101))]]], (41716 ^ _779530) ^ [_1600240, _1600242, _1600244] : [-(_1600240 = _1600242), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600244)), _1600240) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600244)), _1600242), 41722 ^ _779530 : [(41723 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41721 ^ [_1600240, _1600242, _1600244]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600244)), _1600240))))], (41725 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Onth(_1600244), _1600240), 41721 ^ [_1600240, _1600242, _1600244]) = hAPP(hAPP(c_List_Onth(_1600244), _1600242), 41721 ^ [_1600240, _1600242, _1600244])]]], (41729 ^ _779530) ^ [_1600555, _1600557, _1600559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600555, tc_HOL_Obool)), _1600557), _1600559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1600555), tc_HOL_Obool)), c_List_Olists(_1600555, _1600557)), c_List_Olists(_1600555, _1600559))))], (41735 ^ _779530) ^ [_1600690, _1600692, _1600694] : [-(hAPP(hAPP(c_List_Onth(_1600690), hAPP(hAPP(c_List_Olist_OCons(_1600690), _1600692), _1600694)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1600692)], (41737 ^ _779530) ^ [_1600733, _1600735, _1600737, _1600739] : [-(hAPP(hAPP(c_List_Onth(_1600733), hAPP(hAPP(c_List_Olist_OCons(_1600733), _1600735), _1600737)), hAPP(c_Nat_OSuc, _1600739)) = hAPP(hAPP(c_List_Onth(_1600733), _1600737), _1600739))], (41739 ^ _779530) ^ [_1600789, _1600791, _1600793, _1600795] : [-(hAPP(hAPP(c_List_Onth(_1600789), hAPP(hAPP(c_List_Olist_OCons(_1600789), _1600791), _1600793)), _1600795) = c_Nat_Onat_Onat__case(_1600789, _1600791, hAPP(c_List_Onth(_1600789), _1600793), _1600795))], (41741 ^ _779530) ^ [_1600862, _1600864, _1600866] : [41743 ^ _779530 : [(41744 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600862), 41742 ^ [_1600862, _1600864, _1600866]), hAPP(c_List_Oset(_1600862), _1600864))))], (41746 ^ _779530) ^ [] : [hBOOL(hAPP(_1600866, 41742 ^ [_1600862, _1600864, _1600866]))]], 41747 ^ _779530 : [(41748 ^ _779530) ^ [_1601046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1601046), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1600862)), _1600864))), -(hBOOL(hAPP(_1600866, hAPP(hAPP(c_List_Onth(_1600862), _1600864), _1601046))))]]], (41754 ^ _779530) ^ [_1601173, _1601175, _1601177] : [41756 ^ _779530 : [(41757 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41755 ^ [_1601173, _1601175, _1601177]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601173)), _1601175))))], (41759 ^ _779530) ^ [] : [hBOOL(hAPP(_1601177, hAPP(hAPP(c_List_Onth(_1601173), _1601175), 41755 ^ [_1601173, _1601175, _1601177])))]], 41760 ^ _779530 : [(41761 ^ _779530) ^ [_1601375] : [hBOOL(hAPP(hAPP(c_member(_1601173), _1601375), hAPP(c_List_Oset(_1601173), _1601175))), -(hBOOL(hAPP(_1601177, _1601375)))]]], (41767 ^ _779530) ^ [_1601492, _1601494, _1601496, _1601498, _1601500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1601492), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601494)), _1601496))), -(hAPP(hAPP(c_List_Onth(_1601498), hAPP(hAPP(c_List_Omap(_1601494, _1601498), _1601500), _1601496)), _1601492) = hAPP(_1601500, hAPP(hAPP(c_List_Onth(_1601494), _1601496), _1601492)))], (41773 ^ _779530) ^ [_1601655, _1601657, _1601659, _1601661] : [hBOOL(hAPP(c_List_Odistinct(_1601655), _1601657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1601659), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601655)), _1601657))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1601661), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601655)), _1601657))), 41784 ^ _779530 : [(41785 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Onth(_1601655), _1601657), _1601659) = hAPP(hAPP(c_List_Onth(_1601655), _1601657), _1601661), -(_1601659 = _1601661)], (41791 ^ _779530) ^ [] : [_1601659 = _1601661, -(hAPP(hAPP(c_List_Onth(_1601655), _1601657), _1601659) = hAPP(hAPP(c_List_Onth(_1601655), _1601657), _1601661))]]], (41815 ^ _779530) ^ [_1602565, _1602567] : [41817 ^ _779530 : [(41818 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41816 ^ [_1602565, _1602567]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602565)), _1602567))))], (41821 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41819 ^ [_1602565, _1602567]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602565)), _1602567))))], (41823 ^ _779530) ^ [] : [41816 ^ [_1602565, _1602567] = 41819 ^ [_1602565, _1602567]], (41825 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1602565), _1602567), 41816 ^ [_1602565, _1602567]) = hAPP(hAPP(c_List_Onth(_1602565), _1602567), 41819 ^ [_1602565, _1602567]))]], -(hBOOL(hAPP(c_List_Odistinct(_1602565), _1602567)))], (41797 ^ _779530) ^ [_1602105, _1602107] : [hBOOL(hAPP(c_List_Odistinct(_1602105), _1602107)), 41800 ^ _779530 : [(41801 ^ _779530) ^ [_1602237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1602237), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602105)), _1602107))), 41804 ^ _779530 : [(41805 ^ _779530) ^ [_1602364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1602364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602105)), _1602107))), -(_1602237 = _1602364), hAPP(hAPP(c_List_Onth(_1602105), _1602107), _1602237) = hAPP(hAPP(c_List_Onth(_1602105), _1602107), _1602364)]]]]], (41829 ^ _779530) ^ [_1602997] : [-(c_List_Olists(_1602997, c_Orderings_Otop__class_Otop(tc_fun(_1602997, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1602997), tc_HOL_Obool)))], (41831 ^ _779530) ^ [_1603035, _1603037, _1603039] : [c_Equiv__Relations_Oequiv(_1603035, _1603037, _1603039), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1603035), c_List_Olists(_1603035, _1603037), c_List_Olistrel(_1603035, _1603039)))], (41837 ^ _779530) ^ [_1603134, _1603136, _1603138] : [c_Relation_Orefl__on(_1603134, _1603136, _1603138), -(c_Relation_Orefl__on(tc_List_Olist(_1603134), c_List_Olists(_1603134, _1603136), c_List_Olistrel(_1603134, _1603138)))], (41843 ^ _779530) ^ [_1603251, _1603253, _1603255] : [hBOOL(hAPP(hAPP(c_member(_1603251), _1603253), hAPP(c_List_Oset(_1603251), _1603255))), 41847 ^ _779530 : [(41848 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41846 ^ [_1603251, _1603253, _1603255]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603251)), _1603255))))], (41850 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1603251), _1603255), 41846 ^ [_1603251, _1603253, _1603255]) = _1603253)]]], (41852 ^ _779530) ^ [_1603439, _1603441, _1603443] : [-(hBOOL(hAPP(hAPP(c_member(_1603439), _1603441), hAPP(c_List_Oset(_1603439), _1603443)))), 41853 ^ _779530 : [(41854 ^ _779530) ^ [_1603513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1603513), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603439)), _1603443))), hAPP(hAPP(c_List_Onth(_1603439), _1603443), _1603513) = _1603441]]], (41862 ^ _779530) ^ [_1603675, _1603677, _1603679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1603675), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603677)), _1603679))), -(hBOOL(hAPP(hAPP(c_member(_1603677), hAPP(hAPP(c_List_Onth(_1603677), _1603679), _1603675)), hAPP(c_List_Oset(_1603677), _1603679))))], (41868 ^ _779530) ^ [_1603833, _1603835, _1603837, _1603839] : [_1603833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1603835), hAPP(hAPP(c_List_Olist_OCons(_1603835), _1603837), _1603839)), _1603833) = _1603837)], (41874 ^ _779530) ^ [_1603940, _1603942, _1603944, _1603946] : [-(_1603940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1603942), hAPP(hAPP(c_List_Olist_OCons(_1603942), _1603944), _1603946)), _1603940) = hAPP(hAPP(c_List_Onth(_1603942), _1603946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1603940), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41880 ^ _779530) ^ [_1604012, _1604014] : [-(hAPP(c_List_Oset(_1604012), _1604014) = hAPP(c_Set_OCollect(_1604012), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1604012), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1604012, 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)), _1604012), 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)), _1604012), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1604012, tc_fun(tc_Nat_Onat, _1604012), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604012, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1604012), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1604012), c_COMBB(_1604012, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1604012), _1604014))))), 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(_1604012)), _1604014))))))], (41882 ^ _779530) ^ [_1604159, _1604161, _1604163, _1604165] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604159)), hAPP(hAPP(c_List_Olist_OCons(_1604159), _1604161), _1604163)), c_List_Olists(_1604159, _1604165))), 41885 ^ _779530 : [(41886 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604159), _1604161), _1604165)))], (41888 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604159)), _1604163), c_List_Olists(_1604159, _1604165))))]]], (41890 ^ _779530) ^ [_1604340, _1604342, _1604344, _1604346] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604340)), hAPP(hAPP(c_List_Olist_OCons(_1604340), _1604342), _1604344)), c_List_Olists(_1604340, _1604346)))), hBOOL(hAPP(hAPP(c_member(_1604340), _1604342), _1604346)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604340)), _1604344), c_List_Olists(_1604340, _1604346)))], (41910 ^ _779530) ^ [_1604802, _1604804, _1604806] : [41912 ^ _779530 : [(41913 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1604802), 41911 ^ [_1604802, _1604804, _1604806]), hAPP(c_List_Oset(_1604802), _1604804))))], (41915 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1604802), 41911 ^ [_1604802, _1604804, _1604806]), _1604806))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604802)), _1604804), c_List_Olists(_1604802, _1604806))))], (41900 ^ _779530) ^ [_1604575, _1604577, _1604579] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1604575)), _1604577), c_List_Olists(_1604575, _1604579))), 41903 ^ _779530 : [(41904 ^ _779530) ^ [_1604683] : [hBOOL(hAPP(hAPP(c_member(_1604575), _1604683), hAPP(c_List_Oset(_1604575), _1604577))), -(hBOOL(hAPP(hAPP(c_member(_1604575), _1604683), _1604579)))]]], (41919 ^ _779530) ^ [_1605037, _1605039, _1605041, _1605043] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1605037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1605039), hAPP(hAPP(c_List_Olist_OCons(_1605039), _1605041), _1605043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1605037)) = _1605041)], (41925 ^ _779530) ^ [_1605156, _1605158, _1605160, _1605162] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1605156) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1605158), hAPP(hAPP(c_List_Olist_OCons(_1605158), _1605160), _1605162)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1605156)) = hAPP(hAPP(c_List_Onth(_1605158), _1605162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1605156)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41931 ^ _779530) ^ [_1605237, _1605239] : [-(c_List_Olists(_1605237, _1605239) = hAPP(c_Set_OCollect(tc_List_Olist(_1605237)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605237), tc_fun(_1605237, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1605237, tc_HOL_Obool), tc_fun(tc_fun(_1605237, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1605237)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1605237, tc_HOL_Obool))), c_List_Oset(_1605237))), _1605239)))], (41933 ^ _779530) ^ [_1605315, _1605317, _1605319] : [-(hAPP(c_List_Oset(_1605315), c_List_Osublist(_1605315, _1605317, _1605319)) = hAPP(c_Set_OCollect(_1605315), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1605315), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1605315, 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)), _1605315), 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)), _1605315), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1605315, tc_fun(tc_Nat_Onat, _1605315), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1605315, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1605315), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1605315), c_COMBB(_1605315, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1605315), _1605317))))), 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(_1605315)), _1605317)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1605319))))))], (41935 ^ _779530) ^ [_1605480, _1605482, _1605484, _1605486] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605480), tc_List_Olist(_1605480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605480), tc_List_Olist(_1605480)), _1605482), _1605484)), c_List_Olistrel(_1605480, _1605486))), 41938 ^ _779530 : [(41939 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605480)), _1605482) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605480)), _1605484))], (41941 ^ _779530) ^ [_1605709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1605709), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605480)), _1605482))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605480, _1605480)), hAPP(hAPP(c_Product__Type_OPair(_1605480, _1605480), hAPP(hAPP(c_List_Onth(_1605480), _1605482), _1605709)), hAPP(hAPP(c_List_Onth(_1605480), _1605484), _1605709))), _1605486)))]]], (41947 ^ _779530) ^ [_1605888, _1605890, _1605892, _1605894] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605888), tc_List_Olist(_1605888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605888), tc_List_Olist(_1605888)), _1605890), _1605892)), c_List_Olistrel(_1605888, _1605894)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605888)), _1605890) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605888)), _1605892), 41953 ^ _779530 : [(41954 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41952 ^ [_1605888, _1605890, _1605892, _1605894]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605888)), _1605890))))], (41956 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605888, _1605888)), hAPP(hAPP(c_Product__Type_OPair(_1605888, _1605888), hAPP(hAPP(c_List_Onth(_1605888), _1605890), 41952 ^ [_1605888, _1605890, _1605892, _1605894])), hAPP(hAPP(c_List_Onth(_1605888), _1605892), 41952 ^ [_1605888, _1605890, _1605892, _1605894]))), _1605894))]]], (41960 ^ _779530) ^ [_1606353, _1606355, _1606357, _1606359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606353), tc_List_Olist(_1606353))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606353), tc_List_Olist(_1606353)), _1606355), _1606357)), c_List_Olexord(_1606353, _1606359))), 41965 ^ _779530 : [(41966 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606353)), _1606355)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606353)), _1606357))))], (41968 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1606353), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606353)), _1606355)), _1606357) = _1606355)]], 41970 ^ _779530 : [(41971 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41969 ^ [_1606353, _1606355, _1606357, _1606359]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606353)), _1606355)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606353)), _1606357)))))], (41973 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1606353), 41969 ^ [_1606353, _1606355, _1606357, _1606359]), _1606355) = hAPP(hAPP(c_List_Otake(_1606353), 41969 ^ [_1606353, _1606355, _1606357, _1606359]), _1606357))], (41975 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606353, _1606353)), hAPP(hAPP(c_Product__Type_OPair(_1606353, _1606353), hAPP(hAPP(c_List_Onth(_1606353), _1606355), 41969 ^ [_1606353, _1606355, _1606357, _1606359])), hAPP(hAPP(c_List_Onth(_1606353), _1606357), 41969 ^ [_1606353, _1606355, _1606357, _1606359]))), _1606359)))]]], (41977 ^ _779530) ^ [_1606893, _1606895, _1606897, _1606899] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606893), tc_List_Olist(_1606893))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606893), tc_List_Olist(_1606893)), _1606895), _1606897)), c_List_Olexord(_1606893, _1606899)))), 41978 ^ _779530 : [(41979 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606893)), _1606895)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606893)), _1606897))), hAPP(hAPP(c_List_Otake(_1606893), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606893)), _1606895)), _1606897) = _1606895], (41985 ^ _779530) ^ [_1607200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607200), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606893)), _1606895)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606893)), _1606897)))), hAPP(hAPP(c_List_Otake(_1606893), _1607200), _1606895) = hAPP(hAPP(c_List_Otake(_1606893), _1607200), _1606897), hBOOL(hAPP(hAPP(c_member(tc_prod(_1606893, _1606893)), hAPP(hAPP(c_Product__Type_OPair(_1606893, _1606893), hAPP(hAPP(c_List_Onth(_1606893), _1606895), _1607200)), hAPP(hAPP(c_List_Onth(_1606893), _1606897), _1607200))), _1606899))]]], (41997 ^ _779530) ^ [_1607554, _1607556, _1607558, _1607560] : [hBOOL(hAPP(c_List_Odistinct(_1607554), _1607556)), -(hBOOL(hAPP(hAPP(c_member(_1607554), _1607558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1607554, tc_HOL_Obool)), hAPP(c_List_Oset(_1607554), _1607556)), hAPP(hAPP(c_Set_Oinsert(_1607554), hAPP(hAPP(c_List_Onth(_1607554), _1607556), _1607560)), c_Orderings_Obot__class_Obot(tc_fun(_1607554, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1607554), hAPP(hAPP(c_List_Olist__update(_1607554, _1607556), _1607560), _1607558))))], (42007 ^ _779530) ^ [_1607768, _1607770, _1607772, _1607774, _1607776] : [-(_1607768 = _1607770), -(hAPP(hAPP(c_List_Onth(_1607772), hAPP(hAPP(c_List_Olist__update(_1607772, _1607774), _1607768), _1607776)), _1607770) = hAPP(hAPP(c_List_Onth(_1607772), _1607774), _1607770))], (42013 ^ _779530) ^ [_1607835, _1607837, _1607839] : [-(hAPP(hAPP(c_List_Olist__update(_1607835, _1607837), _1607839), hAPP(hAPP(c_List_Onth(_1607835), _1607837), _1607839)) = _1607837)], (42015 ^ _779530) ^ [_1607879, _1607881, _1607883, _1607885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607879), _1607881)), -(hAPP(hAPP(c_List_Onth(_1607883), hAPP(hAPP(c_List_Otake(_1607883), _1607881), _1607885)), _1607879) = hAPP(hAPP(c_List_Onth(_1607883), _1607885), _1607879))], (42021 ^ _779530) ^ [_1608018, _1608020, _1608022, _1608024, _1608026, _1608028] : [-(hAPP(hAPP(c_List_Omap(_1608018, _1608020), _1608022), hAPP(hAPP(c_List_Olist__update(_1608018, _1608024), _1608026), _1608028)) = hAPP(hAPP(c_List_Olist__update(_1608020, hAPP(hAPP(c_List_Omap(_1608018, _1608020), _1608022), _1608024)), _1608026), hAPP(_1608022, _1608028)))], (42023 ^ _779530) ^ [_1608090, _1608092, _1608094, _1608096, _1608098] : [-(hAPP(hAPP(c_List_Otake(_1608090), _1608092), hAPP(hAPP(c_List_Omap(_1608094, _1608090), _1608096), _1608098)) = hAPP(hAPP(c_List_Omap(_1608094, _1608090), _1608096), hAPP(hAPP(c_List_Otake(_1608094), _1608092), _1608098)))], (42025 ^ _779530) ^ [_1608155, _1608157, _1608159, _1608161] : [-(hAPP(hAPP(c_List_Otake(_1608155), hAPP(c_Nat_OSuc, _1608157)), hAPP(hAPP(c_List_Olist_OCons(_1608155), _1608159), _1608161)) = hAPP(hAPP(c_List_Olist_OCons(_1608155), _1608159), hAPP(hAPP(c_List_Otake(_1608155), _1608157), _1608161)))], (42027 ^ _779530) ^ [_1608219, _1608221, _1608223, _1608225, _1608227] : [-(hAPP(hAPP(c_List_Olist__update(_1608219, hAPP(hAPP(c_List_Olist_OCons(_1608219), _1608221), _1608223)), _1608225), _1608227) = c_Nat_Onat_Onat__case(tc_List_Olist(_1608219), hAPP(hAPP(c_List_Olist_OCons(_1608219), _1608227), _1608223), hAPP(hAPP(c_COMBB(tc_List_Olist(_1608219), tc_List_Olist(_1608219), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1608219), _1608221)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1608219, tc_List_Olist(_1608219)), c_List_Olist__update(_1608219, _1608223)), _1608227)), _1608225))], (42029 ^ _779530) ^ [_1608316, _1608318, _1608320, _1608322] : [-(hAPP(hAPP(c_List_Olist__update(_1608316, hAPP(hAPP(c_List_Olist_OCons(_1608316), _1608318), _1608320)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1608322) = hAPP(hAPP(c_List_Olist_OCons(_1608316), _1608322), _1608320))], (42031 ^ _779530) ^ [_1608370, _1608372, _1608374, _1608376, _1608378] : [-(hAPP(hAPP(c_List_Olist__update(_1608370, hAPP(hAPP(c_List_Olist_OCons(_1608370), _1608372), _1608374)), hAPP(c_Nat_OSuc, _1608376)), _1608378) = hAPP(hAPP(c_List_Olist_OCons(_1608370), _1608372), hAPP(hAPP(c_List_Olist__update(_1608370, _1608374), _1608376), _1608378)))], (42033 ^ _779530) ^ [_1608438, _1608440, _1608442, _1608444, _1608446, _1608448] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1608438, _1608440), hAPP(hAPP(c_List_Ozip(_1608438, _1608440), _1608442), _1608444)), _1608446), _1608448) = hAPP(hAPP(c_List_Ozip(_1608438, _1608440), hAPP(hAPP(c_List_Olist__update(_1608438, _1608442), _1608446), hAPP(c_Product__Type_Ofst(_1608438, _1608440), _1608448))), hAPP(hAPP(c_List_Olist__update(_1608440, _1608444), _1608446), hAPP(c_Product__Type_Osnd(_1608438, _1608440), _1608448))))], (42035 ^ _779530) ^ [_1608531, _1608533, _1608535, _1608537, _1608539] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1608531, _1608533)), _1608535), hAPP(hAPP(c_List_Ozip(_1608531, _1608533), _1608537), _1608539)) = hAPP(hAPP(c_List_Ozip(_1608531, _1608533), hAPP(hAPP(c_List_Otake(_1608531), _1608535), _1608537)), hAPP(hAPP(c_List_Otake(_1608533), _1608535), _1608539)))], (42037 ^ _779530) ^ [_1608607, _1608609, _1608611, _1608613, _1608615, _1608617, _1608619] : [-(hAPP(hAPP(c_List_Ozip(_1608607, _1608609), hAPP(hAPP(c_List_Olist__update(_1608607, _1608611), _1608613), _1608615)), hAPP(hAPP(c_List_Olist__update(_1608609, _1608617), _1608613), _1608619)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1608607, _1608609), hAPP(hAPP(c_List_Ozip(_1608607, _1608609), _1608611), _1608617)), _1608613), hAPP(hAPP(c_Product__Type_OPair(_1608607, _1608609), _1608615), _1608619)))], (42039 ^ _779530) ^ [_1608699, _1608701, _1608703, _1608705] : [hBOOL(hAPP(hAPP(c_member(_1608699), _1608701), hAPP(c_List_Oset(_1608699), hAPP(hAPP(c_List_Otake(_1608699), _1608703), _1608705)))), -(hBOOL(hAPP(hAPP(c_member(_1608699), _1608701), hAPP(c_List_Oset(_1608699), _1608705))))], (42045 ^ _779530) ^ [_1608844, _1608846, _1608848, _1608850] : [-(hAPP(hAPP(c_List_Otake(_1608844), _1608846), hAPP(hAPP(c_List_Otake(_1608844), _1608848), _1608850)) = hAPP(hAPP(c_List_Otake(_1608844), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1608846), _1608848)), _1608850))], (42047 ^ _779530) ^ [_1608903, _1608905, _1608907, _1608909, _1608911] : [-(hAPP(hAPP(c_List_Olist__update(_1608903, hAPP(hAPP(c_List_Olist__update(_1608903, _1608905), _1608907), _1608909)), _1608907), _1608911) = hAPP(hAPP(c_List_Olist__update(_1608903, _1608905), _1608907), _1608911))], (42049 ^ _779530) ^ [_1608957, _1608959, _1608961, _1608963, _1608965, _1608967] : [-(_1608957 = _1608959), -(hAPP(hAPP(c_List_Olist__update(_1608961, hAPP(hAPP(c_List_Olist__update(_1608961, _1608963), _1608957), _1608965)), _1608959), _1608967) = hAPP(hAPP(c_List_Olist__update(_1608961, hAPP(hAPP(c_List_Olist__update(_1608961, _1608963), _1608959), _1608967)), _1608957), _1608965))], (42055 ^ _779530) ^ [_1609037, _1609039, _1609041] : [hBOOL(hAPP(c_List_Odistinct(_1609037), _1609039)), -(hBOOL(hAPP(c_List_Odistinct(_1609037), hAPP(hAPP(c_List_Otake(_1609037), _1609041), _1609039))))], (42061 ^ _779530) ^ [_1609148, _1609150, _1609152] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609148, tc_HOL_Obool)), hAPP(c_List_Oset(_1609148), hAPP(hAPP(c_List_Otake(_1609148), _1609150), _1609152))), hAPP(c_List_Oset(_1609148), _1609152))))], (42063 ^ _779530) ^ [_1609203, _1609205, _1609207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609203)), _1609205)), _1609207)), -(hAPP(hAPP(c_List_Otake(_1609203), _1609207), _1609205) = _1609205)], (42069 ^ _779530) ^ [_1609322, _1609324, _1609326, _1609328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609322)), _1609324)), _1609326)), -(hAPP(hAPP(c_List_Olist__update(_1609322, _1609324), _1609326), _1609328) = _1609324)], (42075 ^ _779530) ^ [_1609445, _1609447, _1609449] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609445)), hAPP(hAPP(c_List_Otake(_1609445), _1609447), _1609449)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609445)), _1609449)), _1609447))], (42077 ^ _779530) ^ [_1609500, _1609502, _1609504, _1609506] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609500)), hAPP(hAPP(c_List_Olist__update(_1609500, _1609502), _1609504), _1609506)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609500)), _1609502))], (42079 ^ _779530) ^ [_1609552, _1609554, _1609556] : [-(c_List_Osublist(_1609552, _1609554, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1609556)) = hAPP(hAPP(c_List_Otake(_1609552), _1609556), _1609554))], (42081 ^ _779530) ^ [_1609594, _1609596, _1609598, _1609600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1609594), _1609596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609598, tc_HOL_Obool)), hAPP(c_List_Oset(_1609598), hAPP(hAPP(c_List_Otake(_1609598), _1609594), _1609600))), hAPP(c_List_Oset(_1609598), hAPP(hAPP(c_List_Otake(_1609598), _1609596), _1609600)))))], (42087 ^ _779530) ^ [_1609757, _1609759, _1609761, _1609763, _1609765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609757, tc_HOL_Obool)), hAPP(c_List_Oset(_1609757), _1609759)), _1609761)), hBOOL(hAPP(hAPP(c_member(_1609757), _1609763), _1609761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609757, tc_HOL_Obool)), hAPP(c_List_Oset(_1609757), hAPP(hAPP(c_List_Olist__update(_1609757, _1609759), _1609765), _1609763))), _1609761)))], (42097 ^ _779530) ^ [_1609990, _1609992, _1609994, _1609996] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609990, tc_HOL_Obool)), hAPP(c_List_Oset(_1609990), hAPP(hAPP(c_List_Olist__update(_1609990, _1609992), _1609994), _1609996))), hAPP(hAPP(c_Set_Oinsert(_1609990), _1609996), hAPP(c_List_Oset(_1609990), _1609992)))))], (42099 ^ _779530) ^ [_1610056, _1610058, _1610060, _1610062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610056), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610058)), _1610060))), -(hAPP(hAPP(c_List_Onth(_1610058), hAPP(hAPP(c_List_Olist__update(_1610058, _1610060), _1610056), _1610062)), _1610056) = _1610062)], (42105 ^ _779530) ^ [_1610195, _1610197, _1610199, _1610201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610197)), _1610199))), 42108 ^ _779530 : [(42109 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1610197, _1610199), _1610195), _1610201) = _1610199, -(hAPP(hAPP(c_List_Onth(_1610197), _1610199), _1610195) = _1610201)], (42115 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Onth(_1610197), _1610199), _1610195) = _1610201, -(hAPP(hAPP(c_List_Olist__update(_1610197, _1610199), _1610195), _1610201) = _1610199)]]], (42121 ^ _779530) ^ [_1610489, _1610491, _1610493, _1610495, _1610497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610489), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610491)), _1610493))), 42124 ^ _779530 : [(42125 ^ _779530) ^ [] : [_1610489 = _1610495, -(hAPP(hAPP(c_List_Onth(_1610491), hAPP(hAPP(c_List_Olist__update(_1610491, _1610493), _1610489), _1610497)), _1610495) = _1610497)], (42131 ^ _779530) ^ [] : [-(_1610489 = _1610495), -(hAPP(hAPP(c_List_Onth(_1610491), hAPP(hAPP(c_List_Olist__update(_1610491, _1610493), _1610489), _1610497)), _1610495) = hAPP(hAPP(c_List_Onth(_1610491), _1610493), _1610495))]]], (42137 ^ _779530) ^ [_1610785, _1610787, _1610789, _1610791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610785), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610787)), _1610789))), -(hBOOL(hAPP(hAPP(c_member(_1610787), _1610791), hAPP(c_List_Oset(_1610787), hAPP(hAPP(c_List_Olist__update(_1610787, _1610789), _1610785), _1610791)))))], (42143 ^ _779530) ^ [_1610956, _1610958, _1610960, _1610962, _1610964, _1610966, _1610968] : [hBOOL(hAPP(hAPP(c_member(_1610956), _1610958), hAPP(c_List_Oset(_1610956), hAPP(hAPP(c_List_Otake(_1610956), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610960)), _1610962)), _1610964)))), -(c_Map_Omap__upds(_1610956, _1610960, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1610956, tc_Option_Ooption(_1610960)), _1610966), _1610958), hAPP(c_Option_Ooption_OSome(_1610960), _1610968)), _1610964, _1610962) = c_Map_Omap__upds(_1610956, _1610960, _1610966, _1610964, _1610962))], (42149 ^ _779530) ^ [_1611153, _1611155, _1611157, _1611159, _1611161, _1611163, _1611165] : [-(hBOOL(hAPP(hAPP(c_member(_1611153), _1611155), hAPP(c_List_Oset(_1611153), hAPP(hAPP(c_List_Otake(_1611153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611157)), _1611159)), _1611161))))), -(c_Map_Omap__upds(_1611153, _1611157, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1611153, tc_Option_Ooption(_1611157)), _1611163), _1611155), hAPP(c_Option_Ooption_OSome(_1611157), _1611165)), _1611161, _1611159) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1611153, tc_Option_Ooption(_1611157)), c_Map_Omap__upds(_1611153, _1611157, _1611163, _1611161, _1611159)), _1611155), hAPP(c_Option_Ooption_OSome(_1611157), _1611165)))], (42155 ^ _779530) ^ [_1611278, _1611280, _1611282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611278, _1611278), tc_HOL_Obool)), _1611280), _1611282)), c_Relation_Orefl__on(_1611278, c_Orderings_Otop__class_Otop(tc_fun(_1611278, tc_HOL_Obool)), _1611282), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1611278), tc_List_Olist(_1611278)), tc_HOL_Obool)), c_List_Olistrel1(_1611278, _1611280)), c_List_Olistrel(_1611278, _1611282))))], (42165 ^ _779530) ^ [_1611495, _1611497, _1611499, _1611501] : [hBOOL(hAPP(hAPP(c_member(_1611495), _1611497), c_Wellfounded_Oacc(_1611495, _1611499))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611495)), _1611501), c_Wellfounded_Oacc(tc_List_Olist(_1611495), c_List_Olistrel1(_1611495, _1611499)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611495)), hAPP(hAPP(c_List_Olist_OCons(_1611495), _1611497), _1611501)), c_Wellfounded_Oacc(tc_List_Olist(_1611495), c_List_Olistrel1(_1611495, _1611499)))))], (42175 ^ _779530) ^ [_1611736, _1611738, _1611740, _1611742, _1611744, _1611746] : [-(c_Map_Omap__add(_1611736, _1611738, _1611740, c_Map_Omap__upds(_1611736, _1611738, _1611742, _1611744, _1611746)) = c_Map_Omap__upds(_1611736, _1611738, c_Map_Omap__add(_1611736, _1611738, _1611740, _1611742), _1611744, _1611746))], (42177 ^ _779530) ^ [_1611787, _1611789, _1611791, _1611793, _1611795, _1611797] : [-(hBOOL(hAPP(hAPP(c_member(_1611787), _1611789), hAPP(c_List_Oset(_1611787), _1611791)))), -(hAPP(c_Map_Omap__upds(_1611787, _1611793, _1611795, _1611791, _1611797), _1611789) = hAPP(_1611795, _1611789))], (42183 ^ _779530) ^ [_1611855, _1611857, _1611859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611855, _1611855), tc_HOL_Obool)), _1611857), _1611859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1611855), tc_List_Olist(_1611855)), tc_HOL_Obool)), c_List_Olistrel1(_1611855, _1611857)), c_List_Olistrel1(_1611855, _1611859))))], (42189 ^ _779530) ^ [_1612006, _1612008, _1612010, _1612012, _1612014] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612006), tc_List_Olist(_1612006))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612006), tc_List_Olist(_1612006)), _1612008), _1612010)), c_List_Olistrel1(_1612006, _1612012))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612006), tc_List_Olist(_1612006))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612006), tc_List_Olist(_1612006)), hAPP(hAPP(c_List_Olist_OCons(_1612006), _1612014), _1612008)), hAPP(hAPP(c_List_Olist_OCons(_1612006), _1612014), _1612010))), c_List_Olistrel1(_1612006, _1612012))))], (42195 ^ _779530) ^ [_1612241, _1612243, _1612245, _1612247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612241), tc_List_Olist(_1612241))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612241), tc_List_Olist(_1612241)), _1612243), _1612245)), c_List_Olistrel1(_1612241, _1612247))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612241)), _1612243) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612241)), _1612245))], (42201 ^ _779530) ^ [_1612410, _1612412, _1612414, _1612416, _1612418, _1612420, _1612422] : [-(c_Map_Omap__upds(_1612410, _1612412, _1612414, hAPP(hAPP(c_List_Olist_OCons(_1612410), _1612416), _1612418), hAPP(hAPP(c_List_Olist_OCons(_1612412), _1612420), _1612422)) = c_Map_Omap__upds(_1612410, _1612412, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1612410, tc_Option_Ooption(_1612412)), _1612414), _1612416), hAPP(c_Option_Ooption_OSome(_1612412), _1612420)), _1612418, _1612422))], (42203 ^ _779530) ^ [_1612492, _1612494, _1612496] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612492)), _1612494), c_Wellfounded_Oacc(tc_List_Olist(_1612492), c_List_Olistrel1(_1612492, _1612496)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612492)), _1612494), c_List_Olists(_1612492, c_Wellfounded_Oacc(_1612492, _1612496)))))], (42209 ^ _779530) ^ [_1612635, _1612637, _1612639] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612635)), _1612637), c_List_Olists(_1612635, c_Wellfounded_Oacc(_1612635, _1612639)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612635)), _1612637), c_Wellfounded_Oacc(tc_List_Olist(_1612635), c_List_Olistrel1(_1612635, _1612639)))))], (42215 ^ _779530) ^ [_1612778, _1612780, _1612782, _1612784, _1612786, _1612788, _1612790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612778)), _1612780)), _1612782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612782), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612784)), _1612786))), -(c_Map_Omap__upds(_1612778, _1612784, _1612788, _1612780, hAPP(hAPP(c_List_Olist__update(_1612784, _1612786), _1612782), _1612790)) = c_Map_Omap__upds(_1612778, _1612784, _1612788, _1612780, _1612786))], (42225 ^ _779530) ^ [_1613013, _1613015, _1613017, _1613019, _1613021, _1613023, _1613025] : [-(hBOOL(hAPP(hAPP(c_member(_1613013), _1613015), hAPP(c_List_Oset(_1613013), _1613017)))), -(c_Map_Omap__upds(_1613013, _1613019, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1613013, tc_Option_Ooption(_1613019)), _1613021), _1613015), hAPP(c_Option_Ooption_OSome(_1613019), _1613023)), _1613017, _1613025) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1613013, tc_Option_Ooption(_1613019)), c_Map_Omap__upds(_1613013, _1613019, _1613021, _1613017, _1613025)), _1613015), hAPP(c_Option_Ooption_OSome(_1613019), _1613023)))], (42231 ^ _779530) ^ [_1613121, _1613123, _1613125, _1613127, _1613129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613121, _1613121)), hAPP(hAPP(c_Product__Type_OPair(_1613121, _1613121), _1613123), _1613125)), _1613127)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613121), tc_List_Olist(_1613121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613121), tc_List_Olist(_1613121)), hAPP(hAPP(c_List_Olist_OCons(_1613121), _1613123), _1613129)), hAPP(hAPP(c_List_Olist_OCons(_1613121), _1613125), _1613129))), c_List_Olistrel1(_1613121, _1613127))))], (42237 ^ _779530) ^ [_1613361, _1613363, _1613365, _1613367, _1613369, _1613371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613361), tc_List_Olist(_1613361))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613361), tc_List_Olist(_1613361)), hAPP(hAPP(c_List_Olist_OCons(_1613361), _1613363), _1613365)), hAPP(hAPP(c_List_Olist_OCons(_1613361), _1613367), _1613369))), c_List_Olistrel1(_1613361, _1613371))), 42242 ^ _779530 : [(42243 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613361, _1613361)), hAPP(hAPP(c_Product__Type_OPair(_1613361, _1613361), _1613363), _1613367)), _1613371)))], (42245 ^ _779530) ^ [] : [-(_1613365 = _1613369)]], 42246 ^ _779530 : [(42247 ^ _779530) ^ [] : [-(_1613363 = _1613367)], (42249 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613361), tc_List_Olist(_1613361))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613361), tc_List_Olist(_1613361)), _1613365), _1613369)), c_List_Olistrel1(_1613361, _1613371))))]]], (42251 ^ _779530) ^ [_1613731, _1613733, _1613735, _1613737, _1613739, _1613741] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613731), tc_List_Olist(_1613731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613731), tc_List_Olist(_1613731)), hAPP(hAPP(c_List_Olist_OCons(_1613731), _1613733), _1613735)), hAPP(hAPP(c_List_Olist_OCons(_1613731), _1613737), _1613739))), c_List_Olistrel1(_1613731, _1613741)))), 42252 ^ _779530 : [(42253 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613731, _1613731)), hAPP(hAPP(c_Product__Type_OPair(_1613731, _1613731), _1613733), _1613737)), _1613741)), _1613735 = _1613739], (42259 ^ _779530) ^ [] : [_1613733 = _1613737, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613731), tc_List_Olist(_1613731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613731), tc_List_Olist(_1613731)), _1613735), _1613739)), c_List_Olistrel1(_1613731, _1613741)))]]], (42267 ^ _779530) ^ [_1614159, _1614161, _1614163, _1614165, _1614167, _1614169] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614159)), _1614161) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614163)), _1614165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614159, tc_HOL_Obool)), hAPP(c_List_Oset(_1614159), _1614161)), _1614167)), -(c_Map_Orestrict__map(_1614159, _1614163, c_Map_Omap__upds(_1614159, _1614163, _1614169, _1614161, _1614165), _1614167) = c_Map_Omap__upds(_1614159, _1614163, c_Map_Orestrict__map(_1614159, _1614163, _1614169, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1614159, tc_HOL_Obool)), _1614167), hAPP(c_List_Oset(_1614159), _1614161))), _1614161, _1614165))], (42277 ^ _779530) ^ [_1614438, _1614440, _1614442, _1614444, _1614446] : [-(c_Map_Odom(_1614438, _1614440, c_Map_Omap__upds(_1614438, _1614440, _1614442, _1614444, _1614446)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1614438, tc_HOL_Obool)), hAPP(c_List_Oset(_1614438), hAPP(hAPP(c_List_Otake(_1614438), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614440)), _1614446)), _1614444))), c_Map_Odom(_1614438, _1614440, _1614442)))], (42279 ^ _779530) ^ [_1614535, _1614537, _1614539, _1614541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614535), tc_List_Olist(_1614535))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614535), tc_List_Olist(_1614535)), _1614537), _1614539)), c_List_Olistrel1(_1614535, _1614541))), 42284 ^ _779530 : [(42285 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614535, _1614535)), hAPP(hAPP(c_Product__Type_OPair(_1614535, _1614535), hAPP(hAPP(c_List_Onth(_1614535), _1614537), 42283 ^ [_1614535, _1614537, _1614539, _1614541])), 42282 ^ [_1614535, _1614537, _1614539, _1614541])), _1614541)))], (42287 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42283 ^ [_1614535, _1614537, _1614539, _1614541]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614535)), _1614537))))], (42289 ^ _779530) ^ [] : [-(_1614539 = hAPP(hAPP(c_List_Olist__update(_1614535, _1614537), 42283 ^ [_1614535, _1614537, _1614539, _1614541]), 42282 ^ [_1614535, _1614537, _1614539, _1614541]))]]], (42291 ^ _779530) ^ [_1614883, _1614885, _1614887, _1614889] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614883), tc_List_Olist(_1614883))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614883), tc_List_Olist(_1614883)), _1614885), _1614887)), c_List_Olistrel1(_1614883, _1614889)))), 42292 ^ _779530 : [(42293 ^ _779530) ^ [_1615016, _1615018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614883, _1614883)), hAPP(hAPP(c_Product__Type_OPair(_1614883, _1614883), hAPP(hAPP(c_List_Onth(_1614883), _1614885), _1615016)), _1615018)), _1614889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1615016), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614883)), _1614885))), _1614887 = hAPP(hAPP(c_List_Olist__update(_1614883, _1614885), _1615016), _1615018)]]], (42305 ^ _779530) ^ [_1615316, _1615318, _1615320, _1615322] : [class_Enum_Oenum(_1615316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615318)), _1615320) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615316)), c_Enum_Oenum__class_Oenum(_1615316)), -(hAPP(hAPP(c_Map_Omap__of(_1615316, _1615318), hAPP(hAPP(c_List_Ozip(_1615316, _1615318), c_Enum_Oenum__class_Oenum(_1615316)), _1615320)), _1615322) = hAPP(c_Option_Ooption_OSome(_1615318), 42312 ^ [_1615316, _1615318, _1615320, _1615322]))], (42316 ^ _779530) ^ [_1615549, _1615551, _1615553, _1615555] : [42319 ^ _779530 : [(42320 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615549, _1615549)), hAPP(hAPP(c_Product__Type_OPair(_1615549, _1615549), 42317 ^ [_1615549, _1615551, _1615553, _1615555]), 42318 ^ [_1615549, _1615551, _1615553, _1615555])), _1615551))], (42322 ^ _779530) ^ [] : [42317 ^ [_1615549, _1615551, _1615553, _1615555] = 42318 ^ [_1615549, _1615551, _1615553, _1615555]], (42324 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615549, _1615549)), hAPP(hAPP(c_Product__Type_OPair(_1615549, _1615549), 42318 ^ [_1615549, _1615551, _1615553, _1615555]), 42317 ^ [_1615549, _1615551, _1615553, _1615555])), _1615551))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615549), tc_List_Olist(_1615549))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615549), tc_List_Olist(_1615549)), _1615553), _1615555)), c_List_Olexord(_1615549, _1615551)))), -(_1615553 = _1615555), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615549), tc_List_Olist(_1615549))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615549), tc_List_Olist(_1615549)), _1615555), _1615553)), c_List_Olexord(_1615549, _1615551))))], (42336 ^ _779530) ^ [_1616095, _1616097, _1616099] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616095, _1616095)), hAPP(hAPP(c_Product__Type_OPair(_1616095, _1616095), 42337 ^ [_1616095, _1616097, _1616099]), 42337 ^ [_1616095, _1616097, _1616099])), _1616097))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616095), tc_List_Olist(_1616095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616095), tc_List_Olist(_1616095)), _1616099), _1616099)), c_List_Olexord(_1616095, _1616097)))], (42343 ^ _779530) ^ [_1616270, _1616272, _1616274, _1616276] : [c_Fun_Oinj__on(_1616270, _1616272, _1616274, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616270, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1616270), tc_fun(_1616270, tc_HOL_Obool), c_List_Oset(_1616270)), _1616276))), -(c_Fun_Oinj__on(tc_List_Olist(_1616270), tc_List_Olist(_1616272), hAPP(c_List_Omap(_1616270, _1616272), _1616274), _1616276))], (42349 ^ _779530) ^ [_1616419, _1616421, _1616423, _1616425, _1616427] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616419, _1616421)), hAPP(hAPP(c_Product__Type_OPair(_1616419, _1616421), _1616423), _1616425)), hAPP(c_List_Oset(tc_prod(_1616419, _1616421)), _1616427))), -(hAPP(hAPP(c_Map_Omap__of(_1616419, _1616421), _1616427), _1616423) = hAPP(c_Option_Ooption_OSome(_1616421), 42352 ^ [_1616419, _1616421, _1616423, _1616425, _1616427]))], (42356 ^ _779530) ^ [_1616602, _1616604, _1616606, _1616608] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1616602, tc_HOL_Obool)), _1616604), _1616606)), hBOOL(hAPP(hAPP(c_member(_1616602), _1616608), _1616604)), -(hBOOL(hAPP(hAPP(c_member(_1616602), _1616608), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616602, tc_HOL_Obool), _1616606))))], (42366 ^ _779530) ^ [_1616799, _1616801, _1616803] : [c_Equiv__Relations_Oequiv(_1616799, _1616801, _1616803), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616799, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1616799), _1616801), _1616803)) = _1616801)], (42372 ^ _779530) ^ [_1616908, _1616910, _1616912] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616908, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1616908, tc_HOL_Obool)), _1616910), _1616912)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1616908, tc_HOL_Obool)), _1616910), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616908, tc_HOL_Obool), _1616912)))], (42374 ^ _779530) ^ [_1616969, _1616971, _1616973, _1616975] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1616969, _1616971), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1616969, tc_HOL_Obool), _1616973)), _1616975) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1616969, tc_HOL_Obool), tc_fun(tc_prod(_1616969, _1616971), tc_HOL_Obool)), _1616973), hAPP(hAPP(c_COMBC(tc_fun(_1616969, tc_HOL_Obool), tc_fun(_1616969, tc_fun(_1616971, tc_HOL_Obool)), tc_fun(tc_prod(_1616969, _1616971), tc_HOL_Obool)), c_Product__Type_OSigma(_1616969, _1616971)), _1616975)))], (42386 ^ _779530) ^ [_1617345, _1617347, _1617349] : [42388 ^ _779530 : [(42389 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1617345, tc_HOL_Obool)), 42387 ^ [_1617345, _1617347, _1617349]), _1617347)))], (42391 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617345, tc_HOL_Obool)), 42387 ^ [_1617345, _1617347, _1617349]), _1617349) = c_Orderings_Obot__class_Obot(tc_fun(_1617345, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617345, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617345, tc_HOL_Obool), _1617347)), _1617349) = c_Orderings_Obot__class_Obot(tc_fun(_1617345, tc_HOL_Obool)))], (42376 ^ _779530) ^ [_1617077, _1617079, _1617081] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617077, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617077, tc_HOL_Obool), _1617079)), _1617081) = c_Orderings_Obot__class_Obot(tc_fun(_1617077, tc_HOL_Obool)), 42379 ^ _779530 : [(42380 ^ _779530) ^ [_1617212] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1617077, tc_HOL_Obool)), _1617212), _1617079)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617077, tc_HOL_Obool)), _1617212), _1617081) = c_Orderings_Obot__class_Obot(tc_fun(_1617077, tc_HOL_Obool)))]]], (42395 ^ _779530) ^ [_1617608, _1617610, _1617612] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617608, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617608, tc_HOL_Obool), _1617610)), _1617612) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617608, tc_HOL_Obool), tc_fun(_1617608, tc_HOL_Obool)), _1617610), hAPP(hAPP(c_COMBC(tc_fun(_1617608, tc_HOL_Obool), tc_fun(_1617608, tc_HOL_Obool), tc_fun(_1617608, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617608, tc_HOL_Obool))), _1617612)))], (42397 ^ _779530) ^ [_1617691, _1617693, _1617695] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617691, tc_HOL_Obool)), _1617693), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617691, tc_HOL_Obool), _1617695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617691, tc_HOL_Obool), tc_fun(_1617691, tc_HOL_Obool)), _1617695), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617691, tc_HOL_Obool)), _1617693)))], (42399 ^ _779530) ^ [_1617758, _1617760, _1617762] : [-(hAPP(c_Relation_ODomain(_1617758, _1617760), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1617758, _1617760), tc_HOL_Obool), _1617762)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1617758, _1617760), tc_HOL_Obool), tc_fun(_1617758, tc_HOL_Obool)), _1617762), c_Relation_ODomain(_1617758, _1617760)))], (42401 ^ _779530) ^ [_1617821, _1617823, _1617825] : [-(hAPP(c_Relation_ORange(_1617821, _1617823), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1617821, _1617823), tc_HOL_Obool), _1617825)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1617821, _1617823), tc_HOL_Obool), tc_fun(_1617823, tc_HOL_Obool)), _1617825), c_Relation_ORange(_1617821, _1617823)))], (42403 ^ _779530) ^ [_1617884, _1617886] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617884, tc_HOL_Obool), _1617886) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617884, tc_HOL_Obool), tc_fun(_1617884, tc_HOL_Obool)), _1617886), c_COMBI(tc_fun(_1617884, tc_HOL_Obool))))], (42405 ^ _779530) ^ [_1617935, _1617937, _1617939, _1617941] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617935, tc_fun(_1617937, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617935, tc_HOL_Obool), _1617939)), _1617941) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617935, tc_HOL_Obool), tc_fun(_1617937, tc_HOL_Obool)), _1617939), hAPP(hAPP(c_COMBC(tc_fun(_1617935, tc_HOL_Obool), tc_fun(_1617935, tc_fun(_1617937, tc_HOL_Obool)), tc_fun(_1617937, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617935, tc_fun(_1617937, tc_HOL_Obool))), _1617941)))], (42407 ^ _779530) ^ [_1618025, _1618027, _1618029, _1618031] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618025, tc_HOL_Obool), tc_fun(_1618027, tc_HOL_Obool)), _1618029), hAPP(hAPP(c_COMBC(tc_fun(_1618025, tc_HOL_Obool), tc_fun(_1618025, tc_fun(_1618027, tc_HOL_Obool)), tc_fun(_1618027, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1618025, tc_fun(_1618027, tc_HOL_Obool))), _1618031)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1618025, tc_fun(_1618027, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618025, tc_HOL_Obool), _1618029)), _1618031))], (42409 ^ _779530) ^ [_1618115, _1618117, _1618119, _1618121] : [-(hAPP(c_Set_Ovimage(_1618115, _1618117, _1618119), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618117, tc_HOL_Obool), _1618121)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618117, tc_HOL_Obool), tc_fun(_1618115, tc_HOL_Obool)), _1618121), c_Set_Ovimage(_1618115, _1618117, _1618119)))], (42411 ^ _779530) ^ [_1618176, _1618178, _1618180] : [class_Complete__Lattice_Ocomplete__lattice(_1618176), class_Orderings_Olinorder(_1618176), 42418 ^ _779530 : [(42419 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1618176), _1618178), c_Complete__Lattice_OSup__class_OSup(_1618176, _1618180))), 42423 ^ _779530 : [(42424 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618176), 42422 ^ [_1618176, _1618178, _1618180]), _1618180)))], (42426 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1618176), _1618178), 42422 ^ [_1618176, _1618178, _1618180])))]]], (42428 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1618176), _1618178), c_Complete__Lattice_OSup__class_OSup(_1618176, _1618180)))), 42429 ^ _779530 : [(42430 ^ _779530) ^ [_1618482] : [hBOOL(hAPP(hAPP(c_member(_1618176), _1618482), _1618180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1618176), _1618178), _1618482))]]]]], (42438 ^ _779530) ^ [_1618636, _1618638] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618636, tc_HOL_Obool), hAPP(c_Set_OPow(_1618636), _1618638)) = _1618638)], (42440 ^ _779530) ^ [_1618672, _1618674] : [-(hAPP(c_Relation_OField(_1618672), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1618672, _1618672), tc_HOL_Obool), _1618674)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618672, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1618672, _1618672), tc_HOL_Obool), tc_fun(_1618672, tc_HOL_Obool), c_Relation_OField(_1618672)), _1618674)))], (42442 ^ _779530) ^ [_1618735, _1618737, _1618739, _1618741] : [-(hAPP(c_Set_Oimage(_1618735, _1618737, _1618739), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618735, tc_HOL_Obool), _1618741)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618735, tc_HOL_Obool), tc_fun(_1618737, tc_HOL_Obool)), _1618741), c_Set_Oimage(_1618735, _1618737, _1618739)))], (42444 ^ _779530) ^ [_1618796] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618796, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1618796, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1618796, tc_HOL_Obool)))], (42446 ^ _779530) ^ [_1618838, _1618840, _1618842] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1618838, tc_HOL_Obool)), _1618840), _1618842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618838, tc_HOL_Obool)), _1618840), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618838, tc_HOL_Obool), _1618842))))], (42452 ^ _779530) ^ [_1618969, _1618971, _1618973] : [class_Complete__Lattice_Ocomplete__lattice(_1618969), 42455 ^ _779530 : [(42466 ^ _779530) ^ [] : [42468 ^ _779530 : [(42469 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618969), 42467 ^ [_1618969, _1618971, _1618973]), _1618971)))], (42471 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618969), 42467 ^ [_1618969, _1618971, _1618973]), _1618973))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618969), c_Complete__Lattice_OSup__class_OSup(_1618969, _1618971)), _1618973)))], (42456 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618969), c_Complete__Lattice_OSup__class_OSup(_1618969, _1618971)), _1618973)), 42459 ^ _779530 : [(42460 ^ _779530) ^ [_1619127] : [hBOOL(hAPP(hAPP(c_member(_1618969), _1619127), _1618971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1618969), _1619127), _1618973)))]]]]], (42475 ^ _779530) ^ [_1619403, _1619405, _1619407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619403, tc_HOL_Obool), tc_HOL_Obool)), _1619405), _1619407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619403, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619403, tc_HOL_Obool), _1619405)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619403, tc_HOL_Obool), _1619407))))], (42481 ^ _779530) ^ [_1619552, _1619554] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1619552), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619552, tc_HOL_Obool), _1619554))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1619552, tc_HOL_Obool)), _1619554)))], (42487 ^ _779530) ^ [_1619663, _1619665] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619663, tc_HOL_Obool), tc_HOL_Obool)), _1619665), hAPP(c_Set_OPow(_1619663), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619663, tc_HOL_Obool), _1619665)))))], (42489 ^ _779530) ^ [_1619712] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619712, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1619712, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1619712, tc_HOL_Obool)))], (42491 ^ _779530) ^ [_1619754, _1619756, _1619758] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619754, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1619754, tc_HOL_Obool), tc_HOL_Obool)), _1619756), _1619758)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619754, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619754, tc_HOL_Obool), _1619756)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619754, tc_HOL_Obool), _1619758)))], (42493 ^ _779530) ^ [_1619824, _1619826, _1619828, _1619830] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619824, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619826, tc_fun(_1619824, tc_HOL_Obool), _1619828), _1619830)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619826, tc_fun(_1619824, tc_HOL_Obool)), _1619830), _1619828))], (42495 ^ _779530) ^ [_1619881, _1619883, _1619885, _1619887] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1619881, tc_fun(_1619883, tc_HOL_Obool)), _1619885), _1619887) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619883, tc_HOL_Obool), hAPP(c_Set_Oimage(_1619881, tc_fun(_1619883, tc_HOL_Obool), _1619887), _1619885)))], (42497 ^ _779530) ^ [_1619938, _1619940, _1619942] : [class_Complete__Lattice_Ocomplete__lattice(_1619938), hBOOL(hAPP(hAPP(c_member(_1619938), _1619940), _1619942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1619938), _1619940), c_Complete__Lattice_OSup__class_OSup(_1619938, _1619942))))], (42507 ^ _779530) ^ [_1620103] : [class_Complete__Lattice_Ocomplete__lattice(_1620103), -(c_Complete__Lattice_OSup__class_OSup(_1620103, c_Orderings_Obot__class_Obot(tc_fun(_1620103, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1620103))], (42513 ^ _779530) ^ [_1620196, _1620198] : [class_Complete__Lattice_Ocomplete__lattice(_1620196), -(c_Complete__Lattice_OSup__class_OSup(_1620196, hAPP(hAPP(c_Set_Oinsert(_1620196), _1620198), c_Orderings_Obot__class_Obot(tc_fun(_1620196, tc_HOL_Obool)))) = _1620198)], (42519 ^ _779530) ^ [_1620303, _1620305, _1620307] : [class_Complete__Lattice_Ocomplete__lattice(_1620303), -(c_Complete__Lattice_OSup__class_OSup(_1620303, hAPP(hAPP(c_Set_Oinsert(_1620303), _1620305), _1620307)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1620303), _1620305), c_Complete__Lattice_OSup__class_OSup(_1620303, _1620307)))], (42525 ^ _779530) ^ [_1620424] : [class_Complete__Lattice_Ocomplete__lattice(_1620424), -(c_Complete__Lattice_OSup__class_OSup(_1620424, c_Orderings_Otop__class_Otop(tc_fun(_1620424, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1620424))], (42531 ^ _779530) ^ [_1620517, _1620519, _1620521] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1620517, tc_HOL_Obool)), _1620519), _1620521) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620517, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1620517, tc_HOL_Obool)), _1620519), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1620517, tc_HOL_Obool)), _1620521), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1620517, tc_HOL_Obool), tc_HOL_Obool))))))], (42533 ^ _779530) ^ [_1620591, _1620593, _1620595, _1620597, _1620599] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1620591, tc_fun(_1620593, tc_HOL_Obool)), _1620595), hAPP(hAPP(c_COMBS(_1620591, tc_fun(_1620593, tc_HOL_Obool), tc_fun(_1620593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620593, tc_HOL_Obool), tc_fun(tc_fun(_1620593, tc_HOL_Obool), tc_fun(_1620593, tc_HOL_Obool)), _1620591), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1620593, tc_HOL_Obool))), _1620597)), _1620599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1620593, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620593, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620591, tc_fun(_1620593, tc_HOL_Obool), _1620597), _1620595))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620593, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620591, tc_fun(_1620593, tc_HOL_Obool), _1620599), _1620595))))], (42535 ^ _779530) ^ [_1620720, _1620722, _1620724] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620720, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620720, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1620720, tc_HOL_Obool), tc_HOL_Obool)), _1620722), _1620724))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620720, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620720, tc_HOL_Obool), _1620722)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620720, tc_HOL_Obool), _1620724)))))], (42537 ^ _779530) ^ [_1620800, _1620802, _1620804] : [class_Complete__Lattice_Ocomplete__lattice(_1620800), -(c_Complete__Lattice_OSup__class_OSup(_1620800, hAPP(hAPP(c_Set_Oinsert(_1620800), _1620802), hAPP(hAPP(c_Set_Oinsert(_1620800), _1620804), c_Orderings_Obot__class_Obot(tc_fun(_1620800, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1620800), _1620802), _1620804))], (42543 ^ _779530) ^ [_1620941, _1620943] : [class_Complete__Lattice_Ocomplete__lattice(_1620941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620941), _1620943)), -(_1620943 = c_Orderings_Obot__class_Obot(tc_fun(_1620941, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1620941, _1620943) = c_Complete__Lattice_OSup__class_OSup(_1620941, _1620943))], (42557 ^ _779530) ^ [_1621113, _1621115] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1621113, tc_HOL_Obool)), _1621115)), 42563 ^ _779530 : [(42564 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1621113, tc_HOL_Obool)), 42562 ^ [_1621113, _1621115]), _1621115)))], (42566 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1621113), 42562 ^ [_1621113, _1621115]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1621113), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621113, tc_HOL_Obool), _1621115))))], (42570 ^ _779530) ^ [_1621371, _1621373, _1621375] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1621371, tc_HOL_Obool)), _1621373), _1621375))), 42576 ^ _779530 : [(42577 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1621371, tc_HOL_Obool)), 42575 ^ [_1621371, _1621373, _1621375]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621371, tc_HOL_Obool)), _1621373), _1621375))))], (42580 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1621371, tc_HOL_Obool)), 42578 ^ [_1621371, _1621373, _1621375]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621371, tc_HOL_Obool)), _1621373), _1621375))))], (42582 ^ _779530) ^ [] : [42575 ^ [_1621371, _1621373, _1621375] = 42578 ^ [_1621371, _1621373, _1621375]], (42584 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1621371, tc_HOL_Obool)), 42575 ^ [_1621371, _1621373, _1621375]), 42578 ^ [_1621371, _1621373, _1621375]) = c_Orderings_Obot__class_Obot(tc_fun(_1621371, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1621371, tc_HOL_Obool)), _1621373), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621371, tc_HOL_Obool), _1621375)) = c_Orderings_Obot__class_Obot(tc_fun(_1621371, tc_HOL_Obool)))], (42588 ^ _779530) ^ [_1621965, _1621967] : [class_Groups_Ocomm__monoid__add(_1621965), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1621965), _1621967) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1621965), hAPP(c_List_Onth(_1621965), _1621967)), 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(_1621965)), _1621967))))], (42594 ^ _779530) ^ [_1622098, _1622100, _1622102, _1622104] : [42596 ^ _779530 : [(42597 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622098), 42595 ^ [_1622098, _1622100, _1622102, _1622104]), hAPP(c_List_Oset(_1622098), _1622100))))], (42599 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1622102, 42595 ^ [_1622098, _1622100, _1622102, _1622104])), hAPP(_1622104, 42595 ^ [_1622098, _1622100, _1622102, _1622104])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1622098, _1622102, _1622100)), c_List_Olist_Olist__size(_1622098, _1622104, _1622100))))], (42613 ^ _779530) ^ [_1622528] : [42615 ^ _779530 : [(42616 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42614 ^ [_1622528]), hAPP(c_List_Oset(tc_Nat_Onat), _1622528))))], (42618 ^ _779530) ^ [] : [42614 ^ [_1622528] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1622528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42603 ^ _779530) ^ [_1622360] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1622360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42606 ^ _779530 : [(42607 ^ _779530) ^ [_1622435] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1622435), hAPP(c_List_Oset(tc_Nat_Onat), _1622360))), -(_1622435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42622 ^ _779530) ^ [_1622684, _1622686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1622686))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1622686), _1622684)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1622686))))], (42628 ^ _779530) ^ [_1622805, _1622807, _1622809] : [class_Groups_Omonoid__add(_1622805), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1622805), hAPP(hAPP(c_List_Olist_OCons(_1622805), _1622807), _1622809)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1622805), _1622807), hAPP(c_List_Omonoid__add__class_Olistsum(_1622805), _1622809)))], (42634 ^ _779530) ^ [_1622934, _1622936, _1622938] : [class_Groups_Omonoid__add(_1622934), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1622934), hAPP(hAPP(c_List_Omap(_1622936, _1622934), hAPP(c_COMBK(_1622934, _1622936), c_Groups_Ozero__class_Ozero(_1622934))), _1622938)) = c_Groups_Ozero__class_Ozero(_1622934))], (42640 ^ _779530) ^ [_1623059, _1623061, _1623063, _1623065, _1623067] : [class_Groups_Ocomm__monoid__add(_1623059), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1623059), hAPP(hAPP(c_List_Omap(_1623061, _1623059), hAPP(hAPP(c_COMBS(_1623061, _1623059, _1623059), hAPP(hAPP(c_COMBB(_1623059, tc_fun(_1623059, _1623059), _1623061), c_Groups_Oplus__class_Oplus(_1623059)), _1623063)), _1623065)), _1623067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1623059), hAPP(c_List_Omonoid__add__class_Olistsum(_1623059), hAPP(hAPP(c_List_Omap(_1623061, _1623059), _1623063), _1623067))), hAPP(c_List_Omonoid__add__class_Olistsum(_1623059), hAPP(hAPP(c_List_Omap(_1623061, _1623059), _1623065), _1623067))))], (42646 ^ _779530) ^ [_1623290, _1623292, _1623294, _1623296, _1623298] : [class_Rings_Osemiring__0(_1623290), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1623290), hAPP(hAPP(c_List_Omap(_1623292, _1623290), hAPP(hAPP(c_COMBB(_1623290, _1623290, _1623292), hAPP(c_Groups_Otimes__class_Otimes(_1623290), _1623294)), _1623296)), _1623298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1623290), _1623294), hAPP(c_List_Omonoid__add__class_Olistsum(_1623290), hAPP(hAPP(c_List_Omap(_1623292, _1623290), _1623296), _1623298))))], (42652 ^ _779530) ^ [_1623473, _1623475, _1623477, _1623479, _1623481] : [class_Rings_Osemiring__0(_1623473), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1623473), hAPP(hAPP(c_List_Omap(_1623475, _1623473), hAPP(hAPP(c_COMBC(_1623475, _1623473, _1623473), hAPP(hAPP(c_COMBB(_1623473, tc_fun(_1623473, _1623473), _1623475), c_Groups_Otimes__class_Otimes(_1623473)), _1623477)), _1623479)), _1623481)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1623473), hAPP(c_List_Omonoid__add__class_Olistsum(_1623473), hAPP(hAPP(c_List_Omap(_1623475, _1623473), _1623477), _1623481))), _1623479))], (42658 ^ _779530) ^ [_1623676, _1623678, _1623680, _1623682, _1623684] : [class_Groups_Oab__group__add(_1623676), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1623676), hAPP(hAPP(c_List_Omap(_1623678, _1623676), hAPP(hAPP(c_COMBS(_1623678, _1623676, _1623676), hAPP(hAPP(c_COMBB(_1623676, tc_fun(_1623676, _1623676), _1623678), c_Groups_Ominus__class_Ominus(_1623676)), _1623680)), _1623682)), _1623684)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1623676), hAPP(c_List_Omonoid__add__class_Olistsum(_1623676), hAPP(hAPP(c_List_Omap(_1623678, _1623676), _1623680), _1623684))), hAPP(c_List_Omonoid__add__class_Olistsum(_1623676), hAPP(hAPP(c_List_Omap(_1623678, _1623676), _1623682), _1623684))))], (42664 ^ _779530) ^ [_1623907, _1623909, _1623911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1623909))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1623909), _1623907), _1623911)) = 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), _1623909)), _1623911)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1623909), _1623907)))], (42670 ^ _779530) ^ [_1624068, _1624070] : [class_Groups_Oordered__ab__group__add__abs(_1624068), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1624068), hAPP(c_Groups_Oabs__class_Oabs(_1624068), hAPP(c_List_Omonoid__add__class_Olistsum(_1624068), _1624070))), hAPP(c_List_Omonoid__add__class_Olistsum(_1624068), hAPP(hAPP(c_List_Omap(_1624068, _1624068), c_Groups_Oabs__class_Oabs(_1624068)), _1624070)))))], (42676 ^ _779530) ^ [_1624209, _1624211, _1624213, _1624215] : [class_Groups_Oab__group__add(_1624209), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1624209), hAPP(c_List_Omonoid__add__class_Olistsum(_1624209), hAPP(hAPP(c_List_Omap(_1624211, _1624209), _1624213), _1624215))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1624209), hAPP(hAPP(c_List_Omap(_1624211, _1624209), hAPP(c_Fun_Ocomp(_1624209, _1624209, _1624211, c_Groups_Ouminus__class_Ouminus(_1624209)), _1624213)), _1624215)))], (42682 ^ _779530) ^ [_1624374, _1624376, _1624378] : [-(c_List_Olist_Olist__size(_1624374, _1624376, _1624378) = 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(_1624374, tc_Nat_Onat), _1624376), _1624378))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624374)), _1624378)))], (42684 ^ _779530) ^ [_1624430, _1624432] : [class_Groups_Ocomm__monoid__add(_1624430), hBOOL(hAPP(c_List_Odistinct(_1624430), _1624432)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1624430), _1624432) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1624430, _1624430), c_COMBI(_1624430)), hAPP(c_List_Oset(_1624430), _1624432)))], (42694 ^ _779530) ^ [_1624607, _1624609, _1624611, _1624613] : [class_Groups_Ocomm__monoid__add(_1624607), hBOOL(hAPP(c_List_Odistinct(_1624609), _1624611)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1624607), hAPP(hAPP(c_List_Omap(_1624609, _1624607), _1624613), _1624611)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1624609, _1624607), _1624613), hAPP(c_List_Oset(_1624609), _1624611)))], (42704 ^ _779530) ^ [_1624806, _1624808, _1624810, _1624812] : [class_Groups_Ocomm__monoid__add(_1624806), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1624806), _1624808), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624810, _1624812))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1624806), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1624806), _1624808), c_List_Oupto(_1624810, _1624812))))], (42710 ^ _779530) ^ [_1624949, _1624951, _1624953, _1624955] : [class_Groups_Ocomm__monoid__add(_1624949), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1624949), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1624949), _1624951), c_List_Oupto(_1624953, _1624955))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1624949), _1624951), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1624953, _1624955))))], (42716 ^ _779530) ^ [_1625092, _1625094, _1625096, _1625098] : [class_Rings_Osemiring__1(_1625092), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1625092), hAPP(hAPP(c_List_Omap(_1625094, _1625092), hAPP(c_COMBK(_1625092, _1625094), _1625096)), _1625098)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1625092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1625092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625094)), _1625098))), _1625096))], (42722 ^ _779530) ^ [_1625251, _1625253, _1625255, _1625257] : [class_Groups_Ocomm__monoid__add(_1625251), 42725 ^ _779530 : [(42726 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1625253), _1625255)), -(c_Nitpick_Osetsum_H(_1625253, _1625251, _1625257, _1625255) = hAPP(c_List_Omonoid__add__class_Olistsum(_1625251), hAPP(hAPP(c_List_Omap(_1625253, _1625251), _1625257), c_Hilbert__Choice_OEps(tc_List_Olist(_1625253), hAPP(hAPP(c_COMBS(tc_List_Olist(_1625253), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1625253)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1625253), tc_fun(_1625253, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1625253, tc_HOL_Obool), tc_fun(tc_fun(_1625253, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1625253)), c_fequal), c_List_Oset(_1625253))), _1625255))), c_List_Odistinct(_1625253))))))], (42732 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1625253), _1625255))), -(c_Nitpick_Osetsum_H(_1625253, _1625251, _1625257, _1625255) = c_Groups_Ozero__class_Ozero(_1625251))]]], (42738 ^ _779530) ^ [_1625639, _1625641, _1625643, _1625645, _1625647] : [class_Groups_Omonoid__add(_1625639), class_Groups_Oordered__ab__semigroup__add(_1625639), 42748 ^ _779530 : [(42749 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625641), 42747 ^ [_1625639, _1625641, _1625643, _1625645, _1625647]), hAPP(c_List_Oset(_1625641), _1625643))))], (42751 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625639), hAPP(_1625645, 42747 ^ [_1625639, _1625641, _1625643, _1625645, _1625647])), hAPP(_1625647, 42747 ^ [_1625639, _1625641, _1625643, _1625645, _1625647])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1625639), hAPP(c_List_Omonoid__add__class_Olistsum(_1625639), hAPP(hAPP(c_List_Omap(_1625641, _1625639), _1625645), _1625643))), hAPP(c_List_Omonoid__add__class_Olistsum(_1625639), hAPP(hAPP(c_List_Omap(_1625641, _1625639), _1625647), _1625643)))))], (42755 ^ _779530) ^ [_1626063, _1626065, _1626067] : [hBOOL(hAPP(_1626063, _1626065)), -(hBOOL(hAPP(_1626063, c_Hilbert__Choice_OEps(_1626067, _1626063))))], (42761 ^ _779530) ^ [_1626156, _1626158] : [42762 ^ _779530 : [(42763 ^ _779530) ^ [_1626202] : [hBOOL(hAPP(_1626156, _1626202))]], -(hBOOL(hAPP(_1626156, c_Hilbert__Choice_OEps(_1626158, _1626156))))], (42767 ^ _779530) ^ [_1626260, _1626262] : [-(c_Hilbert__Choice_OEps(_1626260, hAPP(c_fequal, _1626262)) = _1626262)], (42769 ^ _779530) ^ [_1626291, _1626293] : [-(c_Hilbert__Choice_OEps(_1626291, hAPP(hAPP(c_COMBC(_1626291, _1626291, tc_HOL_Obool), c_fequal), _1626293)) = _1626293)], (42771 ^ _779530) ^ [_1626344, _1626346] : [hBOOL(hAPP(_1626344, c_Hilbert__Choice_OEps(_1626346, _1626344))), -(hBOOL(hAPP(_1626344, 42774 ^ [_1626344, _1626346])))], (42778 ^ _779530) ^ [_1626443, _1626445] : [42779 ^ _779530 : [(42780 ^ _779530) ^ [_1626489] : [hBOOL(hAPP(_1626443, _1626489))]], -(hBOOL(hAPP(_1626443, c_Hilbert__Choice_OEps(_1626445, _1626443))))], (42784 ^ _779530) ^ [_1626549, _1626551] : [42785 ^ _779530 : [(42786 ^ _779530) ^ [_1626595] : [hBOOL(hAPP(_1626549, _1626595))]], -(hBOOL(hAPP(_1626549, c_Hilbert__Choice_OEps(_1626551, _1626549))))], (42790 ^ _779530) ^ [_1626653, _1626655, _1626657] : [42791 ^ _779530 : [(42792 ^ _779530) ^ [_1626707] : [hBOOL(hAPP(_1626653, _1626707))]], _1626655 = c_Hilbert__Choice_OEps(_1626657, _1626653), -(hBOOL(hAPP(_1626653, _1626655)))], (42800 ^ _779530) ^ [_1626822, _1626824] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626822), _1626824)), -(c_Nitpick_Ocard_H(_1626822, _1626824) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626822)), c_Hilbert__Choice_OEps(tc_List_Olist(_1626822), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626822), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626822)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626822), tc_fun(_1626822, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626822, tc_HOL_Obool), tc_fun(tc_fun(_1626822, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626822)), c_fequal), c_List_Oset(_1626822))), _1626824))), c_List_Odistinct(_1626822)))))], (42806 ^ _779530) ^ [_1627059, _1627061] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627059), _1627061))), -(c_Nitpick_Ocard_H(_1627059, _1627061) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42812 ^ _779530) ^ [_1627104, _1627106, _1627108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627104), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627106)), _1627108))), -(c_List_Obutlast(_1627106, hAPP(hAPP(c_List_Otake(_1627106), _1627104), _1627108)) = hAPP(hAPP(c_List_Otake(_1627106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1627104), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627108))], (42818 ^ _779530) ^ [_1627257, _1627259, _1627261, _1627263] : [-(hAPP(hAPP(c_List_Omap(_1627257, _1627259), _1627261), c_List_Obutlast(_1627257, _1627263)) = c_List_Obutlast(_1627259, hAPP(hAPP(c_List_Omap(_1627257, _1627259), _1627261), _1627263)))], (42820 ^ _779530) ^ [_1627310, _1627312, _1627314] : [hBOOL(hAPP(hAPP(c_member(_1627310), _1627312), hAPP(c_List_Oset(_1627310), c_List_Obutlast(_1627310, _1627314)))), -(hBOOL(hAPP(hAPP(c_member(_1627310), _1627312), hAPP(c_List_Oset(_1627310), _1627314))))], (42826 ^ _779530) ^ [_1627443, _1627445, _1627447, _1627449] : [-(c_Hilbert__Choice_OEps(tc_prod(_1627443, _1627445), hAPP(c_Product__Type_Oprod_Oprod__case(_1627443, _1627445, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1627443, tc_fun(_1627445, tc_HOL_Obool), tc_fun(_1627445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1627445, tc_HOL_Obool), tc_fun(_1627445, tc_HOL_Obool)), _1627443), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1627445)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1627443), c_fconj), hAPP(c_fequal, _1627447)))), hAPP(c_fequal, _1627449)))) = hAPP(hAPP(c_Product__Type_OPair(_1627443, _1627445), _1627447), _1627449))], (42828 ^ _779530) ^ [_1627549, _1627551, _1627553] : [-(c_Hilbert__Choice_OEps(tc_prod(_1627549, _1627551), _1627553) = c_Hilbert__Choice_OEps(tc_prod(_1627549, _1627551), hAPP(c_Product__Type_Oprod_Oprod__case(_1627549, _1627551, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1627551, tc_prod(_1627549, _1627551)), tc_fun(_1627551, tc_HOL_Obool), _1627549), hAPP(c_COMBB(tc_prod(_1627549, _1627551), tc_HOL_Obool, _1627551), _1627553)), c_Product__Type_OPair(_1627549, _1627551)))))], (42830 ^ _779530) ^ [_1627627, _1627629, _1627631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1627627), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627629)), _1627631))), -(hAPP(hAPP(c_List_Otake(_1627629), _1627627), c_List_Obutlast(_1627629, _1627631)) = hAPP(hAPP(c_List_Otake(_1627629), _1627627), _1627631))], (42836 ^ _779530) ^ [_1627768, _1627770] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627768)), c_List_Obutlast(_1627768, _1627770)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627768)), _1627770)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42838 ^ _779530) ^ [_1627816, _1627818, _1627820] : [-(c_Hilbert__Choice_OEps(tc_prod(_1627816, _1627818), hAPP(c_Product__Type_Oprod_Oprod__case(_1627816, _1627818, tc_HOL_Obool), _1627820)) = c_Hilbert__Choice_OEps(tc_prod(_1627816, _1627818), hAPP(hAPP(c_COMBS(tc_prod(_1627816, _1627818), _1627818, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1627816, tc_fun(_1627818, tc_HOL_Obool), tc_prod(_1627816, _1627818)), _1627820), c_Product__Type_Ofst(_1627816, _1627818))), c_Product__Type_Osnd(_1627816, _1627818))))], (42840 ^ _779530) ^ [_1627897, _1627899] : [-(c_List_Obutlast(_1627897, _1627899) = hAPP(hAPP(c_List_Otake(_1627897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627897)), _1627899)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627899))], (42842 ^ _779530) ^ [_1627961, _1627963, _1627965, _1627967] : [_1627961 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627963)), _1627965)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1627963, hAPP(hAPP(c_List_Olist__update(_1627963, _1627965), _1627961), _1627967)) = c_List_Obutlast(_1627963, _1627965))], (42848 ^ _779530) ^ [_1628092, _1628094, _1628096, _1628098] : [-(_1628092 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628094)), _1628096)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1628094, hAPP(hAPP(c_List_Olist__update(_1628094, _1628096), _1628092), _1628098)) = hAPP(hAPP(c_List_Olist__update(_1628094, c_List_Obutlast(_1628094, _1628096)), _1628092), _1628098))], (42854 ^ _779530) ^ [_1628171, _1628173, _1628175, _1628177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1628171), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628173)), _1628175))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1628171), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628173)), _1628177))), 42864 ^ _779530 : [(42865 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42863 ^ [_1628171, _1628173, _1628175, _1628177]), _1628171)))], (42867 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Onth(_1628173), _1628175), 42863 ^ [_1628171, _1628173, _1628175, _1628177]) = hAPP(hAPP(c_List_Onth(_1628173), _1628177), 42863 ^ [_1628171, _1628173, _1628175, _1628177])]], -(hAPP(hAPP(c_List_Otake(_1628173), _1628171), _1628175) = hAPP(hAPP(c_List_Otake(_1628173), _1628171), _1628177))], (42871 ^ _779530) ^ [_1628588, _1628590] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1628588))), c_List_Otranspose(_1628588, _1628590)) = c_List_Ofoldr(tc_List_Olist(_1628588), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1628588)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1628588))), _1628590, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42873 ^ _779530) ^ [_1628649, _1628651, _1628653, _1628655] : [-(c_List_Otranspose(_1628649, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1628651), tc_List_Olist(_1628649)), hAPP(c_List_Omap(_1628651, _1628649), _1628653)), _1628655)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1628651), tc_List_Olist(_1628649)), hAPP(c_List_Omap(_1628651, _1628649), _1628653)), c_List_Otranspose(_1628651, _1628655)))], (42875 ^ _779530) ^ [_1628722, _1628724, _1628726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628722), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1628724))), c_List_Otranspose(_1628724, _1628726)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1628724)), c_List_Otranspose(_1628724, _1628726)), _1628722) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1628724), _1628724), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628724), tc_Nat_Onat, _1628724), c_List_Onth(_1628724)), _1628722)), hAPP(c_List_Ofilter(tc_List_Olist(_1628724), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1628724)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628722)), c_Nat_Osize__class_Osize(tc_List_Olist(_1628724)))), _1628726)))], (42881 ^ _779530) ^ [_1628965, _1628967, _1628969, _1628971, _1628973] : [class_Groups_Ocomm__monoid__add(_1628965), hBOOL(hAPP(hAPP(c_member(_1628967), _1628969), hAPP(c_List_Oset(_1628967), _1628971))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1628965), hAPP(hAPP(c_List_Omap(_1628967, _1628965), _1628973), _1628971)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1628965), hAPP(_1628973, _1628969)), hAPP(c_List_Omonoid__add__class_Olistsum(_1628965), hAPP(hAPP(c_List_Omap(_1628967, _1628965), _1628973), c_List_Oremove1(_1628967, _1628969, _1628971)))))], (42891 ^ _779530) ^ [_1629214, _1629216, _1629218, _1629220, _1629222] : [-(hAPP(c_List_Ofilter(_1629214, _1629216), hAPP(hAPP(c_List_Omap(_1629218, _1629214), _1629220), _1629222)) = hAPP(hAPP(c_List_Omap(_1629218, _1629214), _1629220), hAPP(c_List_Ofilter(_1629218, hAPP(c_Fun_Ocomp(_1629214, tc_HOL_Obool, _1629218, _1629216), _1629220)), _1629222)))], (42893 ^ _779530) ^ [_1629283, _1629285, _1629287] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1629283, tc_HOL_Obool)), hAPP(c_List_Oset(_1629283), hAPP(c_List_Ofilter(_1629283, _1629285), _1629287))), hAPP(c_List_Oset(_1629283), _1629287))))], (42895 ^ _779530) ^ [_1629336, _1629338, _1629340] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629336)), hAPP(c_List_Ofilter(_1629336, _1629338), _1629340))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629336)), _1629340))))], (42907 ^ _779530) ^ [_1629606, _1629608, _1629610] : [42909 ^ _779530 : [(42910 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629606), 42908 ^ [_1629606, _1629608, _1629610]), hAPP(c_List_Oset(_1629606), _1629610))))], (42912 ^ _779530) ^ [] : [hBOOL(hAPP(_1629608, 42908 ^ [_1629606, _1629608, _1629610]))]], -(hAPP(c_List_Ofilter(_1629606, _1629608), _1629610) = _1629610)], (42897 ^ _779530) ^ [_1629406, _1629408, _1629410] : [hAPP(c_List_Ofilter(_1629406, _1629408), _1629410) = _1629410, 42900 ^ _779530 : [(42901 ^ _779530) ^ [_1629497] : [hBOOL(hAPP(hAPP(c_member(_1629406), _1629497), hAPP(c_List_Oset(_1629406), _1629410))), -(hBOOL(hAPP(_1629408, _1629497)))]]], (42916 ^ _779530) ^ [_1629798, _1629800, _1629802] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629798)), hAPP(c_List_Ofilter(_1629798, _1629800), _1629802))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629798)), hAPP(c_List_Ofilter(_1629798, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1629798), c_fNot), _1629800)), _1629802))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629798)), _1629802))], (42918 ^ _779530) ^ [_1629889, _1629891, _1629893, _1629895] : [_1629889 = _1629891, -(c_List_Oremove1(_1629893, _1629889, hAPP(hAPP(c_List_Olist_OCons(_1629893), _1629891), _1629895)) = _1629895)], (42924 ^ _779530) ^ [_1629988, _1629990, _1629992, _1629994] : [-(_1629988 = _1629990), -(c_List_Oremove1(_1629992, _1629988, hAPP(hAPP(c_List_Olist_OCons(_1629992), _1629990), _1629994)) = hAPP(hAPP(c_List_Olist_OCons(_1629992), _1629990), c_List_Oremove1(_1629992, _1629988, _1629994)))], (42930 ^ _779530) ^ [_1630069, _1630071, _1630073, _1630075] : [hBOOL(hAPP(_1630069, _1630071)), -(hAPP(c_List_Ofilter(_1630073, _1630069), hAPP(hAPP(c_List_Olist_OCons(_1630073), _1630071), _1630075)) = hAPP(hAPP(c_List_Olist_OCons(_1630073), _1630071), hAPP(c_List_Ofilter(_1630073, _1630069), _1630075)))], (42936 ^ _779530) ^ [_1630204, _1630206, _1630208, _1630210] : [-(hBOOL(hAPP(_1630204, _1630206))), -(hAPP(c_List_Ofilter(_1630208, _1630204), hAPP(hAPP(c_List_Olist_OCons(_1630208), _1630206), _1630210)) = hAPP(c_List_Ofilter(_1630208, _1630204), _1630210))], (42942 ^ _779530) ^ [_1630268, _1630270, _1630272, _1630274] : [-(hAPP(c_List_Ofilter(_1630268, _1630270), hAPP(c_List_Ofilter(_1630268, _1630272), _1630274)) = hAPP(c_List_Ofilter(_1630268, hAPP(hAPP(c_COMBS(_1630268, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1630268), c_fconj), _1630272)), _1630270)), _1630274))], (42944 ^ _779530) ^ [_1630335, _1630337, _1630339, _1630341] : [-(hAPP(c_List_Ofilter(_1630335, _1630337), c_List_Oremove1(_1630335, _1630339, _1630341)) = c_List_Oremove1(_1630335, _1630339, hAPP(c_List_Ofilter(_1630335, _1630337), _1630341)))], (42946 ^ _779530) ^ [_1630384, _1630386, _1630388, _1630390] : [-(c_List_Oremove1(_1630384, _1630386, c_List_Oremove1(_1630384, _1630388, _1630390)) = c_List_Oremove1(_1630384, _1630388, c_List_Oremove1(_1630384, _1630386, _1630390)))], (42948 ^ _779530) ^ [_1630425, _1630427, _1630429, _1630431] : [-(hBOOL(hAPP(_1630425, _1630427))), -(c_List_Oremove1(_1630429, _1630427, hAPP(c_List_Ofilter(_1630429, _1630425), _1630431)) = hAPP(c_List_Ofilter(_1630429, _1630425), _1630431))], (42954 ^ _779530) ^ [_1630483, _1630485, _1630487] : [hBOOL(hAPP(c_List_Odistinct(_1630483), _1630485)), -(hBOOL(hAPP(c_List_Odistinct(_1630483), c_List_Oremove1(_1630483, _1630487, _1630485))))], (42960 ^ _779530) ^ [_1630586, _1630588, _1630590] : [hBOOL(hAPP(c_List_Odistinct(_1630586), _1630588)), -(hBOOL(hAPP(c_List_Odistinct(_1630586), hAPP(c_List_Ofilter(_1630586, _1630590), _1630588))))], (42966 ^ _779530) ^ [_1630689, _1630691, _1630693] : [-(hBOOL(hAPP(hAPP(c_member(_1630689), _1630691), hAPP(c_List_Oset(_1630689), _1630693)))), -(c_List_Oremove1(_1630689, _1630691, _1630693) = _1630693)], (42972 ^ _779530) ^ [_1630742, _1630744, _1630746, _1630748] : [-(hBOOL(hAPP(hAPP(c_member(_1630742), _1630744), hAPP(c_List_Oset(_1630742), _1630746)))), hBOOL(hAPP(hAPP(c_member(_1630742), _1630744), hAPP(c_List_Oset(_1630742), c_List_Oremove1(_1630742, _1630748, _1630746))))], (42978 ^ _779530) ^ [_1630865, _1630867, _1630869, _1630871] : [-(_1630865 = _1630867), 42981 ^ _779530 : [(42982 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630869), _1630865), hAPP(c_List_Oset(_1630869), c_List_Oremove1(_1630869, _1630867, _1630871)))), -(hBOOL(hAPP(hAPP(c_member(_1630869), _1630865), hAPP(c_List_Oset(_1630869), _1630871))))], (42988 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630869), _1630865), hAPP(c_List_Oset(_1630869), _1630871))), -(hBOOL(hAPP(hAPP(c_member(_1630869), _1630865), hAPP(c_List_Oset(_1630869), c_List_Oremove1(_1630869, _1630867, _1630871)))))]]], (42994 ^ _779530) ^ [_1631166, _1631168, _1631170] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631166, tc_HOL_Obool)), hAPP(c_List_Oset(_1631166), c_List_Oremove1(_1631166, _1631168, _1631170))), hAPP(c_List_Oset(_1631166), _1631170))))], (42996 ^ _779530) ^ [_1631217, _1631219, _1631221] : [-(hAPP(c_List_Oset(_1631217), hAPP(c_List_Ofilter(_1631217, _1631219), _1631221)) = hAPP(c_Set_OCollect(_1631217), hAPP(hAPP(c_COMBS(_1631217, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631217), c_fconj), hAPP(hAPP(c_COMBC(_1631217, tc_fun(_1631217, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631217)), hAPP(c_List_Oset(_1631217), _1631221)))), _1631219)))], (42998 ^ _779530) ^ [_1631300, _1631302, _1631304, _1631306, _1631308] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631300)), hAPP(c_List_Ofilter(_1631300, _1631302), hAPP(hAPP(c_List_Omap(_1631304, _1631300), _1631306), _1631308))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631304)), hAPP(c_List_Ofilter(_1631304, hAPP(c_Fun_Ocomp(_1631300, tc_HOL_Obool, _1631304, _1631302), _1631306)), _1631308)))], (43000 ^ _779530) ^ [_1631374, _1631376, _1631378, _1631380] : [hBOOL(hAPP(hAPP(c_member(_1631374), _1631376), hAPP(c_List_Oset(_1631374), _1631378))), -(hBOOL(hAPP(_1631380, _1631376))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631374)), hAPP(c_List_Ofilter(_1631374, _1631380), _1631378))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631374)), _1631378))))], (43010 ^ _779530) ^ [_1631548, _1631550, _1631552] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1631548, tc_HOL_Obool)), hAPP(c_List_Oset(_1631548), _1631550)), hAPP(hAPP(c_Set_Oinsert(_1631548), _1631552), c_Orderings_Obot__class_Obot(tc_fun(_1631548, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1631548), hAPP(c_List_Ofilter(_1631548, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1631548), c_fNot), hAPP(hAPP(c_COMBC(_1631548, _1631548, tc_HOL_Obool), c_fequal), _1631552))), _1631550)))], (43012 ^ _779530) ^ [_1631635, _1631637, _1631639] : [hBOOL(hAPP(c_List_Odistinct(_1631635), _1631637)), -(hAPP(c_List_Ofilter(_1631635, hAPP(hAPP(c_COMBC(_1631635, tc_fun(_1631635, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631635)), hAPP(c_List_Oset(_1631635), c_List_Osublist(_1631635, _1631637, _1631639)))), _1631637) = c_List_Osublist(_1631635, _1631637, _1631639))], (43018 ^ _779530) ^ [_1631790, _1631792, _1631794] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631790)), hAPP(c_List_Ofilter(_1631790, _1631792), _1631794)) = 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(_1631790)), _1631794)))), hAPP(hAPP(c_COMBB(_1631790, tc_HOL_Obool, tc_Nat_Onat), _1631792), hAPP(c_List_Onth(_1631790), _1631794))))))], (43020 ^ _779530) ^ [_1631882, _1631884, _1631886] : [hBOOL(hAPP(hAPP(c_member(_1631882), _1631884), hAPP(c_List_Oset(_1631882), _1631886))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631882)), c_List_Oremove1(_1631882, _1631884, _1631886)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631882)), _1631886)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43026 ^ _779530) ^ [_1632027, _1632029, _1632031] : [-(hBOOL(hAPP(hAPP(c_member(_1632027), _1632029), hAPP(c_List_Oset(_1632027), _1632031)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632027)), c_List_Oremove1(_1632027, _1632029, _1632031)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632027)), _1632031))], (43032 ^ _779530) ^ [_1632097, _1632099, _1632101] : [hBOOL(hAPP(c_List_Odistinct(_1632097), _1632099)), -(hAPP(c_List_Oset(_1632097), c_List_Oremove1(_1632097, _1632101, _1632099)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632097, tc_HOL_Obool)), hAPP(c_List_Oset(_1632097), _1632099)), hAPP(hAPP(c_Set_Oinsert(_1632097), _1632101), c_Orderings_Obot__class_Obot(tc_fun(_1632097, tc_HOL_Obool)))))], (43038 ^ _779530) ^ [_1632260, _1632262, _1632264, _1632266] : [-(c_List_Omap__filter(_1632260, _1632262, _1632264, _1632266) = hAPP(hAPP(c_List_Omap(_1632260, _1632262), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1632262), _1632262, _1632260, c_Option_Othe(_1632262)), _1632264)), hAPP(c_List_Ofilter(_1632260, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1632260), c_fNot), hAPP(hAPP(c_COMBC(_1632260, tc_Option_Ooption(_1632262), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1632262), tc_fun(tc_Option_Ooption(_1632262), tc_HOL_Obool), _1632260), c_fequal), _1632264)), c_Option_Ooption_ONone(_1632262)))), _1632266)))], (43040 ^ _779530) ^ [_1632362, _1632364, _1632366, _1632368, _1632370] : [-(hAPP(hAPP(c_List_Omap(_1632362, _1632364), _1632366), hAPP(c_List_Ofilter(_1632362, _1632368), _1632370)) = c_List_Omap__filter(_1632362, _1632364, hAPP(hAPP(c_COMBC(_1632362, tc_Option_Ooption(_1632364), tc_Option_Ooption(_1632364)), hAPP(hAPP(c_COMBS(_1632362, tc_Option_Ooption(_1632364), tc_fun(tc_Option_Ooption(_1632364), tc_Option_Ooption(_1632364))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1632364), tc_fun(tc_Option_Ooption(_1632364), tc_Option_Ooption(_1632364))), _1632362), c_If(tc_Option_Ooption(_1632364))), _1632368)), hAPP(hAPP(c_COMBB(_1632364, tc_Option_Ooption(_1632364), _1632362), c_Option_Ooption_OSome(_1632364)), _1632366))), c_Option_Ooption_ONone(_1632364)), _1632370))], (43042 ^ _779530) ^ [_1632488, _1632490, _1632492, _1632494, _1632496, _1632498] : [hAPP(hAPP(c_Map_Omap__of(_1632488, _1632490), _1632492), _1632494) = hAPP(c_Option_Ooption_OSome(_1632490), _1632496), hBOOL(hAPP(hAPP(_1632498, _1632494), _1632496)), -(hAPP(hAPP(c_Map_Omap__of(_1632488, _1632490), hAPP(c_List_Ofilter(tc_prod(_1632488, _1632490), hAPP(c_Product__Type_Oprod_Oprod__case(_1632488, _1632490, tc_HOL_Obool), _1632498)), _1632492)), _1632494) = hAPP(c_Option_Ooption_OSome(_1632490), _1632496))], (43052 ^ _779530) ^ [_1632731, _1632733, _1632735, _1632737, _1632739] : [-(c_List_Omap__filter(_1632731, _1632733, _1632735, hAPP(hAPP(c_List_Olist_OCons(_1632731), _1632737), _1632739)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1632733), _1632733, c_List_Omap__filter(_1632731, _1632733, _1632735, _1632739), hAPP(hAPP(c_COMBC(_1632733, tc_List_Olist(_1632733), tc_List_Olist(_1632733)), c_List_Olist_OCons(_1632733)), c_List_Omap__filter(_1632731, _1632733, _1632735, _1632739))), hAPP(_1632735, _1632737)))], (43054 ^ _779530) ^ [_1632814, _1632816, _1632818, _1632820] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1632814, tc_Nat_Onat), _1632814), c_Product__Type_Ofst(_1632814, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1632814, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1632814, tc_Nat_Onat)), _1632816), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1632814, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1632814, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1632814, tc_Nat_Onat), _1632818), _1632820))) = hAPP(hAPP(c_List_Omap(tc_prod(_1632814, tc_Nat_Onat), _1632814), c_Product__Type_Ofst(_1632814, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1632814, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1632814, tc_Nat_Onat)), _1632816), c_Product__Type_Osnd(_1632814, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1632814, tc_Nat_Onat), _1632818), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1632820)))))], (43056 ^ _779530) ^ [_1632957, _1632959, _1632961] : [class_Orderings_Olinorder(_1632957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1632957), _1632959)), -(c_List_Olinorder__class_Osorted__list__of__set(_1632957, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1632957, tc_HOL_Obool)), _1632959), hAPP(hAPP(c_Set_Oinsert(_1632957), _1632961), c_Orderings_Obot__class_Obot(tc_fun(_1632957, tc_HOL_Obool))))) = c_List_Oremove1(_1632957, _1632961, c_List_Olinorder__class_Osorted__list__of__set(_1632957, _1632959)))], (43066 ^ _779530) ^ [_1633164, _1633166] : [-(c_List_Ofoldr(tc_List_Olist(_1633164), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1633164)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1633164))), c_List_Otranspose(_1633164, _1633166), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1633164))), hAPP(c_List_Ofilter(tc_List_Olist(_1633164), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1633164)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1633164), tc_List_Olist(_1633164), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1633164)))), _1633166)))], (43068 ^ _779530) ^ [_1633261, _1633263] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1633261)), c_List_Olist_ONil(_1633261)), c_List_Olists(_1633261, _1633263))))], (43070 ^ _779530) ^ [_1633300, _1633302, _1633304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633300), tc_List_Olist(_1633300))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633300), tc_List_Olist(_1633300)), c_List_Olist_ONil(_1633300)), _1633302)), c_List_Olistrel(_1633300, _1633304))), -(_1633302 = c_List_Olist_ONil(_1633300))], (43076 ^ _779530) ^ [_1633447, _1633449, _1633451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633447), tc_List_Olist(_1633447))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633447), tc_List_Olist(_1633447)), _1633449), c_List_Olist_ONil(_1633447))), c_List_Olistrel(_1633447, _1633451))), -(_1633449 = c_List_Olist_ONil(_1633447))], (43092 ^ _779530) ^ [_1633817, _1633819, _1633821] : [43094 ^ _779530 : [(43095 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1633817), 43093 ^ [_1633817, _1633819, _1633821]), hAPP(c_List_Oset(_1633817), _1633821))))], (43097 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1633819, 43093 ^ [_1633817, _1633819, _1633821])))]], -(hAPP(c_List_Ofilter(_1633817, _1633819), _1633821) = c_List_Olist_ONil(_1633817))], (43082 ^ _779530) ^ [_1633612, _1633614, _1633616] : [hAPP(c_List_Ofilter(_1633612, _1633614), _1633616) = c_List_Olist_ONil(_1633612), 43085 ^ _779530 : [(43086 ^ _779530) ^ [_1633709] : [hBOOL(hAPP(hAPP(c_member(_1633612), _1633709), hAPP(c_List_Oset(_1633612), _1633616))), hBOOL(hAPP(_1633614, _1633709))]]], (43101 ^ _779530) ^ [_1633934, _1633936] : [-(hAPP(c_List_Ofilter(_1633934, _1633936), c_List_Olist_ONil(_1633934)) = c_List_Olist_ONil(_1633934))], (43103 ^ _779530) ^ [_1633969, _1633971, _1633973] : [-(c_List_Omap__filter(_1633969, _1633971, _1633973, c_List_Olist_ONil(_1633969)) = c_List_Olist_ONil(_1633971))], (43105 ^ _779530) ^ [_1634005] : [-(c_List_Otranspose(_1634005, c_List_Olist_ONil(tc_List_Olist(_1634005))) = c_List_Olist_ONil(tc_List_Olist(_1634005)))], (43107 ^ _779530) ^ [_1634039, _1634041, _1634043, _1634045] : [-(c_List_Ofoldr(_1634039, _1634041, _1634043, c_List_Olist_ONil(_1634039), _1634045) = _1634045)], (43109 ^ _779530) ^ [_1634076, _1634078] : [-(c_List_Otranspose(_1634076, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1634076)), c_List_Olist_ONil(_1634076)), _1634078)) = c_List_Otranspose(_1634076, _1634078))], (43121 ^ _779530) ^ [_1634344, _1634346] : [43123 ^ _779530 : [(43124 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634344)), 43122 ^ [_1634344, _1634346]), hAPP(c_List_Oset(tc_List_Olist(_1634344)), _1634346))))], (43126 ^ _779530) ^ [] : [43122 ^ [_1634344, _1634346] = c_List_Olist_ONil(_1634344)]], -(c_List_Otranspose(_1634344, _1634346) = c_List_Olist_ONil(tc_List_Olist(_1634344)))], (43111 ^ _779530) ^ [_1634134, _1634136] : [c_List_Otranspose(_1634134, _1634136) = c_List_Olist_ONil(tc_List_Olist(_1634134)), 43114 ^ _779530 : [(43115 ^ _779530) ^ [_1634229] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634134)), _1634229), hAPP(c_List_Oset(tc_List_Olist(_1634134)), _1634136))), -(_1634229 = c_List_Olist_ONil(_1634134))]]], (43130 ^ _779530) ^ [_1634539] : [class_Groups_Omonoid__add(_1634539), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1634539), c_List_Olist_ONil(_1634539)) = c_Groups_Ozero__class_Ozero(_1634539))], (43136 ^ _779530) ^ [_1634630] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634630)), c_List_Olist_ONil(_1634630)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43138 ^ _779530) ^ [_1634677, _1634679] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634677)), _1634679) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1634679 = c_List_Olist_ONil(_1634677))], (43144 ^ _779530) ^ [_1634768, _1634770] : [_1634770 = c_List_Olist_ONil(_1634768), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634768)), _1634770) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43150 ^ _779530) ^ [_1634880, _1634882] : [hAPP(c_List_Oset(_1634880), _1634882) = c_Orderings_Obot__class_Obot(tc_fun(_1634880, tc_HOL_Obool)), -(_1634882 = c_List_Olist_ONil(_1634880))], (43156 ^ _779530) ^ [_1634977, _1634979] : [_1634979 = c_List_Olist_ONil(_1634977), -(hAPP(c_List_Oset(_1634977), _1634979) = c_Orderings_Obot__class_Obot(tc_fun(_1634977, tc_HOL_Obool)))], (43162 ^ _779530) ^ [_1635095, _1635097] : [c_Orderings_Obot__class_Obot(tc_fun(_1635095, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635095), _1635097), -(_1635097 = c_List_Olist_ONil(_1635095))], (43168 ^ _779530) ^ [_1635192, _1635194] : [_1635194 = c_List_Olist_ONil(_1635192), -(c_Orderings_Obot__class_Obot(tc_fun(_1635192, tc_HOL_Obool)) = hAPP(c_List_Oset(_1635192), _1635194))], (43174 ^ _779530) ^ [_1635295] : [-(hAPP(c_List_Oset(_1635295), c_List_Olist_ONil(_1635295)) = c_Orderings_Obot__class_Obot(tc_fun(_1635295, tc_HOL_Obool)))], (43176 ^ _779530) ^ [_1635330, _1635332, _1635334] : [-(hAPP(hAPP(c_List_Olist__update(_1635330, c_List_Olist_ONil(_1635330)), _1635332), _1635334) = c_List_Olist_ONil(_1635330))], (43178 ^ _779530) ^ [_1635370, _1635372, _1635374] : [-(hAPP(hAPP(c_List_Olist__update(_1635370, c_List_Olist_ONil(_1635370)), _1635372), _1635374) = c_List_Olist_ONil(_1635370))], (43180 ^ _779530) ^ [_1635431, _1635433, _1635435, _1635437] : [hAPP(hAPP(c_List_Olist__update(_1635431, _1635433), _1635435), _1635437) = c_List_Olist_ONil(_1635431), -(_1635433 = c_List_Olist_ONil(_1635431))], (43186 ^ _779530) ^ [_1635534, _1635536, _1635538, _1635540] : [_1635536 = c_List_Olist_ONil(_1635534), -(hAPP(hAPP(c_List_Olist__update(_1635534, _1635536), _1635538), _1635540) = c_List_Olist_ONil(_1635534))], (43192 ^ _779530) ^ [_1635643, _1635645] : [-(c_List_Olist_Olist__size(_1635643, _1635645, c_List_Olist_ONil(_1635643)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43194 ^ _779530) ^ [_1635674, _1635676] : [-(hAPP(hAPP(c_List_Otake(_1635674), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635676) = c_List_Olist_ONil(_1635674))], (43206 ^ _779530) ^ [_1635839, _1635841, _1635843] : [43207 ^ _779530 : [(43208 ^ _779530) ^ [] : [_1635841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43210 ^ _779530) ^ [] : [_1635843 = c_List_Olist_ONil(_1635839)]], -(hAPP(hAPP(c_List_Otake(_1635839), _1635841), _1635843) = c_List_Olist_ONil(_1635839))], (43196 ^ _779530) ^ [_1635727, _1635729, _1635731] : [hAPP(hAPP(c_List_Otake(_1635727), _1635729), _1635731) = c_List_Olist_ONil(_1635727), -(_1635729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1635731 = c_List_Olist_ONil(_1635727))], (43214 ^ _779530) ^ [_1635982, _1635984] : [-(hAPP(hAPP(c_List_Otake(_1635982), _1635984), c_List_Olist_ONil(_1635982)) = c_List_Olist_ONil(_1635982))], (43216 ^ _779530) ^ [_1636019, _1636021, _1636023, _1636025] : [-(c_Map_Omap__upds(_1636019, _1636021, _1636023, _1636025, c_List_Olist_ONil(_1636021)) = _1636023)], (43218 ^ _779530) ^ [_1636056, _1636058, _1636060, _1636062] : [-(c_Map_Omap__upds(_1636056, _1636058, _1636060, c_List_Olist_ONil(_1636056), _1636062) = _1636060)], (43220 ^ _779530) ^ [_1636093, _1636095] : [-(c_Enum_On__lists(_1636093, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1636095) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1636093)), c_List_Olist_ONil(_1636093)), c_List_Olist_ONil(tc_List_Olist(_1636093))))], (43222 ^ _779530) ^ [_1636147, _1636149] : [_1636147 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1636149, _1636147, c_List_Olist_ONil(_1636149)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1636149)), c_List_Olist_ONil(_1636149)), c_List_Olist_ONil(tc_List_Olist(_1636149))))], (43228 ^ _779530) ^ [_1636262, _1636264] : [-(_1636262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1636264, _1636262, c_List_Olist_ONil(_1636264)) = c_List_Olist_ONil(tc_List_Olist(_1636264)))], (43234 ^ _779530) ^ [_1636325, _1636327, _1636329] : [hAPP(hAPP(c_List_Olist_OCons(_1636325), _1636327), _1636329) = c_List_Olist_ONil(_1636325)], (43236 ^ _779530) ^ [_1636377, _1636379, _1636381] : [c_List_Olist_ONil(_1636377) = hAPP(hAPP(c_List_Olist_OCons(_1636377), _1636379), _1636381)], (43238 ^ _779530) ^ [_1636414] : [-(c_Enum_Osublists(_1636414, c_List_Olist_ONil(_1636414)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1636414)), c_List_Olist_ONil(_1636414)), c_List_Olist_ONil(tc_List_Olist(_1636414))))], (43240 ^ _779530) ^ [_1636458, _1636460, _1636462] : [-(hAPP(hAPP(c_List_Ozip(_1636458, _1636460), _1636462), c_List_Olist_ONil(_1636460)) = c_List_Olist_ONil(tc_prod(_1636458, _1636460)))], (43242 ^ _779530) ^ [_1636501, _1636503, _1636505] : [-(hAPP(hAPP(c_List_Ozip(_1636501, _1636503), c_List_Olist_ONil(_1636501)), _1636505) = c_List_Olist_ONil(tc_prod(_1636501, _1636503)))], (43244 ^ _779530) ^ [_1636544] : [class_Orderings_Olinorder(_1636544), -(c_List_Olinorder__class_Osorted__list__of__set(_1636544, c_Orderings_Obot__class_Obot(tc_fun(_1636544, tc_HOL_Obool))) = c_List_Olist_ONil(_1636544))], (43250 ^ _779530) ^ [_1636637, _1636639] : [-(c_List_Osublist(_1636637, c_List_Olist_ONil(_1636637), _1636639) = c_List_Olist_ONil(_1636637))], (43252 ^ _779530) ^ [_1636670, _1636672, _1636674] : [-(c_Enum_Oproduct(_1636670, _1636672, c_List_Olist_ONil(_1636670), _1636674) = c_List_Olist_ONil(tc_prod(_1636670, _1636672)))], (43254 ^ _779530) ^ [_1636709, _1636711] : [-(c_List_Olistrelp(_1636709, _1636711, c_List_Olist_ONil(_1636709), c_List_Olist_ONil(_1636709)))], (43256 ^ _779530) ^ [_1636740, _1636742] : [-(c_List_Olistrelp(_1636740, _1636742, c_List_Olist_ONil(_1636740), c_List_Olist_ONil(_1636740)))], (43258 ^ _779530) ^ [_1636771] : [-(hBOOL(hAPP(c_List_Odistinct(_1636771), c_List_Olist_ONil(_1636771))))], (43260 ^ _779530) ^ [_1636800, _1636802, _1636804] : [-(hAPP(hAPP(c_Map_Omap__of(_1636800, _1636802), c_List_Olist_ONil(tc_prod(_1636800, _1636802))), _1636804) = c_Option_Ooption_ONone(_1636802))], (43262 ^ _779530) ^ [_1636843, _1636845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1636843), _1636845)), -(c_List_Oupto(_1636845, _1636843) = c_List_Olist_ONil(tc_Int_Oint))], (43268 ^ _779530) ^ [_1636935, _1636937] : [-(_1636935 = c_List_Olist_ONil(_1636937)), hBOOL(hAPP(c_List_Odistinct(_1636937), _1636935)), -(hBOOL(hAPP(c_List_Odistinct(_1636937), c_List_Obutlast(_1636937, _1636935))))], (43278 ^ _779530) ^ [_1637086] : [-(c_List_Obutlast(_1637086, c_List_Olist_ONil(_1637086)) = c_List_Olist_ONil(_1637086))], (43280 ^ _779530) ^ [_1637128, _1637130, _1637132] : [_1637128 = c_List_Olist_ONil(_1637130), -(c_List_Obutlast(_1637130, hAPP(hAPP(c_List_Olist_OCons(_1637130), _1637132), _1637128)) = c_List_Olist_ONil(_1637130))], (43286 ^ _779530) ^ [_1637231, _1637233, _1637235] : [-(_1637231 = c_List_Olist_ONil(_1637233)), -(c_List_Obutlast(_1637233, hAPP(hAPP(c_List_Olist_OCons(_1637233), _1637235), _1637231)) = hAPP(hAPP(c_List_Olist_OCons(_1637233), _1637235), c_List_Obutlast(_1637233, _1637231)))], (43292 ^ _779530) ^ [_1637295, _1637297] : [-(c_List_Oremove1(_1637295, _1637297, c_List_Olist_ONil(_1637295)) = c_List_Olist_ONil(_1637295))], (43294 ^ _779530) ^ [_1637349, _1637351, _1637353, _1637355] : [hAPP(hAPP(c_List_Omap(_1637349, _1637351), _1637353), _1637355) = c_List_Olist_ONil(_1637351), -(_1637355 = c_List_Olist_ONil(_1637349))], (43300 ^ _779530) ^ [_1637452, _1637454, _1637456, _1637458] : [_1637458 = c_List_Olist_ONil(_1637452), -(hAPP(hAPP(c_List_Omap(_1637452, _1637454), _1637456), _1637458) = c_List_Olist_ONil(_1637454))], (43306 ^ _779530) ^ [_1637561, _1637563, _1637565] : [-(hAPP(hAPP(c_List_Omap(_1637561, _1637563), _1637565), c_List_Olist_ONil(_1637561)) = c_List_Olist_ONil(_1637563))], (43308 ^ _779530) ^ [_1637622, _1637624, _1637626, _1637628] : [c_List_Olist_ONil(_1637622) = hAPP(hAPP(c_List_Omap(_1637624, _1637622), _1637626), _1637628), -(_1637628 = c_List_Olist_ONil(_1637624))], (43314 ^ _779530) ^ [_1637725, _1637727, _1637729, _1637731] : [_1637731 = c_List_Olist_ONil(_1637727), -(c_List_Olist_ONil(_1637725) = hAPP(hAPP(c_List_Omap(_1637727, _1637725), _1637729), _1637731))], (43320 ^ _779530) ^ [_1637834, _1637836] : [-(c_List_Osublist(_1637834, _1637836, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1637834))], (43322 ^ _779530) ^ [_1637865, _1637867, _1637869] : [-(hAPP(hAPP(c_Map_Omap__of(_1637865, _1637867), c_List_Olist_ONil(tc_prod(_1637865, _1637867))), _1637869) = c_Option_Ooption_ONone(_1637867))], (43324 ^ _779530) ^ [_1637923, _1637925] : [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(_1637923)), _1637925))), _1637925 = c_List_Olist_ONil(_1637923)], (43330 ^ _779530) ^ [_1638017, _1638019] : [-(_1638019 = c_List_Olist_ONil(_1638017)), -(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(_1638017)), _1638019))))], (43336 ^ _779530) ^ [_1638066, _1638068, _1638070] : [-(hAPP(hAPP(c_List_Otake(_1638066), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1638066), _1638068), _1638070)) = hAPP(hAPP(c_List_Olist_OCons(_1638066), _1638068), c_List_Olist_ONil(_1638066)))], (43338 ^ _779530) ^ [_1638134, _1638136, _1638138] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638134), tc_List_Olist(_1638134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638134), tc_List_Olist(_1638134)), c_List_Olist_ONil(_1638134)), _1638136)), c_List_Olistrel1(_1638134, _1638138)))], (43340 ^ _779530) ^ [_1638208, _1638210, _1638212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638208), tc_List_Olist(_1638208))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638208), tc_List_Olist(_1638208)), _1638210), c_List_Olist_ONil(_1638208))), c_List_Olistrel1(_1638208, _1638212)))], (43342 ^ _779530) ^ [_1638267, _1638269] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638267), tc_List_Olist(_1638267))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638267), tc_List_Olist(_1638267)), c_List_Olist_ONil(_1638267)), c_List_Olist_ONil(_1638267))), c_List_Olistrel(_1638267, _1638269))))], (43344 ^ _779530) ^ [_1638341, _1638343, _1638345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638341), tc_List_Olist(_1638341))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638341), tc_List_Olist(_1638341)), _1638343), c_List_Olist_ONil(_1638341))), c_List_Olexord(_1638341, _1638345)))], (43346 ^ _779530) ^ [_1638415, _1638417, _1638419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638415), tc_List_Olist(_1638415))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638415), tc_List_Olist(_1638415)), c_List_Olist_ONil(_1638415)), _1638417)), c_List_Olex(_1638415, _1638419)))], (43348 ^ _779530) ^ [_1638489, _1638491, _1638493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638489), tc_List_Olist(_1638489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638489), tc_List_Olist(_1638489)), _1638491), c_List_Olist_ONil(_1638489))), c_List_Olex(_1638489, _1638493)))], (43350 ^ _779530) ^ [_1638548, _1638550, _1638552, _1638554] : [-(hAPP(hAPP(c_List_Otake(_1638548), _1638550), hAPP(hAPP(c_List_Olist_OCons(_1638548), _1638552), _1638554)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1638548), c_List_Olist_ONil(_1638548), hAPP(hAPP(c_COMBB(tc_List_Olist(_1638548), tc_List_Olist(_1638548), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1638548), _1638552)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1638548), tc_List_Olist(_1638548)), c_List_Otake(_1638548)), _1638554)), _1638550))], (43352 ^ _779530) ^ [_1638646, _1638648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638646), _1638648)), -(c_List_Oupto(_1638646, _1638648) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1638646), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1638646), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1638648)))], (43358 ^ _779530) ^ [_1638763, _1638765] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1638763), _1638765))), -(c_List_Oupto(_1638763, _1638765) = c_List_Olist_ONil(tc_Int_Oint))], (43364 ^ _779530) ^ [_1638821, _1638823, _1638825] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638821)), -(c_List_Osublist(_1638823, hAPP(hAPP(c_List_Olist_OCons(_1638823), _1638825), c_List_Olist_ONil(_1638823)), _1638821) = hAPP(hAPP(c_List_Olist_OCons(_1638823), _1638825), c_List_Olist_ONil(_1638823)))], (43370 ^ _779530) ^ [_1638946, _1638948, _1638950] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638946))), -(c_List_Osublist(_1638948, hAPP(hAPP(c_List_Olist_OCons(_1638948), _1638950), c_List_Olist_ONil(_1638948)), _1638946) = c_List_Olist_ONil(_1638948))], (43376 ^ _779530) ^ [_1639004] : [-(c_List_Olists(_1639004, c_Orderings_Obot__class_Obot(tc_fun(_1639004, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639004)), c_List_Olist_ONil(_1639004)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639004), tc_HOL_Obool))))], (43378 ^ _779530) ^ [_1639069, _1639071, _1639073, _1639075] : [_1639069 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1639071), _1639069), hAPP(hAPP(c_List_Olist_OCons(_1639071), _1639073), _1639075)) = c_List_Olist_ONil(_1639071))], (43384 ^ _779530) ^ [_1639180, _1639182, _1639184, _1639186] : [-(_1639180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1639182), _1639180), hAPP(hAPP(c_List_Olist_OCons(_1639182), _1639184), _1639186)) = hAPP(hAPP(c_List_Olist_OCons(_1639182), _1639184), hAPP(hAPP(c_List_Otake(_1639182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1639180), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1639186)))], (43390 ^ _779530) ^ [_1639269, _1639271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639269)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639271))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639269), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639271)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639269)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639269)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639271))))], (43396 ^ _779530) ^ [_1639428, _1639430] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639428)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639430)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639428), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1639430)) = c_List_Olist_ONil(tc_Int_Oint))], (43402 ^ _779530) ^ [_1639486, _1639488] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1639486), tc_List_Olist(_1639486), c_List_Olistrel(_1639486, _1639488)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639486)), c_List_Olist_ONil(_1639486)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639486), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639486)), c_List_Olist_ONil(_1639486)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639486), tc_HOL_Obool))))], (43404 ^ _779530) ^ [_1639563, _1639565] : [-(c_List_Oset__Cons(_1639563, _1639565, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1639563)), c_List_Olist_ONil(_1639563)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1639563), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1639563, tc_List_Olist(_1639563), hAPP(hAPP(c_COMBC(_1639563, tc_List_Olist(_1639563), tc_List_Olist(_1639563)), c_List_Olist_OCons(_1639563)), c_List_Olist_ONil(_1639563))), _1639565))], (43406 ^ _779530) ^ [_1639653, _1639655, _1639657, _1639659] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639653) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1639655), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639653)), hAPP(hAPP(c_List_Olist_OCons(_1639655), _1639657), _1639659)) = c_List_Olist_ONil(_1639655))], (43412 ^ _779530) ^ [_1639776, _1639778, _1639780, _1639782] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1639778), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639776)), hAPP(hAPP(c_List_Olist_OCons(_1639778), _1639780), _1639782)) = hAPP(hAPP(c_List_Olist_OCons(_1639778), _1639780), hAPP(hAPP(c_List_Otake(_1639778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1639776)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1639782)))], (43418 ^ _779530) ^ [_1639865, _1639867, _1639869, _1639871] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639865)), _1639867))), c_List_Ofoldr(tc_List_Olist(_1639869), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1639869)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1639869))), _1639871, 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(_1639865)), _1639867)), c_List_Ofoldr(tc_List_Olist(_1639869), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1639869)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639869), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1639869)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1639869)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1639869), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1639869)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1639869), tc_List_Olist(_1639869), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1639869)))), _1639871), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (43420 ^ _779530) ^ [_1640034, _1640036] : [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), _1640034), _1640036))), 43423 ^ _779530 : [(43424 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1640034), _1640036)), -(c_List_Oupto(_1640034, _1640036) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1640034), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1640034), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1640036)))], (43430 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1640034), _1640036))), -(c_List_Oupto(_1640034, _1640036) = c_List_Olist_ONil(tc_Int_Oint))]]], (43436 ^ _779530) ^ [_1640288, _1640290, _1640292] : [-(c_List_Osublist(_1640288, _1640290, _1640292) = hAPP(hAPP(c_List_Omap(tc_prod(_1640288, tc_Nat_Onat), _1640288), c_Product__Type_Ofst(_1640288, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1640288, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1640288, 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(_1640288, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1640288, tc_Nat_Onat))), _1640292)), hAPP(hAPP(c_List_Ozip(_1640288, tc_Nat_Onat), _1640290), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640288)), _1640290))))))], (43438 ^ _779530) ^ [_1640400, _1640402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640400), _1640402)), -(c_List_Oupt(_1640400, _1640402) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1640400), c_List_Oupt(hAPP(c_Nat_OSuc, _1640400), _1640402)))], (43444 ^ _779530) ^ [_1640511, _1640513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640511), _1640513))), -(c_List_Oupt(_1640511, _1640513) = c_List_Olist_ONil(tc_Nat_Onat))], (43450 ^ _779530) ^ [_1640557] : [-(c_List_Oupt(_1640557, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (43452 ^ _779530) ^ [_1640583, _1640585] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1640583), _1640585)) = c_List_Oupt(_1640583, _1640585))], (43454 ^ _779530) ^ [_1640620, _1640622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1640620), _1640622)), -(c_List_Oupt(_1640622, _1640620) = c_List_Olist_ONil(tc_Nat_Onat))], (43470 ^ _779530) ^ [_1640830, _1640832] : [43471 ^ _779530 : [(43472 ^ _779530) ^ [] : [_1640832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43474 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1640832), _1640830))]], -(c_List_Oupt(_1640830, _1640832) = c_List_Olist_ONil(tc_Nat_Onat))], (43460 ^ _779530) ^ [_1640728, _1640730] : [c_List_Oupt(_1640728, _1640730) = c_List_Olist_ONil(tc_Nat_Onat), -(_1640730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1640730), _1640728)))], (43478 ^ _779530) ^ [_1640963, _1640965] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1640963, _1640965))))], (43480 ^ _779530) ^ [_1640993, _1640995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640993), _1640995)), -(c_List_Oupt(_1640993, _1640995) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1640993), c_List_Oupt(hAPP(c_Nat_OSuc, _1640993), _1640995)))], (43486 ^ _779530) ^ [_1641110, _1641112, _1641114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1641110), _1641112)), _1641114)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1641112), c_List_Oupt(_1641110, _1641114)) = c_List_Oupt(_1641110, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1641110), _1641112)))], (43492 ^ _779530) ^ [_1641247, _1641249] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1641247), _1641249) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1641247, _1641249)))], (43494 ^ _779530) ^ [_1641284, _1641286] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1641284, _1641286)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1641284), _1641286))], (43496 ^ _779530) ^ [_1641321, _1641323] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1641321, _1641323)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1641323), _1641321))], (43498 ^ _779530) ^ [_1641367, _1641369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641367)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641369))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641367), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641369)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641367)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641367)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641369))))], (43504 ^ _779530) ^ [_1641520, _1641522] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641520)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641522)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641520), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1641522)) = c_List_Olist_ONil(tc_Nat_Onat))], (43510 ^ _779530) ^ [_1641599, _1641601, _1641603, _1641605] : [c_List_Oupt(_1641599, _1641601) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1641603), _1641605), 43513 ^ _779530 : [(43514 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641599), _1641601)))], (43516 ^ _779530) ^ [] : [-(_1641599 = _1641603)], (43518 ^ _779530) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1641599), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1641601) = _1641605)]]], (43520 ^ _779530) ^ [_1641772, _1641774, _1641776, _1641778] : [-(c_List_Oupt(_1641772, _1641774) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1641776), _1641778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641772), _1641774)), _1641772 = _1641776, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1641772), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1641774) = _1641778], (43534 ^ _779530) ^ [_1642013, _1642015] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1642013, _1642015)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1642013), hAPP(c_Nat_OSuc, _1642015)))], (43536 ^ _779530) ^ [_1642053, _1642055] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1642053, _1642055) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1642053, hAPP(c_Nat_OSuc, _1642055))))], (43538 ^ _779530) ^ [_1642091] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1642091) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1642091)))], (43540 ^ _779530) ^ [_1642123, _1642125, _1642127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1642123), _1642125)), _1642127)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1642123, _1642127)), _1642125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1642123), _1642125))], (43546 ^ _779530) ^ [_1642254, _1642256] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1642254, _1642256) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1642254), hAPP(c_Nat_OSuc, _1642256))))], (43548 ^ _779530) ^ [_1642295, _1642297] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1642295, _1642297) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1642295), _1642297)))], (43550 ^ _779530) ^ [_1642333] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1642333) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1642333))))], (43552 ^ _779530) ^ [_1642368, _1642370] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1642368), hAPP(c_List_Onth(_1642368), _1642370)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642368)), _1642370))) = _1642370)], (43554 ^ _779530) ^ [_1642417, _1642419, _1642421, _1642423] : [class_Groups_Ocomm__monoid__add(_1642417), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1642417), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1642417), _1642419), c_List_Oupt(_1642421, _1642423))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1642417), _1642419), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1642421, _1642423))))], (43560 ^ _779530) ^ [_1642560, _1642562, _1642564, _1642566] : [class_Groups_Ocomm__monoid__add(_1642560), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1642560), _1642562), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1642564, _1642566))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1642560), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1642560), _1642562), c_List_Oupt(_1642564, _1642566))))], (43566 ^ _779530) ^ [_1642703, _1642705, _1642707, _1642709, _1642711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642703), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1642705), _1642707))), -(hAPP(hAPP(c_List_Onth(_1642709), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1642709), _1642711), c_List_Oupt(_1642707, _1642705))), _1642703) = hAPP(_1642711, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1642707), _1642703)))], (43572 ^ _779530) ^ [_1642866, _1642868, _1642870, _1642872] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1642866, tc_Nat_Onat), _1642866), c_Product__Type_Ofst(_1642866, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1642866, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1642866, 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(_1642866, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1642866, tc_Nat_Onat))), _1642868)), hAPP(hAPP(c_List_Ozip(_1642866, tc_Nat_Onat), _1642870), c_List_Oupt(_1642872, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1642872), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642866)), _1642870)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1642866, tc_Nat_Onat), _1642866), c_Product__Type_Ofst(_1642866, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1642866, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1642866, 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(_1642866, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1642866, 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(_1642866, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1642866, tc_Nat_Onat))), _1642872))), _1642868)), hAPP(hAPP(c_List_Ozip(_1642866, tc_Nat_Onat), _1642870), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642866)), _1642870))))))], (43574 ^ _779530) ^ [_1643071, _1643073, _1643075] : [43575 ^ _779530 : [(43576 ^ _779530) ^ [] : [-(_1643071 = c_List_Olist_ONil(tc_List_Olist(_1643073)))], (43578 ^ _779530) ^ [] : [_1643075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 43582 ^ _779530 : [(43583 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43581 ^ [_1643071, _1643073, _1643075]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1643073))), _1643071))))], (43585 ^ _779530) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643073)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1643073)), _1643071), 43581 ^ [_1643071, _1643073, _1643075])) = _1643075]], -(c_List_Otranspose(_1643073, _1643071) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1643073)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1643073)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1643073), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1643073)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1643073)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1643073), hAPP(hAPP(c_COMBB(tc_List_Olist(_1643073), tc_fun(tc_Nat_Onat, _1643073), tc_Nat_Onat), c_List_Onth(_1643073)), hAPP(c_List_Onth(tc_List_Olist(_1643073)), _1643071))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1643073))), _1643071)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1643075)))], (43589 ^ _779530) ^ [_1643599, _1643601, _1643603, _1643605, _1643607] : [_1643599 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1643601, _1643603, _1643605), _1643599), _1643607) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643603), _1643601), c_List_Olist_ONil(_1643603)), _1643607))], (43595 ^ _779530) ^ [_1643722, _1643724, _1643726, _1643728, _1643730] : [-(_1643722 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1643724, _1643726, _1643728), _1643722), _1643730) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1643726), _1643724), tc_prod(_1643726, _1643724), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643726), _1643724), c_List_Olist_ONil(_1643726)), _1643730), hAPP(c_Product__Type_Oprod_Oprod__case(_1643726, _1643724, tc_prod(tc_List_Olist(_1643726), _1643724)), hAPP(hAPP(c_COMBC(_1643726, tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724)), tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1643726), _1643724), tc_prod(tc_List_Olist(_1643726), _1643724)), tc_fun(tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724)), tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724))), _1643726), c_COMBB(tc_prod(tc_List_Olist(_1643726), _1643724), tc_prod(tc_List_Olist(_1643726), _1643724), _1643724)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1643726), tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724))), tc_fun(tc_prod(tc_List_Olist(_1643726), _1643724), tc_prod(tc_List_Olist(_1643726), _1643724)), _1643726), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1643726), _1643724, tc_prod(tc_List_Olist(_1643726), _1643724))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1643726), tc_List_Olist(_1643726)), tc_fun(tc_List_Olist(_1643726), tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724))), _1643726), hAPP(c_COMBB(tc_List_Olist(_1643726), tc_fun(_1643724, tc_prod(tc_List_Olist(_1643726), _1643724)), tc_List_Olist(_1643726)), c_Product__Type_OPair(tc_List_Olist(_1643726), _1643724))), c_List_Olist_OCons(_1643726))))), hAPP(c_Lazy__Sequence_Oanamorph(_1643724, _1643726, _1643728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1643722), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1643728, _1643730)))], (43601 ^ _779530) ^ [_1644018] : [-(c_List_Olistset(_1644018, c_List_Olist_ONil(tc_fun(_1644018, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1644018)), c_List_Olist_ONil(_1644018)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1644018), tc_HOL_Obool))))], (43603 ^ _779530) ^ [_1644068, _1644070, _1644072, _1644074, _1644076] : [-(hAPP(hAPP(c_List_Ozip(_1644068, _1644070), _1644072), hAPP(hAPP(c_List_Olist_OCons(_1644070), _1644074), _1644076)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1644068, _1644070)), _1644068, c_List_Olist_ONil(tc_prod(_1644068, _1644070)), hAPP(hAPP(c_COMBC(_1644068, tc_fun(tc_List_Olist(_1644068), tc_List_Olist(tc_prod(_1644068, _1644070))), tc_fun(tc_List_Olist(_1644068), tc_List_Olist(tc_prod(_1644068, _1644070)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1644068, _1644070)), tc_List_Olist(tc_prod(_1644068, _1644070))), tc_fun(tc_fun(tc_List_Olist(_1644068), tc_List_Olist(tc_prod(_1644068, _1644070))), tc_fun(tc_List_Olist(_1644068), tc_List_Olist(tc_prod(_1644068, _1644070)))), _1644068), c_COMBB(tc_List_Olist(tc_prod(_1644068, _1644070)), tc_List_Olist(tc_prod(_1644068, _1644070)), tc_List_Olist(_1644068))), hAPP(hAPP(c_COMBB(tc_prod(_1644068, _1644070), tc_fun(tc_List_Olist(tc_prod(_1644068, _1644070)), tc_List_Olist(tc_prod(_1644068, _1644070))), _1644068), c_List_Olist_OCons(tc_prod(_1644068, _1644070))), hAPP(hAPP(c_COMBC(_1644068, _1644070, tc_prod(_1644068, _1644070)), c_Product__Type_OPair(_1644068, _1644070)), _1644074)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1644068), tc_List_Olist(_1644070), tc_List_Olist(tc_prod(_1644068, _1644070))), c_List_Ozip(_1644068, _1644070)), _1644076))), _1644072))], (43605 ^ _779530) ^ [_1644295, _1644297, _1644299, _1644301, _1644303, _1644305] : [-(hAPP(c_List_Olist_Olist__case(_1644295, _1644297, _1644299, _1644301), hAPP(hAPP(c_List_Olist_OCons(_1644297), _1644303), _1644305)) = hAPP(hAPP(_1644301, _1644303), _1644305))], (43607 ^ _779530) ^ [_1644350, _1644352, _1644354, _1644356] : [-(hAPP(c_List_Olist_Olist__case(_1644350, _1644352, _1644354, _1644356), c_List_Olist_ONil(_1644352)) = _1644354)], (43609 ^ _779530) ^ [_1644389, _1644391, _1644393] : [-(c_List_Olistset(_1644389, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1644389, tc_HOL_Obool)), _1644391), _1644393)) = c_List_Oset__Cons(_1644389, _1644391, c_List_Olistset(_1644389, _1644393)))], (43611 ^ _779530) ^ [_1644437, _1644439, _1644441, _1644443, _1644445] : [-(hAPP(hAPP(c_List_Ozip(_1644437, _1644439), hAPP(hAPP(c_List_Olist_OCons(_1644437), _1644441), _1644443)), _1644445) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1644437, _1644439)), _1644439, c_List_Olist_ONil(tc_prod(_1644437, _1644439)), hAPP(hAPP(c_COMBC(_1644439, tc_fun(tc_List_Olist(_1644439), tc_List_Olist(tc_prod(_1644437, _1644439))), tc_fun(tc_List_Olist(_1644439), tc_List_Olist(tc_prod(_1644437, _1644439)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1644437, _1644439)), tc_List_Olist(tc_prod(_1644437, _1644439))), tc_fun(tc_fun(tc_List_Olist(_1644439), tc_List_Olist(tc_prod(_1644437, _1644439))), tc_fun(tc_List_Olist(_1644439), tc_List_Olist(tc_prod(_1644437, _1644439)))), _1644439), c_COMBB(tc_List_Olist(tc_prod(_1644437, _1644439)), tc_List_Olist(tc_prod(_1644437, _1644439)), tc_List_Olist(_1644439))), hAPP(hAPP(c_COMBB(tc_prod(_1644437, _1644439), tc_fun(tc_List_Olist(tc_prod(_1644437, _1644439)), tc_List_Olist(tc_prod(_1644437, _1644439))), _1644439), c_List_Olist_OCons(tc_prod(_1644437, _1644439))), hAPP(c_Product__Type_OPair(_1644437, _1644439), _1644441)))), hAPP(c_List_Ozip(_1644437, _1644439), _1644443))), _1644445))], (43613 ^ _779530) ^ [_1644638, _1644640] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1644638)), c_List_Otranspose__rel(_1644638)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1644638)), c_List_Olist_ONil(_1644638)), _1644640))), -(c_List_Otranspose(_1644638, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1644638)), c_List_Olist_ONil(_1644638)), _1644640)) = c_List_Otranspose(_1644638, _1644640))], (43619 ^ _779530) ^ [_1644797, _1644799, _1644801] : [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), _1644797), _1644799))), -(hBOOL(hAPP(hAPP(_1644801, _1644797), _1644799))), 43626 ^ _779530 : [(43627 ^ _779530) ^ [] : [-(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), 43624 ^ [_1644797, _1644799, _1644801]), 43625 ^ [_1644797, _1644799, _1644801]))))], (43635 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1644801, 43624 ^ [_1644797, _1644799, _1644801]), 43625 ^ [_1644797, _1644799, _1644801]))], (43629 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43624 ^ [_1644797, _1644799, _1644801]), 43625 ^ [_1644797, _1644799, _1644801])), -(hBOOL(hAPP(hAPP(_1644801, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43624 ^ [_1644797, _1644799, _1644801]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43625 ^ [_1644797, _1644799, _1644801])))]]], (43639 ^ _779530) ^ [_1645288] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1645288)), c_List_Otranspose__rel(_1645288)), c_List_Olist_ONil(tc_List_Olist(_1645288)))), -(c_List_Otranspose(_1645288, c_List_Olist_ONil(tc_List_Olist(_1645288))) = c_List_Olist_ONil(tc_List_Olist(_1645288)))], (43645 ^ _779530) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (43647 ^ _779530) ^ [_1645433, _1645435, _1645437, _1645439, _1645441, _1645443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645433)), _1645435)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645437)), _1645439))), -(c_Map_Omap__upds(_1645433, _1645437, _1645441, hAPP(hAPP(c_List_Oappend(_1645433), _1645435), hAPP(hAPP(c_List_Olist_OCons(_1645433), _1645443), c_List_Olist_ONil(_1645433))), _1645439) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1645433, tc_Option_Ooption(_1645437)), c_Map_Omap__upds(_1645433, _1645437, _1645441, _1645435, _1645439)), _1645443), hAPP(c_Option_Ooption_OSome(_1645437), hAPP(hAPP(c_List_Onth(_1645437), _1645439), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645433)), _1645435)))))], (43653 ^ _779530) ^ [_1645708, _1645710, _1645712, _1645714, _1645716] : [hAPP(hAPP(c_List_Oappend(_1645708), _1645710), hAPP(hAPP(c_List_Olist_OCons(_1645708), _1645712), c_List_Olist_ONil(_1645708))) = hAPP(hAPP(c_List_Oappend(_1645708), _1645714), hAPP(hAPP(c_List_Olist_OCons(_1645708), _1645716), c_List_Olist_ONil(_1645708))), 43656 ^ _779530 : [(43657 ^ _779530) ^ [] : [-(_1645710 = _1645714)], (43659 ^ _779530) ^ [] : [-(_1645712 = _1645716)]]], (43661 ^ _779530) ^ [_1645885, _1645887, _1645889, _1645891, _1645893] : [-(hAPP(hAPP(c_List_Oappend(_1645885), _1645887), hAPP(hAPP(c_List_Olist_OCons(_1645885), _1645889), c_List_Olist_ONil(_1645885))) = hAPP(hAPP(c_List_Oappend(_1645885), _1645891), hAPP(hAPP(c_List_Olist_OCons(_1645885), _1645893), c_List_Olist_ONil(_1645885)))), _1645887 = _1645891, _1645889 = _1645893], (43671 ^ _779530) ^ [_1646124, _1646126, _1646128, _1646130, _1646132] : [hAPP(hAPP(c_List_Olist_OCons(_1646124), _1646126), _1646128) = hAPP(hAPP(c_List_Oappend(_1646124), _1646130), _1646132), 43676 ^ _779530 : [(43677 ^ _779530) ^ [] : [-(_1646130 = c_List_Olist_ONil(_1646124))], (43679 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1646124), _1646126), _1646128) = _1646132)]], 43681 ^ _779530 : [(43682 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1646124), _1646126), 43680 ^ [_1646124, _1646126, _1646128, _1646130, _1646132]) = _1646130)], (43684 ^ _779530) ^ [] : [-(_1646128 = hAPP(hAPP(c_List_Oappend(_1646124), 43680 ^ [_1646124, _1646126, _1646128, _1646130, _1646132]), _1646132))]]], (43686 ^ _779530) ^ [_1646417, _1646419, _1646421, _1646423, _1646425] : [-(hAPP(hAPP(c_List_Olist_OCons(_1646417), _1646419), _1646421) = hAPP(hAPP(c_List_Oappend(_1646417), _1646423), _1646425)), 43687 ^ _779530 : [(43688 ^ _779530) ^ [] : [_1646423 = c_List_Olist_ONil(_1646417), hAPP(hAPP(c_List_Olist_OCons(_1646417), _1646419), _1646421) = _1646425], (43694 ^ _779530) ^ [_1646600] : [hAPP(hAPP(c_List_Olist_OCons(_1646417), _1646419), _1646600) = _1646423, _1646421 = hAPP(hAPP(c_List_Oappend(_1646417), _1646600), _1646425)]]], (43702 ^ _779530) ^ [_1646788, _1646790, _1646792, _1646794, _1646796] : [hAPP(hAPP(c_List_Oappend(_1646788), _1646790), _1646792) = hAPP(hAPP(c_List_Olist_OCons(_1646788), _1646794), _1646796), 43707 ^ _779530 : [(43708 ^ _779530) ^ [] : [-(_1646790 = c_List_Olist_ONil(_1646788))], (43710 ^ _779530) ^ [] : [-(_1646792 = hAPP(hAPP(c_List_Olist_OCons(_1646788), _1646794), _1646796))]], 43712 ^ _779530 : [(43713 ^ _779530) ^ [] : [-(_1646790 = hAPP(hAPP(c_List_Olist_OCons(_1646788), _1646794), 43711 ^ [_1646788, _1646790, _1646792, _1646794, _1646796]))], (43715 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1646788), 43711 ^ [_1646788, _1646790, _1646792, _1646794, _1646796]), _1646792) = _1646796)]]], (43717 ^ _779530) ^ [_1647081, _1647083, _1647085, _1647087, _1647089] : [-(hAPP(hAPP(c_List_Oappend(_1647081), _1647083), _1647085) = hAPP(hAPP(c_List_Olist_OCons(_1647081), _1647087), _1647089)), 43718 ^ _779530 : [(43719 ^ _779530) ^ [] : [_1647083 = c_List_Olist_ONil(_1647081), _1647085 = hAPP(hAPP(c_List_Olist_OCons(_1647081), _1647087), _1647089)], (43725 ^ _779530) ^ [_1647264] : [_1647083 = hAPP(hAPP(c_List_Olist_OCons(_1647081), _1647087), _1647264), hAPP(hAPP(c_List_Oappend(_1647081), _1647264), _1647085) = _1647089]]], (43733 ^ _779530) ^ [_1647428, _1647430, _1647432, _1647434, _1647436, _1647438] : [hAPP(hAPP(c_List_Olist_OCons(_1647428), _1647430), _1647432) = _1647434, _1647436 = hAPP(hAPP(c_List_Oappend(_1647428), _1647432), _1647438), -(hAPP(hAPP(c_List_Olist_OCons(_1647428), _1647430), _1647436) = hAPP(hAPP(c_List_Oappend(_1647428), _1647434), _1647438))], (43743 ^ _779530) ^ [_1647637, _1647639, _1647641, _1647643] : [-(hAPP(hAPP(c_List_Oappend(_1647637), hAPP(hAPP(c_List_Olist_OCons(_1647637), _1647639), _1647641)), _1647643) = hAPP(hAPP(c_List_Olist_OCons(_1647637), _1647639), hAPP(hAPP(c_List_Oappend(_1647637), _1647641), _1647643)))], (43745 ^ _779530) ^ [_1647698, _1647700, _1647702, _1647704, _1647706] : [-(hAPP(hAPP(c_List_Omap(_1647698, _1647700), _1647702), hAPP(hAPP(c_List_Oappend(_1647698), _1647704), _1647706)) = hAPP(hAPP(c_List_Oappend(_1647700), hAPP(hAPP(c_List_Omap(_1647698, _1647700), _1647702), _1647704)), hAPP(hAPP(c_List_Omap(_1647698, _1647700), _1647702), _1647706)))], (43747 ^ _779530) ^ [_1647772, _1647774, _1647776, _1647778] : [-(hAPP(c_List_Ofilter(_1647772, _1647774), hAPP(hAPP(c_List_Oappend(_1647772), _1647776), _1647778)) = hAPP(hAPP(c_List_Oappend(_1647772), hAPP(c_List_Ofilter(_1647772, _1647774), _1647776)), hAPP(c_List_Ofilter(_1647772, _1647774), _1647778)))], (43749 ^ _779530) ^ [_1647835, _1647837, _1647839, _1647841, _1647843, _1647845] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647835)), _1647837) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647839)), _1647841), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647835)), _1647843) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647839)), _1647845), -(hAPP(hAPP(c_List_Ozip(_1647835, _1647839), hAPP(hAPP(c_List_Oappend(_1647835), _1647837), _1647843)), hAPP(hAPP(c_List_Oappend(_1647839), _1647841), _1647845)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1647835, _1647839)), hAPP(hAPP(c_List_Ozip(_1647835, _1647839), _1647837), _1647841)), hAPP(hAPP(c_List_Ozip(_1647835, _1647839), _1647843), _1647845)))], (43759 ^ _779530) ^ [_1648144, _1648146, _1648148, _1648150] : [-(hAPP(c_Map_Omap__of(_1648144, _1648146), hAPP(hAPP(c_List_Oappend(tc_prod(_1648144, _1648146)), _1648148), _1648150)) = c_Map_Omap__add(_1648144, _1648146, hAPP(c_Map_Omap__of(_1648144, _1648146), _1648150), hAPP(c_Map_Omap__of(_1648144, _1648146), _1648148)))], (43761 ^ _779530) ^ [_1648207, _1648209, _1648211, _1648213, _1648215, _1648217] : [hAPP(hAPP(c_List_Oappend(_1648207), _1648209), _1648211) = _1648213, _1648215 = hAPP(hAPP(c_List_Oappend(_1648207), _1648211), _1648217), -(hAPP(hAPP(c_List_Oappend(_1648207), _1648209), _1648215) = hAPP(hAPP(c_List_Oappend(_1648207), _1648213), _1648217))], (43771 ^ _779530) ^ [_1648437, _1648439, _1648441, _1648443] : [hAPP(hAPP(c_List_Oappend(_1648437), _1648439), _1648441) = hAPP(hAPP(c_List_Oappend(_1648437), _1648443), _1648441), -(_1648439 = _1648443)], (43777 ^ _779530) ^ [_1648546, _1648548, _1648550, _1648552] : [_1648548 = _1648552, -(hAPP(hAPP(c_List_Oappend(_1648546), _1648548), _1648550) = hAPP(hAPP(c_List_Oappend(_1648546), _1648552), _1648550))], (43783 ^ _779530) ^ [_1648682, _1648684, _1648686, _1648688] : [hAPP(hAPP(c_List_Oappend(_1648682), _1648684), _1648686) = hAPP(hAPP(c_List_Oappend(_1648682), _1648684), _1648688), -(_1648686 = _1648688)], (43789 ^ _779530) ^ [_1648791, _1648793, _1648795, _1648797] : [_1648795 = _1648797, -(hAPP(hAPP(c_List_Oappend(_1648791), _1648793), _1648795) = hAPP(hAPP(c_List_Oappend(_1648791), _1648793), _1648797))], (43795 ^ _779530) ^ [_1648930, _1648932, _1648934, _1648936, _1648938] : [hAPP(hAPP(c_List_Oappend(_1648930), _1648932), _1648934) = hAPP(hAPP(c_List_Oappend(_1648930), _1648936), _1648938), 43801 ^ _779530 : [(43802 ^ _779530) ^ [] : [-(_1648932 = hAPP(hAPP(c_List_Oappend(_1648930), _1648936), 43798 ^ [_1648930, _1648932, _1648934, _1648936, _1648938]))], (43804 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1648930), 43798 ^ [_1648930, _1648932, _1648934, _1648936, _1648938]), _1648934) = _1648938)]], 43805 ^ _779530 : [(43806 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1648930), _1648932), 43798 ^ [_1648930, _1648932, _1648934, _1648936, _1648938]) = _1648936)], (43808 ^ _779530) ^ [] : [-(_1648934 = hAPP(hAPP(c_List_Oappend(_1648930), 43798 ^ [_1648930, _1648932, _1648934, _1648936, _1648938]), _1648938))]]], (43810 ^ _779530) ^ [_1649261, _1649263, _1649265, _1649267, _1649269] : [-(hAPP(hAPP(c_List_Oappend(_1649261), _1649263), _1649265) = hAPP(hAPP(c_List_Oappend(_1649261), _1649267), _1649269)), 43811 ^ _779530 : [(43812 ^ _779530) ^ [_1649373] : [_1649263 = hAPP(hAPP(c_List_Oappend(_1649261), _1649267), _1649373), hAPP(hAPP(c_List_Oappend(_1649261), _1649373), _1649265) = _1649269], (43818 ^ _779530) ^ [_1649485] : [hAPP(hAPP(c_List_Oappend(_1649261), _1649263), _1649485) = _1649267, _1649265 = hAPP(hAPP(c_List_Oappend(_1649261), _1649485), _1649269)]]], (43826 ^ _779530) ^ [_1649649, _1649651, _1649653, _1649655] : [-(hAPP(hAPP(c_List_Oappend(_1649649), hAPP(hAPP(c_List_Oappend(_1649649), _1649651), _1649653)), _1649655) = hAPP(hAPP(c_List_Oappend(_1649649), _1649651), hAPP(hAPP(c_List_Oappend(_1649649), _1649653), _1649655)))], (43828 ^ _779530) ^ [_1649731, _1649733, _1649735, _1649737] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649731)), hAPP(hAPP(c_List_Oappend(_1649731), _1649733), _1649735)), c_List_Olists(_1649731, _1649737))), 43831 ^ _779530 : [(43832 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649731)), _1649733), c_List_Olists(_1649731, _1649737))))], (43834 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649731)), _1649735), c_List_Olists(_1649731, _1649737))))]]], (43836 ^ _779530) ^ [_1649922, _1649924, _1649926, _1649928] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649922)), hAPP(hAPP(c_List_Oappend(_1649922), _1649924), _1649926)), c_List_Olists(_1649922, _1649928)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649922)), _1649924), c_List_Olists(_1649922, _1649928))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1649922)), _1649926), c_List_Olists(_1649922, _1649928)))], (43846 ^ _779530) ^ [_1650149, _1650151, _1650153, _1650155, _1650157, _1650159] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650149)), _1650151) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650153)), _1650155), -(c_Map_Omap__upds(_1650149, _1650153, _1650157, hAPP(hAPP(c_List_Oappend(_1650149), _1650151), _1650159), _1650155) = c_Map_Omap__upds(_1650149, _1650153, _1650157, _1650151, _1650155))], (43852 ^ _779530) ^ [_1650302, _1650304, _1650306, _1650308, _1650310, _1650312] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650302)), _1650304) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650306)), _1650308), -(c_Map_Omap__upds(_1650302, _1650306, _1650310, _1650304, hAPP(hAPP(c_List_Oappend(_1650306), _1650308), _1650312)) = c_Map_Omap__upds(_1650302, _1650306, _1650310, _1650304, _1650308))], (43858 ^ _779530) ^ [_1650455, _1650457, _1650459] : [-(hAPP(c_List_Oset(_1650455), hAPP(hAPP(c_List_Oappend(_1650455), _1650457), _1650459)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1650455, tc_HOL_Obool)), hAPP(c_List_Oset(_1650455), _1650457)), hAPP(c_List_Oset(_1650455), _1650459)))], (43860 ^ _779530) ^ [_1650516, _1650518, _1650520] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650516)), hAPP(hAPP(c_List_Oappend(_1650516), _1650518), _1650520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650516)), _1650518)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650516)), _1650520)))], (43862 ^ _779530) ^ [_1650578, _1650580, _1650582] : [class_Groups_Omonoid__add(_1650578), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1650578), hAPP(hAPP(c_List_Oappend(_1650578), _1650580), _1650582)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1650578), hAPP(c_List_Omonoid__add__class_Olistsum(_1650578), _1650580)), hAPP(c_List_Omonoid__add__class_Olistsum(_1650578), _1650582)))], (43868 ^ _779530) ^ [_1650717, _1650719, _1650721, _1650723, _1650725, _1650727] : [-(c_List_Ofoldr(_1650717, _1650719, _1650721, hAPP(hAPP(c_List_Oappend(_1650717), _1650723), _1650725), _1650727) = c_List_Ofoldr(_1650717, _1650719, _1650721, _1650723, c_List_Ofoldr(_1650717, _1650719, _1650721, _1650725, _1650727)))], (43870 ^ _779530) ^ [_1650788, _1650790, _1650792] : [_1650788 = c_List_Olist_ONil(_1650790), -(c_List_Obutlast(_1650790, hAPP(hAPP(c_List_Oappend(_1650790), _1650792), _1650788)) = c_List_Obutlast(_1650790, _1650792))], (43876 ^ _779530) ^ [_1650893, _1650895, _1650897] : [-(_1650893 = c_List_Olist_ONil(_1650895)), -(c_List_Obutlast(_1650895, hAPP(hAPP(c_List_Oappend(_1650895), _1650897), _1650893)) = hAPP(hAPP(c_List_Oappend(_1650895), _1650897), c_List_Obutlast(_1650895, _1650893)))], (43882 ^ _779530) ^ [_1650957, _1650959, _1650961] : [_1650957 = _1650959, -(_1650957 = hAPP(hAPP(c_List_Oappend(_1650961), c_List_Olist_ONil(_1650961)), _1650959))], (43888 ^ _779530) ^ [_1651074, _1651076, _1651078] : [hAPP(hAPP(c_List_Oappend(_1651074), _1651076), _1651078) = _1651078, -(_1651076 = c_List_Olist_ONil(_1651074))], (43894 ^ _779530) ^ [_1651169, _1651171, _1651173] : [_1651171 = c_List_Olist_ONil(_1651169), -(hAPP(hAPP(c_List_Oappend(_1651169), _1651171), _1651173) = _1651173)], (43900 ^ _779530) ^ [_1651288, _1651290, _1651292] : [hAPP(hAPP(c_List_Oappend(_1651288), _1651290), _1651292) = _1651290, -(_1651292 = c_List_Olist_ONil(_1651288))], (43906 ^ _779530) ^ [_1651383, _1651385, _1651387] : [_1651387 = c_List_Olist_ONil(_1651383), -(hAPP(hAPP(c_List_Oappend(_1651383), _1651385), _1651387) = _1651385)], (43912 ^ _779530) ^ [_1651502, _1651504, _1651506] : [hAPP(hAPP(c_List_Oappend(_1651502), _1651504), _1651506) = c_List_Olist_ONil(_1651502), 43915 ^ _779530 : [(43916 ^ _779530) ^ [] : [-(_1651504 = c_List_Olist_ONil(_1651502))], (43918 ^ _779530) ^ [] : [-(_1651506 = c_List_Olist_ONil(_1651502))]]], (43920 ^ _779530) ^ [_1651631, _1651633, _1651635] : [-(hAPP(hAPP(c_List_Oappend(_1651631), _1651633), _1651635) = c_List_Olist_ONil(_1651631)), _1651633 = c_List_Olist_ONil(_1651631), _1651635 = c_List_Olist_ONil(_1651631)], (43930 ^ _779530) ^ [_1651812, _1651814, _1651816] : [_1651812 = hAPP(hAPP(c_List_Oappend(_1651814), _1651816), _1651812), -(_1651816 = c_List_Olist_ONil(_1651814))], (43936 ^ _779530) ^ [_1651907, _1651909, _1651911] : [_1651911 = c_List_Olist_ONil(_1651909), -(_1651907 = hAPP(hAPP(c_List_Oappend(_1651909), _1651911), _1651907))], (43942 ^ _779530) ^ [_1652026, _1652028, _1652030] : [_1652026 = hAPP(hAPP(c_List_Oappend(_1652028), _1652026), _1652030), -(_1652030 = c_List_Olist_ONil(_1652028))], (43948 ^ _779530) ^ [_1652121, _1652123, _1652125] : [_1652125 = c_List_Olist_ONil(_1652123), -(_1652121 = hAPP(hAPP(c_List_Oappend(_1652123), _1652121), _1652125))], (43954 ^ _779530) ^ [_1652222, _1652224] : [-(hAPP(hAPP(c_List_Oappend(_1652222), _1652224), c_List_Olist_ONil(_1652222)) = _1652224)], (43956 ^ _779530) ^ [_1652275, _1652277, _1652279] : [c_List_Olist_ONil(_1652275) = hAPP(hAPP(c_List_Oappend(_1652275), _1652277), _1652279), 43959 ^ _779530 : [(43960 ^ _779530) ^ [] : [-(_1652277 = c_List_Olist_ONil(_1652275))], (43962 ^ _779530) ^ [] : [-(_1652279 = c_List_Olist_ONil(_1652275))]]], (43964 ^ _779530) ^ [_1652404, _1652406, _1652408] : [-(c_List_Olist_ONil(_1652404) = hAPP(hAPP(c_List_Oappend(_1652404), _1652406), _1652408)), _1652406 = c_List_Olist_ONil(_1652404), _1652408 = c_List_Olist_ONil(_1652404)], (43974 ^ _779530) ^ [_1652567, _1652569] : [-(hAPP(hAPP(c_List_Oappend(_1652567), c_List_Olist_ONil(_1652567)), _1652569) = _1652569)], (43976 ^ _779530) ^ [_1652602, _1652604, _1652606, _1652608] : [-(hAPP(hAPP(c_List_Onth(_1652602), hAPP(hAPP(c_List_Oappend(_1652602), _1652604), hAPP(hAPP(c_List_Olist_OCons(_1652602), _1652606), _1652608))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652602)), _1652604)) = _1652606)], (43978 ^ _779530) ^ [_1652662, _1652664, _1652666, _1652668] : [-(hAPP(hAPP(c_List_Onth(_1652662), hAPP(hAPP(c_List_Oappend(_1652662), _1652664), _1652666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652662)), _1652664)), _1652668)) = hAPP(hAPP(c_List_Onth(_1652662), _1652666), _1652668))], (43980 ^ _779530) ^ [_1652728, _1652730, _1652732, _1652734] : [-(hAPP(hAPP(c_List_Otake(_1652728), _1652730), hAPP(hAPP(c_List_Oappend(_1652728), _1652732), _1652734)) = hAPP(hAPP(c_List_Oappend(_1652728), hAPP(hAPP(c_List_Otake(_1652728), _1652730), _1652732)), hAPP(hAPP(c_List_Otake(_1652728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1652730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652728)), _1652732))), _1652734)))], (43982 ^ _779530) ^ [_1652810, _1652812, _1652814, _1652816, _1652818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652810), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652812)), _1652814))), -(hAPP(hAPP(c_List_Olist__update(_1652812, hAPP(hAPP(c_List_Oappend(_1652812), _1652814), _1652816)), _1652810), _1652818) = hAPP(hAPP(c_List_Oappend(_1652812), hAPP(hAPP(c_List_Olist__update(_1652812, _1652814), _1652810), _1652818)), _1652816))], (43988 ^ _779530) ^ [_1652985, _1652987, _1652989, _1652991, _1652993] : [-(hAPP(hAPP(c_List_Olist__update(_1652985, hAPP(hAPP(c_List_Oappend(_1652985), _1652987), hAPP(hAPP(c_List_Olist_OCons(_1652985), _1652989), _1652991))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652985)), _1652987)), _1652993) = hAPP(hAPP(c_List_Oappend(_1652985), _1652987), hAPP(hAPP(c_List_Olist_OCons(_1652985), _1652993), _1652991)))], (43990 ^ _779530) ^ [_1653079, _1653081, _1653083, _1653085] : [hBOOL(hAPP(hAPP(c_member(_1653079), _1653081), hAPP(c_List_Oset(_1653079), _1653083))), -(c_List_Oremove1(_1653079, _1653081, hAPP(hAPP(c_List_Oappend(_1653079), _1653083), _1653085)) = hAPP(hAPP(c_List_Oappend(_1653079), c_List_Oremove1(_1653079, _1653081, _1653083)), _1653085))], (43996 ^ _779530) ^ [_1653226, _1653228, _1653230, _1653232] : [-(hBOOL(hAPP(hAPP(c_member(_1653226), _1653228), hAPP(c_List_Oset(_1653226), _1653230)))), -(c_List_Oremove1(_1653226, _1653228, hAPP(hAPP(c_List_Oappend(_1653226), _1653230), _1653232)) = hAPP(hAPP(c_List_Oappend(_1653226), _1653230), c_List_Oremove1(_1653226, _1653228, _1653232)))], (44002 ^ _779530) ^ [_1653304, _1653306, _1653308, _1653310] : [44003 ^ _779530 : [(44004 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1653304), _1653306), hAPP(c_List_Oset(_1653304), c_List_Obutlast(_1653304, _1653308))))], (44006 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1653304), _1653306), hAPP(c_List_Oset(_1653304), c_List_Obutlast(_1653304, _1653310))))]], -(hBOOL(hAPP(hAPP(c_member(_1653304), _1653306), hAPP(c_List_Oset(_1653304), c_List_Obutlast(_1653304, hAPP(hAPP(c_List_Oappend(_1653304), _1653308), _1653310))))))], (44010 ^ _779530) ^ [_1653529, _1653531, _1653533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1653529), _1653531)), -(c_List_Oupt(_1653529, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653531), _1653533)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1653529, _1653531)), c_List_Oupt(_1653531, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653531), _1653533))))], (44016 ^ _779530) ^ [_1653672, _1653674, _1653676] : [-(c_List_Obutlast(_1653672, hAPP(hAPP(c_List_Oappend(_1653672), _1653674), hAPP(hAPP(c_List_Olist_OCons(_1653672), _1653676), c_List_Olist_ONil(_1653672)))) = _1653674)], (44018 ^ _779530) ^ [_1653720, _1653722, _1653724, _1653726, _1653728, _1653730] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653720), tc_List_Olist(_1653720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653720), tc_List_Olist(_1653720)), hAPP(hAPP(c_List_Oappend(_1653720), _1653722), _1653728)), hAPP(hAPP(c_List_Oappend(_1653720), _1653724), _1653730))), c_List_Olistrel1(_1653720, _1653726)))), 44019 ^ _779530 : [(44020 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653720), tc_List_Olist(_1653720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653720), tc_List_Olist(_1653720)), _1653722), _1653724)), c_List_Olistrel1(_1653720, _1653726))), _1653728 = _1653730], (44026 ^ _779530) ^ [] : [_1653722 = _1653724, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653720), tc_List_Olist(_1653720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653720), tc_List_Olist(_1653720)), _1653728), _1653730)), c_List_Olistrel1(_1653720, _1653726)))]]], (44034 ^ _779530) ^ [_1654168, _1654170, _1654172, _1654174, _1654176] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654168), tc_List_Olist(_1654168))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654168), tc_List_Olist(_1654168)), _1654170), _1654172)), c_List_Olexord(_1654168, _1654174))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654168), tc_List_Olist(_1654168))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654168), tc_List_Olist(_1654168)), hAPP(hAPP(c_List_Oappend(_1654168), _1654176), _1654170)), hAPP(hAPP(c_List_Oappend(_1654168), _1654176), _1654172))), c_List_Olexord(_1654168, _1654174))))], (44040 ^ _779530) ^ [_1654403] : [-(c_List_Oreturn__list(_1654403) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1654403))], (44042 ^ _779530) ^ [_1654449, _1654451, _1654453] : [hBOOL(hAPP(c_List_Odistinct(_1654449), hAPP(hAPP(c_List_Oappend(_1654449), _1654451), _1654453))), 44045 ^ _779530 : [(44046 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1654449), _1654451)))], (44048 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1654449), _1654453)))], (44050 ^ _779530) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654449, tc_HOL_Obool)), hAPP(c_List_Oset(_1654449), _1654451)), hAPP(c_List_Oset(_1654449), _1654453)) = c_Orderings_Obot__class_Obot(tc_fun(_1654449, tc_HOL_Obool)))]]], (44052 ^ _779530) ^ [_1654666, _1654668, _1654670] : [-(hBOOL(hAPP(c_List_Odistinct(_1654666), hAPP(hAPP(c_List_Oappend(_1654666), _1654668), _1654670)))), hBOOL(hAPP(c_List_Odistinct(_1654666), _1654668)), hBOOL(hAPP(c_List_Odistinct(_1654666), _1654670)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1654666, tc_HOL_Obool)), hAPP(c_List_Oset(_1654666), _1654668)), hAPP(c_List_Oset(_1654666), _1654670)) = c_Orderings_Obot__class_Obot(tc_fun(_1654666, tc_HOL_Obool))], (44066 ^ _779530) ^ [_1654962, _1654964, _1654966, _1654968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654962), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654964)), _1654966))), -(hAPP(hAPP(c_List_Onth(_1654964), hAPP(hAPP(c_List_Oappend(_1654964), _1654966), _1654968)), _1654962) = hAPP(hAPP(c_List_Onth(_1654964), _1654966), _1654962))], (44072 ^ _779530) ^ [_1655109, _1655111, _1655113, _1655115] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655109), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655111)), _1655113)))), -(hAPP(hAPP(c_List_Onth(_1655111), hAPP(hAPP(c_List_Oappend(_1655111), _1655113), _1655115)), _1655109) = hAPP(hAPP(c_List_Onth(_1655111), _1655115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655109), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655111)), _1655113))))], (44078 ^ _779530) ^ [_1655218, _1655220, _1655222, _1655224, _1655226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655218), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655220)), _1655222))), -(hAPP(hAPP(c_List_Olist__update(_1655220, hAPP(hAPP(c_List_Oappend(_1655220), _1655222), _1655224)), _1655218), _1655226) = hAPP(hAPP(c_List_Oappend(_1655220), hAPP(hAPP(c_List_Olist__update(_1655220, _1655222), _1655218), _1655226)), _1655224))], (44084 ^ _779530) ^ [_1655387, _1655389, _1655391, _1655393, _1655395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655387), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655389)), _1655391)))), -(hAPP(hAPP(c_List_Olist__update(_1655389, hAPP(hAPP(c_List_Oappend(_1655389), _1655391), _1655393)), _1655387), _1655395) = hAPP(hAPP(c_List_Oappend(_1655389), _1655391), hAPP(hAPP(c_List_Olist__update(_1655389, _1655393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655387), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655389)), _1655391))), _1655395)))], (44090 ^ _779530) ^ [_1655490, _1655492, _1655494] : [-(c_Enum_Osublists(_1655490, hAPP(hAPP(c_List_Olist_OCons(_1655490), _1655492), _1655494)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1655490)), tc_List_Olist(tc_List_Olist(_1655490))), c_Enum_Osublists(_1655490, _1655494)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1655490)), tc_List_Olist(tc_List_Olist(_1655490)), tc_List_Olist(tc_List_Olist(_1655490))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1655490)), tc_fun(tc_List_Olist(tc_List_Olist(_1655490)), tc_List_Olist(tc_List_Olist(_1655490))), tc_List_Olist(tc_List_Olist(_1655490))), c_List_Oappend(tc_List_Olist(_1655490))), hAPP(c_List_Omap(tc_List_Olist(_1655490), tc_List_Olist(_1655490)), hAPP(c_List_Olist_OCons(_1655490), _1655492)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1655490))))))], (44092 ^ _779530) ^ [_1655624, _1655626, _1655628, _1655630, _1655632] : [-(c_Enum_Oproduct(_1655624, _1655626, hAPP(hAPP(c_List_Olist_OCons(_1655624), _1655628), _1655630), _1655632) = hAPP(hAPP(c_List_Oappend(tc_prod(_1655624, _1655626)), hAPP(hAPP(c_List_Omap(_1655626, tc_prod(_1655624, _1655626)), hAPP(c_Product__Type_OPair(_1655624, _1655626), _1655628)), _1655632)), c_Enum_Oproduct(_1655624, _1655626, _1655630, _1655632)))], (44094 ^ _779530) ^ [_1655702, _1655704, _1655706, _1655708] : [-(c_List_Osublist(_1655702, hAPP(hAPP(c_List_Oappend(_1655702), _1655704), _1655706), _1655708) = hAPP(hAPP(c_List_Oappend(_1655702), c_List_Osublist(_1655702, _1655704, _1655708)), c_List_Osublist(_1655702, _1655706, 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(_1655702)), _1655704)))), _1655708)))))], (44096 ^ _779530) ^ [_1655781, _1655783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655781), _1655783)), -(c_List_Oupt(_1655781, hAPP(c_Nat_OSuc, _1655783)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1655781, _1655783)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1655783), c_List_Olist_ONil(tc_Nat_Onat))))], (44102 ^ _779530) ^ [_1655919, _1655921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655919), _1655921)), -(c_List_Oupt(_1655919, hAPP(c_Nat_OSuc, _1655921)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1655919, _1655921)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1655921), c_List_Olist_ONil(tc_Nat_Onat))))], (44108 ^ _779530) ^ [_1656042, _1656044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656042), _1656044))), -(c_List_Oupt(_1656042, hAPP(c_Nat_OSuc, _1656044)) = c_List_Olist_ONil(tc_Nat_Onat))], (44114 ^ _779530) ^ [_1656091, _1656093, _1656095, _1656097, _1656099, _1656101, _1656103, _1656105] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656091, _1656091)), hAPP(hAPP(c_Product__Type_OPair(_1656091, _1656091), _1656093), _1656095)), _1656097)), _1656099 = hAPP(hAPP(c_List_Oappend(_1656091), _1656101), hAPP(hAPP(c_List_Olist_OCons(_1656091), _1656093), _1656103)), _1656105 = hAPP(hAPP(c_List_Oappend(_1656091), _1656101), hAPP(hAPP(c_List_Olist_OCons(_1656091), _1656095), _1656103)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656091), tc_List_Olist(_1656091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656091), tc_List_Olist(_1656091)), _1656099), _1656105)), c_List_Olistrel1(_1656091, _1656097))))], (44128 ^ _779530) ^ [_1656470, _1656472, _1656474, _1656476, _1656478, _1656480, _1656482] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656470, _1656470)), hAPP(hAPP(c_Product__Type_OPair(_1656470, _1656470), _1656472), _1656474)), _1656476)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656470), tc_List_Olist(_1656470))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656470), tc_List_Olist(_1656470)), hAPP(hAPP(c_List_Oappend(_1656470), _1656478), hAPP(hAPP(c_List_Olist_OCons(_1656470), _1656472), _1656480))), hAPP(hAPP(c_List_Oappend(_1656470), _1656478), hAPP(hAPP(c_List_Olist_OCons(_1656470), _1656474), _1656482)))), c_List_Olexord(_1656470, _1656476))))], (44134 ^ _779530) ^ [_1656719, _1656721, _1656723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656719), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656721)), _1656723))), -(hAPP(hAPP(c_List_Otake(_1656721), hAPP(c_Nat_OSuc, _1656719)), _1656723) = hAPP(hAPP(c_List_Oappend(_1656721), hAPP(hAPP(c_List_Otake(_1656721), _1656719), _1656723)), hAPP(hAPP(c_List_Olist_OCons(_1656721), hAPP(hAPP(c_List_Onth(_1656721), _1656723), _1656719)), c_List_Olist_ONil(_1656721))))], (44140 ^ _779530) ^ [_1656939, _1656941, _1656943, _1656945, _1656947, _1656949] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656939), tc_List_Olist(_1656939))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656939), tc_List_Olist(_1656939)), hAPP(hAPP(c_List_Oappend(_1656939), _1656941), hAPP(hAPP(c_List_Olist_OCons(_1656939), _1656943), c_List_Olist_ONil(_1656939)))), hAPP(hAPP(c_List_Oappend(_1656939), _1656945), hAPP(hAPP(c_List_Olist_OCons(_1656939), _1656947), c_List_Olist_ONil(_1656939))))), c_List_Olistrel1(_1656939, _1656949))), 44145 ^ _779530 : [(44146 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656939), tc_List_Olist(_1656939))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656939), tc_List_Olist(_1656939)), _1656941), _1656945)), c_List_Olistrel1(_1656939, _1656949))))], (44148 ^ _779530) ^ [] : [-(_1656943 = _1656947)]], 44149 ^ _779530 : [(44150 ^ _779530) ^ [] : [-(_1656941 = _1656945)], (44152 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656939, _1656939)), hAPP(hAPP(c_Product__Type_OPair(_1656939, _1656939), _1656943), _1656947)), _1656949)))]]], (44154 ^ _779530) ^ [_1657349, _1657351, _1657353, _1657355, _1657357, _1657359] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657349), tc_List_Olist(_1657349))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657349), tc_List_Olist(_1657349)), hAPP(hAPP(c_List_Oappend(_1657349), _1657351), hAPP(hAPP(c_List_Olist_OCons(_1657349), _1657353), c_List_Olist_ONil(_1657349)))), hAPP(hAPP(c_List_Oappend(_1657349), _1657355), hAPP(hAPP(c_List_Olist_OCons(_1657349), _1657357), c_List_Olist_ONil(_1657349))))), c_List_Olistrel1(_1657349, _1657359)))), 44155 ^ _779530 : [(44156 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657349), tc_List_Olist(_1657349))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657349), tc_List_Olist(_1657349)), _1657351), _1657355)), c_List_Olistrel1(_1657349, _1657359))), _1657353 = _1657357], (44162 ^ _779530) ^ [] : [_1657351 = _1657355, hBOOL(hAPP(hAPP(c_member(tc_prod(_1657349, _1657349)), hAPP(hAPP(c_Product__Type_OPair(_1657349, _1657349), _1657353), _1657357)), _1657359))]]], (44170 ^ _779530) ^ [_1657817, _1657819, _1657821, _1657823] : [-(c_List_Osublist(_1657817, hAPP(hAPP(c_List_Olist_OCons(_1657817), _1657819), _1657821), _1657823) = hAPP(hAPP(c_List_Oappend(_1657817), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1657817)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657823)), hAPP(hAPP(c_List_Olist_OCons(_1657817), _1657819), c_List_Olist_ONil(_1657817))), c_List_Olist_ONil(_1657817))), c_List_Osublist(_1657817, _1657821, 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)), _1657823)))))], (44172 ^ _779530) ^ [_1657904] : [c_List_Onat__list(_1657904), -(c_List_Oembed__list(c_List_Oreturn__list(_1657904)) = _1657904)], (44178 ^ _779530) ^ [_1657985, _1657987, _1657989, _1657991] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657985), tc_List_Olist(_1657985))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657985), tc_List_Olist(_1657985)), _1657987), _1657989)), c_List_Olistrel1(_1657985, _1657991))), 44183 ^ _779530 : [(44184 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1657985, _1657985)), hAPP(hAPP(c_Product__Type_OPair(_1657985, _1657985), 44181 ^ [_1657985, _1657987, _1657989, _1657991]), 44182 ^ [_1657985, _1657987, _1657989, _1657991])), _1657991)))], (44188 ^ _779530) ^ [] : [-(_1657987 = hAPP(hAPP(c_List_Oappend(_1657985), 44185 ^ [_1657985, _1657987, _1657989, _1657991]), hAPP(hAPP(c_List_Olist_OCons(_1657985), 44181 ^ [_1657985, _1657987, _1657989, _1657991]), 44186 ^ [_1657985, _1657987, _1657989, _1657991])))], (44190 ^ _779530) ^ [] : [-(_1657989 = hAPP(hAPP(c_List_Oappend(_1657985), 44185 ^ [_1657985, _1657987, _1657989, _1657991]), hAPP(hAPP(c_List_Olist_OCons(_1657985), 44182 ^ [_1657985, _1657987, _1657989, _1657991]), 44186 ^ [_1657985, _1657987, _1657989, _1657991])))]]], (44192 ^ _779530) ^ [_1658390] : [-(c_List_Oembed__list(_1658390) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1658390))], (44194 ^ _779530) ^ [_1658418, _1658420] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1658418), _1658420) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1658418)), c_List_Oembed__list(_1658420))))], (44196 ^ _779530) ^ [_1658461, _1658463, _1658465, _1658467, _1658469] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658461), tc_List_Olist(_1658461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658461), tc_List_Olist(_1658461)), hAPP(hAPP(c_List_Oappend(_1658461), _1658463), _1658465)), hAPP(hAPP(c_List_Oappend(_1658461), _1658463), _1658467))), c_List_Olexord(_1658461, _1658469))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658461, _1658461)), hAPP(hAPP(c_Product__Type_OPair(_1658461, _1658461), 44201 ^ [_1658461, _1658463, _1658465, _1658467, _1658469]), 44201 ^ [_1658461, _1658463, _1658465, _1658467, _1658469])), _1658469))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658461), tc_List_Olist(_1658461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658461), tc_List_Olist(_1658461)), _1658465), _1658467)), c_List_Olexord(_1658461, _1658469))))], (44207 ^ _779530) ^ [_1658780, _1658782] : [-(hAPP(c_List_Orotate1(_1658780), _1658782) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1658780), _1658780, c_List_Olist_ONil(_1658780), hAPP(hAPP(c_COMBB(tc_List_Olist(_1658780), tc_fun(tc_List_Olist(_1658780), tc_List_Olist(_1658780)), _1658780), hAPP(c_COMBC(tc_List_Olist(_1658780), tc_List_Olist(_1658780), tc_List_Olist(_1658780)), c_List_Oappend(_1658780))), hAPP(hAPP(c_COMBC(_1658780, tc_List_Olist(_1658780), tc_List_Olist(_1658780)), c_List_Olist_OCons(_1658780)), c_List_Olist_ONil(_1658780)))), _1658782))], (44209 ^ _779530) ^ [_1658889, _1658891] : [hBOOL(hAPP(c_List_Odistinct(_1658889), hAPP(c_List_Orotate1(_1658889), _1658891))), -(hBOOL(hAPP(c_List_Odistinct(_1658889), _1658891)))], (44215 ^ _779530) ^ [_1658988, _1658990] : [hBOOL(hAPP(c_List_Odistinct(_1658988), _1658990)), -(hBOOL(hAPP(c_List_Odistinct(_1658988), hAPP(c_List_Orotate1(_1658988), _1658990))))], (44221 ^ _779530) ^ [_1659093, _1659095] : [-(hAPP(c_List_Oset(_1659093), hAPP(c_List_Orotate1(_1659093), _1659095)) = hAPP(c_List_Oset(_1659093), _1659095))], (44223 ^ _779530) ^ [_1659133, _1659135] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659133)), hAPP(c_List_Orotate1(_1659133), _1659135)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659133)), _1659135))], (44225 ^ _779530) ^ [_1659192, _1659194] : [hAPP(c_List_Orotate1(_1659192), _1659194) = c_List_Olist_ONil(_1659192), -(_1659194 = c_List_Olist_ONil(_1659192))], (44231 ^ _779530) ^ [_1659283, _1659285] : [_1659285 = c_List_Olist_ONil(_1659283), -(hAPP(c_List_Orotate1(_1659283), _1659285) = c_List_Olist_ONil(_1659283))], (44237 ^ _779530) ^ [_1659378, _1659380, _1659382, _1659384] : [-(hAPP(c_List_Orotate1(_1659378), c_List_Olist_ONil(_1659378)) = c_List_Olist_ONil(_1659378))], (44239 ^ _779530) ^ [_1659413, _1659415, _1659417, _1659419] : [-(hAPP(c_List_Orotate1(_1659415), hAPP(hAPP(c_List_Olist_OCons(_1659415), _1659417), _1659419)) = hAPP(hAPP(c_List_Oappend(_1659415), _1659419), hAPP(hAPP(c_List_Olist_OCons(_1659415), _1659417), c_List_Olist_ONil(_1659415))))], (44241 ^ _779530) ^ [_1659475, _1659477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659475)), _1659477)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1659475), _1659477) = _1659477)], (44247 ^ _779530) ^ [_1659586, _1659588, _1659590, _1659592, _1659594] : [class_Groups_Omonoid__add(_1659586), 44253 ^ _779530 : [(44254 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1659588), 44252 ^ [_1659586, _1659588, _1659590, _1659592, _1659594]), hAPP(c_List_Oset(_1659588), _1659590))))], (44256 ^ _779530) ^ [] : [hBOOL(hAPP(_1659592, 44252 ^ [_1659586, _1659588, _1659590, _1659592, _1659594]))], (44258 ^ _779530) ^ [] : [hAPP(_1659594, 44252 ^ [_1659586, _1659588, _1659590, _1659592, _1659594]) = c_Groups_Ozero__class_Ozero(_1659586)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1659586), hAPP(hAPP(c_List_Omap(_1659588, _1659586), _1659594), hAPP(c_List_Ofilter(_1659588, _1659592), _1659590))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1659586), hAPP(hAPP(c_List_Omap(_1659588, _1659586), _1659594), _1659590)))], (44262 ^ _779530) ^ [_1659977, _1659979, _1659981] : [-(c_List_Opartition(_1659977, _1659979, _1659981) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659977), tc_List_Olist(_1659977)), hAPP(c_List_Ofilter(_1659977, _1659979), _1659981)), hAPP(c_List_Ofilter(_1659977, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1659977, c_fNot), _1659979)), _1659981)))], (44264 ^ _779530) ^ [_1660041, _1660043, _1660045] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1660041), tc_List_Olist(_1660041)), c_List_Opartition(_1660041, _1660043, _1660045)) = hAPP(c_List_Ofilter(_1660041, _1660043), _1660045))], (44266 ^ _779530) ^ [_1660088, _1660090, _1660092, _1660094, _1660096] : [c_List_Opartition(_1660088, _1660090, _1660092) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660088), tc_List_Olist(_1660088)), _1660094), _1660096), 44269 ^ _779530 : [(44270 ^ _779530) ^ [_1660241] : [hBOOL(hAPP(hAPP(c_member(_1660088), _1660241), hAPP(c_List_Oset(_1660088), _1660094))), -(hBOOL(hAPP(_1660090, _1660241)))], (44276 ^ _779530) ^ [_1660350] : [hBOOL(hAPP(hAPP(c_member(_1660088), _1660350), hAPP(c_List_Oset(_1660088), _1660096))), hBOOL(hAPP(_1660090, _1660350))]]], (44282 ^ _779530) ^ [_1660470, _1660472] : [-(c_List_Opartition(_1660470, _1660472, c_List_Olist_ONil(_1660470)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660470), tc_List_Olist(_1660470)), c_List_Olist_ONil(_1660470)), c_List_Olist_ONil(_1660470)))], (44284 ^ _779530) ^ [_1660518, _1660520, _1660522, _1660524] : [-(c_List_Opartition(_1660518, _1660520, hAPP(hAPP(c_List_Olist_OCons(_1660518), _1660522), _1660524)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1660518), tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1660518), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1660518), tc_fun(tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), tc_fun(tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), tc_List_Olist(_1660518)), c_COMBS(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_fun(tc_List_Olist(_1660518), tc_fun(tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), tc_List_Olist(_1660518)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_fun(tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_List_Olist(_1660518)), hAPP(c_If(tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), hAPP(_1660520, _1660522)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1660518), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_List_Olist(_1660518)), c_Product__Type_OPair(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), hAPP(c_List_Olist_OCons(_1660518), _1660522))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1660518), tc_fun(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518))), tc_fun(tc_fun(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_fun(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), tc_List_Olist(_1660518)), c_COMBB(tc_List_Olist(_1660518), tc_prod(tc_List_Olist(_1660518), tc_List_Olist(_1660518)), tc_List_Olist(_1660518))), c_Product__Type_OPair(tc_List_Olist(_1660518), tc_List_Olist(_1660518)))), hAPP(c_List_Olist_OCons(_1660518), _1660522)))), c_List_Opartition(_1660518, _1660520, _1660524)))], (44286 ^ _779530) ^ [_1660937, _1660939, _1660941] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1660937), tc_List_Olist(_1660937)), c_List_Opartition(_1660937, _1660939, _1660941)) = hAPP(c_List_Ofilter(_1660937, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1660937, c_fNot), _1660939)), _1660941))], (44288 ^ _779530) ^ [_1660992, _1660994, _1660996, _1660998, _1661000] : [c_List_Opartition(_1660992, _1660994, _1660996) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660992), tc_List_Olist(_1660992)), _1660998), _1661000), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1660992, tc_HOL_Obool)), hAPP(c_List_Oset(_1660992), _1660998)), hAPP(c_List_Oset(_1660992), _1661000)) = hAPP(c_List_Oset(_1660992), _1660996))], (44294 ^ _779530) ^ [_1661161, _1661163, _1661165, _1661167] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1661161)), c_List_Otranspose__rel(_1661161)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661161)), hAPP(hAPP(c_List_Olist_OCons(_1661161), _1661163), _1661165)), _1661167))), -(c_List_Otranspose(_1661161, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661161)), hAPP(hAPP(c_List_Olist_OCons(_1661161), _1661163), _1661165)), _1661167)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661161)), hAPP(hAPP(c_List_Olist_OCons(_1661161), _1661163), c_List_Oconcat(_1661161, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661161), tc_List_Olist(_1661161)), c_List_Olist_Olist__case(tc_List_Olist(_1661161), _1661161, c_List_Olist_ONil(_1661161), hAPP(hAPP(c_COMBB(tc_List_Olist(_1661161), tc_fun(tc_List_Olist(_1661161), tc_List_Olist(_1661161)), _1661161), c_COMBK(tc_List_Olist(_1661161), tc_List_Olist(_1661161))), hAPP(hAPP(c_COMBC(_1661161, tc_List_Olist(_1661161), tc_List_Olist(_1661161)), c_List_Olist_OCons(_1661161)), c_List_Olist_ONil(_1661161))))), _1661167)))), c_List_Otranspose(_1661161, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1661161)), _1661165), c_List_Oconcat(tc_List_Olist(_1661161), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1661161), tc_List_Olist(tc_List_Olist(_1661161))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1661161)), _1661161, c_List_Olist_ONil(tc_List_Olist(_1661161)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1661161), tc_List_Olist(tc_List_Olist(_1661161))), _1661161), hAPP(hAPP(c_COMBC(tc_List_Olist(_1661161), tc_List_Olist(tc_List_Olist(_1661161)), tc_List_Olist(tc_List_Olist(_1661161))), c_List_Olist_OCons(tc_List_Olist(_1661161))), c_List_Olist_ONil(tc_List_Olist(_1661161)))))), _1661167))))))], (44300 ^ _779530) ^ [_1661694, _1661696, _1661698, _1661700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661694), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661696)), _1661698))), -(hAPP(hAPP(c_List_Olist__update(_1661696, _1661698), _1661694), _1661700) = hAPP(hAPP(c_List_Oappend(_1661696), hAPP(hAPP(c_List_Otake(_1661696), _1661694), _1661698)), hAPP(hAPP(c_List_Olist_OCons(_1661696), _1661700), hAPP(hAPP(c_List_Odrop(_1661696), hAPP(c_Nat_OSuc, _1661694)), _1661698))))], (44306 ^ _779530) ^ [_1661887, _1661889, _1661891] : [-(hAPP(hAPP(c_List_Odrop(_1661887), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1661887), _1661889), _1661891)) = _1661891)], (44308 ^ _779530) ^ [_1661930, _1661932, _1661934, _1661936] : [-(hAPP(hAPP(c_List_Odrop(_1661930), hAPP(c_Nat_OSuc, _1661932)), hAPP(hAPP(c_List_Olist_OCons(_1661930), _1661934), _1661936)) = hAPP(hAPP(c_List_Odrop(_1661930), _1661932), _1661936))], (44310 ^ _779530) ^ [_1661986, _1661988, _1661990, _1661992, _1661994] : [hAPP(hAPP(c_List_Odrop(_1661986), _1661988), _1661990) = hAPP(hAPP(c_List_Olist_OCons(_1661986), _1661992), _1661994), -(hAPP(hAPP(c_List_Onth(_1661986), _1661990), _1661988) = _1661992)], (44316 ^ _779530) ^ [_1662117, _1662119, _1662121, _1662123] : [-(hAPP(hAPP(c_List_Odrop(_1662117), _1662119), hAPP(hAPP(c_List_Otake(_1662117), _1662121), _1662123)) = hAPP(hAPP(c_List_Otake(_1662117), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1662121), _1662119)), hAPP(hAPP(c_List_Odrop(_1662117), _1662119), _1662123)))], (44318 ^ _779530) ^ [_1662184, _1662186, _1662188, _1662190] : [-(hAPP(hAPP(c_List_Otake(_1662184), _1662186), hAPP(hAPP(c_List_Odrop(_1662184), _1662188), _1662190)) = hAPP(hAPP(c_List_Odrop(_1662184), _1662188), hAPP(hAPP(c_List_Otake(_1662184), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662186), _1662188)), _1662190)))], (44320 ^ _779530) ^ [_1662251, _1662253, _1662255] : [hBOOL(hAPP(c_List_Odistinct(_1662251), _1662253)), -(hBOOL(hAPP(c_List_Odistinct(_1662251), hAPP(hAPP(c_List_Odrop(_1662251), _1662255), _1662253))))], (44326 ^ _779530) ^ [_1662362, _1662364, _1662366, _1662368, _1662370] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1662362, _1662364)), _1662366), hAPP(hAPP(c_List_Ozip(_1662362, _1662364), _1662368), _1662370)) = hAPP(hAPP(c_List_Ozip(_1662362, _1662364), hAPP(hAPP(c_List_Odrop(_1662362), _1662366), _1662368)), hAPP(hAPP(c_List_Odrop(_1662364), _1662366), _1662370)))], (44328 ^ _779530) ^ [_1662438, _1662440, _1662442] : [-(c_List_Obutlast(_1662438, hAPP(hAPP(c_List_Odrop(_1662438), _1662440), _1662442)) = hAPP(hAPP(c_List_Odrop(_1662438), _1662440), c_List_Obutlast(_1662438, _1662442)))], (44330 ^ _779530) ^ [_1662487, _1662489, _1662491] : [-(hAPP(hAPP(c_List_Odrop(_1662487), _1662489), c_List_Obutlast(_1662487, _1662491)) = c_List_Obutlast(_1662487, hAPP(hAPP(c_List_Odrop(_1662487), _1662489), _1662491)))], (44332 ^ _779530) ^ [_1662536, _1662538, _1662540, _1662542] : [-(hAPP(hAPP(c_List_Odrop(_1662536), _1662538), hAPP(hAPP(c_List_Odrop(_1662536), _1662540), _1662542)) = hAPP(hAPP(c_List_Odrop(_1662536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662538), _1662540)), _1662542))], (44334 ^ _779530) ^ [_1662595, _1662597] : [-(hAPP(hAPP(c_List_Odrop(_1662595), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1662597) = _1662597)], (44336 ^ _779530) ^ [_1662628, _1662630, _1662632, _1662634] : [hBOOL(hAPP(hAPP(c_member(_1662628), _1662630), hAPP(c_List_Oset(_1662628), hAPP(hAPP(c_List_Odrop(_1662628), _1662632), _1662634)))), -(hBOOL(hAPP(hAPP(c_member(_1662628), _1662630), hAPP(c_List_Oset(_1662628), _1662634))))], (44342 ^ _779530) ^ [_1662773, _1662775, _1662777] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662773)), hAPP(hAPP(c_List_Odrop(_1662773), _1662775), _1662777)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662773)), _1662777)), _1662775))], (44344 ^ _779530) ^ [_1662828, _1662830, _1662832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1662828, tc_HOL_Obool)), hAPP(c_List_Oset(_1662828), hAPP(hAPP(c_List_Odrop(_1662828), _1662830), _1662832))), hAPP(c_List_Oset(_1662828), _1662832))))], (44346 ^ _779530) ^ [_1662883, _1662885, _1662887] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1662883), c_List_Oupt(_1662885, _1662887)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662885), _1662883), _1662887))], (44348 ^ _779530) ^ [_1662928, _1662930] : [-(hAPP(hAPP(c_List_Odrop(_1662928), _1662930), c_List_Olist_ONil(_1662928)) = c_List_Olist_ONil(_1662928))], (44350 ^ _779530) ^ [_1662965, _1662967, _1662969, _1662971, _1662973] : [-(hAPP(hAPP(c_List_Odrop(_1662965), _1662967), hAPP(hAPP(c_List_Omap(_1662969, _1662965), _1662971), _1662973)) = hAPP(hAPP(c_List_Omap(_1662969, _1662965), _1662971), hAPP(hAPP(c_List_Odrop(_1662969), _1662967), _1662973)))], (44352 ^ _779530) ^ [_1663030, _1663032, _1663034] : [-(hAPP(hAPP(c_List_Oappend(_1663030), hAPP(hAPP(c_List_Otake(_1663030), _1663032), _1663034)), hAPP(hAPP(c_List_Odrop(_1663030), _1663032), _1663034)) = _1663034)], (44354 ^ _779530) ^ [_1663081] : [-(c_List_Oconcat(_1663081, c_List_Olist_ONil(tc_List_Olist(_1663081))) = c_List_Olist_ONil(_1663081))], (44356 ^ _779530) ^ [_1663113, _1663115, _1663117] : [-(c_List_Oconcat(_1663113, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1663113)), _1663115), _1663117)) = hAPP(hAPP(c_List_Oappend(_1663113), _1663115), c_List_Oconcat(_1663113, _1663117)))], (44368 ^ _779530) ^ [_1663385, _1663387] : [44370 ^ _779530 : [(44371 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663385)), 44369 ^ [_1663385, _1663387]), hAPP(c_List_Oset(tc_List_Olist(_1663385)), _1663387))))], (44373 ^ _779530) ^ [] : [44369 ^ [_1663385, _1663387] = c_List_Olist_ONil(_1663385)]], -(c_List_Olist_ONil(_1663385) = c_List_Oconcat(_1663385, _1663387))], (44358 ^ _779530) ^ [_1663179, _1663181] : [c_List_Olist_ONil(_1663179) = c_List_Oconcat(_1663179, _1663181), 44361 ^ _779530 : [(44362 ^ _779530) ^ [_1663270] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663179)), _1663270), hAPP(c_List_Oset(tc_List_Olist(_1663179)), _1663181))), -(_1663270 = c_List_Olist_ONil(_1663179))]]], (44387 ^ _779530) ^ [_1663797, _1663799] : [44389 ^ _779530 : [(44390 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663797)), 44388 ^ [_1663797, _1663799]), hAPP(c_List_Oset(tc_List_Olist(_1663797)), _1663799))))], (44392 ^ _779530) ^ [] : [44388 ^ [_1663797, _1663799] = c_List_Olist_ONil(_1663797)]], -(c_List_Oconcat(_1663797, _1663799) = c_List_Olist_ONil(_1663797))], (44377 ^ _779530) ^ [_1663591, _1663593] : [c_List_Oconcat(_1663591, _1663593) = c_List_Olist_ONil(_1663591), 44380 ^ _779530 : [(44381 ^ _779530) ^ [_1663682] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663591)), _1663682), hAPP(c_List_Oset(tc_List_Olist(_1663591)), _1663593))), -(_1663682 = c_List_Olist_ONil(_1663591))]]], (44396 ^ _779530) ^ [_1663988, _1663990, _1663992, _1663994] : [-(hAPP(hAPP(c_List_Omap(_1663988, _1663990), _1663992), c_List_Oconcat(_1663988, _1663994)) = c_List_Oconcat(_1663990, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1663988), tc_List_Olist(_1663990)), hAPP(c_List_Omap(_1663988, _1663990), _1663992)), _1663994)))], (44398 ^ _779530) ^ [_1664051, _1664053, _1664055] : [-(hAPP(c_List_Ofilter(_1664051, _1664053), c_List_Oconcat(_1664051, _1664055)) = c_List_Oconcat(_1664051, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1664051), tc_List_Olist(_1664051)), c_List_Ofilter(_1664051, _1664053)), _1664055)))], (44400 ^ _779530) ^ [_1664106, _1664108, _1664110, _1664112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1664106), _1664108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664110, tc_HOL_Obool)), hAPP(c_List_Oset(_1664110), hAPP(hAPP(c_List_Odrop(_1664110), _1664108), _1664112))), hAPP(c_List_Oset(_1664110), hAPP(hAPP(c_List_Odrop(_1664110), _1664106), _1664112)))))], (44406 ^ _779530) ^ [_1664287, _1664289, _1664291] : [hAPP(hAPP(c_List_Odrop(_1664287), _1664289), _1664291) = c_List_Olist_ONil(_1664287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664287)), _1664291)), _1664289)))], (44412 ^ _779530) ^ [_1664406, _1664408, _1664410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664406)), _1664410)), _1664408)), -(hAPP(hAPP(c_List_Odrop(_1664406), _1664408), _1664410) = c_List_Olist_ONil(_1664406))], (44418 ^ _779530) ^ [_1664531, _1664533, _1664535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664531)), _1664533)), _1664535)), -(hAPP(hAPP(c_List_Odrop(_1664531), _1664535), _1664533) = c_List_Olist_ONil(_1664531))], (44424 ^ _779530) ^ [_1664654, _1664656, _1664658, _1664660] : [-(hAPP(hAPP(c_List_Odrop(_1664654), _1664656), hAPP(hAPP(c_List_Oappend(_1664654), _1664658), _1664660)) = hAPP(hAPP(c_List_Oappend(_1664654), hAPP(hAPP(c_List_Odrop(_1664654), _1664656), _1664658)), hAPP(hAPP(c_List_Odrop(_1664654), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664656), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664654)), _1664658))), _1664660)))], (44426 ^ _779530) ^ [_1664757, _1664759, _1664761, _1664763] : [hAPP(hAPP(c_List_Oappend(_1664757), _1664759), _1664761) = _1664763, 44429 ^ _779530 : [(44430 ^ _779530) ^ [] : [-(_1664759 = hAPP(hAPP(c_List_Otake(_1664757), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664757)), _1664759)), _1664763))], (44432 ^ _779530) ^ [] : [-(_1664761 = hAPP(hAPP(c_List_Odrop(_1664757), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664757)), _1664759)), _1664763))]]], (44434 ^ _779530) ^ [_1664936, _1664938, _1664940, _1664942] : [-(hAPP(hAPP(c_List_Oappend(_1664936), _1664938), _1664940) = _1664942), _1664938 = hAPP(hAPP(c_List_Otake(_1664936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664936)), _1664938)), _1664942), _1664940 = hAPP(hAPP(c_List_Odrop(_1664936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664936)), _1664938)), _1664942)], (44444 ^ _779530) ^ [_1665151, _1665153] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665151)), c_List_Oconcat(_1665151, _1665153)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1665151), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1665151))), _1665153)))], (44446 ^ _779530) ^ [_1665204, _1665206, _1665208, _1665210] : [-(hAPP(hAPP(c_List_Odrop(_1665204), _1665206), hAPP(hAPP(c_List_Olist_OCons(_1665204), _1665208), _1665210)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1665204), hAPP(hAPP(c_List_Olist_OCons(_1665204), _1665208), _1665210), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1665204), tc_List_Olist(_1665204)), c_List_Odrop(_1665204)), _1665210), _1665206))], (44448 ^ _779530) ^ [_1665280, _1665282] : [-(hAPP(c_List_Oset(_1665280), c_List_Oconcat(_1665280, _1665282)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1665280), tc_fun(_1665280, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1665280)), _1665282)), c_List_Oset(_1665280)))], (44450 ^ _779530) ^ [_1665336, _1665338, _1665340] : [-(c_List_Oconcat(_1665336, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1665336)), _1665338), _1665340)) = hAPP(hAPP(c_List_Oappend(_1665336), c_List_Oconcat(_1665336, _1665338)), c_List_Oconcat(_1665336, _1665340)))], (44452 ^ _779530) ^ [_1665405, _1665407, _1665409, _1665411] : [_1665405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1665407), _1665405), hAPP(hAPP(c_List_Olist_OCons(_1665407), _1665409), _1665411)) = hAPP(hAPP(c_List_Olist_OCons(_1665407), _1665409), _1665411))], (44458 ^ _779530) ^ [_1665528, _1665530, _1665532, _1665534] : [-(_1665528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1665530), _1665528), hAPP(hAPP(c_List_Olist_OCons(_1665530), _1665532), _1665534)) = hAPP(hAPP(c_List_Odrop(_1665530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1665528), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1665534))], (44464 ^ _779530) ^ [_1665600, _1665602, _1665604, _1665606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1665600), _1665602)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665604)), _1665606))), -(hAPP(hAPP(c_List_Onth(_1665604), hAPP(hAPP(c_List_Odrop(_1665604), _1665600), _1665606)), _1665602) = hAPP(hAPP(c_List_Onth(_1665604), _1665606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1665600), _1665602)))], (44470 ^ _779530) ^ [_1665801, _1665803, _1665805, _1665807, _1665809] : [hAPP(hAPP(c_List_Oappend(_1665801), _1665803), _1665805) = hAPP(hAPP(c_List_Oappend(_1665801), _1665807), _1665809), 44473 ^ _779530 : [(44474 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665803)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665807))), 44477 ^ _779530 : [(44478 ^ _779530) ^ [] : [-(_1665803 = hAPP(hAPP(c_List_Otake(_1665801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665803)), _1665807))], (44480 ^ _779530) ^ [] : [-(_1665805 = hAPP(hAPP(c_List_Oappend(_1665801), hAPP(hAPP(c_List_Odrop(_1665801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665803)), _1665807)), _1665809))]]], (44482 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665803)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665807)))), 44485 ^ _779530 : [(44486 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1665801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665807)), _1665803) = _1665807)], (44488 ^ _779530) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1665801), hAPP(hAPP(c_List_Odrop(_1665801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665801)), _1665807)), _1665803)), _1665805) = _1665809)]]]]], (44490 ^ _779530) ^ [_1666314, _1666316, _1666318, _1666320, _1666322] : [-(hAPP(hAPP(c_List_Oappend(_1666314), _1666316), _1666318) = hAPP(hAPP(c_List_Oappend(_1666314), _1666320), _1666322)), 44493 ^ _779530 : [(44494 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666316)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666320))))], (44496 ^ _779530) ^ [] : [_1666316 = hAPP(hAPP(c_List_Otake(_1666314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666316)), _1666320), _1666318 = hAPP(hAPP(c_List_Oappend(_1666314), hAPP(hAPP(c_List_Odrop(_1666314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666316)), _1666320)), _1666322)]], 44501 ^ _779530 : [(44502 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666316)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666320)))], (44504 ^ _779530) ^ [] : [hAPP(hAPP(c_List_Otake(_1666314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666320)), _1666316) = _1666320, hAPP(hAPP(c_List_Oappend(_1666314), hAPP(hAPP(c_List_Odrop(_1666314), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666314)), _1666320)), _1666316)), _1666318) = _1666322]]], (44512 ^ _779530) ^ [_1666902, _1666904, _1666906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1666902), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666904)), _1666906))), -(hAPP(hAPP(c_List_Olist_OCons(_1666904), hAPP(hAPP(c_List_Onth(_1666904), _1666906), _1666902)), hAPP(hAPP(c_List_Odrop(_1666904), hAPP(c_Nat_OSuc, _1666902)), _1666906)) = hAPP(hAPP(c_List_Odrop(_1666904), _1666902), _1666906))], (44518 ^ _779530) ^ [_1667075, _1667077, _1667079, _1667081] : [-(c_List_Otranspose(_1667075, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1667075)), hAPP(hAPP(c_List_Olist_OCons(_1667075), _1667077), _1667079)), _1667081)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1667075)), hAPP(hAPP(c_List_Olist_OCons(_1667075), _1667077), c_List_Oconcat(_1667075, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1667075), tc_List_Olist(_1667075)), c_List_Olist_Olist__case(tc_List_Olist(_1667075), _1667075, c_List_Olist_ONil(_1667075), hAPP(hAPP(c_COMBB(tc_List_Olist(_1667075), tc_fun(tc_List_Olist(_1667075), tc_List_Olist(_1667075)), _1667075), c_COMBK(tc_List_Olist(_1667075), tc_List_Olist(_1667075))), hAPP(hAPP(c_COMBC(_1667075, tc_List_Olist(_1667075), tc_List_Olist(_1667075)), c_List_Olist_OCons(_1667075)), c_List_Olist_ONil(_1667075))))), _1667081)))), c_List_Otranspose(_1667075, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1667075)), _1667079), c_List_Oconcat(tc_List_Olist(_1667075), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1667075), tc_List_Olist(tc_List_Olist(_1667075))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1667075)), _1667075, c_List_Olist_ONil(tc_List_Olist(_1667075)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1667075), tc_List_Olist(tc_List_Olist(_1667075))), _1667075), hAPP(hAPP(c_COMBC(tc_List_Olist(_1667075), tc_List_Olist(tc_List_Olist(_1667075)), tc_List_Olist(tc_List_Olist(_1667075))), c_List_Olist_OCons(tc_List_Olist(_1667075))), c_List_Olist_ONil(tc_List_Olist(_1667075)))))), _1667081))))))], (44520 ^ _779530) ^ [_1667316, _1667318, _1667320, _1667322] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1667318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667316)), hAPP(hAPP(c_List_Olist_OCons(_1667318), _1667320), _1667322)) = hAPP(hAPP(c_List_Olist_OCons(_1667318), _1667320), _1667322))], (44526 ^ _779530) ^ [_1667451, _1667453, _1667455, _1667457] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667451) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1667453), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667451)), hAPP(hAPP(c_List_Olist_OCons(_1667453), _1667455), _1667457)) = hAPP(hAPP(c_List_Odrop(_1667453), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1667451)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1667457))], (44532 ^ _779530) ^ [_1667532, _1667534, _1667536, _1667538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667532), _1667534)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667536)), _1667538))), -(hAPP(hAPP(c_List_Otake(_1667536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667532), _1667534)), _1667538) = hAPP(hAPP(c_List_Oappend(_1667536), hAPP(hAPP(c_List_Otake(_1667536), _1667532), _1667538)), hAPP(hAPP(c_List_Otake(_1667536), _1667534), hAPP(hAPP(c_List_Odrop(_1667536), _1667532), _1667538))))], (44538 ^ _779530) ^ [_1667741, _1667743, _1667745] : [44540 ^ _779530 : [(44541 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667741), tc_List_Olist(_1667741))), 44539 ^ [_1667741, _1667743, _1667745]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1667741), tc_List_Olist(_1667741))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1667741), tc_List_Olist(_1667741)), _1667743), _1667745)))))], (44543 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1667741), tc_List_Olist(_1667741), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1667741), tc_fun(tc_List_Olist(_1667741), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667741), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1667741), tc_Nat_Onat), tc_fun(tc_List_Olist(_1667741), tc_HOL_Obool)), tc_List_Olist(_1667741)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1667741))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1667741)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1667741))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1667741)))), 44539 ^ [_1667741, _1667743, _1667745]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667741))), _1667743) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667741))), _1667745), 44548 ^ _779530 : [(44549 ^ _779530) ^ [] : [c_List_Oconcat(_1667741, _1667743) = c_List_Oconcat(_1667741, _1667745), -(_1667743 = _1667745)], (44555 ^ _779530) ^ [] : [_1667743 = _1667745, -(c_List_Oconcat(_1667741, _1667743) = c_List_Oconcat(_1667741, _1667745))]]], (44561 ^ _779530) ^ [_1668468, _1668470, _1668472] : [c_List_Oconcat(_1668468, _1668470) = c_List_Oconcat(_1668468, _1668472), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1668468))), _1668470) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1668468))), _1668472), 44571 ^ _779530 : [(44572 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668468), tc_List_Olist(_1668468))), 44570 ^ [_1668468, _1668470, _1668472]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1668468), tc_List_Olist(_1668468))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1668468), tc_List_Olist(_1668468)), _1668470), _1668472)))))], (44574 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1668468), tc_List_Olist(_1668468), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668468), tc_fun(tc_List_Olist(_1668468), tc_Nat_Onat), tc_fun(tc_List_Olist(_1668468), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1668468), tc_Nat_Onat), tc_fun(tc_List_Olist(_1668468), tc_HOL_Obool)), tc_List_Olist(_1668468)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1668468))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1668468)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1668468))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1668468)))), 44570 ^ [_1668468, _1668470, _1668472]))]], -(_1668470 = _1668472)], (44578 ^ _779530) ^ [_1669109, _1669111, _1669113, _1669115] : [-(c_List_Oconcat(_1669109, hAPP(hAPP(c_List_Omap(_1669111, tc_List_Olist(_1669109)), hAPP(hAPP(c_COMBC(_1669111, tc_List_Olist(_1669109), tc_List_Olist(_1669109)), hAPP(hAPP(c_COMBB(_1669109, tc_fun(tc_List_Olist(_1669109), tc_List_Olist(_1669109)), _1669111), c_List_Olist_OCons(_1669109)), _1669113)), c_List_Olist_ONil(_1669109))), _1669115)) = hAPP(hAPP(c_List_Omap(_1669111, _1669109), _1669113), _1669115))], (44580 ^ _779530) ^ [_1669196, _1669198, _1669200, _1669202, _1669204] : [-(hAPP(hAPP(c_List_Ozip(_1669196, _1669198), hAPP(hAPP(c_List_Oappend(_1669196), _1669200), _1669202)), _1669204) = hAPP(hAPP(c_List_Oappend(tc_prod(_1669196, _1669198)), hAPP(hAPP(c_List_Ozip(_1669196, _1669198), _1669200), hAPP(hAPP(c_List_Otake(_1669198), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669196)), _1669200)), _1669204))), hAPP(hAPP(c_List_Ozip(_1669196, _1669198), _1669202), hAPP(hAPP(c_List_Odrop(_1669198), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669196)), _1669200)), _1669204))))], (44582 ^ _779530) ^ [_1669303, _1669305, _1669307, _1669309, _1669311] : [-(hAPP(hAPP(c_List_Ozip(_1669303, _1669305), _1669307), hAPP(hAPP(c_List_Oappend(_1669305), _1669309), _1669311)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1669303, _1669305)), hAPP(hAPP(c_List_Ozip(_1669303, _1669305), hAPP(hAPP(c_List_Otake(_1669303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669305)), _1669309)), _1669307)), _1669309)), hAPP(hAPP(c_List_Ozip(_1669303, _1669305), hAPP(hAPP(c_List_Odrop(_1669303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669305)), _1669309)), _1669307)), _1669311)))], (44584 ^ _779530) ^ [_1669410, _1669412, _1669414] : [-(c_Enum_On__lists(_1669410, hAPP(c_Nat_OSuc, _1669412), _1669414) = c_List_Oconcat(tc_List_Olist(_1669410), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669410), tc_List_Olist(tc_List_Olist(_1669410))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669410), tc_List_Olist(_1669410), tc_List_Olist(tc_List_Olist(_1669410))), hAPP(hAPP(c_COMBB(tc_fun(_1669410, tc_List_Olist(_1669410)), tc_fun(tc_List_Olist(_1669410), tc_List_Olist(tc_List_Olist(_1669410))), tc_List_Olist(_1669410)), c_List_Omap(_1669410, tc_List_Olist(_1669410))), hAPP(c_COMBC(_1669410, tc_List_Olist(_1669410), tc_List_Olist(_1669410)), c_List_Olist_OCons(_1669410)))), _1669414)), c_Enum_On__lists(_1669410, _1669412, _1669414))))], (44586 ^ _779530) ^ [_1669530, _1669532, _1669534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669530), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669532)), _1669534))), -(_1669534 = hAPP(hAPP(c_List_Oappend(_1669532), hAPP(hAPP(c_List_Otake(_1669532), _1669530), _1669534)), hAPP(hAPP(c_List_Olist_OCons(_1669532), hAPP(hAPP(c_List_Onth(_1669532), _1669534), _1669530)), hAPP(hAPP(c_List_Odrop(_1669532), hAPP(c_Nat_OSuc, _1669530)), _1669534))))], (44592 ^ _779530) ^ [_1669719, _1669721] : [-(c_List_Oconcat(tc_List_Olist(_1669719), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669719), tc_List_Olist(tc_List_Olist(_1669719))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1669719)), _1669719, c_List_Olist_ONil(tc_List_Olist(_1669719)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1669719), tc_List_Olist(tc_List_Olist(_1669719))), _1669719), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669719), tc_List_Olist(tc_List_Olist(_1669719)), tc_List_Olist(tc_List_Olist(_1669719))), c_List_Olist_OCons(tc_List_Olist(_1669719))), c_List_Olist_ONil(tc_List_Olist(_1669719)))))), _1669721)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669719), tc_List_Olist(_1669719)), c_List_Otl(_1669719)), hAPP(c_List_Ofilter(tc_List_Olist(_1669719), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1669719)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669719), tc_List_Olist(_1669719), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1669719)))), _1669721)))], (44594 ^ _779530) ^ [_1669871, _1669873] : [-(c_List_Oconcat(_1669871, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669871), tc_List_Olist(_1669871)), c_List_Olist_Olist__case(tc_List_Olist(_1669871), _1669871, c_List_Olist_ONil(_1669871), hAPP(hAPP(c_COMBB(tc_List_Olist(_1669871), tc_fun(tc_List_Olist(_1669871), tc_List_Olist(_1669871)), _1669871), c_COMBK(tc_List_Olist(_1669871), tc_List_Olist(_1669871))), hAPP(hAPP(c_COMBC(_1669871, tc_List_Olist(_1669871), tc_List_Olist(_1669871)), c_List_Olist_OCons(_1669871)), c_List_Olist_ONil(_1669871))))), _1669873)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669871), _1669871), c_List_Ohd(_1669871)), hAPP(c_List_Ofilter(tc_List_Olist(_1669871), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1669871)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669871), tc_List_Olist(_1669871), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1669871)))), _1669873)))], (44596 ^ _779530) ^ [_1670014, _1670016, _1670018] : [-(hAPP(hAPP(c_List_Odrop(_1670014), _1670016), hAPP(c_List_Otl(_1670014), _1670018)) = hAPP(c_List_Otl(_1670014), hAPP(hAPP(c_List_Odrop(_1670014), _1670016), _1670018)))], (44598 ^ _779530) ^ [_1670067, _1670069, _1670071] : [-(hAPP(c_List_Otl(_1670067), hAPP(hAPP(c_List_Odrop(_1670067), _1670069), _1670071)) = hAPP(hAPP(c_List_Odrop(_1670067), _1670069), hAPP(c_List_Otl(_1670067), _1670071)))], (44600 ^ _779530) ^ [_1670120, _1670122, _1670124, _1670126] : [-(hAPP(hAPP(c_List_Omap(_1670120, _1670122), _1670124), hAPP(c_List_Otl(_1670120), _1670126)) = hAPP(c_List_Otl(_1670122), hAPP(hAPP(c_List_Omap(_1670120, _1670122), _1670124), _1670126)))], (44602 ^ _779530) ^ [_1670177] : [-(hAPP(c_List_Otl(_1670177), c_List_Olist_ONil(_1670177)) = c_List_Olist_ONil(_1670177))], (44604 ^ _779530) ^ [_1670209, _1670211] : [hBOOL(hAPP(c_List_Odistinct(_1670209), _1670211)), -(hBOOL(hAPP(c_List_Odistinct(_1670209), hAPP(c_List_Otl(_1670209), _1670211))))], (44610 ^ _779530) ^ [_1670312, _1670314, _1670316] : [-(hAPP(c_List_Ohd(_1670312), hAPP(hAPP(c_List_Olist_OCons(_1670312), _1670314), _1670316)) = _1670314)], (44612 ^ _779530) ^ [_1670352, _1670354, _1670356] : [-(hAPP(c_List_Otl(_1670352), hAPP(hAPP(c_List_Olist_OCons(_1670352), _1670354), _1670356)) = _1670356)], (44614 ^ _779530) ^ [_1670388, _1670390, _1670392] : [-(_1670388 = c_List_Olist_ONil(_1670390)), -(hAPP(hAPP(c_List_Otake(_1670390), hAPP(c_Nat_OSuc, _1670392)), _1670388) = hAPP(hAPP(c_List_Olist_OCons(_1670390), hAPP(c_List_Ohd(_1670390), _1670388)), hAPP(hAPP(c_List_Otake(_1670390), _1670392), hAPP(c_List_Otl(_1670390), _1670388))))], (44620 ^ _779530) ^ [_1670461, _1670463, _1670465] : [-(_1670461 = c_List_Olist_ONil(_1670463)), -(hAPP(c_List_Otl(_1670463), hAPP(hAPP(c_List_Oappend(_1670463), _1670461), _1670465)) = hAPP(hAPP(c_List_Oappend(_1670463), hAPP(c_List_Otl(_1670463), _1670461)), _1670465))], (44626 ^ _779530) ^ [_1670523, _1670525] : [-(_1670523 = c_List_Olist_ONil(_1670525)), -(hAPP(c_List_Orotate1(_1670525), _1670523) = hAPP(hAPP(c_List_Oappend(_1670525), hAPP(c_List_Otl(_1670525), _1670523)), hAPP(hAPP(c_List_Olist_OCons(_1670525), hAPP(c_List_Ohd(_1670525), _1670523)), c_List_Olist_ONil(_1670525))))], (44632 ^ _779530) ^ [_1670594, _1670596, _1670598] : [-(hAPP(hAPP(c_List_Otake(_1670594), _1670596), hAPP(c_List_Otl(_1670594), _1670598)) = hAPP(c_List_Otl(_1670594), hAPP(hAPP(c_List_Otake(_1670594), hAPP(c_Nat_OSuc, _1670596)), _1670598)))], (44634 ^ _779530) ^ [_1670650, _1670652, _1670654] : [-(hAPP(hAPP(c_List_Odrop(_1670650), hAPP(c_Nat_OSuc, _1670652)), _1670654) = hAPP(hAPP(c_List_Odrop(_1670650), _1670652), hAPP(c_List_Otl(_1670650), _1670654)))], (44636 ^ _779530) ^ [_1670697, _1670699, _1670701, _1670703] : [-(_1670697 = c_List_Olist_ONil(_1670699)), -(hAPP(c_List_Ohd(_1670701), hAPP(hAPP(c_List_Omap(_1670699, _1670701), _1670703), _1670697)) = hAPP(_1670703, hAPP(c_List_Ohd(_1670699), _1670697)))], (44642 ^ _779530) ^ [_1670773, _1670775, _1670777] : [_1670773 = c_List_Olist_ONil(_1670775), -(hAPP(c_List_Ohd(_1670775), hAPP(hAPP(c_List_Oappend(_1670775), _1670773), _1670777)) = hAPP(c_List_Ohd(_1670775), _1670777))], (44648 ^ _779530) ^ [_1670886, _1670888, _1670890] : [-(_1670886 = c_List_Olist_ONil(_1670888)), -(hAPP(c_List_Ohd(_1670888), hAPP(hAPP(c_List_Oappend(_1670888), _1670886), _1670890)) = hAPP(c_List_Ohd(_1670888), _1670886))], (44654 ^ _779530) ^ [_1670942, _1670944, _1670946] : [-(_1670942 = c_List_Olist_ONil(_1670944)), -(hAPP(c_List_Ohd(_1670944), hAPP(hAPP(c_List_Oappend(_1670944), _1670942), _1670946)) = hAPP(c_List_Ohd(_1670944), _1670942))], (44660 ^ _779530) ^ [_1671000, _1671002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1671000), _1671002)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1671000, _1671002)) = _1671000)], (44666 ^ _779530) ^ [_1671099, _1671101, _1671103] : [-(hAPP(c_List_Otl(_1671099), hAPP(hAPP(c_List_Oappend(_1671099), _1671101), _1671103)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1671099), _1671099, hAPP(c_List_Otl(_1671099), _1671103), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1671099), tc_List_Olist(_1671099)), _1671099), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671099), tc_List_Olist(_1671099), tc_List_Olist(_1671099)), c_List_Oappend(_1671099)), _1671103))), _1671101))], (44668 ^ _779530) ^ [_1671185, _1671187] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671185)), hAPP(c_List_Otl(_1671185), _1671187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671185)), _1671187)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44670 ^ _779530) ^ [_1671231, _1671233] : [-(_1671231 = c_List_Olist_ONil(_1671233)), -(hBOOL(hAPP(hAPP(c_member(_1671233), hAPP(c_List_Ohd(_1671233), _1671231)), hAPP(c_List_Oset(_1671233), _1671231))))], (44676 ^ _779530) ^ [_1671286, _1671288, _1671290] : [-(hAPP(c_List_Otl(_1671286), hAPP(hAPP(c_List_Otake(_1671286), _1671288), _1671290)) = hAPP(hAPP(c_List_Otake(_1671286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1671288), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1671286), _1671290)))], (44678 ^ _779530) ^ [_1671341, _1671343] : [-(_1671341 = c_List_Olist_ONil(_1671343)), -(hAPP(c_List_Ohd(_1671343), _1671341) = hAPP(hAPP(c_List_Onth(_1671343), _1671341), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44684 ^ _779530) ^ [_1671391, _1671393, _1671395] : [-(_1671391 = c_List_Olist_ONil(_1671393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1671395), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671393)), _1671391))), -(hAPP(c_List_Ohd(_1671393), hAPP(hAPP(c_List_Odrop(_1671393), _1671395), _1671391)) = hAPP(hAPP(c_List_Onth(_1671393), _1671391), _1671395))], (44694 ^ _779530) ^ [_1671590, _1671592, _1671594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1671590), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671592)), _1671594))), -(hAPP(hAPP(c_List_Oappend(_1671592), hAPP(hAPP(c_List_Otake(_1671592), _1671590), _1671594)), hAPP(hAPP(c_List_Olist_OCons(_1671592), hAPP(c_List_Ohd(_1671592), hAPP(hAPP(c_List_Odrop(_1671592), _1671590), _1671594))), c_List_Olist_ONil(_1671592))) = hAPP(hAPP(c_List_Otake(_1671592), hAPP(c_Nat_OSuc, _1671590)), _1671594))], (44700 ^ _779530) ^ [_1671793, _1671795] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671793)), c_List_Oremdups(_1671793, c_List_Oconcat(_1671793, _1671795))) = hAPP(c_Finite__Set_Ocard(_1671793), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1671793), tc_fun(_1671793, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1671793)), _1671795)), c_List_Oset(_1671793))))], (44702 ^ _779530) ^ [_1671859, _1671861] : [class_Lattices_Oab__semigroup__idem__mult(_1671859), -(_1671861 = c_List_Olist_ONil(_1671859)), -(hAPP(c_Finite__Set_Ofold1(_1671859, c_Groups_Otimes__class_Otimes(_1671859)), hAPP(c_List_Oset(_1671859), _1671861)) = hAPP(c_List_Ofoldl(_1671859, _1671859, c_Groups_Otimes__class_Otimes(_1671859), hAPP(c_List_Ohd(_1671859), _1671861)), hAPP(c_List_Otl(_1671859), _1671861)))], (44712 ^ _779530) ^ [_1672019, _1672021] : [-(hBOOL(hAPP(c_List_Odistinct(_1672019), c_List_Oremdups(_1672019, _1672021))))], (44714 ^ _779530) ^ [_1672051, _1672053] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672051)), c_List_Oremdups(_1672051, _1672053))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672051)), _1672053))))], (44716 ^ _779530) ^ [_1672098, _1672100, _1672102, _1672104, _1672106, _1672108, _1672110] : [-(hAPP(c_List_Ofoldl(_1672098, _1672100, _1672102, _1672104), hAPP(hAPP(c_List_Omap(_1672106, _1672100), _1672108), _1672110)) = hAPP(c_List_Ofoldl(_1672098, _1672106, hAPP(hAPP(c_COMBC(_1672098, tc_fun(_1672106, _1672100), tc_fun(_1672106, _1672098)), hAPP(hAPP(c_COMBB(tc_fun(_1672100, _1672098), tc_fun(tc_fun(_1672106, _1672100), tc_fun(_1672106, _1672098)), _1672098), c_COMBB(_1672100, _1672098, _1672106)), _1672102)), _1672108), _1672104), _1672110))], (44718 ^ _779530) ^ [_1672200, _1672202, _1672204, _1672206] : [-(c_List_Oremdups(_1672200, hAPP(hAPP(c_List_Omap(_1672202, _1672200), _1672204), c_List_Oremdups(_1672202, _1672206))) = c_List_Oremdups(_1672200, hAPP(hAPP(c_List_Omap(_1672202, _1672200), _1672204), _1672206)))], (44720 ^ _779530) ^ [_1672256, _1672258] : [-(hAPP(c_List_Oset(_1672256), c_List_Oremdups(_1672256, _1672258)) = hAPP(c_List_Oset(_1672256), _1672258))], (44722 ^ _779530) ^ [_1672294, _1672296, _1672298, _1672300, _1672302, _1672304] : [-(hAPP(c_List_Ofoldl(_1672294, _1672296, _1672298, _1672300), hAPP(hAPP(c_List_Olist_OCons(_1672296), _1672302), _1672304)) = hAPP(c_List_Ofoldl(_1672294, _1672296, _1672298, hAPP(hAPP(_1672298, _1672300), _1672302)), _1672304))], (44724 ^ _779530) ^ [_1672357, _1672359] : [hBOOL(hAPP(c_List_Odistinct(_1672357), _1672359)), -(c_List_Oremdups(_1672357, _1672359) = _1672359)], (44730 ^ _779530) ^ [_1672463, _1672465] : [c_List_Oremdups(_1672463, _1672465) = _1672465, -(hBOOL(hAPP(c_List_Odistinct(_1672463), _1672465)))], (44736 ^ _779530) ^ [_1672550, _1672552] : [hBOOL(hAPP(c_List_Odistinct(_1672550), _1672552)), -(c_List_Oremdups(_1672550, _1672552) = _1672552)], (44742 ^ _779530) ^ [_1672643, _1672645, _1672647] : [-(c_List_Oremdups(_1672643, hAPP(c_List_Ofilter(_1672643, _1672645), _1672647)) = hAPP(c_List_Ofilter(_1672643, _1672645), c_List_Oremdups(_1672643, _1672647)))], (44744 ^ _779530) ^ [_1672688, _1672690, _1672692] : [class_Groups_Oab__semigroup__add(_1672688), -(c_List_Ofoldr(_1672688, _1672688, c_Groups_Oplus__class_Oplus(_1672688), _1672690, _1672692) = hAPP(c_List_Ofoldl(_1672688, _1672688, c_Groups_Oplus__class_Oplus(_1672688), _1672692), _1672690))], (44750 ^ _779530) ^ [_1672801, _1672803, _1672805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1672801), _1672803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1672801), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1672803), _1672805))))], (44756 ^ _779530) ^ [_1672916, _1672918, _1672920] : [class_Groups_Omonoid__add(_1672916), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672916), _1672918), hAPP(c_List_Ofoldl(_1672916, _1672916, c_Groups_Oplus__class_Oplus(_1672916), c_Groups_Ozero__class_Ozero(_1672916)), _1672920)) = hAPP(c_List_Ofoldl(_1672916, _1672916, c_Groups_Oplus__class_Oplus(_1672916), _1672918), _1672920))], (44762 ^ _779530) ^ [_1673053, _1673055, _1673057, _1673059] : [class_Groups_Osemigroup__add(_1673053), -(hAPP(c_List_Ofoldl(_1673053, _1673053, c_Groups_Oplus__class_Oplus(_1673053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1673053), _1673055), _1673057)), _1673059) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1673053), _1673055), hAPP(c_List_Ofoldl(_1673053, _1673053, c_Groups_Oplus__class_Oplus(_1673053), _1673057), _1673059)))], (44768 ^ _779530) ^ [_1673204, _1673206] : [-(c_List_Oremdups(_1673204, c_List_Oremdups(_1673204, _1673206)) = c_List_Oremdups(_1673204, _1673206))], (44770 ^ _779530) ^ [_1673253, _1673255] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673253)), c_List_Oremdups(_1673253, _1673255)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673253)), _1673255), -(c_List_Oremdups(_1673253, _1673255) = _1673255)], (44776 ^ _779530) ^ [_1673366, _1673368] : [c_List_Oremdups(_1673366, _1673368) = _1673368, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673366)), c_List_Oremdups(_1673366, _1673368)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673366)), _1673368))], (44782 ^ _779530) ^ [_1673485, _1673487, _1673489, _1673491] : [-(hAPP(c_List_Ofoldl(_1673485, _1673487, _1673489, _1673491), c_List_Olist_ONil(_1673487)) = _1673491)], (44784 ^ _779530) ^ [_1673539, _1673541] : [c_List_Oremdups(_1673539, _1673541) = c_List_Olist_ONil(_1673539), -(_1673541 = c_List_Olist_ONil(_1673539))], (44790 ^ _779530) ^ [_1673626, _1673628] : [_1673628 = c_List_Olist_ONil(_1673626), -(c_List_Oremdups(_1673626, _1673628) = c_List_Olist_ONil(_1673626))], (44796 ^ _779530) ^ [_1673734, _1673736] : [c_List_Olist_ONil(_1673734) = c_List_Oremdups(_1673734, _1673736), -(_1673736 = c_List_Olist_ONil(_1673734))], (44802 ^ _779530) ^ [_1673821, _1673823] : [_1673823 = c_List_Olist_ONil(_1673821), -(c_List_Olist_ONil(_1673821) = c_List_Oremdups(_1673821, _1673823))], (44808 ^ _779530) ^ [_1673914] : [-(c_List_Oremdups(_1673914, c_List_Olist_ONil(_1673914)) = c_List_Olist_ONil(_1673914))], (44810 ^ _779530) ^ [_1673944, _1673946, _1673948, _1673950, _1673952, _1673954] : [-(hAPP(c_List_Ofoldl(_1673944, _1673946, _1673948, _1673950), hAPP(hAPP(c_List_Oappend(_1673946), _1673952), _1673954)) = hAPP(c_List_Ofoldl(_1673944, _1673946, _1673948, hAPP(c_List_Ofoldl(_1673944, _1673946, _1673948, _1673950), _1673952)), _1673954))], (44812 ^ _779530) ^ [_1674009, _1674011, _1674013] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1674009), tc_List_Olist(_1674009), c_List_Oappend(_1674009), _1674011), _1674013) = hAPP(hAPP(c_List_Oappend(_1674009), _1674011), c_List_Oconcat(_1674009, _1674013)))], (44814 ^ _779530) ^ [_1674061, _1674063, _1674065] : [hBOOL(hAPP(c_List_Odistinct(_1674061), _1674063)), -(c_List_Oremove1(_1674061, _1674065, c_List_Oremdups(_1674061, _1674063)) = c_List_Oremdups(_1674061, c_List_Oremove1(_1674061, _1674065, _1674063)))], (44820 ^ _779530) ^ [_1674176] : [class_Groups_Omonoid__add(_1674176), -(c_List_Omonoid__add__class_Olistsum(_1674176) = c_List_Ofoldl(_1674176, _1674176, c_Groups_Oplus__class_Oplus(_1674176), c_Groups_Ozero__class_Ozero(_1674176)))], (44826 ^ _779530) ^ [_1674271, _1674273] : [-(c_List_Oconcat(_1674271, _1674273) = hAPP(c_List_Ofoldl(tc_List_Olist(_1674271), tc_List_Olist(_1674271), c_List_Oappend(_1674271), c_List_Olist_ONil(_1674271)), _1674273))], (44828 ^ _779530) ^ [_1674315, _1674317, _1674319] : [class_Groups_Omonoid__add(_1674315), -(hAPP(c_List_Ofoldl(_1674315, _1674315, c_Groups_Oplus__class_Oplus(_1674315), _1674317), _1674319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1674315), _1674317), c_List_Ofoldr(_1674315, _1674315, c_Groups_Oplus__class_Oplus(_1674315), _1674319, c_Groups_Ozero__class_Ozero(_1674315))))], (44834 ^ _779530) ^ [_1674448, _1674450] : [class_Groups_Omonoid__add(_1674448), -(hAPP(c_List_Ofoldl(_1674448, _1674448, c_Groups_Oplus__class_Oplus(_1674448), c_Groups_Ozero__class_Ozero(_1674448)), _1674450) = c_List_Ofoldr(_1674448, _1674448, c_Groups_Oplus__class_Oplus(_1674448), _1674450, c_Groups_Ozero__class_Ozero(_1674448)))], (44840 ^ _779530) ^ [_1674582, _1674584] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674582), _1674584) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44843 ^ _779530 : [(44844 ^ _779530) ^ [] : [-(_1674582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44846 ^ _779530) ^ [_1674696] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1674696), hAPP(c_List_Oset(tc_Nat_Onat), _1674584))), -(_1674696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (44852 ^ _779530) ^ [_1674793, _1674795] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674793), _1674795) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1674793 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44858 ^ _779530 : [(44859 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44857 ^ [_1674793, _1674795]), hAPP(c_List_Oset(tc_Nat_Onat), _1674795))))], (44861 ^ _779530) ^ [] : [44857 ^ [_1674793, _1674795] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44865 ^ _779530) ^ [_1675031, _1675033, _1675035] : [hBOOL(hAPP(hAPP(c_member(_1675031), _1675033), hAPP(c_List_Oset(_1675031), _1675035))), -(c_List_Oremdups(_1675031, hAPP(hAPP(c_List_Olist_OCons(_1675031), _1675033), _1675035)) = c_List_Oremdups(_1675031, _1675035))], (44871 ^ _779530) ^ [_1675156, _1675158, _1675160] : [-(hBOOL(hAPP(hAPP(c_member(_1675156), _1675158), hAPP(c_List_Oset(_1675156), _1675160)))), -(c_List_Oremdups(_1675156, hAPP(hAPP(c_List_Olist_OCons(_1675156), _1675158), _1675160)) = hAPP(hAPP(c_List_Olist_OCons(_1675156), _1675158), c_List_Oremdups(_1675156, _1675160)))], (44877 ^ _779530) ^ [_1675230, _1675232] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675230)), c_List_Oremdups(_1675230, _1675232)) = hAPP(c_Finite__Set_Ocard(_1675230), hAPP(c_List_Oset(_1675230), _1675232)))], (44879 ^ _779530) ^ [_1675275, _1675277] : [class_Complete__Lattice_Ocomplete__lattice(_1675275), -(c_Complete__Lattice_OSup__class_OSup(_1675275, hAPP(c_List_Oset(_1675275), _1675277)) = hAPP(c_List_Ofoldl(_1675275, _1675275, c_Lattices_Osemilattice__sup__class_Osup(_1675275), c_Orderings_Obot__class_Obot(_1675275)), _1675277))], (44885 ^ _779530) ^ [_1675390, _1675392, _1675394] : [class_Lattices_Olattice(_1675390), -(c_Big__Operators_Olattice__class_OSup__fin(_1675390, hAPP(c_List_Oset(_1675390), hAPP(hAPP(c_List_Olist_OCons(_1675390), _1675392), _1675394))) = hAPP(c_List_Ofoldl(_1675390, _1675390, c_Lattices_Osemilattice__sup__class_Osup(_1675390), _1675392), _1675394))], (44891 ^ _779530) ^ [_1675519, _1675521, _1675523] : [class_Lattices_Olattice(_1675519), -(c_Big__Operators_Olattice__class_OInf__fin(_1675519, hAPP(c_List_Oset(_1675519), hAPP(hAPP(c_List_Olist_OCons(_1675519), _1675521), _1675523))) = hAPP(c_List_Ofoldl(_1675519, _1675519, c_Lattices_Osemilattice__inf__class_Oinf(_1675519), _1675521), _1675523))], (44897 ^ _779530) ^ [_1675648, _1675650, _1675652] : [class_Orderings_Olinorder(_1675648), -(c_Big__Operators_Olinorder__class_OMin(_1675648, hAPP(c_List_Oset(_1675648), hAPP(hAPP(c_List_Olist_OCons(_1675648), _1675650), _1675652))) = hAPP(c_List_Ofoldl(_1675648, _1675648, c_Orderings_Oord__class_Omin(_1675648), _1675650), _1675652))], (44903 ^ _779530) ^ [_1675777, _1675779, _1675781] : [class_Orderings_Olinorder(_1675777), -(c_Big__Operators_Olinorder__class_OMax(_1675777, hAPP(c_List_Oset(_1675777), hAPP(hAPP(c_List_Olist_OCons(_1675777), _1675779), _1675781))) = hAPP(c_List_Ofoldl(_1675777, _1675777, c_Orderings_Oord__class_Omax(_1675777), _1675779), _1675781))], (44909 ^ _779530) ^ [_1675906, _1675908, _1675910] : [class_Orderings_Olinorder(_1675906), -(c_Big__Operators_Olattice_OInf__fin(_1675906, c_Orderings_Oord__class_Omin(_1675906), hAPP(c_List_Oset(_1675906), hAPP(hAPP(c_List_Olist_OCons(_1675906), _1675908), _1675910))) = hAPP(c_List_Ofoldl(_1675906, _1675906, c_Orderings_Oord__class_Omin(_1675906), _1675908), _1675910))], (44915 ^ _779530) ^ [_1676041, _1676043, _1676045] : [class_Orderings_Olinorder(_1676041), -(c_Big__Operators_Olattice_OSup__fin(_1676041, c_Orderings_Oord__class_Omax(_1676041), hAPP(c_List_Oset(_1676041), hAPP(hAPP(c_List_Olist_OCons(_1676041), _1676043), _1676045))) = hAPP(c_List_Ofoldl(_1676041, _1676041, c_Orderings_Oord__class_Omax(_1676041), _1676043), _1676045))], (44921 ^ _779530) ^ [_1676176, _1676178, _1676180, _1676182] : [class_Complete__Lattice_Ocomplete__lattice(_1676176), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1676178, _1676176), hAPP(c_List_Oset(_1676178), _1676180)), _1676182) = hAPP(c_List_Ofoldl(_1676176, _1676178, hAPP(c_COMBC(_1676178, _1676176, _1676176), hAPP(hAPP(c_COMBB(_1676176, tc_fun(_1676176, _1676176), _1676178), c_Lattices_Osemilattice__sup__class_Osup(_1676176)), _1676182)), c_Orderings_Obot__class_Obot(_1676176)), _1676180))], (44927 ^ _779530) ^ [_1676347, _1676349, _1676351, _1676353, _1676355] : [-(c_Map_Omap__upds(_1676347, _1676349, _1676351, _1676353, _1676355) = hAPP(c_List_Ofoldl(tc_fun(_1676347, tc_Option_Ooption(_1676349)), tc_prod(_1676347, _1676349), hAPP(hAPP(c_COMBB(tc_fun(_1676347, tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349)))), tc_fun(tc_prod(_1676347, _1676349), tc_fun(_1676347, tc_Option_Ooption(_1676349))), tc_fun(_1676347, tc_Option_Ooption(_1676349))), c_Product__Type_Oprod_Oprod__case(_1676347, _1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349)))), hAPP(hAPP(c_COMBC(tc_fun(_1676347, tc_Option_Ooption(_1676349)), tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676347, tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349))))), hAPP(hAPP(c_COMBB(tc_fun(_1676347, tc_fun(tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349))))), tc_fun(tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676347, tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349))))), tc_fun(_1676347, tc_Option_Ooption(_1676349))), c_COMBC(_1676347, tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349))))), hAPP(hAPP(c_COMBB(tc_fun(_1676347, tc_fun(tc_Option_Ooption(_1676349), tc_fun(_1676347, tc_Option_Ooption(_1676349)))), tc_fun(_1676347, tc_fun(tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349))))), tc_fun(_1676347, tc_Option_Ooption(_1676349))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1676349), tc_fun(_1676347, tc_Option_Ooption(_1676349))), tc_fun(tc_fun(_1676349, tc_Option_Ooption(_1676349)), tc_fun(_1676349, tc_fun(_1676347, tc_Option_Ooption(_1676349)))), _1676347), c_COMBB(tc_Option_Ooption(_1676349), tc_fun(_1676347, tc_Option_Ooption(_1676349)), _1676349))), c_Fun_Ofun__upd(_1676347, tc_Option_Ooption(_1676349))))), c_Option_Ooption_OSome(_1676349))), _1676351), hAPP(hAPP(c_List_Ozip(_1676347, _1676349), _1676353), _1676355)))], (44929 ^ _779530) ^ [_1676654, _1676656] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1676654), hAPP(c_List_Oset(tc_Nat_Onat), _1676656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1676654), 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)), _1676656))))], (44935 ^ _779530) ^ [_1676759, _1676761, _1676763] : [-(_1676759 = c_List_Olist_ONil(_1676761)), -(hAPP(c_List_Ohd(_1676761), hAPP(c_List_Orotate(_1676761, _1676763), _1676759)) = hAPP(hAPP(c_List_Onth(_1676761), _1676759), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1676763, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676761)), _1676759))))], (44941 ^ _779530) ^ [_1676829, _1676831, _1676833] : [-(hAPP(c_List_Orotate(_1676829, _1676831), _1676833) = hAPP(hAPP(c_List_Oappend(_1676829), hAPP(hAPP(c_List_Odrop(_1676829), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1676831, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676829)), _1676833))), _1676833)), hAPP(hAPP(c_List_Otake(_1676829), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1676831, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676829)), _1676833))), _1676833)))], (44943 ^ _779530) ^ [_1676908, _1676910, _1676912] : [-(hAPP(c_List_Orotate1(_1676908), hAPP(c_List_Orotate(_1676908, _1676910), _1676912)) = hAPP(c_List_Orotate(_1676908, _1676910), hAPP(c_List_Orotate1(_1676908), _1676912)))], (44945 ^ _779530) ^ [_1676975, _1676977, _1676979] : [hAPP(c_List_Orotate(_1676975, _1676977), _1676979) = c_List_Olist_ONil(_1676975), -(_1676979 = c_List_Olist_ONil(_1676975))], (44951 ^ _779530) ^ [_1677070, _1677072, _1677074] : [_1677074 = c_List_Olist_ONil(_1677070), -(hAPP(c_List_Orotate(_1677070, _1677072), _1677074) = c_List_Olist_ONil(_1677070))], (44957 ^ _779530) ^ [_1677171, _1677173, _1677175] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677171)), hAPP(c_List_Orotate(_1677171, _1677173), _1677175)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677171)), _1677175))], (44959 ^ _779530) ^ [_1677218, _1677220, _1677222, _1677224] : [-(hAPP(c_List_Orotate(_1677218, _1677220), hAPP(c_List_Orotate(_1677218, _1677222), _1677224)) = hAPP(c_List_Orotate(_1677218, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1677220), _1677222)), _1677224))], (44961 ^ _779530) ^ [_1677289, _1677291, _1677293] : [hBOOL(hAPP(c_List_Odistinct(_1677289), hAPP(c_List_Orotate(_1677289, _1677291), _1677293))), -(hBOOL(hAPP(c_List_Odistinct(_1677289), _1677293)))], (44967 ^ _779530) ^ [_1677392, _1677394, _1677396] : [hBOOL(hAPP(c_List_Odistinct(_1677392), _1677396)), -(hBOOL(hAPP(c_List_Odistinct(_1677392), hAPP(c_List_Orotate(_1677392, _1677394), _1677396))))], (44973 ^ _779530) ^ [_1677501, _1677503, _1677505] : [-(hAPP(c_List_Oset(_1677501), hAPP(c_List_Orotate(_1677501, _1677503), _1677505)) = hAPP(c_List_Oset(_1677501), _1677505))], (44975 ^ _779530) ^ [_1677544, _1677546, _1677548, _1677550, _1677552] : [-(hAPP(c_List_Orotate(_1677544, _1677546), hAPP(hAPP(c_List_Omap(_1677548, _1677544), _1677550), _1677552)) = hAPP(hAPP(c_List_Omap(_1677548, _1677544), _1677550), hAPP(c_List_Orotate(_1677548, _1677546), _1677552)))], (44977 ^ _779530) ^ [_1677605, _1677607, _1677609] : [-(hAPP(c_List_Orotate(_1677605, _1677607), _1677609) = hAPP(c_List_Orotate(_1677605, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1677607, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677605)), _1677609))), _1677609))], (44979 ^ _779530) ^ [_1677655, _1677657, _1677659] : [-(hAPP(c_List_Orotate(_1677655, hAPP(c_Nat_OSuc, _1677657)), _1677659) = hAPP(c_List_Orotate1(_1677655), hAPP(c_List_Orotate(_1677655, _1677657), _1677659)))], (44981 ^ _779530) ^ [_1677702] : [-(c_List_Orotate(_1677702, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1677702)))], (44983 ^ _779530) ^ [_1677732, _1677734, _1677736] : [-(c_List_Orotate(_1677732, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1677734), _1677736)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1677732), tc_List_Olist(_1677732), tc_List_Olist(_1677732), c_List_Orotate(_1677732, _1677734)), c_List_Orotate(_1677732, _1677736)))], (44985 ^ _779530) ^ [_1677788, _1677790, _1677792] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1677788, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677790)), _1677792)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1677790, _1677788), _1677792) = _1677792)], (44991 ^ _779530) ^ [_1677901, _1677903, _1677905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677901)), _1677903)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1677901, _1677905), _1677903) = _1677903)], (44997 ^ _779530) ^ [_1678016, _1678018, _1678020, _1678022] : [44998 ^ _779530 : [(44999 ^ _779530) ^ [_1678113, _1678115] : [_1678016 = hAPP(hAPP(c_List_Olist_OCons(_1678018), _1678115), _1678113)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1678018), tc_List_Olist(_1678018))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678018), tc_List_Olist(_1678018)), _1678020), hAPP(hAPP(c_List_Oappend(_1678018), _1678020), _1678016))), c_List_Olexord(_1678018, _1678022))))], (45003 ^ _779530) ^ [_1678212, _1678214, _1678216] : [class_Orderings_Olinorder(_1678212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1678212), _1678214)), -(c_List_Olinorder__class_Osorted__list__of__set(_1678212, hAPP(hAPP(c_Set_Oinsert(_1678212), _1678216), _1678214)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678212, _1678212, c_COMBI(_1678212)), _1678216), c_List_Olinorder__class_Osorted__list__of__set(_1678212, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1678212, tc_HOL_Obool)), _1678214), hAPP(hAPP(c_Set_Oinsert(_1678212), _1678216), c_Orderings_Obot__class_Obot(tc_fun(_1678212, tc_HOL_Obool)))))))], (45013 ^ _779530) ^ [_1678451, _1678453, _1678455, _1678457, _1678459] : [class_Orderings_Olinorder(_1678451), -(hAPP(c_List_Oset(_1678453), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678453, _1678451, _1678455), _1678457), _1678459)) = hAPP(hAPP(c_Set_Oinsert(_1678453), _1678457), hAPP(c_List_Oset(_1678453), _1678459)))], (45019 ^ _779530) ^ [_1678588, _1678590, _1678592, _1678594] : [class_Orderings_Olinorder(_1678588), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678590, _1678588, _1678592), _1678594), c_List_Olist_ONil(_1678590)) = hAPP(hAPP(c_List_Olist_OCons(_1678590), _1678594), c_List_Olist_ONil(_1678590)))], (45025 ^ _779530) ^ [_1678711, _1678713, _1678715, _1678717, _1678719, _1678721] : [class_Orderings_Olinorder(_1678711), 45028 ^ _779530 : [(45029 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1678711), hAPP(_1678713, _1678715)), hAPP(_1678713, _1678717))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678719, _1678711, _1678713), _1678715), hAPP(hAPP(c_List_Olist_OCons(_1678719), _1678717), _1678721)) = hAPP(hAPP(c_List_Olist_OCons(_1678719), _1678715), hAPP(hAPP(c_List_Olist_OCons(_1678719), _1678717), _1678721)))], (45035 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1678711), hAPP(_1678713, _1678715)), hAPP(_1678713, _1678717)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678719, _1678711, _1678713), _1678715), hAPP(hAPP(c_List_Olist_OCons(_1678719), _1678717), _1678721)) = hAPP(hAPP(c_List_Olist_OCons(_1678719), _1678717), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678719, _1678711, _1678713), _1678715), _1678721)))]]], (45041 ^ _779530) ^ [_1679093, _1679095, _1679097, _1679099, _1679101, _1679103] : [class_Orderings_Olinorder(_1679093), -(hBOOL(hAPP(_1679095, _1679097))), -(hAPP(c_List_Ofilter(_1679099, _1679095), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679099, _1679093, _1679101), _1679097), _1679103)) = hAPP(c_List_Ofilter(_1679099, _1679095), _1679103))], (45051 ^ _779530) ^ [_1679239, _1679241, _1679243] : [class_Orderings_Olinorder(_1679239), -(c_List_Oremove1(_1679239, _1679241, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679239, _1679239, c_COMBI(_1679239)), _1679241), _1679243)) = _1679243)], (45057 ^ _779530) ^ [_1679348, _1679350, _1679352, _1679354, _1679356, _1679358] : [class_Orderings_Olinorder(_1679348), -(hAPP(_1679350, _1679352) = hAPP(_1679350, _1679354)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679356, _1679348, _1679350), _1679354), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679356, _1679348, _1679350), _1679352), _1679358)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679356, _1679348, _1679350), _1679352), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679356, _1679348, _1679350), _1679354), _1679358)))], (45067 ^ _779530) ^ [_1679538, _1679540, _1679542, _1679544] : [class_Orderings_Olinorder(_1679538), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679538, _1679538, c_COMBI(_1679538)), _1679540), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679538, _1679538, c_COMBI(_1679538)), _1679542), _1679544)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679538, _1679538, c_COMBI(_1679538)), _1679542), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679538, _1679538, c_COMBI(_1679538)), _1679540), _1679544)))], (45073 ^ _779530) ^ [_1679713, _1679715, _1679717, _1679719, _1679721] : [class_Orderings_Olinorder(_1679713), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679715)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679715, _1679713, _1679717), _1679719), _1679721)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679715)), _1679721)))], (45079 ^ _779530) ^ [_1679848, _1679850, _1679852, _1679854, _1679856] : [class_Orderings_Olinorder(_1679848), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679850, _1679848, _1679852), _1679854), _1679856) = c_List_Olist_ONil(_1679850)], (45085 ^ _779530) ^ [_1679954, _1679956, _1679958, _1679960, _1679962] : [class_Orderings_Olinorder(_1679954), 45088 ^ _779530 : [(45089 ^ _779530) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1679956), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679956, _1679954, _1679958), _1679960), _1679962))), 45092 ^ _779530 : [(45093 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679956), _1679960), hAPP(c_List_Oset(_1679956), _1679962)))], (45095 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1679956), _1679962)))]]], (45097 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1679956), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1679956, _1679954, _1679958), _1679960), _1679962)))), -(hBOOL(hAPP(hAPP(c_member(_1679956), _1679960), hAPP(c_List_Oset(_1679956), _1679962)))), hBOOL(hAPP(c_List_Odistinct(_1679956), _1679962))]]], (45107 ^ _779530) ^ [_1680356, _1680358, _1680360, _1680362, _1680364] : [class_Orderings_Olinorder(_1680356), hBOOL(hAPP(hAPP(c_member(_1680358), _1680360), hAPP(c_List_Oset(_1680358), _1680362))), c_List_Olinorder__class_Osorted(_1680356, hAPP(hAPP(c_List_Omap(_1680358, _1680356), _1680364), _1680362)), hAPP(c_List_Ohd(_1680358), hAPP(c_List_Ofilter(_1680358, hAPP(hAPP(c_COMBB(_1680356, tc_HOL_Obool, _1680358), hAPP(c_fequal, hAPP(_1680364, _1680360))), _1680364)), _1680362)) = _1680360, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680358, _1680356, _1680364), _1680360), c_List_Oremove1(_1680358, _1680360, _1680362)) = _1680362)], (45125 ^ _779530) ^ [_1680735, _1680737, _1680739, _1680741, _1680743] : [class_Orderings_Olinorder(_1680735), -(hBOOL(hAPP(hAPP(c_member(_1680735), hAPP(_1680737, _1680739)), hAPP(c_Set_Oimage(_1680741, _1680735, _1680737), hAPP(c_List_Oset(_1680741), _1680743))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1680741, _1680735, _1680737, _1680739, _1680743) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1680741, _1680735, _1680737), _1680739), _1680743))], (45135 ^ _779530) ^ [_1680907] : [class_Orderings_Olinorder(_1680907), -(c_List_Olinorder__class_Osorted(_1680907, c_List_Olist_ONil(_1680907)))], (45141 ^ _779530) ^ [_1680984, _1680986] : [class_Orderings_Olinorder(_1680984), -(c_List_Olinorder__class_Osorted(_1680984, hAPP(hAPP(c_List_Olist_OCons(_1680984), _1680986), c_List_Olist_ONil(_1680984))))], (45147 ^ _779530) ^ [_1681079, _1681081, _1681083, _1681085, _1681087] : [class_Orderings_Olinorder(_1681079), 45150 ^ _779530 : [(45151 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1681079, hAPP(hAPP(c_List_Omap(_1681081, _1681079), _1681083), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681081, _1681079, _1681083), _1681085), _1681087))), -(c_List_Olinorder__class_Osorted(_1681079, hAPP(hAPP(c_List_Omap(_1681081, _1681079), _1681083), _1681087)))], (45157 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1681079, hAPP(hAPP(c_List_Omap(_1681081, _1681079), _1681083), _1681087)), -(c_List_Olinorder__class_Osorted(_1681079, hAPP(hAPP(c_List_Omap(_1681081, _1681079), _1681083), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681081, _1681079, _1681083), _1681085), _1681087))))]]], (45163 ^ _779530) ^ [_1681386, _1681388, _1681390] : [class_Orderings_Olinorder(_1681386), 45166 ^ _779530 : [(45167 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1681386, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681386, _1681386, c_COMBI(_1681386)), _1681388), _1681390)), -(c_List_Olinorder__class_Osorted(_1681386, _1681390))], (45173 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1681386, _1681390), -(c_List_Olinorder__class_Osorted(_1681386, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681386, _1681386, c_COMBI(_1681386)), _1681388), _1681390)))]]], (45179 ^ _779530) ^ [_1681633, _1681635] : [class_Orderings_Olinorder(_1681633), c_List_Olinorder__class_Osorted(_1681633, _1681635), -(c_List_Olinorder__class_Osorted(_1681633, c_List_Oremdups(_1681633, _1681635)))], (45189 ^ _779530) ^ [_1681766, _1681768, _1681770, _1681772, _1681774] : [class_Orderings_Olinorder(_1681766), -(c_List_Olinorder__class_Osorted(_1681766, hAPP(hAPP(c_List_Omap(_1681768, _1681766), _1681770), hAPP(c_List_Ofilter(_1681768, hAPP(hAPP(c_COMBC(_1681768, _1681766, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1681766, tc_fun(_1681766, tc_HOL_Obool), _1681768), c_fequal), _1681770)), hAPP(_1681772, _1681774))), _1681774))))], (45195 ^ _779530) ^ [_1681929] : [class_Orderings_Olinorder(_1681929), -(c_List_Olinorder__class_Osorted(_1681929, c_List_Olist_ONil(_1681929)))], (45201 ^ _779530) ^ [_1682006, _1682008] : [class_Orderings_Olinorder(_1682006), -(_1682008 = c_List_Olist_ONil(_1682006)), c_List_Olinorder__class_Osorted(_1682006, _1682008), -(c_List_Olinorder__class_Osorted(_1682006, c_List_Obutlast(_1682006, _1682008)))], (45215 ^ _779530) ^ [_1682198, _1682200] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1682198, _1682200)))], (45217 ^ _779530) ^ [_1682226, _1682228] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1682226, _1682228)))], (45219 ^ _779530) ^ [_1682254, _1682256, _1682258] : [class_Orderings_Olinorder(_1682254), c_List_Olinorder__class_Osorted(_1682254, _1682256), -(c_List_Olinorder__class_Osorted(_1682254, c_List_Olinorder__class_Oinsort__insert__key(_1682254, _1682254, c_COMBI(_1682254), _1682258, _1682256)))], (45229 ^ _779530) ^ [_1682401, _1682403, _1682405] : [class_Orderings_Olinorder(_1682401), c_List_Olinorder__class_Osorted(_1682401, _1682403), -(c_List_Olinorder__class_Osorted(_1682401, c_List_Oremove1(_1682401, _1682405, _1682403)))], (45239 ^ _779530) ^ [_1682540, _1682542, _1682544] : [class_Orderings_Olinorder(_1682540), -(c_List_Olinorder__class_Osorted(_1682540, hAPP(c_List_Ofilter(_1682540, hAPP(hAPP(c_COMBC(_1682540, _1682540, tc_HOL_Obool), c_fequal), hAPP(_1682542, _1682544))), _1682544)))], (45245 ^ _779530) ^ [_1682655, _1682657, _1682659, _1682661, _1682663] : [class_Orderings_Olinorder(_1682655), hBOOL(hAPP(c_List_Odistinct(_1682657), _1682659)), -(hBOOL(hAPP(c_List_Odistinct(_1682657), c_List_Olinorder__class_Oinsort__insert__key(_1682657, _1682655, _1682661, _1682663, _1682659))))], (45255 ^ _779530) ^ [_1682822, _1682824, _1682826] : [class_Orderings_Olinorder(_1682822), c_List_Olinorder__class_Osorted(_1682822, _1682824), -(c_List_Olinorder__class_Osorted(_1682822, hAPP(hAPP(c_List_Otake(_1682822), _1682826), _1682824)))], (45265 ^ _779530) ^ [_1682969, _1682971, _1682973, _1682975] : [class_Orderings_Olinorder(_1682969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1682969), _1682971), _1682973)), c_List_Olinorder__class_Osorted(_1682969, hAPP(hAPP(c_List_Olist_OCons(_1682969), _1682973), _1682975)), -(c_List_Olinorder__class_Osorted(_1682969, hAPP(hAPP(c_List_Olist_OCons(_1682969), _1682971), hAPP(hAPP(c_List_Olist_OCons(_1682969), _1682973), _1682975))))], (45279 ^ _779530) ^ [_1683222, _1683224, _1683226, _1683228] : [class_Orderings_Olinorder(_1683222), 45282 ^ _779530 : [(45283 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1683222, hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683224), hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683226), _1683228))), 45286 ^ _779530 : [(45287 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683222), _1683224), _1683226)))], (45289 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683222, hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683226), _1683228)))]]], (45291 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683222, hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683224), hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683226), _1683228)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683222), _1683224), _1683226)), c_List_Olinorder__class_Osorted(_1683222, hAPP(hAPP(c_List_Olist_OCons(_1683222), _1683226), _1683228))]]], (45301 ^ _779530) ^ [_1683608, _1683610, _1683612] : [class_Orderings_Olinorder(_1683608), c_List_Olinorder__class_Osorted(_1683608, _1683610), hBOOL(hAPP(c_List_Odistinct(_1683608), _1683610)), c_List_Olinorder__class_Osorted(_1683608, _1683612), hBOOL(hAPP(c_List_Odistinct(_1683608), _1683612)), hAPP(c_List_Oset(_1683608), _1683610) = hAPP(c_List_Oset(_1683608), _1683612), -(_1683610 = _1683612)], (45327 ^ _779530) ^ [_1683991, _1683993] : [class_Orderings_Olinorder(_1683991), c_List_Olinorder__class_Osorted(_1683991, _1683993), -(c_List_Olinorder__class_Osorted(_1683991, hAPP(c_List_Otl(_1683991), _1683993)))], (45337 ^ _779530) ^ [_1684128, _1684130, _1684132, _1684134, _1684136] : [class_Orderings_Olinorder(_1684128), c_List_Olinorder__class_Osorted(_1684128, hAPP(hAPP(c_List_Omap(_1684130, _1684128), _1684132), _1684134)), -(c_List_Olinorder__class_Osorted(_1684128, hAPP(hAPP(c_List_Omap(_1684130, _1684128), _1684132), hAPP(c_List_Ofilter(_1684130, _1684136), _1684134))))], (45347 ^ _779530) ^ [_1684315, _1684317, _1684319, _1684321, _1684323] : [class_Orderings_Olinorder(_1684315), c_List_Olinorder__class_Osorted(_1684315, hAPP(hAPP(c_List_Omap(_1684317, _1684315), _1684319), _1684321)), -(c_List_Olinorder__class_Osorted(_1684315, hAPP(hAPP(c_List_Omap(_1684317, _1684315), _1684319), c_List_Olinorder__class_Oinsort__insert__key(_1684317, _1684315, _1684319, _1684323, _1684321))))], (45357 ^ _779530) ^ [_1684502, _1684504, _1684506, _1684508, _1684510] : [class_Orderings_Olinorder(_1684502), c_List_Olinorder__class_Osorted(_1684502, hAPP(hAPP(c_List_Omap(_1684504, _1684502), _1684506), _1684508)), -(c_List_Olinorder__class_Osorted(_1684502, hAPP(hAPP(c_List_Omap(_1684504, _1684502), _1684506), c_List_Oremove1(_1684504, _1684510, _1684508))))], (45367 ^ _779530) ^ [_1684685, _1684687, _1684689] : [class_Orderings_Olinorder(_1684685), c_List_Olinorder__class_Osorted(_1684685, _1684687), -(c_List_Olinorder__class_Osorted(_1684685, hAPP(hAPP(c_List_Odrop(_1684685), _1684689), _1684687)))], (45377 ^ _779530) ^ [_1684832, _1684834, _1684836] : [class_Orderings_Olinorder(_1684832), 45380 ^ _779530 : [(45381 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1684832, hAPP(hAPP(c_List_Olist_OCons(_1684832), _1684834), _1684836)), 45384 ^ _779530 : [(45385 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1684832, _1684836))], (45387 ^ _779530) ^ [_1685018] : [hBOOL(hAPP(hAPP(c_member(_1684832), _1685018), hAPP(c_List_Oset(_1684832), _1684836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1684832), _1684834), _1685018)))]]], (45393 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1684832, hAPP(hAPP(c_List_Olist_OCons(_1684832), _1684834), _1684836))), c_List_Olinorder__class_Osorted(_1684832, _1684836), 45399 ^ _779530 : [(45400 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684832), 45398 ^ [_1684832, _1684834, _1684836]), hAPP(c_List_Oset(_1684832), _1684836))))], (45402 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1684832), _1684834), 45398 ^ [_1684832, _1684834, _1684836]))]]]]], (45406 ^ _779530) ^ [_1685357, _1685359, _1685361] : [class_Orderings_Olinorder(_1685357), 45409 ^ _779530 : [(45410 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1685357, hAPP(hAPP(c_List_Oappend(_1685357), _1685359), _1685361)), 45413 ^ _779530 : [(45414 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1685357, _1685359))], (45416 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1685357, _1685361))], (45418 ^ _779530) ^ [_1685593] : [hBOOL(hAPP(hAPP(c_member(_1685357), _1685593), hAPP(c_List_Oset(_1685357), _1685359))), 45421 ^ _779530 : [(45422 ^ _779530) ^ [_1685703] : [hBOOL(hAPP(hAPP(c_member(_1685357), _1685703), hAPP(c_List_Oset(_1685357), _1685361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1685357), _1685593), _1685703)))]]]]], (45428 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1685357, hAPP(hAPP(c_List_Oappend(_1685357), _1685359), _1685361))), c_List_Olinorder__class_Osorted(_1685357, _1685359), c_List_Olinorder__class_Osorted(_1685357, _1685361), 45438 ^ _779530 : [(45439 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685357), 45437 ^ [_1685357, _1685359, _1685361]), hAPP(c_List_Oset(_1685357), _1685359))))], (45442 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1685357), 45440 ^ [_1685357, _1685359, _1685361]), hAPP(c_List_Oset(_1685357), _1685361))))], (45444 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1685357), 45437 ^ [_1685357, _1685359, _1685361]), 45440 ^ [_1685357, _1685359, _1685361]))]]]]], (45448 ^ _779530) ^ [_1686205, _1686207, _1686209, _1686211, _1686213, _1686215] : [class_Orderings_Olinorder(_1686205), c_List_Olinorder__class_Osorted(_1686205, hAPP(hAPP(c_List_Omap(_1686207, _1686205), _1686209), _1686211)), hBOOL(hAPP(_1686213, _1686215)), -(hAPP(c_List_Ofilter(_1686207, _1686213), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1686207, _1686205, _1686209), _1686215), _1686211)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1686207, _1686205, _1686209), _1686215), hAPP(c_List_Ofilter(_1686207, _1686213), _1686211)))], (45462 ^ _779530) ^ [_1686494, _1686496, _1686498] : [class_Orderings_Olinorder(_1686494), 45465 ^ _779530 : [(45466 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1686494, hAPP(hAPP(c_List_Olist_OCons(_1686494), _1686496), _1686498)), 45469 ^ _779530 : [(45476 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1686494, _1686498))], (45470 ^ _779530) ^ [_1686662] : [hBOOL(hAPP(hAPP(c_member(_1686494), _1686662), hAPP(c_List_Oset(_1686494), _1686498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686494), _1686496), _1686662)))]]], (45478 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1686494, hAPP(hAPP(c_List_Olist_OCons(_1686494), _1686496), _1686498))), 45482 ^ _779530 : [(45483 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686494), 45481 ^ [_1686494, _1686496, _1686498]), hAPP(c_List_Oset(_1686494), _1686498))))], (45485 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686494), _1686496), 45481 ^ [_1686494, _1686496, _1686498]))]], c_List_Olinorder__class_Osorted(_1686494, _1686498)]]], (45491 ^ _779530) ^ [_1687020, _1687022, _1687024] : [class_Orderings_Olinorder(_1687020), hBOOL(hAPP(hAPP(c_member(_1687020), _1687022), hAPP(c_List_Oset(_1687020), _1687024))), -(c_List_Olinorder__class_Oinsort__insert__key(_1687020, _1687020, c_COMBI(_1687020), _1687022, _1687024) = _1687024)], (45501 ^ _779530) ^ [_1687191, _1687193, _1687195] : [class_Orderings_Olinorder(_1687191), -(hAPP(c_List_Oset(_1687191), c_List_Olinorder__class_Oinsort__insert__key(_1687191, _1687191, c_COMBI(_1687191), _1687193, _1687195)) = hAPP(hAPP(c_Set_Oinsert(_1687191), _1687193), hAPP(c_List_Oset(_1687191), _1687195)))], (45507 ^ _779530) ^ [_1687320, _1687322] : [class_Orderings_Olinorder(_1687320), hBOOL(hAPP(c_Finite__Set_Ofinite(_1687320), _1687322)), 45514 ^ _779530 : [(45515 ^ _779530) ^ [] : [-(hAPP(c_List_Oset(_1687320), c_List_Olinorder__class_Osorted__list__of__set(_1687320, _1687322)) = _1687322)], (45517 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1687320, c_List_Olinorder__class_Osorted__list__of__set(_1687320, _1687322)))], (45519 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1687320), c_List_Olinorder__class_Osorted__list__of__set(_1687320, _1687322))))]]], (45521 ^ _779530) ^ [_1687541, _1687543, _1687545] : [class_Orderings_Olinorder(_1687541), hBOOL(hAPP(hAPP(c_member(_1687541), _1687543), hAPP(c_List_Oset(_1687541), _1687545))), c_List_Olinorder__class_Osorted(_1687541, _1687545), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687541, _1687541, c_COMBI(_1687541)), _1687543), c_List_Oremove1(_1687541, _1687543, _1687545)) = _1687545)], (45535 ^ _779530) ^ [_1687782, _1687784, _1687786, _1687788] : [class_Orderings_Olinorder(_1687782), c_List_Olinorder__class_Osorted(_1687782, _1687784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1687786), _1687788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687782)), _1687784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1687782), hAPP(hAPP(c_List_Onth(_1687782), _1687784), _1687786)), hAPP(hAPP(c_List_Onth(_1687782), _1687784), _1687788))))], (45553 ^ _779530) ^ [_1688109, _1688111] : [class_Orderings_Olinorder(_1688109), 45556 ^ _779530 : [(45571 ^ _779530) ^ [] : [45573 ^ _779530 : [(45574 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45572 ^ [_1688109, _1688111]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688109)), _1688111))))], (45577 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45575 ^ [_1688109, _1688111]), 45572 ^ [_1688109, _1688111])))], (45579 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688109), hAPP(hAPP(c_List_Onth(_1688109), _1688111), 45575 ^ [_1688109, _1688111])), hAPP(hAPP(c_List_Onth(_1688109), _1688111), 45572 ^ [_1688109, _1688111])))]], -(c_List_Olinorder__class_Osorted(_1688109, _1688111))], (45557 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1688109, _1688111), 45560 ^ _779530 : [(45561 ^ _779530) ^ [_1688280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688280), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688109)), _1688111))), 45564 ^ _779530 : [(45565 ^ _779530) ^ [_1688397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1688397), _1688280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688109), hAPP(hAPP(c_List_Onth(_1688109), _1688111), _1688397)), hAPP(hAPP(c_List_Onth(_1688109), _1688111), _1688280))))]]]]]]], (45583 ^ _779530) ^ [_1688833, _1688835, _1688837, _1688839, _1688841] : [class_Orderings_Olinorder(_1688833), c_Fun_Oinj__on(_1688835, _1688833, _1688837, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1688835, tc_HOL_Obool)), hAPP(c_List_Oset(_1688835), _1688839)), hAPP(c_List_Oset(_1688835), _1688841))), c_List_Olinorder__class_Osorted(_1688833, hAPP(hAPP(c_List_Omap(_1688835, _1688833), _1688837), _1688839)), hBOOL(hAPP(c_List_Odistinct(_1688833), hAPP(hAPP(c_List_Omap(_1688835, _1688833), _1688837), _1688839))), c_List_Olinorder__class_Osorted(_1688833, hAPP(hAPP(c_List_Omap(_1688835, _1688833), _1688837), _1688841)), hBOOL(hAPP(c_List_Odistinct(_1688833), hAPP(hAPP(c_List_Omap(_1688835, _1688833), _1688837), _1688841))), hAPP(c_List_Oset(_1688835), _1688839) = hAPP(c_List_Oset(_1688835), _1688841), -(_1688839 = _1688841)], (45613 ^ _779530) ^ [_1689416, _1689418, _1689420, _1689422, _1689424] : [class_Orderings_Olinorder(_1689416), hBOOL(hAPP(hAPP(c_member(_1689416), hAPP(_1689418, _1689420)), hAPP(c_Set_Oimage(_1689422, _1689416, _1689418), hAPP(c_List_Oset(_1689422), _1689424)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1689422, _1689416, _1689418, _1689420, _1689424) = _1689424)], (45623 ^ _779530) ^ [_1689611, _1689613, _1689615] : [class_Orderings_Olinorder(_1689611), -(hBOOL(hAPP(hAPP(c_member(_1689611), _1689613), hAPP(c_List_Oset(_1689611), _1689615)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1689611, _1689611, c_COMBI(_1689611), _1689613, _1689615) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1689611, _1689611, c_COMBI(_1689611)), _1689613), _1689615))], (45633 ^ _779530) ^ [_1689767, _1689769, _1689771] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1689767), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1689767))), _1689769))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689771), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1689767))), _1689769))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1689767), _1689767), hAPP(hAPP(c_COMBC(tc_List_Olist(_1689767), tc_Nat_Onat, _1689767), c_List_Onth(_1689767)), _1689771)), hAPP(c_List_Ofilter(tc_List_Olist(_1689767), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1689767)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689771)), c_Nat_Osize__class_Osize(tc_List_Olist(_1689767)))), c_List_Otranspose(_1689767, _1689769))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1689767)), _1689769), _1689771))], (45643 ^ _779530) ^ [_1690094, _1690096, _1690098, _1690100] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1690094), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1690094))), _1690096))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1690094))), c_List_Otranspose(_1690094, _1690096)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690100), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1690094))), hAPP(c_List_Ofilter(tc_List_Olist(_1690094), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1690094)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690098)), c_Nat_Osize__class_Osize(tc_List_Olist(_1690094)))), _1690096)))), -(hAPP(hAPP(c_List_Onth(_1690094), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1690094)), c_List_Otranspose(_1690094, _1690096)), _1690098)), _1690100) = hAPP(hAPP(c_List_Onth(_1690094), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1690094)), _1690096), _1690100)), _1690098))], (45657 ^ _779530) ^ [_1690517, _1690519] : [-(c_Fun_Oinj__on(tc_List_Olist(_1690517), tc_List_Olist(_1690517), c_List_Orev(_1690517), _1690519))], (45659 ^ _779530) ^ [_1690550, _1690552] : [-(hAPP(c_List_Orev(_1690550), c_List_Oconcat(_1690550, _1690552)) = c_List_Oconcat(_1690550, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1690550), tc_List_Olist(_1690550)), c_List_Orev(_1690550)), hAPP(c_List_Orev(tc_List_Olist(_1690550)), _1690552))))], (45661 ^ _779530) ^ [_1690608, _1690610, _1690612, _1690614] : [-(hAPP(c_List_Orev(_1690608), hAPP(hAPP(c_List_Omap(_1690610, _1690608), _1690612), _1690614)) = hAPP(hAPP(c_List_Omap(_1690610, _1690608), _1690612), hAPP(c_List_Orev(_1690610), _1690614)))], (45663 ^ _779530) ^ [_1690665, _1690667] : [-(hAPP(c_List_Oset(_1690665), hAPP(c_List_Orev(_1690665), _1690667)) = hAPP(c_List_Oset(_1690665), _1690667))], (45665 ^ _779530) ^ [_1690705, _1690707, _1690709, _1690711] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690705)), _1690707) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690709)), _1690711), -(hAPP(hAPP(c_List_Ozip(_1690705, _1690709), hAPP(c_List_Orev(_1690705), _1690707)), hAPP(c_List_Orev(_1690709), _1690711)) = hAPP(c_List_Orev(tc_prod(_1690705, _1690709)), hAPP(hAPP(c_List_Ozip(_1690705, _1690709), _1690707), _1690711)))], (45671 ^ _779530) ^ [_1690904, _1690906, _1690908] : [hAPP(hAPP(c_List_Olist_OCons(_1690904), _1690906), c_List_Olist_ONil(_1690904)) = hAPP(c_List_Orev(_1690904), _1690908), -(_1690908 = hAPP(hAPP(c_List_Olist_OCons(_1690904), _1690906), c_List_Olist_ONil(_1690904)))], (45677 ^ _779530) ^ [_1691029, _1691031, _1691033] : [_1691033 = hAPP(hAPP(c_List_Olist_OCons(_1691029), _1691031), c_List_Olist_ONil(_1691029)), -(hAPP(hAPP(c_List_Olist_OCons(_1691029), _1691031), c_List_Olist_ONil(_1691029)) = hAPP(c_List_Orev(_1691029), _1691033))], (45683 ^ _779530) ^ [_1691178, _1691180, _1691182] : [hAPP(c_List_Orev(_1691178), _1691180) = hAPP(hAPP(c_List_Olist_OCons(_1691178), _1691182), c_List_Olist_ONil(_1691178)), -(_1691180 = hAPP(hAPP(c_List_Olist_OCons(_1691178), _1691182), c_List_Olist_ONil(_1691178)))], (45689 ^ _779530) ^ [_1691303, _1691305, _1691307] : [_1691305 = hAPP(hAPP(c_List_Olist_OCons(_1691303), _1691307), c_List_Olist_ONil(_1691303)), -(hAPP(c_List_Orev(_1691303), _1691305) = hAPP(hAPP(c_List_Olist_OCons(_1691303), _1691307), c_List_Olist_ONil(_1691303)))], (45695 ^ _779530) ^ [_1691449, _1691451] : [hBOOL(hAPP(c_List_Odistinct(_1691449), hAPP(c_List_Orev(_1691449), _1691451))), -(hBOOL(hAPP(c_List_Odistinct(_1691449), _1691451)))], (45701 ^ _779530) ^ [_1691548, _1691550] : [hBOOL(hAPP(c_List_Odistinct(_1691548), _1691550)), -(hBOOL(hAPP(c_List_Odistinct(_1691548), hAPP(c_List_Orev(_1691548), _1691550))))], (45707 ^ _779530) ^ [_1691653, _1691655, _1691657] : [-(hAPP(c_List_Orev(_1691653), hAPP(c_List_Ofilter(_1691653, _1691655), _1691657)) = hAPP(c_List_Ofilter(_1691653, _1691655), hAPP(c_List_Orev(_1691653), _1691657)))], (45709 ^ _779530) ^ [_1691720, _1691722, _1691724] : [hAPP(c_List_Orev(_1691720), _1691722) = hAPP(c_List_Orev(_1691720), _1691724), -(_1691722 = _1691724)], (45715 ^ _779530) ^ [_1691815, _1691817, _1691819] : [_1691817 = _1691819, -(hAPP(c_List_Orev(_1691815), _1691817) = hAPP(c_List_Orev(_1691815), _1691819))], (45721 ^ _779530) ^ [_1691934, _1691936, _1691938] : [hAPP(c_List_Orev(_1691934), _1691936) = _1691938, -(_1691936 = hAPP(c_List_Orev(_1691934), _1691938))], (45727 ^ _779530) ^ [_1692029, _1692031, _1692033] : [_1692031 = hAPP(c_List_Orev(_1692029), _1692033), -(hAPP(c_List_Orev(_1692029), _1692031) = _1692033)], (45733 ^ _779530) ^ [_1692130, _1692132] : [-(hAPP(c_List_Orev(_1692130), hAPP(c_List_Orev(_1692130), _1692132)) = _1692132)], (45735 ^ _779530) ^ [_1692165, _1692167] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692165)), hAPP(c_List_Orev(_1692165), _1692167)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692165)), _1692167))], (45737 ^ _779530) ^ [_1692209, _1692211] : [class_Groups_Ocomm__monoid__add(_1692209), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1692209), hAPP(c_List_Orev(_1692209), _1692211)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1692209), _1692211))], (45743 ^ _779530) ^ [_1692329, _1692331] : [hAPP(c_List_Orev(_1692329), _1692331) = c_List_Olist_ONil(_1692329), -(_1692331 = c_List_Olist_ONil(_1692329))], (45749 ^ _779530) ^ [_1692420, _1692422] : [_1692422 = c_List_Olist_ONil(_1692420), -(hAPP(c_List_Orev(_1692420), _1692422) = c_List_Olist_ONil(_1692420))], (45755 ^ _779530) ^ [_1692532, _1692534] : [c_List_Olist_ONil(_1692532) = hAPP(c_List_Orev(_1692532), _1692534), -(_1692534 = c_List_Olist_ONil(_1692532))], (45761 ^ _779530) ^ [_1692623, _1692625] : [_1692625 = c_List_Olist_ONil(_1692623), -(c_List_Olist_ONil(_1692623) = hAPP(c_List_Orev(_1692623), _1692625))], (45767 ^ _779530) ^ [_1692720] : [-(hAPP(c_List_Orev(_1692720), c_List_Olist_ONil(_1692720)) = c_List_Olist_ONil(_1692720))], (45769 ^ _779530) ^ [_1692752, _1692754, _1692756] : [-(hAPP(c_List_Orev(_1692752), hAPP(hAPP(c_List_Oappend(_1692752), _1692754), _1692756)) = hAPP(hAPP(c_List_Oappend(_1692752), hAPP(c_List_Orev(_1692752), _1692756)), hAPP(c_List_Orev(_1692752), _1692754)))], (45771 ^ _779530) ^ [_1692810, _1692812, _1692814, _1692816, _1692818] : [-(hAPP(c_List_Ofoldl(_1692810, _1692812, _1692814, _1692816), _1692818) = c_List_Ofoldr(_1692812, _1692810, hAPP(c_COMBC(_1692810, _1692812, _1692810), _1692814), hAPP(c_List_Orev(_1692812), _1692818), _1692816))], (45773 ^ _779530) ^ [_1692867, _1692869, _1692871, _1692873, _1692875] : [-(c_List_Ofoldr(_1692867, _1692869, _1692871, _1692873, _1692875) = hAPP(c_List_Ofoldl(_1692869, _1692867, hAPP(c_COMBC(_1692867, _1692869, _1692869), _1692871), _1692875), hAPP(c_List_Orev(_1692867), _1692873)))], (45775 ^ _779530) ^ [_1692945, _1692947, _1692949, _1692951] : [hAPP(c_List_Orev(_1692945), _1692947) = hAPP(hAPP(c_List_Olist_OCons(_1692945), _1692949), _1692951), -(_1692947 = hAPP(hAPP(c_List_Oappend(_1692945), hAPP(c_List_Orev(_1692945), _1692951)), hAPP(hAPP(c_List_Olist_OCons(_1692945), _1692949), c_List_Olist_ONil(_1692945))))], (45781 ^ _779530) ^ [_1693094, _1693096, _1693098, _1693100] : [_1693096 = hAPP(hAPP(c_List_Oappend(_1693094), hAPP(c_List_Orev(_1693094), _1693100)), hAPP(hAPP(c_List_Olist_OCons(_1693094), _1693098), c_List_Olist_ONil(_1693094))), -(hAPP(c_List_Orev(_1693094), _1693096) = hAPP(hAPP(c_List_Olist_OCons(_1693094), _1693098), _1693100))], (45787 ^ _779530) ^ [_1693249, _1693251, _1693253] : [-(hAPP(c_List_Orev(_1693249), hAPP(hAPP(c_List_Olist_OCons(_1693249), _1693251), _1693253)) = hAPP(hAPP(c_List_Oappend(_1693249), hAPP(c_List_Orev(_1693249), _1693253)), hAPP(hAPP(c_List_Olist_OCons(_1693249), _1693251), c_List_Olist_ONil(_1693249))))], (45789 ^ _779530) ^ [_1693312, _1693314] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693312), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1693312))), c_List_Otranspose(_1693312, _1693314)))))], (45791 ^ _779530) ^ [_1693358, _1693360] : [-(hAPP(c_List_Orev(_1693358), _1693360) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693358), _1693358, hAPP(c_COMBC(_1693358, tc_List_Olist(_1693358), tc_List_Olist(_1693358)), c_List_Olist_OCons(_1693358)), c_List_Olist_ONil(_1693358)), _1693360))], (45793 ^ _779530) ^ [_1693413, _1693415, _1693417] : [-(hAPP(c_List_Orev(_1693413), hAPP(hAPP(c_List_Otake(_1693413), _1693415), _1693417)) = hAPP(hAPP(c_List_Odrop(_1693413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693413)), _1693417)), _1693415)), hAPP(c_List_Orev(_1693413), _1693417)))], (45795 ^ _779530) ^ [_1693479, _1693481, _1693483] : [-(hAPP(c_List_Orev(_1693479), hAPP(hAPP(c_List_Odrop(_1693479), _1693481), _1693483)) = hAPP(hAPP(c_List_Otake(_1693479), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693479)), _1693483)), _1693481)), hAPP(c_List_Orev(_1693479), _1693483)))], (45797 ^ _779530) ^ [_1693545, _1693547, _1693549] : [-(hAPP(c_List_Orotate(_1693545, _1693547), hAPP(c_List_Orev(_1693545), _1693549)) = hAPP(c_List_Orev(_1693545), hAPP(c_List_Orotate(_1693545, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693545)), _1693549)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1693547, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693545)), _1693549)))), _1693549)))], (45799 ^ _779530) ^ [_1693618, _1693620, _1693622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1693618), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693620)), _1693622))), -(hAPP(hAPP(c_List_Onth(_1693620), hAPP(c_List_Orev(_1693620), _1693622)), _1693618) = hAPP(hAPP(c_List_Onth(_1693620), _1693622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693620)), _1693622)), hAPP(c_Nat_OSuc, _1693618))))], (45805 ^ _779530) ^ [_1693795, _1693797, _1693799, _1693801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1693795), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693797)), _1693799))), -(hAPP(c_List_Orev(_1693797), hAPP(hAPP(c_List_Olist__update(_1693797, _1693799), _1693795), _1693801)) = hAPP(hAPP(c_List_Olist__update(_1693797, hAPP(c_List_Orev(_1693797), _1693799)), 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(_1693797)), _1693799)), _1693795)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1693801))], (45811 ^ _779530) ^ [_1693994, _1693996, _1693998, _1694000] : [class_Orderings_Olinorder(_1693994), c_List_Olinorder__class_Osorted(_1693994, hAPP(c_List_Orev(_1693994), _1693996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1693998), _1694000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694000), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693994)), _1693996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1693994), hAPP(hAPP(c_List_Onth(_1693994), _1693996), _1694000)), hAPP(hAPP(c_List_Onth(_1693994), _1693996), _1693998))))], (45829 ^ _779530) ^ [_1694331, _1694333, _1694335] : [class_Orderings_Olinorder(_1694331), c_List_Olinorder__class_Osorted(_1694331, hAPP(c_List_Orev(_1694331), _1694333)), 45836 ^ _779530 : [(45837 ^ _779530) ^ [] : [_1694333 = c_List_Olist_ONil(_1694331), -(c_List_Ofoldr(_1694331, _1694331, c_Orderings_Oord__class_Omax(_1694331), _1694333, _1694335) = _1694335)], (45843 ^ _779530) ^ [] : [-(_1694333 = c_List_Olist_ONil(_1694331)), -(c_List_Ofoldr(_1694331, _1694331, c_Orderings_Oord__class_Omax(_1694331), _1694333, _1694335) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1694331), hAPP(hAPP(c_List_Onth(_1694331), _1694333), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1694335))]]], (45849 ^ _779530) ^ [_1694645, _1694647] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694645), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1694645))), _1694647))), 45852 ^ _779530 : [(45853 ^ _779530) ^ [] : [_1694647 = c_List_Olist_ONil(tc_List_Olist(_1694645)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694645))), c_List_Otranspose(_1694645, _1694647)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45859 ^ _779530) ^ [] : [-(_1694647 = c_List_Olist_ONil(tc_List_Olist(_1694645))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694645))), c_List_Otranspose(_1694645, _1694647)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694645)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1694645)), _1694647), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (45865 ^ _779530) ^ [_1694955, _1694957, _1694959] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694955), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1694955))), _1694957))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694959), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694955))), _1694957))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694955))), hAPP(c_List_Ofilter(tc_List_Olist(_1694955), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1694955)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694959)), c_Nat_Osize__class_Osize(tc_List_Olist(_1694955)))), c_List_Otranspose(_1694955, _1694957))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694955)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1694955)), _1694957), _1694959)))], (45875 ^ _779530) ^ [_1695264, _1695266] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695264), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1695264))), _1695266))), -(c_List_Otranspose(_1695264, c_List_Otranspose(_1695264, _1695266)) = c_List_OtakeWhile(tc_List_Olist(_1695264), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695264)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695264), tc_List_Olist(_1695264), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695264))), _1695266))], (45881 ^ _779530) ^ [_1695457, _1695459] : [class_Orderings_Olinorder(_1695457), 45888 ^ _779530 : [(45889 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45886 ^ [_1695457, _1695459]), 45887 ^ [_1695457, _1695459])))], (45891 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45887 ^ [_1695457, _1695459]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695457)), _1695459))))], (45893 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695457), hAPP(hAPP(c_List_Onth(_1695457), _1695459), 45886 ^ [_1695457, _1695459])), hAPP(hAPP(c_List_Onth(_1695457), _1695459), 45887 ^ [_1695457, _1695459])))]], -(c_List_Olinorder__class_Osorted(_1695457, _1695459))], (45897 ^ _779530) ^ [_1695832, _1695834, _1695836] : [class_Orderings_Olinorder(_1695832), c_List_Olinorder__class_Osorted(_1695832, _1695834), -(c_List_Olinorder__class_Osorted(_1695832, c_List_OtakeWhile(_1695832, _1695836, _1695834)))], (45907 ^ _779530) ^ [_1695967, _1695969, _1695971, _1695973, _1695975] : [-(hBOOL(hAPP(_1695967, _1695969))), -(c_List_OtakeWhile(_1695971, _1695967, hAPP(hAPP(c_List_Oappend(_1695971), _1695973), hAPP(hAPP(c_List_Olist_OCons(_1695971), _1695969), _1695975))) = c_List_OtakeWhile(_1695971, _1695967, _1695973))], (45913 ^ _779530) ^ [_1696035, _1696037] : [-(c_List_OtakeWhile(_1696035, _1696037, c_List_Olist_ONil(_1696035)) = c_List_Olist_ONil(_1696035))], (45915 ^ _779530) ^ [_1696068, _1696070, _1696072] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696068)), c_List_OtakeWhile(_1696068, _1696070, _1696072))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696068)), _1696072))))], (45917 ^ _779530) ^ [_1696118, _1696120, _1696122] : [-(c_List_OtakeWhile(_1696118, _1696120, _1696122) = hAPP(hAPP(c_List_Otake(_1696118), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696118)), c_List_OtakeWhile(_1696118, _1696120, _1696122))), _1696122))], (45919 ^ _779530) ^ [_1696168, _1696170, _1696172] : [hBOOL(hAPP(c_List_Odistinct(_1696168), _1696170)), -(hBOOL(hAPP(c_List_Odistinct(_1696168), c_List_OtakeWhile(_1696168, _1696172, _1696170))))], (45925 ^ _779530) ^ [_1696286, _1696288, _1696290, _1696292] : [hBOOL(hAPP(_1696286, _1696288)), -(c_List_OtakeWhile(_1696290, _1696286, hAPP(hAPP(c_List_Olist_OCons(_1696290), _1696288), _1696292)) = hAPP(hAPP(c_List_Olist_OCons(_1696290), _1696288), c_List_OtakeWhile(_1696290, _1696286, _1696292)))], (45931 ^ _779530) ^ [_1696413, _1696415, _1696417, _1696419] : [-(hBOOL(hAPP(_1696413, _1696415))), -(c_List_OtakeWhile(_1696417, _1696413, hAPP(hAPP(c_List_Olist_OCons(_1696417), _1696415), _1696419)) = c_List_Olist_ONil(_1696417))], (45937 ^ _779530) ^ [_1696471, _1696473, _1696475, _1696477] : [hBOOL(hAPP(hAPP(c_member(_1696471), _1696473), hAPP(c_List_Oset(_1696471), c_List_OtakeWhile(_1696471, _1696475, _1696477)))), 45940 ^ _779530 : [(45941 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696471), _1696473), hAPP(c_List_Oset(_1696471), _1696477))))], (45943 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1696475, _1696473)))]]], (45955 ^ _779530) ^ [_1696852, _1696854, _1696856] : [45957 ^ _779530 : [(45958 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696852), 45956 ^ [_1696852, _1696854, _1696856]), hAPP(c_List_Oset(_1696852), _1696856))))], (45960 ^ _779530) ^ [] : [hBOOL(hAPP(_1696854, 45956 ^ [_1696852, _1696854, _1696856]))]], -(c_List_OtakeWhile(_1696852, _1696854, _1696856) = _1696856)], (45945 ^ _779530) ^ [_1696656, _1696658, _1696660] : [c_List_OtakeWhile(_1696656, _1696658, _1696660) = _1696660, 45948 ^ _779530 : [(45949 ^ _779530) ^ [_1696743] : [hBOOL(hAPP(hAPP(c_member(_1696656), _1696743), hAPP(c_List_Oset(_1696656), _1696660))), -(hBOOL(hAPP(_1696658, _1696743)))]]], (45964 ^ _779530) ^ [_1697040, _1697042, _1697044, _1697046, _1697048] : [-(hAPP(hAPP(c_List_Ozip(_1697040, _1697042), c_List_OtakeWhile(_1697040, _1697044, _1697046)), _1697048) = c_List_OtakeWhile(tc_prod(_1697040, _1697042), hAPP(c_Fun_Ocomp(_1697040, tc_HOL_Obool, tc_prod(_1697040, _1697042), _1697044), c_Product__Type_Ofst(_1697040, _1697042)), hAPP(hAPP(c_List_Ozip(_1697040, _1697042), _1697046), _1697048)))], (45966 ^ _779530) ^ [_1697114, _1697116, _1697118, _1697120, _1697122] : [-(hAPP(hAPP(c_List_Ozip(_1697114, _1697116), _1697118), c_List_OtakeWhile(_1697116, _1697120, _1697122)) = c_List_OtakeWhile(tc_prod(_1697114, _1697116), hAPP(c_Fun_Ocomp(_1697116, tc_HOL_Obool, tc_prod(_1697114, _1697116), _1697120), c_Product__Type_Osnd(_1697114, _1697116)), hAPP(hAPP(c_List_Ozip(_1697114, _1697116), _1697118), _1697122)))], (45968 ^ _779530) ^ [_1697188, _1697190, _1697192, _1697194, _1697196] : [-(c_List_OtakeWhile(_1697188, _1697190, hAPP(hAPP(c_List_Omap(_1697192, _1697188), _1697194), _1697196)) = hAPP(hAPP(c_List_Omap(_1697192, _1697188), _1697194), c_List_OtakeWhile(_1697192, hAPP(c_Fun_Ocomp(_1697188, tc_HOL_Obool, _1697192, _1697190), _1697194), _1697196)))], (45970 ^ _779530) ^ [_1697253, _1697255, _1697257, _1697259, _1697261] : [hBOOL(hAPP(hAPP(c_member(_1697253), _1697255), hAPP(c_List_Oset(_1697253), _1697257))), -(hBOOL(hAPP(_1697259, _1697255))), -(c_List_OtakeWhile(_1697253, _1697259, hAPP(hAPP(c_List_Oappend(_1697253), _1697257), _1697261)) = c_List_OtakeWhile(_1697253, _1697259, _1697257))], (45980 ^ _779530) ^ [_1697411, _1697413, _1697415, _1697417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697413)), c_List_OtakeWhile(_1697413, _1697415, _1697417)))), -(hAPP(hAPP(c_List_Onth(_1697413), c_List_OtakeWhile(_1697413, _1697415, _1697417)), _1697411) = hAPP(hAPP(c_List_Onth(_1697413), _1697417), _1697411))], (45986 ^ _779530) ^ [_1697564, _1697566, _1697568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697564)), c_List_OtakeWhile(_1697564, _1697566, _1697568))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697564)), _1697568))), hBOOL(hAPP(_1697566, hAPP(hAPP(c_List_Onth(_1697564), _1697568), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697564)), c_List_OtakeWhile(_1697564, _1697566, _1697568)))))], (45992 ^ _779530) ^ [_1697732, _1697734, _1697736, _1697738, _1697740] : [-(c_Map_Omap__upds(_1697732, _1697734, _1697736, _1697738, _1697740) = c_Map_Omap__add(_1697732, _1697734, _1697736, hAPP(c_Map_Omap__of(_1697732, _1697734), hAPP(c_List_Orev(tc_prod(_1697732, _1697734)), hAPP(hAPP(c_List_Ozip(_1697732, _1697734), _1697738), _1697740)))))], (45994 ^ _779530) ^ [_1697797, _1697799, _1697801, _1697803, _1697805] : [class_Orderings_Olinorder(_1697797), c_List_Olinorder__class_Osorted(_1697797, hAPP(c_List_Orev(_1697797), hAPP(hAPP(c_List_Omap(_1697799, _1697797), _1697801), _1697803))), -(hAPP(c_List_Ofilter(_1697799, hAPP(hAPP(c_COMBB(_1697797, tc_HOL_Obool, _1697799), hAPP(c_Orderings_Oord__class_Oless(_1697797), _1697805)), _1697801)), _1697803) = c_List_OtakeWhile(_1697799, hAPP(hAPP(c_COMBB(_1697797, tc_HOL_Obool, _1697799), hAPP(c_Orderings_Oord__class_Oless(_1697797), _1697805)), _1697801), _1697803))], (46004 ^ _779530) ^ [_1698044, _1698046, _1698048] : [hBOOL(hAPP(c_List_Odistinct(_1698044), _1698046)), hBOOL(hAPP(hAPP(c_member(_1698044), _1698048), hAPP(c_List_Oset(_1698044), _1698046))), -(c_List_OtakeWhile(_1698044, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698044), c_fNot), hAPP(hAPP(c_COMBC(_1698044, _1698044, tc_HOL_Obool), c_fequal), _1698048)), hAPP(c_List_Orev(_1698044), _1698046)) = hAPP(c_List_Orev(_1698044), hAPP(c_List_Otl(_1698044), c_List_OdropWhile(_1698044, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698044), c_fNot), hAPP(hAPP(c_COMBC(_1698044, _1698044, tc_HOL_Obool), c_fequal), _1698048)), _1698046))))], (46014 ^ _779530) ^ [_1698335, _1698337, _1698339] : [hBOOL(hAPP(c_List_Odistinct(_1698335), _1698337)), hBOOL(hAPP(hAPP(c_member(_1698335), _1698339), hAPP(c_List_Oset(_1698335), _1698337))), -(c_List_OdropWhile(_1698335, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698335), c_fNot), hAPP(hAPP(c_COMBC(_1698335, _1698335, tc_HOL_Obool), c_fequal), _1698339)), hAPP(c_List_Orev(_1698335), _1698337)) = hAPP(hAPP(c_List_Olist_OCons(_1698335), _1698339), hAPP(c_List_Orev(_1698335), c_List_OtakeWhile(_1698335, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698335), c_fNot), hAPP(hAPP(c_COMBC(_1698335, _1698335, tc_HOL_Obool), c_fequal), _1698339)), _1698337))))], (46024 ^ _779530) ^ [_1698632, _1698634, _1698636] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698632)), c_List_OdropWhile(_1698632, _1698634, _1698636))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698632)), _1698636))))], (46026 ^ _779530) ^ [_1698697, _1698699, _1698701, _1698703] : [hBOOL(hAPP(_1698697, _1698699)), -(c_List_OdropWhile(_1698701, _1698697, hAPP(hAPP(c_List_Olist_OCons(_1698701), _1698699), _1698703)) = c_List_OdropWhile(_1698701, _1698697, _1698703))], (46032 ^ _779530) ^ [_1698808, _1698810, _1698812, _1698814] : [-(hBOOL(hAPP(_1698808, _1698810))), -(c_List_OdropWhile(_1698812, _1698808, hAPP(hAPP(c_List_Olist_OCons(_1698812), _1698810), _1698814)) = hAPP(hAPP(c_List_Olist_OCons(_1698812), _1698810), _1698814))], (46038 ^ _779530) ^ [_1698872, _1698874, _1698876] : [hBOOL(hAPP(c_List_Odistinct(_1698872), _1698874)), -(hBOOL(hAPP(c_List_Odistinct(_1698872), c_List_OdropWhile(_1698872, _1698876, _1698874))))], (46044 ^ _779530) ^ [_1698975, _1698977] : [-(c_List_OdropWhile(_1698975, _1698977, c_List_Olist_ONil(_1698975)) = c_List_Olist_ONil(_1698975))], (46056 ^ _779530) ^ [_1699226, _1699228, _1699230] : [46058 ^ _779530 : [(46059 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699226), 46057 ^ [_1699226, _1699228, _1699230]), hAPP(c_List_Oset(_1699226), _1699230))))], (46061 ^ _779530) ^ [] : [hBOOL(hAPP(_1699228, 46057 ^ [_1699226, _1699228, _1699230]))]], -(c_List_OdropWhile(_1699226, _1699228, _1699230) = c_List_Olist_ONil(_1699226))], (46046 ^ _779530) ^ [_1699026, _1699028, _1699030] : [c_List_OdropWhile(_1699026, _1699028, _1699030) = c_List_Olist_ONil(_1699026), 46049 ^ _779530 : [(46050 ^ _779530) ^ [_1699117] : [hBOOL(hAPP(hAPP(c_member(_1699026), _1699117), hAPP(c_List_Oset(_1699026), _1699030))), -(hBOOL(hAPP(_1699028, _1699117)))]]], (46065 ^ _779530) ^ [_1699418, _1699420, _1699422] : [class_Orderings_Olinorder(_1699418), c_List_Olinorder__class_Osorted(_1699418, _1699420), -(c_List_Olinorder__class_Osorted(_1699418, c_List_OdropWhile(_1699418, _1699422, _1699420)))], (46075 ^ _779530) ^ [_1699557, _1699559, _1699561] : [-(hAPP(hAPP(c_List_Oappend(_1699557), c_List_OtakeWhile(_1699557, _1699559, _1699561)), c_List_OdropWhile(_1699557, _1699559, _1699561)) = _1699561)], (46077 ^ _779530) ^ [_1699599, _1699601, _1699603] : [-(c_List_OdropWhile(_1699599, _1699601, _1699603) = c_List_Olist_ONil(_1699599)), hBOOL(hAPP(_1699601, hAPP(c_List_Ohd(_1699599), c_List_OdropWhile(_1699599, _1699601, _1699603))))], (46083 ^ _779530) ^ [_1699705, _1699707, _1699709, _1699711, _1699713] : [-(c_List_OdropWhile(_1699705, _1699707, hAPP(hAPP(c_List_Omap(_1699709, _1699705), _1699711), _1699713)) = hAPP(hAPP(c_List_Omap(_1699709, _1699705), _1699711), c_List_OdropWhile(_1699709, hAPP(c_Fun_Ocomp(_1699705, tc_HOL_Obool, _1699709, _1699707), _1699711), _1699713)))], (46085 ^ _779530) ^ [_1699770, _1699772, _1699774, _1699776, _1699778] : [hBOOL(hAPP(hAPP(c_member(_1699770), _1699772), hAPP(c_List_Oset(_1699770), _1699774))), -(hBOOL(hAPP(_1699776, _1699772))), -(c_List_OdropWhile(_1699770, _1699776, hAPP(hAPP(c_List_Oappend(_1699770), _1699774), _1699778)) = hAPP(hAPP(c_List_Oappend(_1699770), c_List_OdropWhile(_1699770, _1699776, _1699774)), _1699778))], (46095 ^ _779530) ^ [_1699968, _1699970, _1699972, _1699974, _1699976] : [c_List_OdropWhile(_1699968, _1699970, _1699972) = hAPP(hAPP(c_List_Olist_OCons(_1699968), _1699974), _1699976), 46098 ^ _779530 : [(46099 ^ _779530) ^ [] : [-(_1699972 = hAPP(hAPP(c_List_Oappend(_1699968), c_List_OtakeWhile(_1699968, _1699970, _1699972)), hAPP(hAPP(c_List_Olist_OCons(_1699968), _1699974), _1699976)))], (46101 ^ _779530) ^ [] : [hBOOL(hAPP(_1699970, _1699974))]]], (46103 ^ _779530) ^ [_1700149, _1700151, _1700153, _1700155, _1700157] : [-(c_List_OdropWhile(_1700149, _1700151, _1700153) = hAPP(hAPP(c_List_Olist_OCons(_1700149), _1700155), _1700157)), _1700153 = hAPP(hAPP(c_List_Oappend(_1700149), c_List_OtakeWhile(_1700149, _1700151, _1700153)), hAPP(hAPP(c_List_Olist_OCons(_1700149), _1700155), _1700157)), -(hBOOL(hAPP(_1700151, _1700155)))], (46113 ^ _779530) ^ [_1700363, _1700365, _1700367] : [-(c_List_OdropWhile(_1700363, _1700365, _1700367) = hAPP(hAPP(c_List_Odrop(_1700363), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700363)), c_List_OtakeWhile(_1700363, _1700365, _1700367))), _1700367))], (46115 ^ _779530) ^ [_1700413, _1700415, _1700417, _1700419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1700413), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700415)), c_List_OdropWhile(_1700415, _1700417, _1700419)))), -(hAPP(hAPP(c_List_Onth(_1700415), c_List_OdropWhile(_1700415, _1700417, _1700419)), _1700413) = hAPP(hAPP(c_List_Onth(_1700415), _1700419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1700413), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700415)), c_List_OtakeWhile(_1700415, _1700417, _1700419)))))], (46121 ^ _779530) ^ [_1700600, _1700602] : [class_Orderings_Olinorder(_1700600), -(c_List_Olinorder__class_Osort__key(_1700600, _1700600, c_COMBI(_1700600), _1700602) = hAPP(c_List_Ofoldl(tc_List_Olist(_1700600), _1700600, hAPP(c_COMBC(_1700600, tc_List_Olist(_1700600), tc_List_Olist(_1700600)), c_List_Olinorder__class_Oinsort__key(_1700600, _1700600, c_COMBI(_1700600))), c_List_Olist_ONil(_1700600)), _1700602))], (46127 ^ _779530) ^ [_1700765, _1700767, _1700769] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700765), tc_List_Olist(_1700765))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700765), tc_List_Olist(_1700765)), c_List_Olist_ONil(_1700765)), _1700767)), c_List_Olexord(_1700765, _1700769))), -(_1700767 = hAPP(hAPP(c_List_Olist_OCons(_1700765), 46130 ^ [_1700765, _1700767, _1700769]), 46131 ^ [_1700765, _1700767, _1700769]))], (46135 ^ _779530) ^ [_1700948, _1700950, _1700952] : [46136 ^ _779530 : [(46137 ^ _779530) ^ [_1701037, _1701039] : [_1700950 = hAPP(hAPP(c_List_Olist_OCons(_1700948), _1701039), _1701037)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700948), tc_List_Olist(_1700948))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700948), tc_List_Olist(_1700948)), c_List_Olist_ONil(_1700948)), _1700950)), c_List_Olexord(_1700948, _1700952))))], (46141 ^ _779530) ^ [_1701132, _1701134] : [class_Orderings_Olinorder(_1701132), -(c_List_Olinorder__class_Osorted(_1701132, c_List_Olinorder__class_Osort__key(_1701132, _1701132, c_COMBI(_1701132), _1701134)))], (46147 ^ _779530) ^ [_1701221, _1701223, _1701225] : [class_Orderings_Olinorder(_1701221), -(c_List_Olinorder__class_Osort__key(_1701223, _1701221, _1701225, c_List_Olist_ONil(_1701223)) = c_List_Olist_ONil(_1701223))], (46153 ^ _779530) ^ [_1701316, _1701318, _1701320, _1701322] : [class_Orderings_Olinorder(_1701316), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701318)), c_List_Olinorder__class_Osort__key(_1701318, _1701316, _1701320, _1701322)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701318)), _1701322))], (46159 ^ _779530) ^ [_1701433, _1701435, _1701437, _1701439, _1701441] : [class_Orderings_Olinorder(_1701433), -(hAPP(c_List_Ofilter(_1701435, _1701437), c_List_Olinorder__class_Osort__key(_1701435, _1701433, _1701439, _1701441)) = c_List_Olinorder__class_Osort__key(_1701435, _1701433, _1701439, hAPP(c_List_Ofilter(_1701435, _1701437), _1701441)))], (46165 ^ _779530) ^ [_1701558, _1701560, _1701562, _1701564] : [class_Orderings_Olinorder(_1701558), 46168 ^ _779530 : [(46169 ^ _779530) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701560), c_List_Olinorder__class_Osort__key(_1701560, _1701558, _1701562, _1701564))), -(hBOOL(hAPP(c_List_Odistinct(_1701560), _1701564)))], (46175 ^ _779530) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701560), _1701564)), -(hBOOL(hAPP(c_List_Odistinct(_1701560), c_List_Olinorder__class_Osort__key(_1701560, _1701558, _1701562, _1701564))))]]], (46181 ^ _779530) ^ [_1701814, _1701816, _1701818, _1701820] : [class_Orderings_Olinorder(_1701814), -(hAPP(c_List_Oset(_1701816), c_List_Olinorder__class_Osort__key(_1701816, _1701814, _1701818, _1701820)) = hAPP(c_List_Oset(_1701816), _1701820))], (46187 ^ _779530) ^ [_1701923, _1701925, _1701927, _1701929] : [class_Orderings_Olinorder(_1701923), -(c_List_Olinorder__class_Osorted(_1701923, hAPP(hAPP(c_List_Omap(_1701925, _1701923), _1701927), c_List_Olinorder__class_Osort__key(_1701925, _1701923, _1701927, _1701929))))], (46193 ^ _779530) ^ [_1702030, _1702032, _1702034, _1702036, _1702038] : [class_Orderings_Olinorder(_1702030), -(c_List_Olinorder__class_Osort__key(_1702032, _1702030, _1702034, hAPP(hAPP(c_List_Olist_OCons(_1702032), _1702036), _1702038)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702032, _1702030, _1702034), _1702036), c_List_Olinorder__class_Osort__key(_1702032, _1702030, _1702034, _1702038)))], (46199 ^ _779530) ^ [_1702167, _1702169] : [class_Orderings_Olinorder(_1702167), -(c_List_Olinorder__class_Osorted__list__of__set(_1702167, hAPP(c_List_Oset(_1702167), _1702169)) = c_List_Olinorder__class_Osort__key(_1702167, _1702167, c_COMBI(_1702167), c_List_Oremdups(_1702167, _1702169)))], (46205 ^ _779530) ^ [_1702277, _1702279, _1702281, _1702283] : [-(_1702277 = c_List_Olist_ONil(_1702279)), 46208 ^ _779530 : [(46209 ^ _779530) ^ [] : [_1702281 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702279)), _1702277)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1702279, hAPP(hAPP(c_List_Olist__update(_1702279, _1702277), _1702281), _1702283)) = _1702283)], (46215 ^ _779530) ^ [] : [-(_1702281 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702279)), _1702277)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1702279, hAPP(hAPP(c_List_Olist__update(_1702279, _1702277), _1702281), _1702283)) = c_List_Olast(_1702279, _1702277))]]], (46221 ^ _779530) ^ [_1702563, _1702565, _1702567] : [46223 ^ _779530 : [(46224 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702563), 46222 ^ [_1702563, _1702565, _1702567]), hAPP(c_List_Oset(_1702563), c_List_OdropWhile(_1702563, _1702565, _1702567)))))], (46226 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1702565, 46222 ^ [_1702563, _1702565, _1702567])))]], -(c_List_OtakeWhile(_1702563, _1702565, _1702567) = hAPP(c_List_Ofilter(_1702563, _1702565), _1702567))], (46230 ^ _779530) ^ [_1702680, _1702682, _1702684, _1702686] : [-(_1702680 = c_List_Olist_ONil(_1702682)), -(c_List_Olast(_1702684, hAPP(hAPP(c_List_Omap(_1702682, _1702684), _1702686), _1702680)) = hAPP(_1702686, c_List_Olast(_1702682, _1702680)))], (46236 ^ _779530) ^ [_1702752, _1702754, _1702756] : [_1702752 = c_List_Olist_ONil(_1702754), -(c_List_Olast(_1702754, hAPP(hAPP(c_List_Oappend(_1702754), _1702756), _1702752)) = c_List_Olast(_1702754, _1702756))], (46242 ^ _779530) ^ [_1702857, _1702859, _1702861] : [-(_1702857 = c_List_Olist_ONil(_1702859)), -(c_List_Olast(_1702859, hAPP(hAPP(c_List_Oappend(_1702859), _1702861), _1702857)) = c_List_Olast(_1702859, _1702857))], (46248 ^ _779530) ^ [_1702909, _1702911, _1702913] : [-(_1702909 = c_List_Olist_ONil(_1702911)), -(c_List_Olast(_1702911, hAPP(hAPP(c_List_Oappend(_1702911), _1702913), _1702909)) = c_List_Olast(_1702911, _1702909))], (46254 ^ _779530) ^ [_1702963, _1702965, _1702967] : [_1702963 = c_List_Olist_ONil(_1702965), -(c_List_Olast(_1702965, hAPP(hAPP(c_List_Oappend(_1702965), _1702967), _1702963)) = c_List_Olast(_1702965, _1702967))], (46260 ^ _779530) ^ [_1703074, _1703076, _1703078] : [_1703074 = c_List_Olist_ONil(_1703076), -(c_List_Olast(_1703076, hAPP(hAPP(c_List_Olist_OCons(_1703076), _1703078), _1703074)) = _1703078)], (46266 ^ _779530) ^ [_1703175, _1703177, _1703179] : [-(_1703175 = c_List_Olist_ONil(_1703177)), -(c_List_Olast(_1703177, hAPP(hAPP(c_List_Olist_OCons(_1703177), _1703179), _1703175)) = c_List_Olast(_1703177, _1703175))], (46272 ^ _779530) ^ [_1703241, _1703243, _1703245] : [_1703241 = c_List_Olist_ONil(_1703243), -(c_List_Olast(_1703243, hAPP(hAPP(c_List_Olist_OCons(_1703243), _1703245), _1703241)) = _1703245)], (46278 ^ _779530) ^ [_1703340, _1703342, _1703344] : [-(_1703340 = c_List_Olist_ONil(_1703342)), -(c_List_Olast(_1703342, hAPP(hAPP(c_List_Olist_OCons(_1703342), _1703344), _1703340)) = c_List_Olast(_1703342, _1703340))], (46284 ^ _779530) ^ [_1703392, _1703394] : [-(_1703392 = c_List_Olist_ONil(_1703394)), -(hBOOL(hAPP(hAPP(c_member(_1703394), c_List_Olast(_1703394, _1703392)), hAPP(c_List_Oset(_1703394), _1703392))))], (46290 ^ _779530) ^ [_1703445, _1703447, _1703449] : [-(c_List_Olast(_1703445, hAPP(hAPP(c_List_Oappend(_1703445), _1703447), hAPP(hAPP(c_List_Olist_OCons(_1703445), _1703449), c_List_Olist_ONil(_1703445)))) = _1703449)], (46292 ^ _779530) ^ [_1703493, _1703495, _1703497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703493), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703495)), _1703497))), -(c_List_Olast(_1703495, hAPP(hAPP(c_List_Odrop(_1703495), _1703493), _1703497)) = c_List_Olast(_1703495, _1703497))], (46298 ^ _779530) ^ [_1703620, _1703622] : [-(_1703620 = c_List_Olist_ONil(_1703622)), -(c_List_Olast(_1703622, hAPP(c_List_Orev(_1703622), _1703620)) = hAPP(c_List_Ohd(_1703622), _1703620))], (46304 ^ _779530) ^ [_1703667, _1703669] : [-(_1703667 = c_List_Olist_ONil(_1703669)), -(hAPP(c_List_Ohd(_1703669), hAPP(c_List_Orev(_1703669), _1703667)) = c_List_Olast(_1703669, _1703667))], (46310 ^ _779530) ^ [_1703718, _1703720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703718), _1703720)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1703718, _1703720)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703720), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46316 ^ _779530) ^ [_1703850, _1703852, _1703854, _1703856] : [hAPP(hAPP(c_List_Oappend(_1703850), _1703852), hAPP(hAPP(c_List_Olist_OCons(_1703850), _1703854), c_List_Olist_ONil(_1703850))) = _1703856, 46319 ^ _779530 : [(46320 ^ _779530) ^ [] : [_1703856 = c_List_Olist_ONil(_1703850)], (46322 ^ _779530) ^ [] : [-(c_List_Obutlast(_1703850, _1703856) = _1703852)], (46324 ^ _779530) ^ [] : [-(c_List_Olast(_1703850, _1703856) = _1703854)]]], (46326 ^ _779530) ^ [_1704039, _1704041, _1704043, _1704045] : [-(hAPP(hAPP(c_List_Oappend(_1704039), _1704041), hAPP(hAPP(c_List_Olist_OCons(_1704039), _1704043), c_List_Olist_ONil(_1704039))) = _1704045), -(_1704045 = c_List_Olist_ONil(_1704039)), c_List_Obutlast(_1704039, _1704045) = _1704041, c_List_Olast(_1704039, _1704045) = _1704043], (46340 ^ _779530) ^ [_1704285, _1704287] : [-(_1704285 = c_List_Olist_ONil(_1704287)), -(hAPP(hAPP(c_List_Oappend(_1704287), c_List_Obutlast(_1704287, _1704285)), hAPP(hAPP(c_List_Olist_OCons(_1704287), c_List_Olast(_1704287, _1704285)), c_List_Olist_ONil(_1704287))) = _1704285)], (46346 ^ _779530) ^ [_1704346, _1704348] : [-(_1704346 = c_List_Olist_ONil(_1704348)), hBOOL(hAPP(c_List_Odistinct(_1704348), _1704346)), -(c_List_OtakeWhile(_1704348, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1704348), c_fNot), hAPP(hAPP(c_COMBC(_1704348, _1704348, tc_HOL_Obool), c_fequal), c_List_Olast(_1704348, _1704346))), _1704346) = c_List_Obutlast(_1704348, _1704346))], (46356 ^ _779530) ^ [_1704539, _1704541] : [-(_1704539 = c_List_Olist_ONil(_1704541)), -(c_List_Olast(_1704541, _1704539) = hAPP(hAPP(c_List_Onth(_1704541), _1704539), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704541)), _1704539)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46362 ^ _779530) ^ [_1704619, _1704621, _1704623] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704619)), _1704621), c_List_Olists(_1704619, _1704623))), -(_1704621 = c_List_Olist_ONil(_1704619)), 46371 ^ _779530 : [(46372 ^ _779530) ^ [] : [-(_1704621 = hAPP(hAPP(c_List_Olist_OCons(_1704619), 46369 ^ [_1704619, _1704621, _1704623]), 46370 ^ [_1704619, _1704621, _1704623]))], (46374 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1704619), 46369 ^ [_1704619, _1704621, _1704623]), _1704623)))], (46376 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704619)), 46370 ^ [_1704619, _1704621, _1704623]), c_List_Olists(_1704619, _1704623))))]]], (46378 ^ _779530) ^ [_1704902, _1704904, _1704906] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704902)), _1704904), c_List_Olists(_1704902, _1704906)))), 46379 ^ _779530 : [(46380 ^ _779530) ^ [] : [_1704904 = c_List_Olist_ONil(_1704902)], (46382 ^ _779530) ^ [_1705030, _1705032] : [_1704904 = hAPP(hAPP(c_List_Olist_OCons(_1704902), _1705032), _1705030), hBOOL(hAPP(hAPP(c_member(_1704902), _1705032), _1704906)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1704902)), _1705030), c_List_Olists(_1704902, _1704906)))]]], (46394 ^ _779530) ^ [_1705268, _1705270, _1705272, _1705274] : [46396 ^ _779530 : [(46397 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46395 ^ [_1705268, _1705270, _1705272, _1705274]), _1705268)))], (46399 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46395 ^ [_1705268, _1705270, _1705272, _1705274]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705270)), _1705272))))], (46401 ^ _779530) ^ [] : [hBOOL(hAPP(_1705274, hAPP(hAPP(c_List_Onth(_1705270), _1705272), 46395 ^ [_1705268, _1705270, _1705272, _1705274])))]], 46404 ^ _779530 : [(46405 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705268), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705270)), _1705272))))], (46407 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1705274, hAPP(hAPP(c_List_Onth(_1705270), _1705272), _1705268))))]], -(c_List_OtakeWhile(_1705270, _1705274, _1705272) = hAPP(hAPP(c_List_Otake(_1705270), _1705268), _1705272))], (46411 ^ _779530) ^ [_1705672, _1705674, _1705676, _1705678] : [46413 ^ _779530 : [(46414 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46412 ^ [_1705672, _1705674, _1705676, _1705678]), _1705672)))], (46416 ^ _779530) ^ [] : [hBOOL(hAPP(_1705674, hAPP(hAPP(c_List_Onth(_1705676), _1705678), 46412 ^ [_1705672, _1705674, _1705676, _1705678])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1705672), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705676)), _1705678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1705672), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705676)), c_List_OtakeWhile(_1705676, _1705674, _1705678)))))], (46424 ^ _779530) ^ [_1705980, _1705982, _1705984, _1705986] : [class_Complete__Lattice_Ocomplete__lattice(_1705980), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1705982, _1705980), hAPP(c_List_Oset(_1705982), _1705984)), _1705986) = hAPP(c_List_Ofoldl(_1705980, _1705982, hAPP(c_COMBC(_1705982, _1705980, _1705980), hAPP(hAPP(c_COMBB(_1705980, tc_fun(_1705980, _1705980), _1705982), c_Lattices_Osemilattice__inf__class_Oinf(_1705980)), _1705986)), c_Orderings_Otop__class_Otop(_1705980)), _1705984))], (46430 ^ _779530) ^ [_1706151, _1706153, _1706155, _1706157, _1706159, _1706161] : [hBOOL(hAPP(hAPP(c_member(_1706151), _1706153), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1706155, tc_fun(_1706151, tc_HOL_Obool)), _1706157), _1706159))), hBOOL(hAPP(hAPP(c_member(_1706155), _1706161), _1706157)), -(hBOOL(hAPP(hAPP(c_member(_1706151), _1706153), hAPP(_1706159, _1706161))))], (46440 ^ _779530) ^ [_1706368, _1706370, _1706372, _1706374, _1706376, _1706378] : [hBOOL(hAPP(hAPP(c_member(_1706368), _1706370), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1706372, tc_fun(_1706368, tc_HOL_Obool)), _1706374), _1706376))), -(hBOOL(hAPP(hAPP(c_member(_1706368), _1706370), hAPP(_1706376, _1706378)))), hBOOL(hAPP(hAPP(c_member(_1706372), _1706378), _1706374))], (46450 ^ _779530) ^ [_1706589, _1706591, _1706593, _1706595, _1706597, _1706599] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1706589, tc_fun(_1706591, tc_HOL_Obool)), _1706593), _1706595), _1706597)), -(hBOOL(hAPP(hAPP(_1706595, _1706599), _1706597))), hBOOL(hAPP(hAPP(c_member(_1706589), _1706599), _1706593))], (46460 ^ _779530) ^ [_1706790, _1706792, _1706794, _1706796, _1706798, _1706800] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1706790, tc_fun(_1706792, tc_HOL_Obool)), _1706794), _1706796), _1706798)), hBOOL(hAPP(hAPP(c_member(_1706790), _1706800), _1706794)), -(hBOOL(hAPP(hAPP(_1706796, _1706800), _1706798)))], (46470 ^ _779530) ^ [_1706987, _1706989, _1706991, _1706993, _1706995, _1706997, _1706999, _1707001] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1706987, tc_fun(_1706989, tc_fun(_1706991, tc_HOL_Obool))), _1706993), _1706995), _1706997), _1706999)), hBOOL(hAPP(hAPP(c_member(_1706987), _1707001), _1706993)), -(hBOOL(hAPP(hAPP(hAPP(_1706995, _1707001), _1706997), _1706999)))], (46480 ^ _779530) ^ [_1707210, _1707212, _1707214, _1707216, _1707218, _1707220, _1707222, _1707224] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707210, tc_fun(_1707212, tc_fun(_1707214, tc_HOL_Obool))), _1707216), _1707218), _1707220), _1707222)), -(hBOOL(hAPP(hAPP(hAPP(_1707218, _1707224), _1707220), _1707222))), hBOOL(hAPP(hAPP(c_member(_1707210), _1707224), _1707216))], (46490 ^ _779530) ^ [_1707437, _1707439, _1707441, _1707443] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1707441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707437, tc_fun(_1707441, tc_HOL_Obool)), _1707439), _1707443)))), 46491 ^ _779530 : [(46492 ^ _779530) ^ [_1707511] : [hBOOL(hAPP(hAPP(c_member(_1707437), _1707511), _1707439)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1707441), hAPP(_1707443, _1707511)))]]], (46500 ^ _779530) ^ [_1707665, _1707667, _1707669, _1707671, _1707673] : [class_Complete__Lattice_Ocomplete__lattice(_1707665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1707667, tc_HOL_Obool)), _1707669), _1707671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707665), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707667, _1707665), _1707671), _1707673)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707667, _1707665), _1707669), _1707673))))], (46510 ^ _779530) ^ [_1707874, _1707876, _1707878, _1707880, _1707882] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707874, tc_HOL_Obool)), _1707876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707878, tc_fun(_1707874, tc_HOL_Obool)), _1707880), _1707882)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1707878, tc_fun(_1707874, tc_HOL_Obool)), _1707880), hAPP(hAPP(c_COMBB(tc_fun(_1707874, tc_HOL_Obool), tc_fun(_1707874, tc_HOL_Obool), _1707878), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707874, tc_HOL_Obool)), _1707876)), _1707882)))], (46512 ^ _779530) ^ [_1707964, _1707966, _1707968, _1707970, _1707972] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1707964, tc_fun(_1707966, tc_HOL_Obool)), _1707968), hAPP(hAPP(c_COMBB(tc_fun(_1707966, tc_HOL_Obool), tc_fun(_1707966, tc_HOL_Obool), _1707964), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707966, tc_HOL_Obool)), _1707970)), _1707972)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1707966, tc_HOL_Obool)), _1707970), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1707964, tc_fun(_1707966, tc_HOL_Obool)), _1707968), _1707972)))], (46514 ^ _779530) ^ [_1708054, _1708056, _1708058, _1708060, _1708062, _1708064] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708054, tc_fun(_1708056, tc_HOL_Obool)), _1708058), hAPP(hAPP(c_COMBC(_1708054, tc_fun(_1708060, tc_fun(_1708056, tc_HOL_Obool)), tc_fun(_1708056, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708060, tc_HOL_Obool), tc_fun(tc_fun(_1708060, tc_fun(_1708056, tc_HOL_Obool)), tc_fun(_1708056, tc_HOL_Obool)), _1708054), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708060, tc_fun(_1708056, tc_HOL_Obool))), _1708062)), _1708064)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708060, tc_fun(_1708056, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1708054, tc_fun(_1708060, tc_HOL_Obool)), _1708058), _1708062)), _1708064))], (46516 ^ _779530) ^ [_1708173, _1708175, _1708177, _1708179, _1708181, _1708183] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708173, tc_fun(_1708175, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1708177, tc_fun(_1708173, tc_HOL_Obool)), _1708179), _1708181)), _1708183) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708177, tc_fun(_1708175, tc_HOL_Obool)), _1708179), hAPP(hAPP(c_COMBC(_1708177, tc_fun(_1708173, tc_fun(_1708175, tc_HOL_Obool)), tc_fun(_1708175, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708173, tc_HOL_Obool), tc_fun(tc_fun(_1708173, tc_fun(_1708175, tc_HOL_Obool)), tc_fun(_1708175, tc_HOL_Obool)), _1708177), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708173, tc_fun(_1708175, tc_HOL_Obool))), _1708181)), _1708183)))], (46518 ^ _779530) ^ [_1708292, _1708294, _1708296, _1708298] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1708292, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1708294, tc_fun(_1708292, tc_HOL_Obool)), _1708296), _1708298)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708294, tc_fun(_1708292, tc_HOL_Obool)), _1708296), hAPP(hAPP(c_COMBB(tc_fun(_1708292, tc_HOL_Obool), tc_fun(_1708292, tc_HOL_Obool), _1708294), c_Groups_Ouminus__class_Ouminus(tc_fun(_1708292, tc_HOL_Obool))), _1708298)))], (46520 ^ _779530) ^ [_1708374, _1708376, _1708378, _1708380] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1708374, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708376, tc_fun(_1708374, tc_HOL_Obool)), _1708378), _1708380)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1708376, tc_fun(_1708374, tc_HOL_Obool)), _1708378), hAPP(hAPP(c_COMBB(tc_fun(_1708374, tc_HOL_Obool), tc_fun(_1708374, tc_HOL_Obool), _1708376), c_Groups_Ouminus__class_Ouminus(tc_fun(_1708374, tc_HOL_Obool))), _1708380)))], (46522 ^ _779530) ^ [_1708456, _1708458, _1708460, _1708462] : [-(hAPP(c_Set_OCollect(_1708456), hAPP(hAPP(c_COMBB(tc_fun(_1708458, tc_HOL_Obool), tc_HOL_Obool, _1708456), c_HOL_OAll(_1708458)), hAPP(hAPP(c_COMBB(tc_fun(_1708458, tc_HOL_Obool), tc_fun(_1708458, tc_HOL_Obool), _1708456), hAPP(c_COMBS(_1708458, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1708458), c_fimplies), hAPP(hAPP(c_COMBC(_1708458, tc_fun(_1708458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1708458)), _1708460)))), _1708462))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708458, tc_fun(_1708456, tc_HOL_Obool)), _1708460), hAPP(hAPP(c_COMBB(tc_fun(_1708456, tc_HOL_Obool), tc_fun(_1708456, tc_HOL_Obool), _1708458), c_Set_OCollect(_1708456)), hAPP(c_COMBC(_1708456, _1708458, tc_HOL_Obool), _1708462))))], (46524 ^ _779530) ^ [_1708590] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708590, tc_HOL_Obool) = c_Set_OBall(_1708590))], (46526 ^ _779530) ^ [_1708645, _1708647, _1708649, _1708651, _1708653, _1708655] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708645, tc_fun(_1708647, tc_fun(_1708649, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1708645, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_fun(_1708647, tc_fun(_1708649, tc_HOL_Obool)), _1708645), hAPP(c_COMBC(_1708647, tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_fun(_1708649, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708649, tc_fun(tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_fun(_1708649, tc_HOL_Obool)), _1708647), c_COMBC(_1708649, tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1708649, tc_prod(_1708647, _1708649)), tc_fun(_1708649, tc_fun(tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_HOL_Obool)), _1708647), hAPP(c_COMBB(tc_prod(_1708647, _1708649), tc_fun(tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool), tc_HOL_Obool), _1708649), c_member(tc_prod(_1708647, _1708649)))), c_Product__Type_OPair(_1708647, _1708649))))), _1708651)), _1708653), _1708655)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708647, _1708649)), hAPP(hAPP(c_Product__Type_OPair(_1708647, _1708649), _1708653), _1708655)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1708645, tc_fun(tc_prod(_1708647, _1708649), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1708645, tc_HOL_Obool))), _1708651))))], (46532 ^ _779530) ^ [_1709128, _1709130, _1709132, _1709134, _1709136, _1709138] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1709130, _1709132)), hAPP(hAPP(c_Product__Type_OPair(_1709130, _1709132), _1709136), _1709138)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1709128, tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1709128, tc_HOL_Obool))), _1709134))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1709128, tc_fun(_1709130, tc_fun(_1709132, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1709128, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_fun(_1709130, tc_fun(_1709132, tc_HOL_Obool)), _1709128), hAPP(c_COMBC(_1709130, tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_fun(_1709132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1709132, tc_fun(tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_fun(_1709132, tc_HOL_Obool)), _1709130), c_COMBC(_1709132, tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1709132, tc_prod(_1709130, _1709132)), tc_fun(_1709132, tc_fun(tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_HOL_Obool)), _1709130), hAPP(c_COMBB(tc_prod(_1709130, _1709132), tc_fun(tc_fun(tc_prod(_1709130, _1709132), tc_HOL_Obool), tc_HOL_Obool), _1709132), c_member(tc_prod(_1709130, _1709132)))), c_Product__Type_OPair(_1709130, _1709132))))), _1709134)), _1709136), _1709138)))], (46538 ^ _779530) ^ [_1709617, _1709619, _1709621, _1709623, _1709625] : [class_Complete__Lattice_Ocomplete__lattice(_1709617), 46541 ^ _779530 : [(46552 ^ _779530) ^ [] : [46554 ^ _779530 : [(46555 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709621), 46553 ^ [_1709617, _1709619, _1709621, _1709623, _1709625]), _1709623)))], (46557 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709617), _1709619), hAPP(_1709625, 46553 ^ [_1709617, _1709619, _1709621, _1709623, _1709625])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709617), _1709619), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1709621, _1709617), _1709623), _1709625))))], (46542 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709617), _1709619), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1709621, _1709617), _1709623), _1709625))), 46545 ^ _779530 : [(46546 ^ _779530) ^ [_1709798] : [hBOOL(hAPP(hAPP(c_member(_1709621), _1709798), _1709623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709617), _1709619), hAPP(_1709625, _1709798))))]]]]], (46571 ^ _779530) ^ [_1710393, _1710395, _1710397, _1710399, _1710401] : [46573 ^ _779530 : [(46574 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710397), 46572 ^ [_1710393, _1710395, _1710397, _1710399, _1710401]), _1710399)))], (46576 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710393, tc_HOL_Obool)), _1710395), hAPP(_1710401, 46572 ^ [_1710393, _1710395, _1710397, _1710399, _1710401])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710393, tc_HOL_Obool)), _1710395), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710397, tc_fun(_1710393, tc_HOL_Obool)), _1710399), _1710401))))], (46561 ^ _779530) ^ [_1710135, _1710137, _1710139, _1710141, _1710143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710135, tc_HOL_Obool)), _1710137), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710139, tc_fun(_1710135, tc_HOL_Obool)), _1710141), _1710143))), 46564 ^ _779530 : [(46565 ^ _779530) ^ [_1710268] : [hBOOL(hAPP(hAPP(c_member(_1710139), _1710268), _1710141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710135, tc_HOL_Obool)), _1710137), hAPP(_1710143, _1710268))))]]], (46580 ^ _779530) ^ [_1710656, _1710658, _1710660, _1710662, _1710664] : [hBOOL(hAPP(hAPP(c_member(_1710656), _1710658), _1710660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710662, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710656, tc_fun(_1710662, tc_HOL_Obool)), _1710660), _1710664)), hAPP(_1710664, _1710658))))], (46586 ^ _779530) ^ [_1710803, _1710805, _1710807, _1710809, _1710811, _1710813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1710803, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1710805, _1710803, _1710807), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710809, tc_fun(_1710805, tc_HOL_Obool)), _1710811), _1710813))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710809, tc_fun(_1710803, tc_HOL_Obool)), _1710811), hAPP(hAPP(c_COMBB(tc_fun(_1710805, tc_HOL_Obool), tc_fun(_1710803, tc_HOL_Obool), _1710809), c_Relation_OImage(_1710805, _1710803, _1710807)), _1710813)))))], (46588 ^ _779530) ^ [_1710897, _1710899, _1710901, _1710903, _1710905, _1710907] : [class_Complete__Lattice_Ocomplete__lattice(_1710897), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710899, _1710897), _1710901), hAPP(hAPP(c_COMBB(tc_fun(_1710903, _1710897), _1710897, _1710899), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710903, _1710897), _1710905)), _1710907)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710903, _1710897), _1710905), hAPP(hAPP(c_COMBB(tc_fun(_1710899, _1710897), _1710897, _1710903), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1710899, _1710897), _1710901)), hAPP(c_COMBC(_1710899, _1710903, _1710897), _1710907))))], (46594 ^ _779530) ^ [_1711106, _1711108, _1711110, _1711112, _1711114, _1711116] : [class_Complete__Lattice_Ocomplete__lattice(_1711106), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711108, tc_fun(_1711110, _1711106)), _1711112), _1711114), _1711116) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711108, _1711106), _1711112), hAPP(hAPP(c_COMBC(_1711108, _1711110, _1711106), _1711114), _1711116)))], (46600 ^ _779530) ^ [_1711257, _1711259, _1711261, _1711263] : [-(hAPP(c_Set_OPow(_1711257), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711259, tc_fun(_1711257, tc_HOL_Obool)), _1711261), _1711263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711259, tc_fun(tc_fun(_1711257, tc_HOL_Obool), tc_HOL_Obool)), _1711261), hAPP(hAPP(c_COMBB(tc_fun(_1711257, tc_HOL_Obool), tc_fun(tc_fun(_1711257, tc_HOL_Obool), tc_HOL_Obool), _1711259), c_Set_OPow(_1711257)), _1711263)))], (46602 ^ _779530) ^ [_1711339, _1711341, _1711343, _1711345, _1711347] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711339, tc_fun(_1711341, tc_HOL_Obool)), _1711343), hAPP(hAPP(c_COMBB(tc_fun(_1711341, tc_HOL_Obool), tc_fun(_1711341, tc_HOL_Obool), _1711339), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711341, tc_HOL_Obool)), _1711345)), _1711347)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711341, tc_HOL_Obool)), _1711345), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711339, tc_fun(_1711341, tc_HOL_Obool)), _1711343), _1711347)))], (46604 ^ _779530) ^ [_1711429, _1711431, _1711433, _1711435, _1711437] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711429, tc_fun(_1711431, tc_HOL_Obool)), _1711433), hAPP(hAPP(c_COMBC(_1711429, tc_fun(_1711431, tc_HOL_Obool), tc_fun(_1711431, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711431, tc_HOL_Obool), tc_fun(tc_fun(_1711431, tc_HOL_Obool), tc_fun(_1711431, tc_HOL_Obool)), _1711429), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711431, tc_HOL_Obool))), _1711435)), _1711437)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711431, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711429, tc_fun(_1711431, tc_HOL_Obool)), _1711433), _1711435)), _1711437))], (46606 ^ _779530) ^ [_1711538, _1711540, _1711542, _1711544, _1711546] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711538, tc_HOL_Obool)), _1711540), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711542, tc_fun(_1711538, tc_HOL_Obool)), _1711544), _1711546)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711542, tc_fun(_1711538, tc_HOL_Obool)), _1711544), hAPP(hAPP(c_COMBB(tc_fun(_1711538, tc_HOL_Obool), tc_fun(_1711538, tc_HOL_Obool), _1711542), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711538, tc_HOL_Obool)), _1711540)), _1711546)))], (46608 ^ _779530) ^ [_1711628, _1711630, _1711632, _1711634, _1711636] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711628, tc_HOL_Obool)), _1711630), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711632, tc_fun(_1711628, tc_HOL_Obool)), _1711634), _1711636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711632, tc_fun(_1711628, tc_HOL_Obool)), _1711634), hAPP(hAPP(c_COMBB(tc_fun(_1711628, tc_HOL_Obool), tc_fun(_1711628, tc_HOL_Obool), _1711632), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711628, tc_HOL_Obool)), _1711630)), _1711636)))], (46610 ^ _779530) ^ [_1711718, _1711720, _1711722, _1711724, _1711726] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711718, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711720, tc_fun(_1711718, tc_HOL_Obool)), _1711722), _1711724)), _1711726) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711720, tc_fun(_1711718, tc_HOL_Obool)), _1711722), hAPP(hAPP(c_COMBC(_1711720, tc_fun(_1711718, tc_HOL_Obool), tc_fun(_1711718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711718, tc_HOL_Obool), tc_fun(tc_fun(_1711718, tc_HOL_Obool), tc_fun(_1711718, tc_HOL_Obool)), _1711720), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711718, tc_HOL_Obool))), _1711724)), _1711726)))], (46612 ^ _779530) ^ [_1711827, _1711829, _1711831, _1711833, _1711835, _1711837, _1711839] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711827, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711829, tc_fun(_1711827, tc_HOL_Obool)), _1711831), _1711833)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711835, tc_fun(_1711827, tc_HOL_Obool)), _1711837), _1711839)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711829, tc_fun(_1711827, tc_HOL_Obool)), _1711831), hAPP(hAPP(c_COMBB(tc_fun(_1711835, tc_fun(_1711827, tc_HOL_Obool)), tc_fun(_1711827, tc_HOL_Obool), _1711829), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1711835, tc_fun(_1711827, tc_HOL_Obool)), _1711837)), hAPP(hAPP(c_COMBC(_1711829, tc_fun(_1711835, tc_fun(_1711827, tc_HOL_Obool)), tc_fun(_1711835, tc_fun(_1711827, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1711827, tc_HOL_Obool), tc_fun(_1711827, tc_HOL_Obool)), tc_fun(tc_fun(_1711835, tc_fun(_1711827, tc_HOL_Obool)), tc_fun(_1711835, tc_fun(_1711827, tc_HOL_Obool))), _1711829), c_COMBB(tc_fun(_1711827, tc_HOL_Obool), tc_fun(_1711827, tc_HOL_Obool), _1711835)), hAPP(hAPP(c_COMBB(tc_fun(_1711827, tc_HOL_Obool), tc_fun(tc_fun(_1711827, tc_HOL_Obool), tc_fun(_1711827, tc_HOL_Obool)), _1711829), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1711827, tc_HOL_Obool))), _1711833))), _1711839))))], (46614 ^ _779530) ^ [_1712030, _1712032, _1712034, _1712036, _1712038] : [class_Complete__Lattice_Ocomplete__lattice(_1712030), class_Orderings_Olinorder(_1712030), 46621 ^ _779530 : [(46622 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1712030), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712032, _1712030), _1712034), _1712036)), _1712038)), 46626 ^ _779530 : [(46627 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712032), 46625 ^ [_1712030, _1712032, _1712034, _1712036, _1712038]), _1712034)))], (46629 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1712030), hAPP(_1712036, 46625 ^ [_1712030, _1712032, _1712034, _1712036, _1712038])), _1712038)))]]], (46631 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1712030), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712032, _1712030), _1712034), _1712036)), _1712038))), 46632 ^ _779530 : [(46633 ^ _779530) ^ [_1712378] : [hBOOL(hAPP(hAPP(c_member(_1712032), _1712378), _1712034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1712030), hAPP(_1712036, _1712378)), _1712038))]]]]], (46641 ^ _779530) ^ [_1712548, _1712550, _1712552, _1712554, _1712556, _1712558] : [-(hAPP(c_Set_Ovimage(_1712548, _1712550, _1712552), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712554, tc_fun(_1712550, tc_HOL_Obool)), _1712556), _1712558)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712554, tc_fun(_1712548, tc_HOL_Obool)), _1712556), hAPP(hAPP(c_COMBB(tc_fun(_1712550, tc_HOL_Obool), tc_fun(_1712548, tc_HOL_Obool), _1712554), c_Set_Ovimage(_1712548, _1712550, _1712552)), _1712558)))], (46653 ^ _779530) ^ [_1712882, _1712884, _1712886, _1712888] : [46655 ^ _779530 : [(46656 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712882), 46654 ^ [_1712882, _1712884, _1712886, _1712888]), _1712886)))], (46658 ^ _779530) ^ [] : [hAPP(_1712888, 46654 ^ [_1712882, _1712884, _1712886, _1712888]) = c_Orderings_Otop__class_Otop(tc_fun(_1712884, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712882, tc_fun(_1712884, tc_HOL_Obool)), _1712886), _1712888) = c_Orderings_Otop__class_Otop(tc_fun(_1712884, tc_HOL_Obool)))], (46643 ^ _779530) ^ [_1712653, _1712655, _1712657, _1712659] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1712653, tc_fun(_1712655, tc_HOL_Obool)), _1712657), _1712659) = c_Orderings_Otop__class_Otop(tc_fun(_1712655, tc_HOL_Obool)), 46646 ^ _779530 : [(46647 ^ _779530) ^ [_1712769] : [hBOOL(hAPP(hAPP(c_member(_1712653), _1712769), _1712657)), -(hAPP(_1712659, _1712769) = c_Orderings_Otop__class_Otop(tc_fun(_1712655, tc_HOL_Obool)))]]], (46672 ^ _779530) ^ [_1713362, _1713364, _1713366, _1713368] : [46674 ^ _779530 : [(46675 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713364), 46673 ^ [_1713362, _1713364, _1713366, _1713368]), _1713366)))], (46677 ^ _779530) ^ [] : [hAPP(_1713368, 46673 ^ [_1713362, _1713364, _1713366, _1713368]) = c_Orderings_Otop__class_Otop(tc_fun(_1713362, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1713362, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713364, tc_fun(_1713362, tc_HOL_Obool)), _1713366), _1713368))], (46662 ^ _779530) ^ [_1713133, _1713135, _1713137, _1713139] : [c_Orderings_Otop__class_Otop(tc_fun(_1713133, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713135, tc_fun(_1713133, tc_HOL_Obool)), _1713137), _1713139), 46665 ^ _779530 : [(46666 ^ _779530) ^ [_1713249] : [hBOOL(hAPP(hAPP(c_member(_1713135), _1713249), _1713137)), -(hAPP(_1713139, _1713249) = c_Orderings_Otop__class_Otop(tc_fun(_1713133, tc_HOL_Obool)))]]], (46681 ^ _779530) ^ [_1713592, _1713594, _1713596, _1713598, _1713600] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713592, tc_fun(_1713594, tc_HOL_Obool)), _1713596), hAPP(hAPP(c_COMBS(_1713592, tc_fun(_1713594, tc_HOL_Obool), tc_fun(_1713594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1713594, tc_HOL_Obool), tc_fun(tc_fun(_1713594, tc_HOL_Obool), tc_fun(_1713594, tc_HOL_Obool)), _1713592), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1713594, tc_HOL_Obool))), _1713598)), _1713600)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1713594, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713592, tc_fun(_1713594, tc_HOL_Obool)), _1713596), _1713598)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713592, tc_fun(_1713594, tc_HOL_Obool)), _1713596), _1713600)))], (46683 ^ _779530) ^ [_1713713, _1713715, _1713717, _1713719, _1713721] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713713, tc_fun(_1713715, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713713, tc_HOL_Obool)), _1713717), _1713719)), _1713721) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1713715, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713713, tc_fun(_1713715, tc_HOL_Obool)), _1713717), _1713721)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713713, tc_fun(_1713715, tc_HOL_Obool)), _1713719), _1713721)))], (46695 ^ _779530) ^ [_1714069, _1714071, _1714073, _1714075, _1714077] : [46697 ^ _779530 : [(46698 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1714073), 46696 ^ [_1714069, _1714071, _1714073, _1714075, _1714077]), _1714075)))], (46700 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1714069), _1714071), hAPP(_1714077, 46696 ^ [_1714069, _1714071, _1714073, _1714075, _1714077])))]], -(hBOOL(hAPP(hAPP(c_member(_1714069), _1714071), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714073, tc_fun(_1714069, tc_HOL_Obool)), _1714075), _1714077))))], (46685 ^ _779530) ^ [_1713826, _1713828, _1713830, _1713832, _1713834] : [hBOOL(hAPP(hAPP(c_member(_1713826), _1713828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1713830, tc_fun(_1713826, tc_HOL_Obool)), _1713832), _1713834))), 46688 ^ _779530 : [(46689 ^ _779530) ^ [_1713950] : [hBOOL(hAPP(hAPP(c_member(_1713830), _1713950), _1713832)), -(hBOOL(hAPP(hAPP(c_member(_1713826), _1713828), hAPP(_1713834, _1713950))))]]], (46704 ^ _779530) ^ [_1714317, _1714319, _1714321, _1714323, _1714325] : [hBOOL(hAPP(hAPP(c_member(_1714317), _1714319), _1714321)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714323, tc_HOL_Obool)), hAPP(_1714325, _1714319)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714317, tc_fun(_1714323, tc_HOL_Obool)), _1714321), _1714325)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714317, tc_fun(_1714323, tc_HOL_Obool)), _1714321), _1714325))], (46710 ^ _779530) ^ [_1714511, _1714513, _1714515, _1714517] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714511, tc_fun(_1714513, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1714511, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1714513, tc_HOL_Obool), tc_fun(_1714513, tc_HOL_Obool), _1714511), hAPP(c_COMBC(_1714513, tc_fun(_1714513, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714513))), _1714515)), _1714517)), -(hBOOL(hAPP(hAPP(c_member(_1714513), _1714517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714511, tc_fun(_1714513, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1714511, tc_HOL_Obool))), _1714515))))], (46716 ^ _779530) ^ [_1714730, _1714732, _1714734, _1714736] : [hBOOL(hAPP(hAPP(c_member(_1714732), _1714736), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714730, tc_fun(_1714732, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1714730, tc_HOL_Obool))), _1714734))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714730, tc_fun(_1714732, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1714730, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1714732, tc_HOL_Obool), tc_fun(_1714732, tc_HOL_Obool), _1714730), hAPP(c_COMBC(_1714732, tc_fun(_1714732, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714732))), _1714734)), _1714736)))], (46722 ^ _779530) ^ [_1714955, _1714957, _1714959, _1714961, _1714963, _1714965] : [hBOOL(hAPP(hAPP(c_member(_1714955), _1714957), _1714959)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714955, tc_fun(_1714961, tc_HOL_Obool)), _1714959), hAPP(hAPP(c_COMBB(tc_fun(_1714961, tc_HOL_Obool), tc_fun(_1714961, tc_HOL_Obool), _1714955), hAPP(c_Set_Oinsert(_1714961), _1714963)), _1714965)) = hAPP(hAPP(c_Set_Oinsert(_1714961), _1714963), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1714955, tc_fun(_1714961, tc_HOL_Obool)), _1714959), _1714965)))], (46728 ^ _779530) ^ [_1715160, _1715162, _1715164, _1715166, _1715168] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715160, tc_fun(_1715162, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1715160), _1715164), _1715166)), _1715168) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715162, tc_HOL_Obool)), hAPP(_1715168, _1715164)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715160, tc_fun(_1715162, tc_HOL_Obool)), _1715166), _1715168)))], (46730 ^ _779530) ^ [_1715255, _1715257, _1715259, _1715261, _1715263] : [_1715255 = c_Orderings_Obot__class_Obot(tc_fun(_1715257, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715259, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715257, tc_fun(_1715259, tc_HOL_Obool)), _1715255), _1715261)), _1715263) = _1715263)], (46736 ^ _779530) ^ [_1715388, _1715390, _1715392, _1715394, _1715396] : [-(_1715388 = c_Orderings_Obot__class_Obot(tc_fun(_1715390, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715392, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715390, tc_fun(_1715392, tc_HOL_Obool)), _1715388), _1715394)), _1715396) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715390, tc_fun(_1715392, tc_HOL_Obool)), _1715388), hAPP(hAPP(c_COMBC(_1715390, tc_fun(_1715392, tc_HOL_Obool), tc_fun(_1715392, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1715392, tc_HOL_Obool), tc_fun(tc_fun(_1715392, tc_HOL_Obool), tc_fun(_1715392, tc_HOL_Obool)), _1715390), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715392, tc_HOL_Obool))), _1715394)), _1715396)))], (46742 ^ _779530) ^ [_1715533, _1715535, _1715537, _1715539, _1715541] : [_1715533 = c_Orderings_Obot__class_Obot(tc_fun(_1715535, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715537, tc_HOL_Obool)), _1715539), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715535, tc_fun(_1715537, tc_HOL_Obool)), _1715533), _1715541)) = _1715539)], (46748 ^ _779530) ^ [_1715666, _1715668, _1715670, _1715672, _1715674] : [-(_1715666 = c_Orderings_Obot__class_Obot(tc_fun(_1715668, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715670, tc_HOL_Obool)), _1715672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715668, tc_fun(_1715670, tc_HOL_Obool)), _1715666), _1715674)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715668, tc_fun(_1715670, tc_HOL_Obool)), _1715666), hAPP(hAPP(c_COMBB(tc_fun(_1715670, tc_HOL_Obool), tc_fun(_1715670, tc_HOL_Obool), _1715668), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715670, tc_HOL_Obool)), _1715672)), _1715674)))], (46754 ^ _779530) ^ [_1715789, _1715791, _1715793, _1715795] : [_1715789 = c_Orderings_Obot__class_Obot(tc_fun(_1715791, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715791, tc_fun(_1715793, tc_HOL_Obool)), _1715789), hAPP(c_COMBK(tc_fun(_1715793, tc_HOL_Obool), _1715791), _1715795)) = c_Orderings_Otop__class_Otop(tc_fun(_1715793, tc_HOL_Obool)))], (46760 ^ _779530) ^ [_1715926, _1715928, _1715930, _1715932] : [-(_1715926 = c_Orderings_Obot__class_Obot(tc_fun(_1715928, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715928, tc_fun(_1715930, tc_HOL_Obool)), _1715926), hAPP(c_COMBK(tc_fun(_1715930, tc_HOL_Obool), _1715928), _1715932)) = _1715932)], (46766 ^ _779530) ^ [_1715994, _1715996, _1715998] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1715994, tc_fun(_1715996, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1715994, tc_HOL_Obool))), _1715998) = c_Orderings_Otop__class_Otop(tc_fun(_1715996, tc_HOL_Obool)))], (46768 ^ _779530) ^ [_1716043, _1716045, _1716047, _1716049] : [class_Complete__Lattice_Ocomplete__lattice(_1716043), -(_1716045 = c_Orderings_Obot__class_Obot(tc_fun(_1716047, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716047, _1716043), _1716045), hAPP(c_COMBK(_1716043, _1716047), _1716049)) = _1716049)], (46778 ^ _779530) ^ [_1716177, _1716179, _1716181, _1716183, _1716185] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716177, tc_fun(_1716179, tc_HOL_Obool)), _1716181), hAPP(hAPP(c_COMBB(tc_fun(_1716179, tc_HOL_Obool), tc_fun(_1716179, tc_HOL_Obool), _1716177), hAPP(c_Set_Oinsert(_1716179), _1716183)), _1716185)) = hAPP(hAPP(c_Set_Oinsert(_1716179), _1716183), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716177, tc_fun(_1716179, tc_HOL_Obool)), _1716181), _1716185)))], (46780 ^ _779530) ^ [_1716261, _1716263, _1716265, _1716267, _1716269] : [-(hAPP(hAPP(c_Set_Oinsert(_1716261), _1716263), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716265, tc_fun(_1716261, tc_HOL_Obool)), _1716267), _1716269)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716265, tc_fun(_1716261, tc_HOL_Obool)), _1716267), hAPP(hAPP(c_COMBB(tc_fun(_1716261, tc_HOL_Obool), tc_fun(_1716261, tc_HOL_Obool), _1716265), hAPP(c_Set_Oinsert(_1716261), _1716263)), _1716269)))], (46782 ^ _779530) ^ [_1716345, _1716347, _1716349, _1716351] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1716345, tc_HOL_Obool), tc_fun(_1716347, tc_HOL_Obool)), _1716349), hAPP(hAPP(c_COMBC(tc_fun(_1716345, tc_HOL_Obool), tc_fun(_1716345, tc_fun(_1716347, tc_HOL_Obool)), tc_fun(_1716347, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716345, tc_fun(_1716347, tc_HOL_Obool))), _1716351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716345, tc_fun(_1716347, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1716345, tc_HOL_Obool), _1716349)), _1716351))], (46784 ^ _779530) ^ [_1716435, _1716437, _1716439, _1716441] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716435, tc_fun(_1716437, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1716435, tc_HOL_Obool), _1716439)), _1716441) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1716435, tc_HOL_Obool), tc_fun(_1716437, tc_HOL_Obool)), _1716439), hAPP(hAPP(c_COMBC(tc_fun(_1716435, tc_HOL_Obool), tc_fun(_1716435, tc_fun(_1716437, tc_HOL_Obool)), tc_fun(_1716437, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716435, tc_fun(_1716437, tc_HOL_Obool))), _1716441)))], (46786 ^ _779530) ^ [_1716525, _1716527, _1716529, _1716531, _1716533, _1716535] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716525, tc_fun(_1716527, tc_HOL_Obool)), _1716529), hAPP(hAPP(c_COMBB(_1716531, tc_fun(_1716527, tc_HOL_Obool), _1716525), _1716533), _1716535)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716531, tc_fun(_1716527, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1716525, _1716531, _1716535), _1716529)), _1716533))], (46788 ^ _779530) ^ [_1716602, _1716604, _1716606, _1716608, _1716610, _1716612] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716602, tc_fun(_1716604, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1716606, _1716602, _1716608), _1716610)), _1716612) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716606, tc_fun(_1716604, tc_HOL_Obool)), _1716610), hAPP(hAPP(c_COMBB(_1716602, tc_fun(_1716604, tc_HOL_Obool), _1716606), _1716612), _1716608)))], (46790 ^ _779530) ^ [_1716679, _1716681, _1716683, _1716685] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716679, tc_fun(_1716681, tc_HOL_Obool)), _1716683), _1716685) = hAPP(c_Set_OCollect(_1716681), hAPP(hAPP(c_COMBB(tc_fun(_1716679, tc_HOL_Obool), tc_HOL_Obool, _1716681), c_HOL_OAll(_1716679)), hAPP(hAPP(c_COMBB(tc_fun(_1716679, tc_HOL_Obool), tc_fun(_1716679, tc_HOL_Obool), _1716681), hAPP(c_COMBS(_1716679, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1716679), c_fimplies), hAPP(hAPP(c_COMBC(_1716679, tc_fun(_1716679, tc_HOL_Obool), tc_HOL_Obool), c_member(_1716679)), _1716683)))), hAPP(hAPP(c_COMBC(_1716681, tc_fun(_1716679, tc_fun(_1716681, tc_HOL_Obool)), tc_fun(_1716679, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1716681, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1716679, tc_fun(_1716681, tc_HOL_Obool)), tc_fun(_1716679, tc_HOL_Obool)), _1716681), c_COMBB(tc_fun(_1716681, tc_HOL_Obool), tc_HOL_Obool, _1716679)), c_member(_1716681))), _1716685)))))], (46792 ^ _779530) ^ [_1716862, _1716864, _1716866, _1716868, _1716870] : [_1716862 = c_Orderings_Obot__class_Obot(tc_fun(_1716864, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1716864, tc_fun(_1716866, tc_HOL_Obool)), _1716862), hAPP(hAPP(c_COMBB(tc_fun(_1716866, tc_HOL_Obool), tc_fun(_1716866, tc_HOL_Obool), _1716864), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1716866, tc_HOL_Obool)), _1716868)), _1716870)) = c_Orderings_Otop__class_Otop(tc_fun(_1716866, tc_HOL_Obool)))], (46798 ^ _779530) ^ [_1717031, _1717033, _1717035, _1717037, _1717039] : [-(_1717031 = c_Orderings_Obot__class_Obot(tc_fun(_1717033, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717033, tc_fun(_1717035, tc_HOL_Obool)), _1717031), hAPP(hAPP(c_COMBB(tc_fun(_1717035, tc_HOL_Obool), tc_fun(_1717035, tc_HOL_Obool), _1717033), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717035, tc_HOL_Obool)), _1717037)), _1717039)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717035, tc_HOL_Obool)), _1717037), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717033, tc_fun(_1717035, tc_HOL_Obool)), _1717031), _1717039)))], (46804 ^ _779530) ^ [_1717157, _1717159, _1717161, _1717163, _1717165] : [_1717157 = c_Orderings_Obot__class_Obot(tc_fun(_1717159, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717159, tc_fun(_1717161, tc_HOL_Obool)), _1717157), hAPP(hAPP(c_COMBC(_1717159, tc_fun(_1717161, tc_HOL_Obool), tc_fun(_1717161, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1717161, tc_HOL_Obool), tc_fun(tc_fun(_1717161, tc_HOL_Obool), tc_fun(_1717161, tc_HOL_Obool)), _1717159), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717161, tc_HOL_Obool))), _1717163)), _1717165)) = c_Orderings_Otop__class_Otop(tc_fun(_1717161, tc_HOL_Obool)))], (46810 ^ _779530) ^ [_1717364, _1717366, _1717368, _1717370, _1717372] : [-(_1717364 = c_Orderings_Obot__class_Obot(tc_fun(_1717366, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717366, tc_fun(_1717368, tc_HOL_Obool)), _1717364), hAPP(hAPP(c_COMBC(_1717366, tc_fun(_1717368, tc_HOL_Obool), tc_fun(_1717368, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1717368, tc_HOL_Obool), tc_fun(tc_fun(_1717368, tc_HOL_Obool), tc_fun(_1717368, tc_HOL_Obool)), _1717366), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717368, tc_HOL_Obool))), _1717370)), _1717372)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717368, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717366, tc_fun(_1717368, tc_HOL_Obool)), _1717364), _1717370)), _1717372))], (46816 ^ _779530) ^ [_1717509, _1717511, _1717513, _1717515, _1717517] : [_1717509 = c_Orderings_Obot__class_Obot(tc_fun(_1717511, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717511, tc_fun(_1717513, tc_HOL_Obool)), _1717509), hAPP(hAPP(c_COMBC(_1717511, tc_fun(_1717513, tc_HOL_Obool), tc_fun(_1717513, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1717513, tc_HOL_Obool), tc_fun(tc_fun(_1717513, tc_HOL_Obool), tc_fun(_1717513, tc_HOL_Obool)), _1717511), c_Groups_Ominus__class_Ominus(tc_fun(_1717513, tc_HOL_Obool))), _1717515)), _1717517)) = c_Orderings_Otop__class_Otop(tc_fun(_1717513, tc_HOL_Obool)))], (46822 ^ _779530) ^ [_1717716, _1717718, _1717720, _1717722, _1717724] : [-(_1717716 = c_Orderings_Obot__class_Obot(tc_fun(_1717718, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717718, tc_fun(_1717720, tc_HOL_Obool)), _1717716), hAPP(hAPP(c_COMBC(_1717718, tc_fun(_1717720, tc_HOL_Obool), tc_fun(_1717720, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1717720, tc_HOL_Obool), tc_fun(tc_fun(_1717720, tc_HOL_Obool), tc_fun(_1717720, tc_HOL_Obool)), _1717718), c_Groups_Ominus__class_Ominus(tc_fun(_1717720, tc_HOL_Obool))), _1717722)), _1717724)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1717720, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717718, tc_fun(_1717720, tc_HOL_Obool)), _1717716), _1717722)), _1717724))], (46828 ^ _779530) ^ [_1717861, _1717863, _1717865, _1717867, _1717869] : [_1717861 = c_Orderings_Obot__class_Obot(tc_fun(_1717863, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1717865, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1717863, tc_fun(_1717865, tc_HOL_Obool)), _1717861), _1717867)), _1717869) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1717865, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1717865, tc_HOL_Obool))), _1717869))], (46834 ^ _779530) ^ [_1718026, _1718028, _1718030, _1718032, _1718034] : [-(_1718026 = c_Orderings_Obot__class_Obot(tc_fun(_1718028, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718030, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718028, tc_fun(_1718030, tc_HOL_Obool)), _1718026), _1718032)), _1718034) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718028, tc_fun(_1718030, tc_HOL_Obool)), _1718026), hAPP(hAPP(c_COMBC(_1718028, tc_fun(_1718030, tc_HOL_Obool), tc_fun(_1718030, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1718030, tc_HOL_Obool), tc_fun(tc_fun(_1718030, tc_HOL_Obool), tc_fun(_1718030, tc_HOL_Obool)), _1718028), c_Groups_Ominus__class_Ominus(tc_fun(_1718030, tc_HOL_Obool))), _1718032)), _1718034)))], (46840 ^ _779530) ^ [_1718171, _1718173, _1718175, _1718177, _1718179] : [_1718171 = c_Orderings_Obot__class_Obot(tc_fun(_1718173, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718175, tc_HOL_Obool)), _1718177), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1718173, tc_fun(_1718175, tc_HOL_Obool)), _1718171), _1718179)) = _1718177)], (46846 ^ _779530) ^ [_1718304, _1718306, _1718308, _1718310, _1718312] : [-(_1718304 = c_Orderings_Obot__class_Obot(tc_fun(_1718306, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718308, tc_HOL_Obool)), _1718310), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1718306, tc_fun(_1718308, tc_HOL_Obool)), _1718304), _1718312)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718306, tc_fun(_1718308, tc_HOL_Obool)), _1718304), hAPP(hAPP(c_COMBB(tc_fun(_1718308, tc_HOL_Obool), tc_fun(_1718308, tc_HOL_Obool), _1718306), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718308, tc_HOL_Obool)), _1718310)), _1718312)))], (46852 ^ _779530) ^ [_1718412, _1718414, _1718416, _1718418, _1718420] : [class_Complete__Lattice_Ocomplete__lattice(_1718412), hBOOL(hAPP(hAPP(c_member(_1718414), _1718416), _1718418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718412), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718414, _1718412), _1718418), _1718420)), hAPP(_1718420, _1718416))))], (46862 ^ _779530) ^ [] : [-(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)))], (46864 ^ _779530) ^ [_1718639, _1718641, _1718643, _1718645, _1718647] : [_1718639 = c_Orderings_Obot__class_Obot(tc_fun(_1718641, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718641, tc_fun(_1718643, tc_HOL_Obool)), _1718639), hAPP(hAPP(c_COMBB(tc_fun(_1718643, tc_HOL_Obool), tc_fun(_1718643, tc_HOL_Obool), _1718641), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718643, tc_HOL_Obool)), _1718645)), _1718647)) = c_Orderings_Otop__class_Otop(tc_fun(_1718643, tc_HOL_Obool)))], (46870 ^ _779530) ^ [_1718808, _1718810, _1718812, _1718814, _1718816] : [-(_1718808 = c_Orderings_Obot__class_Obot(tc_fun(_1718810, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1718810, tc_fun(_1718812, tc_HOL_Obool)), _1718808), hAPP(hAPP(c_COMBB(tc_fun(_1718812, tc_HOL_Obool), tc_fun(_1718812, tc_HOL_Obool), _1718810), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718812, tc_HOL_Obool)), _1718814)), _1718816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1718812, tc_HOL_Obool)), _1718814), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1718810, tc_fun(_1718812, tc_HOL_Obool)), _1718808), _1718816)))], (46876 ^ _779530) ^ [_1718916, _1718918, _1718920] : [-(c_List_Olistsp(_1718916, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1718916, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1718916, tc_fun(_1718916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718916)), _1718918)), hAPP(hAPP(c_COMBC(_1718916, tc_fun(_1718916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1718916)), _1718920))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1718916), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1718916), tc_fun(tc_List_Olist(_1718916), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1718916))), c_List_Olists(_1718916, _1718918))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1718916), tc_fun(tc_List_Olist(_1718916), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1718916))), c_List_Olists(_1718916, _1718920))))], (46878 ^ _779530) ^ [_1719048, _1719050, _1719052, _1719054] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1719048)), _1719050), c_List_Olists(_1719048, _1719052))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1719048)), _1719050), c_List_Olists(_1719048, _1719054))), -(hBOOL(hAPP(c_List_Olistsp(_1719048, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1719048, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1719048, tc_fun(_1719048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1719048)), _1719052)), hAPP(hAPP(c_COMBC(_1719048, tc_fun(_1719048, tc_HOL_Obool), tc_HOL_Obool), c_member(_1719048)), _1719054))), _1719050)))], (46888 ^ _779530) ^ [_1719325, _1719327] : [-(hBOOL(hAPP(c_List_Olistsp(_1719325, _1719327), c_List_Olist_ONil(_1719325))))], (46900 ^ _779530) ^ [_1719634, _1719636, _1719638, _1719640, _1719642, _1719644, _1719646] : [46902 ^ _779530 : [(46903 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719634), 46901 ^ [_1719634, _1719636, _1719638, _1719640, _1719642, _1719644, _1719646]), _1719640)))], (46905 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1719642, 46901 ^ [_1719634, _1719636, _1719638, _1719640, _1719642, _1719644, _1719646]), _1719644), _1719646))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1719634, tc_fun(_1719636, tc_fun(_1719638, tc_HOL_Obool))), _1719640), _1719642), _1719644), _1719646)))], (46890 ^ _779530) ^ [_1719387, _1719389, _1719391, _1719393, _1719395, _1719397, _1719399] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1719387, tc_fun(_1719389, tc_fun(_1719391, tc_HOL_Obool))), _1719393), _1719395), _1719397), _1719399)), 46893 ^ _779530 : [(46894 ^ _779530) ^ [_1719515] : [hBOOL(hAPP(hAPP(c_member(_1719387), _1719515), _1719393)), -(hBOOL(hAPP(hAPP(hAPP(_1719395, _1719515), _1719397), _1719399)))]]], (46919 ^ _779530) ^ [_1720136, _1720138, _1720140, _1720142, _1720144] : [46921 ^ _779530 : [(46922 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720136), 46920 ^ [_1720136, _1720138, _1720140, _1720142, _1720144]), _1720140)))], (46924 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1720142, 46920 ^ [_1720136, _1720138, _1720140, _1720142, _1720144]), _1720144))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1720136, tc_fun(_1720138, tc_HOL_Obool)), _1720140), _1720142), _1720144)))], (46909 ^ _779530) ^ [_1719918, _1719920, _1719922, _1719924, _1719926] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1719918, tc_fun(_1719920, tc_HOL_Obool)), _1719922), _1719924), _1719926)), 46912 ^ _779530 : [(46913 ^ _779530) ^ [_1720027] : [hBOOL(hAPP(hAPP(c_member(_1719918), _1720027), _1719922)), -(hBOOL(hAPP(hAPP(_1719924, _1720027), _1719926)))]]], (46928 ^ _779530) ^ [_1720380, _1720382, _1720384, _1720386] : [hBOOL(hAPP(c_List_Olistsp(_1720380, _1720382), hAPP(hAPP(c_List_Oappend(_1720380), _1720384), _1720386))), 46931 ^ _779530 : [(46932 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1720380, _1720382), _1720384)))], (46934 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1720380, _1720382), _1720386)))]]], (46936 ^ _779530) ^ [_1720529, _1720531, _1720533, _1720535] : [-(hBOOL(hAPP(c_List_Olistsp(_1720529, _1720531), hAPP(hAPP(c_List_Oappend(_1720529), _1720533), _1720535)))), hBOOL(hAPP(c_List_Olistsp(_1720529, _1720531), _1720533)), hBOOL(hAPP(c_List_Olistsp(_1720529, _1720531), _1720535))], (46946 ^ _779530) ^ [_1720714, _1720716] : [-(hBOOL(hAPP(c_List_Olistsp(_1720714, _1720716), c_List_Olist_ONil(_1720714))))], (46948 ^ _779530) ^ [_1720746, _1720748, _1720750, _1720752] : [hBOOL(hAPP(c_List_Olistsp(_1720746, _1720748), _1720750)), hBOOL(hAPP(c_List_Olistsp(_1720746, _1720752), _1720750)), -(hBOOL(hAPP(c_List_Olistsp(_1720746, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1720746, tc_HOL_Obool)), _1720748), _1720752)), _1720750)))], (46958 ^ _779530) ^ [_1720935, _1720937, _1720939] : [-(c_List_Olistsp(_1720935, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1720935, tc_HOL_Obool)), _1720937), _1720939)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1720935), tc_HOL_Obool)), c_List_Olistsp(_1720935, _1720937)), c_List_Olistsp(_1720935, _1720939)))], (46960 ^ _779530) ^ [_1721016, _1721018, _1721020, _1721022] : [hBOOL(hAPP(c_List_Olistsp(_1721016, hAPP(hAPP(c_COMBS(_1721016, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1721016), c_fconj), _1721018)), _1721020)), _1721022)), 46963 ^ _779530 : [(46964 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1721016, _1721018), _1721022)))], (46966 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1721016, _1721020), _1721022)))]]], (46968 ^ _779530) ^ [_1721189, _1721191, _1721193, _1721195] : [-(hBOOL(hAPP(c_List_Olistsp(_1721189, hAPP(hAPP(c_COMBS(_1721189, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1721189), c_fconj), _1721191)), _1721193)), _1721195))), hBOOL(hAPP(c_List_Olistsp(_1721189, _1721191), _1721195)), hBOOL(hAPP(c_List_Olistsp(_1721189, _1721193), _1721195))], (46978 ^ _779530) ^ [_1721419, _1721421, _1721423, _1721425] : [hBOOL(hAPP(c_List_Olistsp(_1721419, _1721421), hAPP(hAPP(c_List_Olist_OCons(_1721419), _1721423), _1721425))), 46981 ^ _779530 : [(46982 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1721421, _1721423)))], (46984 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1721419, _1721421), _1721425)))]]], (46986 ^ _779530) ^ [_1721562, _1721564, _1721566, _1721568] : [-(hBOOL(hAPP(c_List_Olistsp(_1721562, _1721564), hAPP(hAPP(c_List_Olist_OCons(_1721562), _1721566), _1721568)))), hBOOL(hAPP(_1721564, _1721566)), hBOOL(hAPP(c_List_Olistsp(_1721562, _1721564), _1721568))], (47006 ^ _779530) ^ [_1721957, _1721959, _1721961] : [47008 ^ _779530 : [(47009 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721957), 47007 ^ [_1721957, _1721959, _1721961]), hAPP(c_List_Oset(_1721957), _1721961))))], (47011 ^ _779530) ^ [] : [hBOOL(hAPP(_1721959, 47007 ^ [_1721957, _1721959, _1721961]))]], -(hBOOL(hAPP(c_List_Olistsp(_1721957, _1721959), _1721961)))], (46996 ^ _779530) ^ [_1721759, _1721761, _1721763] : [hBOOL(hAPP(c_List_Olistsp(_1721759, _1721761), _1721763)), 46999 ^ _779530 : [(47000 ^ _779530) ^ [_1721848] : [hBOOL(hAPP(hAPP(c_member(_1721759), _1721848), hAPP(c_List_Oset(_1721759), _1721763))), -(hBOOL(hAPP(_1721761, _1721848)))]]], (47015 ^ _779530) ^ [_1722147, _1722149, _1722151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722147, tc_HOL_Obool)), _1722149), _1722151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1722147), tc_HOL_Obool)), c_List_Olistsp(_1722147, _1722149)), c_List_Olistsp(_1722147, _1722151))))], (47021 ^ _779530) ^ [_1722300, _1722302, _1722304] : [hBOOL(hAPP(c_List_Olistsp(_1722300, hAPP(hAPP(c_COMBC(_1722300, tc_fun(_1722300, tc_HOL_Obool), tc_HOL_Obool), c_member(_1722300)), _1722302)), _1722304)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1722300)), _1722304), c_List_Olists(_1722300, _1722302))))], (47027 ^ _779530) ^ [_1722439, _1722441, _1722443] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1722439)), _1722443), c_List_Olists(_1722439, _1722441))), -(hBOOL(hAPP(c_List_Olistsp(_1722439, hAPP(hAPP(c_COMBC(_1722439, tc_fun(_1722439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1722439)), _1722441)), _1722443)))], (47033 ^ _779530) ^ [_1722584, _1722586, _1722588, _1722590, _1722592, _1722594, _1722596, _1722598] : [c_Fun_Oinj__on(_1722584, _1722586, _1722588, _1722590), 47039 ^ _779530 : [(47040 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1722592), 47038 ^ [_1722584, _1722586, _1722588, _1722590, _1722592, _1722594, _1722596, _1722598]), _1722594)))], (47042 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722584, tc_HOL_Obool)), hAPP(_1722596, 47038 ^ [_1722584, _1722586, _1722588, _1722590, _1722592, _1722594, _1722596, _1722598])), _1722590))]], hBOOL(hAPP(hAPP(c_member(_1722592), _1722598), _1722594)), -(hAPP(c_Set_Oimage(_1722584, _1722586, _1722588), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722592, tc_fun(_1722584, tc_HOL_Obool)), _1722594), _1722596)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722592, tc_fun(_1722586, tc_HOL_Obool)), _1722594), hAPP(hAPP(c_COMBB(tc_fun(_1722584, tc_HOL_Obool), tc_fun(_1722586, tc_HOL_Obool), _1722592), c_Set_Oimage(_1722584, _1722586, _1722588)), _1722596)))], (47050 ^ _779530) ^ [_1723073, _1723075] : [class_Complete__Lattice_Ocomplete__lattice(_1723073), -(c_Complete__Lattice_OSup__class_OSup(_1723073, _1723075) = c_Complete__Lattice_OInf__class_OInf(_1723073, hAPP(c_Set_OCollect(_1723073), hAPP(hAPP(c_COMBB(tc_fun(_1723073, tc_HOL_Obool), tc_HOL_Obool, _1723073), c_HOL_OAll(_1723073)), hAPP(hAPP(c_COMBB(tc_fun(_1723073, tc_HOL_Obool), tc_fun(_1723073, tc_HOL_Obool), _1723073), hAPP(c_COMBS(_1723073, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1723073), c_fimplies), hAPP(hAPP(c_COMBC(_1723073, tc_fun(_1723073, tc_HOL_Obool), tc_HOL_Obool), c_member(_1723073)), _1723075)))), hAPP(c_COMBC(_1723073, _1723073, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1723073)))))))], (47056 ^ _779530) ^ [_1723314, _1723316] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1723314), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1723314, tc_HOL_Obool), _1723316)))), 47057 ^ _779530 : [(47058 ^ _779530) ^ [_1723378] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1723314, tc_HOL_Obool)), _1723378), _1723316)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1723314), _1723378))]]], (47066 ^ _779530) ^ [_1723522, _1723524, _1723526, _1723528] : [hBOOL(hAPP(hAPP(c_member(_1723522), _1723524), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1723522, tc_HOL_Obool), _1723526))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1723522, tc_HOL_Obool)), _1723528), _1723526)), -(hBOOL(hAPP(hAPP(c_member(_1723522), _1723524), _1723528)))], (47076 ^ _779530) ^ [_1723719, _1723721, _1723723, _1723725] : [hBOOL(hAPP(hAPP(c_member(_1723719), _1723721), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1723719, tc_HOL_Obool), _1723723))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1723719, tc_HOL_Obool)), _1723725), _1723723)), -(hBOOL(hAPP(hAPP(c_member(_1723719), _1723721), _1723725)))], (47086 ^ _779530) ^ [_1723916, _1723918] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1723916, tc_HOL_Obool), _1723918) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1723916, tc_HOL_Obool), tc_fun(_1723916, tc_HOL_Obool)), _1723918), c_COMBI(tc_fun(_1723916, tc_HOL_Obool))))], (47088 ^ _779530) ^ [_1723967, _1723969, _1723971, _1723973] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1723967, tc_HOL_Obool), hAPP(c_Set_Oimage(_1723969, tc_fun(_1723967, tc_HOL_Obool), _1723971), _1723973)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1723969, tc_fun(_1723967, tc_HOL_Obool)), _1723973), _1723971))], (47090 ^ _779530) ^ [_1724024, _1724026, _1724028, _1724030] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1724024, tc_fun(_1724026, tc_HOL_Obool)), _1724028), _1724030) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724026, tc_HOL_Obool), hAPP(c_Set_Oimage(_1724024, tc_fun(_1724026, tc_HOL_Obool), _1724030), _1724028)))], (47092 ^ _779530) ^ [_1724081, _1724083, _1724085] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724081, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1724081, tc_HOL_Obool)), _1724083), _1724085)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1724081, tc_HOL_Obool)), _1724083), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724081, tc_HOL_Obool), _1724085)))], (47094 ^ _779530) ^ [_1724142, _1724144, _1724146] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724142, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1724142, tc_HOL_Obool), tc_HOL_Obool)), _1724144), _1724146)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1724142, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724142, tc_HOL_Obool), _1724144)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724142, tc_HOL_Obool), _1724146)))], (47096 ^ _779530) ^ [_1724212, _1724214] : [class_Complete__Lattice_Ocomplete__lattice(_1724212), -(c_Complete__Lattice_OInf__class_OInf(_1724212, hAPP(hAPP(c_Set_Oinsert(_1724212), _1724214), c_Orderings_Obot__class_Obot(tc_fun(_1724212, tc_HOL_Obool)))) = _1724214)], (47102 ^ _779530) ^ [_1724319] : [class_Complete__Lattice_Ocomplete__lattice(_1724319), -(c_Complete__Lattice_OInf__class_OInf(_1724319, c_Orderings_Obot__class_Obot(tc_fun(_1724319, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1724319))], (47108 ^ _779530) ^ [_1724412] : [class_Complete__Lattice_Ocomplete__lattice(_1724412), -(c_Complete__Lattice_OInf__class_OInf(_1724412, c_Orderings_Otop__class_Otop(tc_fun(_1724412, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1724412))], (47114 ^ _779530) ^ [_1724505, _1724507, _1724509] : [class_Complete__Lattice_Ocomplete__lattice(_1724505), -(c_Complete__Lattice_OInf__class_OInf(_1724505, hAPP(hAPP(c_Set_Oinsert(_1724505), _1724507), _1724509)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1724505), _1724507), c_Complete__Lattice_OInf__class_OInf(_1724505, _1724509)))], (47120 ^ _779530) ^ [_1724626, _1724628, _1724630] : [class_Complete__Lattice_Ocomplete__lattice(_1724626), hBOOL(hAPP(hAPP(c_member(_1724626), _1724628), _1724630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1724626), c_Complete__Lattice_OInf__class_OInf(_1724626, _1724630)), _1724628)))], (47130 ^ _779530) ^ [_1724791, _1724793] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724791, tc_HOL_Obool), _1724793) = hAPP(c_Set_OCollect(_1724791), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1724791, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1724791), c_HOL_OAll(tc_fun(_1724791, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1724791, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1724791, tc_HOL_Obool), tc_HOL_Obool), _1724791), hAPP(c_COMBS(tc_fun(_1724791, 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(_1724791, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1724791, tc_HOL_Obool), tc_fun(tc_fun(_1724791, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1724791, tc_HOL_Obool))), _1724793)))), c_member(_1724791)))))], (47132 ^ _779530) ^ [_1724919, _1724921, _1724923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1724919, tc_HOL_Obool), tc_HOL_Obool)), _1724921), _1724923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1724919, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724919, tc_HOL_Obool), _1724923)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724919, tc_HOL_Obool), _1724921))))], (47138 ^ _779530) ^ [_1725068] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1725068, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1725068, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1725068, tc_HOL_Obool)))], (47140 ^ _779530) ^ [_1725110, _1725112, _1725114] : [class_Complete__Lattice_Ocomplete__lattice(_1725110), 47143 ^ _779530 : [(47154 ^ _779530) ^ [] : [47156 ^ _779530 : [(47157 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725110), 47155 ^ [_1725110, _1725112, _1725114]), _1725114)))], (47159 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725110), _1725112), 47155 ^ [_1725110, _1725112, _1725114]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725110), _1725112), c_Complete__Lattice_OInf__class_OInf(_1725110, _1725114))))], (47144 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725110), _1725112), c_Complete__Lattice_OInf__class_OInf(_1725110, _1725114))), 47147 ^ _779530 : [(47148 ^ _779530) ^ [_1725268] : [hBOOL(hAPP(hAPP(c_member(_1725110), _1725268), _1725114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725110), _1725112), _1725268)))]]]]], (47163 ^ _779530) ^ [_1725544, _1725546, _1725548] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1725544, tc_HOL_Obool)), _1725546), _1725548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1725544, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1725544, tc_HOL_Obool), _1725548)), _1725546)))], (47169 ^ _779530) ^ [_1725675, _1725677, _1725679] : [class_Complete__Lattice_Ocomplete__lattice(_1725675), class_Orderings_Olinorder(_1725675), 47176 ^ _779530 : [(47177 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1725675), c_Complete__Lattice_OInf__class_OInf(_1725675, _1725677)), _1725679)), 47181 ^ _779530 : [(47182 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725675), 47180 ^ [_1725675, _1725677, _1725679]), _1725677)))], (47184 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1725675), 47180 ^ [_1725675, _1725677, _1725679]), _1725679)))]]], (47186 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1725675), c_Complete__Lattice_OInf__class_OInf(_1725675, _1725677)), _1725679))), 47187 ^ _779530 : [(47188 ^ _779530) ^ [_1725981] : [hBOOL(hAPP(hAPP(c_member(_1725675), _1725981), _1725677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1725675), _1725981), _1725679))]]]]], (47196 ^ _779530) ^ [_1726135] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726135, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1726135, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1726135, tc_HOL_Obool)))], (47198 ^ _779530) ^ [_1726177, _1726179, _1726181] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1726177, tc_HOL_Obool)), _1726179), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726177, tc_HOL_Obool), _1726181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1726177, tc_HOL_Obool), tc_fun(_1726177, tc_HOL_Obool)), _1726181), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1726177, tc_HOL_Obool)), _1726179)))], (47200 ^ _779530) ^ [_1726244, _1726246, _1726248] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726244, tc_HOL_Obool)), _1726246), _1726248) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726244, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1726244, tc_HOL_Obool)), _1726246), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1726244, tc_HOL_Obool)), _1726248), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1726244, tc_HOL_Obool), tc_HOL_Obool))))))], (47202 ^ _779530) ^ [_1726318, _1726320, _1726322, _1726324, _1726326] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1726318, tc_fun(_1726320, tc_HOL_Obool)), _1726322), hAPP(hAPP(c_COMBS(_1726318, tc_fun(_1726320, tc_HOL_Obool), tc_fun(_1726320, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726320, tc_HOL_Obool), tc_fun(tc_fun(_1726320, tc_HOL_Obool), tc_fun(_1726320, tc_HOL_Obool)), _1726318), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726320, tc_HOL_Obool))), _1726324)), _1726326)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726320, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726320, tc_HOL_Obool), hAPP(c_Set_Oimage(_1726318, tc_fun(_1726320, tc_HOL_Obool), _1726324), _1726322))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726320, tc_HOL_Obool), hAPP(c_Set_Oimage(_1726318, tc_fun(_1726320, tc_HOL_Obool), _1726326), _1726322))))], (47204 ^ _779530) ^ [_1726447, _1726449, _1726451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1726447, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1726447, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726447, tc_HOL_Obool), _1726449)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726447, tc_HOL_Obool), _1726451))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1726447, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1726447, tc_HOL_Obool), tc_HOL_Obool)), _1726449), _1726451)))))], (47206 ^ _779530) ^ [_1726527, _1726529, _1726531] : [class_Complete__Lattice_Ocomplete__lattice(_1726527), -(c_Complete__Lattice_OInf__class_OInf(_1726527, hAPP(hAPP(c_Set_Oinsert(_1726527), _1726529), hAPP(hAPP(c_Set_Oinsert(_1726527), _1726531), c_Orderings_Obot__class_Obot(tc_fun(_1726527, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1726527), _1726529), _1726531))], (47212 ^ _779530) ^ [_1726668, _1726670] : [class_Complete__Lattice_Ocomplete__lattice(_1726668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1726668), _1726670)), -(_1726670 = c_Orderings_Obot__class_Obot(tc_fun(_1726668, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1726668, _1726670) = c_Complete__Lattice_OInf__class_OInf(_1726668, _1726670))], (47226 ^ _779530) ^ [_1726840, _1726842] : [class_Complete__Lattice_Ocomplete__lattice(_1726840), -(c_Complete__Lattice_OInf__class_OInf(_1726840, hAPP(c_List_Oset(_1726840), _1726842)) = hAPP(c_List_Ofoldl(_1726840, _1726840, c_Lattices_Osemilattice__inf__class_Oinf(_1726840), c_Orderings_Otop__class_Otop(_1726840)), _1726842))], (47232 ^ _779530) ^ [_1726955, _1726957] : [class_Complete__Lattice_Ocomplete__lattice(_1726955), -(c_Complete__Lattice_OInf__class_OInf(_1726955, _1726957) = c_Complete__Lattice_OSup__class_OSup(_1726955, hAPP(c_Set_OCollect(_1726955), hAPP(hAPP(c_COMBB(tc_fun(_1726955, tc_HOL_Obool), tc_HOL_Obool, _1726955), c_HOL_OAll(_1726955)), hAPP(hAPP(c_COMBB(tc_fun(_1726955, tc_HOL_Obool), tc_fun(_1726955, tc_HOL_Obool), _1726955), hAPP(c_COMBS(_1726955, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1726955), c_fimplies), hAPP(hAPP(c_COMBC(_1726955, tc_fun(_1726955, tc_HOL_Obool), tc_HOL_Obool), c_member(_1726955)), _1726957)))), c_Orderings_Oord__class_Oless__eq(_1726955))))))], (47238 ^ _779530) ^ [_1727206, _1727208, _1727210, _1727212, _1727214] : [c_List_Olist__all2(_1727206, _1727208, _1727210, _1727212, _1727214), 47241 ^ _779530 : [(47242 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727206)), _1727212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727208)), _1727214))], (47244 ^ _779530) ^ [_1727372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1727206, _1727208)), _1727372), hAPP(c_List_Oset(tc_prod(_1727206, _1727208)), hAPP(hAPP(c_List_Ozip(_1727206, _1727208), _1727212), _1727214)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1727206, _1727208, tc_HOL_Obool), _1727210), _1727372)))]]], (47250 ^ _779530) ^ [_1727531, _1727533, _1727535, _1727537, _1727539] : [-(c_List_Olist__all2(_1727531, _1727533, _1727535, _1727537, _1727539)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727531)), _1727537) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727533)), _1727539), 47256 ^ _779530 : [(47257 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1727531, _1727533)), 47255 ^ [_1727531, _1727533, _1727535, _1727537, _1727539]), hAPP(c_List_Oset(tc_prod(_1727531, _1727533)), hAPP(hAPP(c_List_Ozip(_1727531, _1727533), _1727537), _1727539)))))], (47259 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1727531, _1727533, tc_HOL_Obool), _1727535), 47255 ^ [_1727531, _1727533, _1727535, _1727537, _1727539]))]]], (47263 ^ _779530) ^ [_1727872, _1727874] : [class_Orderings_Olinorder(_1727872), 47266 ^ _779530 : [(47267 ^ _779530) ^ [] : [c_List_Olinorder__class_Osorted(_1727872, _1727874), -(_1727874 = c_List_Olist_ONil(_1727872)), 47276 ^ _779530 : [(47277 ^ _779530) ^ [] : [-(_1727874 = hAPP(hAPP(c_List_Olist_OCons(_1727872), 47275 ^ [_1727872, _1727874]), 47274 ^ [_1727872, _1727874]))], (47285 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727872, 47274 ^ [_1727872, _1727874]))], (47279 ^ _779530) ^ [_1728206] : [hBOOL(hAPP(hAPP(c_member(_1727872), _1728206), hAPP(c_List_Oset(_1727872), 47274 ^ [_1727872, _1727874]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727872), 47275 ^ [_1727872, _1727874]), _1728206)))]]], (47287 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727872, _1727874)), 47288 ^ _779530 : [(47289 ^ _779530) ^ [] : [_1727874 = c_List_Olist_ONil(_1727872)], (47291 ^ _779530) ^ [_1728432, _1728434] : [_1727874 = hAPP(hAPP(c_List_Olist_OCons(_1727872), _1728432), _1728434), 47297 ^ _779530 : [(47298 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727872), 47296 ^ [_1727872, _1727874, _1728432, _1728434]), hAPP(c_List_Oset(_1727872), _1728434))))], (47300 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727872), _1728432), 47296 ^ [_1727872, _1727874, _1728432, _1728434]))]], c_List_Olinorder__class_Osorted(_1727872, _1728434)]]]]], (47306 ^ _779530) ^ [_1728741, _1728743, _1728745, _1728747, _1728749, _1728751, _1728753] : [c_List_Olist__all2(_1728741, _1728743, _1728745, _1728747, _1728749), c_List_Olist__all2(_1728741, _1728743, _1728745, _1728751, _1728753), -(c_List_Olist__all2(_1728741, _1728743, _1728745, hAPP(hAPP(c_List_Oappend(_1728741), _1728747), _1728751), hAPP(hAPP(c_List_Oappend(_1728743), _1728749), _1728753)))], (47316 ^ _779530) ^ [_1728940, _1728942, _1728944, _1728946, _1728948, _1728950, _1728952] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728940)), _1728942) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728944)), _1728946), 47319 ^ _779530 : [(47320 ^ _779530) ^ [] : [c_List_Olist__all2(_1728940, _1728944, _1728948, hAPP(hAPP(c_List_Oappend(_1728940), _1728942), _1728950), hAPP(hAPP(c_List_Oappend(_1728944), _1728946), _1728952)), 47323 ^ _779530 : [(47324 ^ _779530) ^ [] : [-(c_List_Olist__all2(_1728940, _1728944, _1728948, _1728942, _1728946))], (47326 ^ _779530) ^ [] : [-(c_List_Olist__all2(_1728940, _1728944, _1728948, _1728950, _1728952))]]], (47328 ^ _779530) ^ [] : [-(c_List_Olist__all2(_1728940, _1728944, _1728948, hAPP(hAPP(c_List_Oappend(_1728940), _1728942), _1728950), hAPP(hAPP(c_List_Oappend(_1728944), _1728946), _1728952))), c_List_Olist__all2(_1728940, _1728944, _1728948, _1728942, _1728946), c_List_Olist__all2(_1728940, _1728944, _1728948, _1728950, _1728952)]]], (47338 ^ _779530) ^ [_1729383, _1729385, _1729387, _1729389] : [c_List_Olist__all2(_1729383, _1729385, _1729387, c_List_Olist_ONil(_1729383), _1729389), -(_1729389 = c_List_Olist_ONil(_1729385))], (47344 ^ _779530) ^ [_1729474, _1729476, _1729478, _1729480] : [_1729480 = c_List_Olist_ONil(_1729476), -(c_List_Olist__all2(_1729474, _1729476, _1729478, c_List_Olist_ONil(_1729474), _1729480))], (47350 ^ _779530) ^ [_1729592, _1729594, _1729596, _1729598] : [c_List_Olist__all2(_1729592, _1729594, _1729596, _1729598, c_List_Olist_ONil(_1729594)), -(_1729598 = c_List_Olist_ONil(_1729592))], (47356 ^ _779530) ^ [_1729683, _1729685, _1729687, _1729689] : [_1729689 = c_List_Olist_ONil(_1729683), -(c_List_Olist__all2(_1729683, _1729685, _1729687, _1729689, c_List_Olist_ONil(_1729685)))], (47362 ^ _779530) ^ [_1729780, _1729782, _1729784, _1729786, _1729788] : [c_List_Olist__all2(_1729780, _1729782, _1729784, _1729786, _1729788), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729780)), _1729786) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729782)), _1729788))], (47368 ^ _779530) ^ [_1729915, _1729917, _1729919] : [_1729915 = _1729917, -(c_List_Olist__all2(_1729919, _1729919, c_fequal, _1729915, _1729917))], (47374 ^ _779530) ^ [_1729996, _1729998, _1730000] : [c_List_Olist__all2(_1730000, _1730000, c_fequal, _1729996, _1729998), -(_1729996 = _1729998)], (47380 ^ _779530) ^ [_1730083, _1730085, _1730087, _1730089, _1730091, _1730093] : [c_List_Olist__all2(_1730083, _1730085, _1730087, _1730089, _1730091), -(c_List_Olist__all2(_1730083, _1730085, _1730087, hAPP(hAPP(c_List_Otake(_1730083), _1730093), _1730089), hAPP(hAPP(c_List_Otake(_1730085), _1730093), _1730091)))], (47386 ^ _779530) ^ [_1730242, _1730244, _1730246, _1730248, _1730250, _1730252, _1730254] : [c_List_Olist__all2(_1730242, _1730244, _1730246, hAPP(hAPP(c_List_Olist_OCons(_1730242), _1730248), _1730250), hAPP(hAPP(c_List_Olist_OCons(_1730244), _1730252), _1730254)), 47389 ^ _779530 : [(47390 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(_1730246, _1730248), _1730252)))], (47392 ^ _779530) ^ [] : [-(c_List_Olist__all2(_1730242, _1730244, _1730246, _1730250, _1730254))]]], (47394 ^ _779530) ^ [_1730405, _1730407, _1730409, _1730411, _1730413, _1730415, _1730417] : [-(c_List_Olist__all2(_1730405, _1730407, _1730409, hAPP(hAPP(c_List_Olist_OCons(_1730405), _1730411), _1730413), hAPP(hAPP(c_List_Olist_OCons(_1730407), _1730415), _1730417))), hBOOL(hAPP(hAPP(_1730409, _1730411), _1730415)), c_List_Olist__all2(_1730405, _1730407, _1730409, _1730413, _1730417)], (47404 ^ _779530) ^ [_1730640, _1730642, _1730644, _1730646, _1730648, _1730650, _1730652] : [c_List_Olist__all2(_1730640, _1730642, _1730644, _1730646, hAPP(hAPP(c_List_Omap(_1730648, _1730642), _1730650), _1730652)), -(c_List_Olist__all2(_1730640, _1730648, hAPP(hAPP(c_COMBC(_1730640, tc_fun(_1730648, _1730642), tc_fun(_1730648, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730642, tc_HOL_Obool), tc_fun(tc_fun(_1730648, _1730642), tc_fun(_1730648, tc_HOL_Obool)), _1730640), c_COMBB(_1730642, tc_HOL_Obool, _1730648)), _1730644)), _1730650), _1730646, _1730652))], (47410 ^ _779530) ^ [_1730837, _1730839, _1730841, _1730843, _1730845, _1730847, _1730849] : [c_List_Olist__all2(_1730837, _1730845, hAPP(hAPP(c_COMBC(_1730837, tc_fun(_1730845, _1730839), tc_fun(_1730845, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730839, tc_HOL_Obool), tc_fun(tc_fun(_1730845, _1730839), tc_fun(_1730845, tc_HOL_Obool)), _1730837), c_COMBB(_1730839, tc_HOL_Obool, _1730845)), _1730841)), _1730847), _1730843, _1730849), -(c_List_Olist__all2(_1730837, _1730839, _1730841, _1730843, hAPP(hAPP(c_List_Omap(_1730845, _1730839), _1730847), _1730849)))], (47416 ^ _779530) ^ [_1731070, _1731072, _1731074, _1731076, _1731078, _1731080, _1731082] : [c_List_Olist__all2(_1731070, _1731072, _1731074, hAPP(hAPP(c_List_Omap(_1731076, _1731070), _1731078), _1731080), _1731082), -(c_List_Olist__all2(_1731076, _1731072, hAPP(hAPP(c_COMBB(_1731070, tc_fun(_1731072, tc_HOL_Obool), _1731076), _1731074), _1731078), _1731080, _1731082))], (47422 ^ _779530) ^ [_1731209, _1731211, _1731213, _1731215, _1731217, _1731219, _1731221] : [c_List_Olist__all2(_1731215, _1731211, hAPP(hAPP(c_COMBB(_1731209, tc_fun(_1731211, tc_HOL_Obool), _1731215), _1731213), _1731217), _1731219, _1731221), -(c_List_Olist__all2(_1731209, _1731211, _1731213, hAPP(hAPP(c_List_Omap(_1731215, _1731209), _1731217), _1731219), _1731221))], (47428 ^ _779530) ^ [_1731354, _1731356, _1731358, _1731360, _1731362, _1731364] : [c_List_Olist__all2(_1731354, _1731356, _1731358, _1731360, _1731362), -(c_List_Olist__all2(_1731354, _1731356, _1731358, hAPP(hAPP(c_List_Odrop(_1731354), _1731364), _1731360), hAPP(hAPP(c_List_Odrop(_1731356), _1731364), _1731362)))], (47434 ^ _779530) ^ [_1731507, _1731509, _1731511, _1731513, _1731515] : [c_List_Olist__all2(_1731507, _1731509, _1731511, hAPP(c_List_Orev(_1731507), _1731513), _1731515), -(c_List_Olist__all2(_1731507, _1731509, _1731511, _1731513, hAPP(c_List_Orev(_1731509), _1731515)))], (47440 ^ _779530) ^ [_1731618, _1731620, _1731622, _1731624, _1731626] : [c_List_Olist__all2(_1731618, _1731620, _1731622, _1731624, hAPP(c_List_Orev(_1731620), _1731626)), -(c_List_Olist__all2(_1731618, _1731620, _1731622, hAPP(c_List_Orev(_1731618), _1731624), _1731626))], (47446 ^ _779530) ^ [_1731759, _1731761, _1731763, _1731765, _1731767] : [c_List_Olist__all2(_1731759, _1731761, _1731763, hAPP(c_List_Orev(_1731759), _1731765), hAPP(c_List_Orev(_1731761), _1731767)), -(c_List_Olist__all2(_1731759, _1731761, _1731763, _1731765, _1731767))], (47452 ^ _779530) ^ [_1731870, _1731872, _1731874, _1731876, _1731878] : [c_List_Olist__all2(_1731870, _1731872, _1731874, _1731876, _1731878), -(c_List_Olist__all2(_1731870, _1731872, _1731874, hAPP(c_List_Orev(_1731870), _1731876), hAPP(c_List_Orev(_1731872), _1731878)))], (47458 ^ _779530) ^ [_1732011, _1732013, _1732015, _1732017, _1732019] : [c_List_Olist__all2(_1732011, _1732013, _1732015, _1732017, _1732019), 47461 ^ _779530 : [(47462 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732011)), _1732017) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732013)), _1732019))], (47464 ^ _779530) ^ [_1732174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732011)), _1732017))), -(hBOOL(hAPP(hAPP(_1732015, hAPP(hAPP(c_List_Onth(_1732011), _1732017), _1732174)), hAPP(hAPP(c_List_Onth(_1732013), _1732019), _1732174))))]]], (47470 ^ _779530) ^ [_1732327, _1732329, _1732331, _1732333, _1732335] : [-(c_List_Olist__all2(_1732327, _1732329, _1732331, _1732333, _1732335)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732327)), _1732333) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732329)), _1732335), 47476 ^ _779530 : [(47477 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47475 ^ [_1732327, _1732329, _1732331, _1732333, _1732335]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732327)), _1732333))))], (47479 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1732331, hAPP(hAPP(c_List_Onth(_1732327), _1732333), 47475 ^ [_1732327, _1732329, _1732331, _1732333, _1732335])), hAPP(hAPP(c_List_Onth(_1732329), _1732335), 47475 ^ [_1732327, _1732329, _1732331, _1732333, _1732335])))]]], (47483 ^ _779530) ^ [_1732687, _1732689, _1732691, _1732693, _1732695, _1732697] : [c_List_Olist__all2(_1732687, _1732689, _1732691, _1732693, _1732695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732697), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732687)), _1732693))), -(hBOOL(hAPP(hAPP(_1732691, hAPP(hAPP(c_List_Onth(_1732687), _1732693), _1732697)), hAPP(hAPP(c_List_Onth(_1732689), _1732695), _1732697))))], (47493 ^ _779530) ^ [_1732904, _1732906, _1732908, _1732910, _1732912, _1732914] : [c_List_Olist__all2(_1732904, _1732906, _1732908, _1732910, _1732912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732914), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732906)), _1732912))), -(hBOOL(hAPP(hAPP(_1732908, hAPP(hAPP(c_List_Onth(_1732904), _1732910), _1732914)), hAPP(hAPP(c_List_Onth(_1732906), _1732912), _1732914))))], (47503 ^ _779530) ^ [_1733121, _1733123, _1733125, _1733127, _1733129, _1733131, _1733133, _1733135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733123)), _1733125))), c_List_Olist__all2(_1733123, _1733127, _1733129, _1733125, _1733131), hBOOL(hAPP(hAPP(_1733129, _1733133), _1733135)), -(c_List_Olist__all2(_1733123, _1733127, _1733129, hAPP(hAPP(c_List_Olist__update(_1733123, _1733125), _1733121), _1733133), hAPP(hAPP(c_List_Olist__update(_1733127, _1733131), _1733121), _1733135)))], (47517 ^ _779530) ^ [_1733420, _1733422, _1733424, _1733426, _1733428, _1733430, _1733432, _1733434] : [c_List_Olist__all2(_1733420, _1733422, _1733424, _1733426, _1733428), hBOOL(hAPP(hAPP(_1733424, _1733430), _1733432)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1733434), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733422)), _1733428))), -(c_List_Olist__all2(_1733420, _1733422, _1733424, hAPP(hAPP(c_List_Olist__update(_1733420, _1733426), _1733434), _1733430), hAPP(hAPP(c_List_Olist__update(_1733422, _1733428), _1733434), _1733432)))], (47531 ^ _779530) ^ [_1733719, _1733721, _1733723, _1733725, _1733727] : [47533 ^ _779530 : [(47534 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1733719, _1733721)), 47532 ^ [_1733719, _1733721, _1733723, _1733725, _1733727]), hAPP(c_List_Oset(tc_prod(_1733719, _1733721)), hAPP(hAPP(c_List_Ozip(_1733719, _1733721), _1733723), _1733725)))))], (47536 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1733719, _1733721, tc_HOL_Obool), _1733727), 47532 ^ [_1733719, _1733721, _1733723, _1733725, _1733727]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733719)), _1733723) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733721)), _1733725), -(c_List_Olist__all2(_1733719, _1733721, _1733727, _1733723, _1733725))], (47544 ^ _779530) ^ [_1734058, _1734060, _1734062] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1734058, tc_HOL_Obool)), _1734060)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1734058), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1734058, tc_HOL_Obool), _1734060))), 47554 ^ _779530 : [(47555 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1734058, tc_HOL_Obool)), 47553 ^ [_1734058, _1734060, _1734062]), _1734060)))], (47557 ^ _779530) ^ [] : [hAPP(c_Finite__Set_Ocard(_1734058), 47553 ^ [_1734058, _1734060, _1734062]) = _1734062]], 47561 ^ _779530 : [(47562 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1734058, tc_HOL_Obool)), 47560 ^ [_1734058, _1734060, _1734062]), _1734060)))], (47565 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1734058, tc_HOL_Obool)), 47563 ^ [_1734058, _1734060, _1734062]), _1734060)))], (47567 ^ _779530) ^ [] : [47560 ^ [_1734058, _1734060, _1734062] = 47563 ^ [_1734058, _1734060, _1734062]], (47569 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1734058, tc_HOL_Obool)), 47560 ^ [_1734058, _1734060, _1734062]), 47563 ^ [_1734058, _1734060, _1734062]) = c_Orderings_Obot__class_Obot(tc_fun(_1734058, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1734062), hAPP(c_Finite__Set_Ocard(tc_fun(_1734058, tc_HOL_Obool)), _1734060)) = hAPP(c_Finite__Set_Ocard(_1734058), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1734058, tc_HOL_Obool), _1734060)))], (47573 ^ _779530) ^ [_1734840, _1734842, _1734844, _1734846] : [47575 ^ _779530 : [(47576 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47574 ^ [_1734840, _1734842, _1734844, _1734846]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734840)), _1734842))))], (47578 ^ _779530) ^ [] : [hBOOL(hAPP(_1734844, hAPP(hAPP(c_List_Onth(_1734840), _1734842), 47574 ^ [_1734840, _1734842, _1734844, _1734846])))]], hBOOL(hAPP(hAPP(c_member(_1734840), _1734846), hAPP(c_List_Oset(_1734840), _1734842))), -(hBOOL(hAPP(_1734844, _1734846)))], (47586 ^ _779530) ^ [_1735136, _1735138, _1735140, _1735142, _1735144] : [c_Fun_Oinj__on(_1735136, _1735138, _1735140, hAPP(hAPP(c_Set_Oinsert(_1735136), _1735142), hAPP(c_List_Oset(_1735136), _1735144))), -(hAPP(hAPP(c_List_Omap(_1735136, _1735138), _1735140), hAPP(c_List_OremoveAll(_1735136, _1735142), _1735144)) = hAPP(c_List_OremoveAll(_1735138, hAPP(_1735140, _1735142)), hAPP(hAPP(c_List_Omap(_1735136, _1735138), _1735140), _1735144)))], (47592 ^ _779530) ^ [_1735315, _1735317, _1735319, _1735321] : [-(hAPP(c_List_OremoveAll(_1735315, _1735317), hAPP(hAPP(c_List_Oappend(_1735315), _1735319), _1735321)) = hAPP(hAPP(c_List_Oappend(_1735315), hAPP(c_List_OremoveAll(_1735315, _1735317), _1735319)), hAPP(c_List_OremoveAll(_1735315, _1735317), _1735321)))], (47594 ^ _779530) ^ [_1735378, _1735380] : [-(hAPP(c_List_OremoveAll(_1735378, _1735380), c_List_Olist_ONil(_1735378)) = c_List_Olist_ONil(_1735378))], (47596 ^ _779530) ^ [_1735409, _1735411, _1735413, _1735415] : [-(hBOOL(hAPP(_1735409, _1735411))), -(hAPP(c_List_OremoveAll(_1735413, _1735411), hAPP(c_List_Ofilter(_1735413, _1735409), _1735415)) = hAPP(c_List_Ofilter(_1735413, _1735409), _1735415))], (47602 ^ _779530) ^ [_1735469, _1735471] : [-(c_List_OremoveAll(_1735469, _1735471) = c_List_Ofilter(_1735469, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1735469), c_fNot), hAPP(c_fequal, _1735471))))], (47604 ^ _779530) ^ [_1735513, _1735515, _1735517] : [hBOOL(hAPP(c_List_Odistinct(_1735513), _1735515)), -(hBOOL(hAPP(c_List_Odistinct(_1735513), hAPP(c_List_OremoveAll(_1735513, _1735517), _1735515))))], (47610 ^ _779530) ^ [_1735635, _1735637, _1735639, _1735641] : [_1735635 = _1735637, -(hAPP(c_List_OremoveAll(_1735639, _1735635), hAPP(hAPP(c_List_Olist_OCons(_1735639), _1735637), _1735641)) = hAPP(c_List_OremoveAll(_1735639, _1735635), _1735641))], (47616 ^ _779530) ^ [_1735750, _1735752, _1735754, _1735756] : [-(_1735750 = _1735752), -(hAPP(c_List_OremoveAll(_1735754, _1735750), hAPP(hAPP(c_List_Olist_OCons(_1735754), _1735752), _1735756)) = hAPP(hAPP(c_List_Olist_OCons(_1735754), _1735752), hAPP(c_List_OremoveAll(_1735754, _1735750), _1735756)))], (47622 ^ _779530) ^ [_1735816, _1735818, _1735820] : [-(hBOOL(hAPP(hAPP(c_member(_1735816), _1735818), hAPP(c_List_Oset(_1735816), _1735820)))), -(hAPP(c_List_OremoveAll(_1735816, _1735818), _1735820) = _1735820)], (47628 ^ _779530) ^ [_1735872, _1735874, _1735876] : [hBOOL(hAPP(c_List_Odistinct(_1735872), _1735874)), -(c_List_Oremove1(_1735872, _1735876, _1735874) = hAPP(c_List_OremoveAll(_1735872, _1735876), _1735874))], (47634 ^ _779530) ^ [_1735979, _1735981, _1735983, _1735985, _1735987] : [c_Fun_Oinj__on(_1735979, _1735981, _1735983, c_Orderings_Otop__class_Otop(tc_fun(_1735979, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1735979, _1735981), _1735983), hAPP(c_List_OremoveAll(_1735979, _1735985), _1735987)) = hAPP(c_List_OremoveAll(_1735981, hAPP(_1735983, _1735985)), hAPP(hAPP(c_List_Omap(_1735979, _1735981), _1735983), _1735987)))], (47640 ^ _779530) ^ [_1736142, _1736144, _1736146] : [-(hAPP(c_List_Oset(_1736142), hAPP(c_List_OremoveAll(_1736142, _1736144), _1736146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1736142, tc_HOL_Obool)), hAPP(c_List_Oset(_1736142), _1736146)), hAPP(hAPP(c_Set_Oinsert(_1736142), _1736144), c_Orderings_Obot__class_Obot(tc_fun(_1736142, tc_HOL_Obool)))))], (47642 ^ _779530) ^ [_1736205, _1736207, _1736209] : [-(hBOOL(hAPP(hAPP(c_member(_1736205), _1736207), hAPP(c_List_Oset(_1736205), _1736209)))), -(c_List_Oinsert(_1736205, _1736207, _1736209) = hAPP(hAPP(c_List_Olist_OCons(_1736205), _1736207), _1736209))], (47648 ^ _779530) ^ [_1736279, _1736281, _1736283] : [hBOOL(hAPP(hAPP(c_member(_1736279), _1736281), hAPP(c_List_Oset(_1736279), _1736283))), -(c_List_Oinsert(_1736279, _1736281, _1736283) = _1736283)], (47654 ^ _779530) ^ [_1736384, _1736386, _1736388] : [-(hBOOL(hAPP(hAPP(c_member(_1736384), _1736386), hAPP(c_List_Oset(_1736384), _1736388)))), -(c_List_Oinsert(_1736384, _1736386, _1736388) = hAPP(hAPP(c_List_Olist_OCons(_1736384), _1736386), _1736388))], (47660 ^ _779530) ^ [_1736448, _1736450, _1736452] : [hBOOL(hAPP(c_List_Odistinct(_1736448), _1736450)), -(hBOOL(hAPP(c_List_Odistinct(_1736448), c_List_Oinsert(_1736448, _1736452, _1736450))))], (47666 ^ _779530) ^ [_1736551, _1736553, _1736555] : [-(c_List_Oinsert(_1736551, _1736553, c_List_Oremdups(_1736551, _1736555)) = c_List_Oremdups(_1736551, c_List_Oinsert(_1736551, _1736553, _1736555)))], (47668 ^ _779530) ^ [_1736592, _1736594, _1736596] : [hBOOL(hAPP(hAPP(c_member(_1736592), _1736594), hAPP(c_List_Oset(_1736592), _1736596))), -(c_List_Oinsert(_1736592, _1736594, _1736596) = _1736596)], (47674 ^ _779530) ^ [_1736703, _1736705, _1736707] : [-(hAPP(c_List_Oset(_1736703), c_List_Oinsert(_1736703, _1736705, _1736707)) = hAPP(hAPP(c_Set_Oinsert(_1736703), _1736705), hAPP(c_List_Oset(_1736703), _1736707)))], (47676 ^ _779530) ^ [_1736752, _1736754] : [-(c_List_Oinsert(_1736752, _1736754, c_List_Olist_ONil(_1736752)) = hAPP(hAPP(c_List_Olist_OCons(_1736752), _1736754), c_List_Olist_ONil(_1736752)))], (47678 ^ _779530) ^ [_1736793, _1736795, _1736797, _1736799] : [-(c_List_Oconcat(_1736793, hAPP(hAPP(c_List_Omap(_1736795, tc_List_Olist(_1736793)), _1736797), _1736799)) = c_List_Omaps(_1736795, _1736793, _1736797, _1736799))], (47680 ^ _779530) ^ [_1736841, _1736843, _1736845, _1736847] : [-(c_List_Omaps(_1736841, _1736843, _1736845, _1736847) = c_List_Oconcat(_1736843, hAPP(hAPP(c_List_Omap(_1736841, tc_List_Olist(_1736843)), _1736845), _1736847)))], (47682 ^ _779530) ^ [_1736889, _1736891, _1736893] : [-(c_List_Omaps(_1736889, _1736891, _1736893, c_List_Olist_ONil(_1736889)) = c_List_Olist_ONil(_1736891))], (47684 ^ _779530) ^ [_1736925, _1736927, _1736929, _1736931, _1736933] : [-(c_List_Omaps(_1736925, _1736927, _1736929, hAPP(hAPP(c_List_Olist_OCons(_1736925), _1736931), _1736933)) = hAPP(hAPP(c_List_Oappend(_1736927), hAPP(_1736929, _1736931)), c_List_Omaps(_1736925, _1736927, _1736929, _1736933)))], (47686 ^ _779530) ^ [_1736985, _1736987] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1736985)), _1736987)), 47692 ^ _779530 : [(47693 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1736985)), 47691 ^ [_1736985, _1736987]), hAPP(c_List_Oset(tc_List_Olist(_1736985)), _1736987))))], (47695 ^ _779530) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1736985), 47691 ^ [_1736985, _1736987]))]], 47699 ^ _779530 : [(47700 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1736985)), 47698 ^ [_1736985, _1736987]), hAPP(c_List_Oset(tc_List_Olist(_1736985)), _1736987))))], (47703 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1736985)), 47701 ^ [_1736985, _1736987]), hAPP(c_List_Oset(tc_List_Olist(_1736985)), _1736987))))], (47705 ^ _779530) ^ [] : [47698 ^ [_1736985, _1736987] = 47701 ^ [_1736985, _1736987]], (47707 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1736985, tc_HOL_Obool)), hAPP(c_List_Oset(_1736985), 47698 ^ [_1736985, _1736987])), hAPP(c_List_Oset(_1736985), 47701 ^ [_1736985, _1736987])) = c_Orderings_Obot__class_Obot(tc_fun(_1736985, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1736985), c_List_Oconcat(_1736985, _1736987))))], (47711 ^ _779530) ^ [_1737702, _1737704, _1737706, _1737708, _1737710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1737702, _1737704)), hAPP(_1737702, _1737706))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1737708, _1737708)), hAPP(hAPP(c_Product__Type_OPair(_1737708, _1737708), _1737704), _1737706)), c_List_Omeasures(_1737708, _1737710))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1737708, _1737708)), hAPP(hAPP(c_Product__Type_OPair(_1737708, _1737708), _1737704), _1737706)), c_List_Omeasures(_1737708, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1737708, tc_Nat_Onat)), _1737702), _1737710)))))], (47721 ^ _779530) ^ [_1737975, _1737977] : [-(c_Wellfounded_Owf(_1737975, c_List_Omeasures(_1737975, _1737977)))], (47723 ^ _779530) ^ [_1738018, _1738020, _1738022] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1738018, _1738018)), hAPP(hAPP(c_Product__Type_OPair(_1738018, _1738018), _1738020), _1738022)), c_List_Omeasures(_1738018, c_List_Olist_ONil(tc_fun(_1738018, tc_Nat_Onat)))))], (47725 ^ _779530) ^ [_1738072, _1738074] : [-(c_List_Omeasures(_1738072, _1738074) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1738072), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1738072, tc_List_Olist(tc_fun(_1738072, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1738072, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1738072, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1738072), c_List_Omap(tc_fun(_1738072, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1738072, tc_Nat_Onat), _1738072, tc_Nat_Onat), c_COMBI(tc_fun(_1738072, tc_Nat_Onat))))), _1738074)))], (47727 ^ _779530) ^ [_1738169, _1738171, _1738173, _1738175, _1738177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1738169, _1738171)), hAPP(_1738169, _1738173))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738175, _1738175)), hAPP(hAPP(c_Product__Type_OPair(_1738175, _1738175), _1738171), _1738173)), c_List_Omeasures(_1738175, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1738175, tc_Nat_Onat)), _1738169), _1738177)))))], (47733 ^ _779530) ^ [_1738364, _1738366, _1738368, _1738370, _1738372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1738364, _1738364)), hAPP(hAPP(c_Product__Type_OPair(_1738364, _1738364), _1738366), _1738368)), c_List_Omeasures(_1738364, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1738364, tc_Nat_Onat)), _1738370), _1738372)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1738370, _1738366)), hAPP(_1738370, _1738368)))), 47740 ^ _779530 : [(47741 ^ _779530) ^ [] : [-(hAPP(_1738370, _1738366) = hAPP(_1738370, _1738368))], (47743 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738364, _1738364)), hAPP(hAPP(c_Product__Type_OPair(_1738364, _1738364), _1738366), _1738368)), c_List_Omeasures(_1738364, _1738372))))]]], (47745 ^ _779530) ^ [_1738643, _1738645, _1738647, _1738649, _1738651] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738643, _1738643)), hAPP(hAPP(c_Product__Type_OPair(_1738643, _1738643), _1738645), _1738647)), c_List_Omeasures(_1738643, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1738643, tc_Nat_Onat)), _1738649), _1738651))))), 47746 ^ _779530 : [(47747 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1738649, _1738645)), hAPP(_1738649, _1738647)))], (47749 ^ _779530) ^ [] : [hAPP(_1738649, _1738645) = hAPP(_1738649, _1738647), hBOOL(hAPP(hAPP(c_member(tc_prod(_1738643, _1738643)), hAPP(hAPP(c_Product__Type_OPair(_1738643, _1738643), _1738645), _1738647)), c_List_Omeasures(_1738643, _1738651)))]]], (47757 ^ _779530) ^ [_1738965, _1738967, _1738969, _1738971] : [-(_1738965 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1738967, tc_HOL_Obool), tc_HOL_Obool))), 47763 ^ _779530 : [(47764 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1738967, tc_HOL_Obool)), 47762 ^ [_1738965, _1738967, _1738969, _1738971]), _1738965)))], (47766 ^ _779530) ^ [] : [c_Fun_Oinj__on(_1738967, _1738969, _1738971, 47762 ^ [_1738965, _1738967, _1738969, _1738971])]], -(c_Fun_Oinj__on(_1738967, _1738969, _1738971, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1738967, tc_HOL_Obool), _1738965)))], (47770 ^ _779530) ^ [_1739226, _1739228, _1739230] : [47772 ^ _779530 : [(47773 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1739226, tc_HOL_Obool)), 47771 ^ [_1739226, _1739228, _1739230]), _1739228)))], (47775 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739226, tc_HOL_Obool)), 47771 ^ [_1739226, _1739228, _1739230]), _1739230))]], -(_1739228 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1739226, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1739226, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1739226, tc_HOL_Obool), _1739228)), _1739230)))], (47783 ^ _779530) ^ [_1739488, _1739490, _1739492, _1739494, _1739496, _1739498, _1739500, _1739502] : [47785 ^ _779530 : [(47786 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739488), 47784 ^ [_1739488, _1739490, _1739492, _1739494, _1739496, _1739498, _1739500, _1739502]), hAPP(c_List_Oset(_1739488), _1739490))))], (47788 ^ _779530) ^ [] : [hAPP(c_Fun_Ocomp(_1739492, _1739492, _1739494, hAPP(_1739496, 47784 ^ [_1739488, _1739490, _1739492, _1739494, _1739496, _1739498, _1739500, _1739502])), _1739498) = hAPP(c_Fun_Ocomp(_1739494, _1739492, _1739494, _1739498), hAPP(_1739500, 47784 ^ [_1739488, _1739490, _1739492, _1739494, _1739496, _1739498, _1739500, _1739502]))]], -(hAPP(c_List_Ofoldl(_1739492, _1739488, hAPP(c_COMBC(_1739488, _1739492, _1739492), _1739496), hAPP(_1739498, _1739502)), _1739490) = hAPP(_1739498, hAPP(c_List_Ofoldl(_1739494, _1739488, hAPP(c_COMBC(_1739488, _1739494, _1739494), _1739500), _1739502), _1739490)))], (47792 ^ _779530) ^ [_1739856, _1739858, _1739860, _1739862, _1739864, _1739866] : [-(_1739856 = c_Orderings_Obot__class_Obot(tc_fun(_1739858, tc_HOL_Obool))), 47798 ^ _779530 : [(47799 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739858), 47797 ^ [_1739856, _1739858, _1739860, _1739862, _1739864, _1739866]), _1739856)))], (47801 ^ _779530) ^ [] : [c_Fun_Oinj__on(_1739860, _1739862, _1739864, hAPP(_1739866, 47797 ^ [_1739856, _1739858, _1739860, _1739862, _1739864, _1739866]))]], -(c_Fun_Oinj__on(_1739860, _1739862, _1739864, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1739858, tc_fun(_1739860, tc_HOL_Obool)), _1739856), _1739866)))], (47805 ^ _779530) ^ [_1740148, _1740150, _1740152, _1740154, _1740156] : [47806 ^ _779530 : [(47807 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740148)), hAPP(hAPP(c_List_Otake(_1740148), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740148)), _1740150)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740152)), _1740154))), _1740150)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740152)), hAPP(hAPP(c_List_Otake(_1740152), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740148)), _1740150)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740152)), _1740154))), _1740154)))], (47809 ^ _779530) ^ [] : [hBOOL(hAPP(_1740156, hAPP(hAPP(c_List_Ozip(_1740148, _1740152), hAPP(hAPP(c_List_Otake(_1740148), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740148)), _1740150)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740152)), _1740154))), _1740150)), hAPP(hAPP(c_List_Otake(_1740152), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740148)), _1740150)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1740152)), _1740154))), _1740154))))]], -(hBOOL(hAPP(_1740156, hAPP(hAPP(c_List_Ozip(_1740148, _1740152), _1740150), _1740154))))], (47813 ^ _779530) ^ [_1740560, _1740562, _1740564, _1740566] : [hAPP(c_List_Oset(_1740560), hAPP(hAPP(c_List_Omap(tc_prod(_1740560, _1740562), _1740560), c_Product__Type_Ofst(_1740560, _1740562)), _1740564)) = hAPP(c_List_Oset(_1740560), hAPP(hAPP(c_List_Omap(tc_prod(_1740560, _1740562), _1740560), c_Product__Type_Ofst(_1740560, _1740562)), _1740566)), 47819 ^ _779530 : [(47820 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740560), 47818 ^ [_1740560, _1740562, _1740564, _1740566]), hAPP(c_List_Oset(_1740560), hAPP(hAPP(c_List_Omap(tc_prod(_1740560, _1740562), _1740560), c_Product__Type_Ofst(_1740560, _1740562)), _1740564)))))], (47822 ^ _779530) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1740560, _1740562), _1740564), 47818 ^ [_1740560, _1740562, _1740564, _1740566]) = hAPP(hAPP(c_Map_Omap__of(_1740560, _1740562), _1740566), 47818 ^ [_1740560, _1740562, _1740564, _1740566])]], -(hAPP(c_Map_Omap__of(_1740560, _1740562), _1740564) = hAPP(c_Map_Omap__of(_1740560, _1740562), _1740566))], (47826 ^ _779530) ^ [_1740998, _1741000, _1741002, _1741004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1740998), _1741000)), 47832 ^ _779530 : [(47833 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740998), 47831 ^ [_1740998, _1741000, _1741002, _1741004]), _1741000)))], (47835 ^ _779530) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1741002), hAPP(_1741004, 47831 ^ [_1740998, _1741000, _1741002, _1741004])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1741002), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1740998, tc_fun(_1741002, tc_HOL_Obool)), _1741000), _1741004))))], (47839 ^ _779530) ^ [_1741285, _1741287] : [47841 ^ _779530 : [(47842 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47840 ^ [_1741285, _1741287]), _1741285)))], (47844 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1741287), 47840 ^ [_1741285, _1741287]))]], -(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)), _1741287), _1741285))], (47848 ^ _779530) ^ [_1741460, _1741462, _1741464] : [c_Wellfounded_OwfP(_1741460, hAPP(_1741462, 47849 ^ [_1741460, _1741462, _1741464])), 47856 ^ _779530 : [(47857 ^ _779530) ^ [] : [hAPP(_1741462, 47854 ^ [_1741460, _1741462, _1741464]) = hAPP(_1741462, 47855 ^ [_1741460, _1741462, _1741464])], (47859 ^ _779530) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1741460, tc_HOL_Obool)), c_Predicate_ODomainP(_1741460, _1741460, hAPP(_1741462, 47854 ^ [_1741460, _1741462, _1741464]))), c_Predicate_ORangeP(_1741460, _1741460, hAPP(_1741462, 47855 ^ [_1741460, _1741462, _1741464]))) = c_Orderings_Obot__class_Obot(tc_fun(_1741460, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1741460, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1741464, tc_fun(_1741460, tc_fun(_1741460, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1741464, tc_HOL_Obool))), _1741462)))], (47863 ^ _779530) ^ [_1741900, _1741902, _1741904, _1741906] : [47865 ^ _779530 : [(47866 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741900), 47864 ^ [_1741900, _1741902, _1741904, _1741906]), hAPP(c_List_Oset(_1741900), _1741902))))], (47868 ^ _779530) ^ [] : [hBOOL(hAPP(_1741904, 47864 ^ [_1741900, _1741902, _1741904, _1741906]))]], -(c_List_OdropWhile(_1741900, _1741904, hAPP(hAPP(c_List_Oappend(_1741900), _1741902), _1741906)) = c_List_OdropWhile(_1741900, _1741904, _1741906))], (47872 ^ _779530) ^ [_1742118, _1742120, _1742122, _1742124, _1742126] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742118)), _1742120) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742122)), _1742124), 47878 ^ _779530 : [(47879 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47877 ^ [_1742118, _1742120, _1742122, _1742124, _1742126]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742118)), _1742120))))], (47881 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(_1742126, hAPP(hAPP(c_List_Onth(_1742118), _1742120), 47877 ^ [_1742118, _1742120, _1742122, _1742124, _1742126])), hAPP(hAPP(c_List_Onth(_1742122), _1742124), 47877 ^ [_1742118, _1742120, _1742122, _1742124, _1742126])))]], -(c_List_Olist__all2(_1742118, _1742122, _1742126, _1742120, _1742124))], (47885 ^ _779530) ^ [_1742476, _1742478, _1742480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1742476), c_Map_Odom(_1742476, _1742478, _1742480))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1742476), c_Orderings_Otop__class_Otop(tc_fun(_1742476, tc_HOL_Obool))))), -(hAPP(_1742480, 47892 ^ [_1742476, _1742478, _1742480]) = c_Option_Ooption_ONone(_1742478))], (47896 ^ _779530) ^ [_1742628, _1742630, _1742632, _1742634, _1742636, _1742638] : [47899 ^ _779530 : [(47900 ^ _779530) ^ [] : [-(_1742628 = hAPP(hAPP(c_Product__Type_OPair(_1742630, _1742632), 47897 ^ [_1742628, _1742630, _1742632, _1742634, _1742636, _1742638]), 47898 ^ [_1742628, _1742630, _1742632, _1742634, _1742636, _1742638]))], (47902 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1742634), _1742636), hAPP(hAPP(_1742638, 47897 ^ [_1742628, _1742630, _1742632, _1742634, _1742636, _1742638]), 47898 ^ [_1742628, _1742630, _1742632, _1742634, _1742636, _1742638])))]], -(hBOOL(hAPP(hAPP(c_member(_1742634), _1742636), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1742630, _1742632, tc_fun(_1742634, tc_HOL_Obool)), _1742638), _1742628))))], (47906 ^ _779530) ^ [_1742953, _1742955, _1742957, _1742959, _1742961, _1742963] : [hBOOL(hAPP(hAPP(c_member(_1742953), _1742955), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1742957, _1742959, tc_fun(_1742953, tc_HOL_Obool)), _1742961), _1742963))), 47911 ^ _779530 : [(47912 ^ _779530) ^ [] : [-(_1742963 = hAPP(hAPP(c_Product__Type_OPair(_1742957, _1742959), 47909 ^ [_1742953, _1742955, _1742957, _1742959, _1742961, _1742963]), 47910 ^ [_1742953, _1742955, _1742957, _1742959, _1742961, _1742963]))], (47914 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742953), _1742955), hAPP(hAPP(_1742961, 47909 ^ [_1742953, _1742955, _1742957, _1742959, _1742961, _1742963]), 47910 ^ [_1742953, _1742955, _1742957, _1742959, _1742961, _1742963]))))]]], (47916 ^ _779530) ^ [_1743222, _1743224] : [class_Orderings_Olinorder(_1743222), hBOOL(hAPP(c_Finite__Set_Ofinite(_1743222), _1743224)), 47924 ^ _779530 : [(47925 ^ _779530) ^ [] : [-(hAPP(c_List_Oset(_1743222), 47923 ^ [_1743222, _1743224]) = _1743224)], (47927 ^ _779530) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743222, 47923 ^ [_1743222, _1743224]))], (47929 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1743222), 47923 ^ [_1743222, _1743224])))], (47931 ^ _779530) ^ [_1743548] : [-(_1743548 = 47923 ^ [_1743222, _1743224]), hAPP(c_List_Oset(_1743222), _1743548) = _1743224, c_List_Olinorder__class_Osorted(_1743222, _1743548), hBOOL(hAPP(c_List_Odistinct(_1743222), _1743548))]]], (47945 ^ _779530) ^ [_1743779, _1743781, _1743783, _1743785] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1743779, tc_Nat_Onat), _1743781), _1743783) = hAPP(c_Nat_OSuc, _1743785), 47949 ^ _779530 : [(47950 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743779), 47948 ^ [_1743779, _1743781, _1743783, _1743785]), _1743783)))], (47952 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1743781, 47948 ^ [_1743779, _1743781, _1743783, _1743785]))))]]], (47954 ^ _779530) ^ [_1743961, _1743963, _1743965] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1743961, _1743963) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1743965, _1743963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743965), _1743961)), -(_1743961 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1743963), 47961 ^ [_1743961, _1743963, _1743965])))], (47965 ^ _779530) ^ [_1744158, _1744160, _1744162, _1744164] : [47967 ^ _779530 : [(47968 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744158), 47966 ^ [_1744158, _1744160, _1744162, _1744164]), hAPP(c_List_Oset(_1744158), _1744160))))], (47970 ^ _779530) ^ [] : [hBOOL(hAPP(_1744162, 47966 ^ [_1744158, _1744160, _1744162, _1744164]))]], -(c_List_OtakeWhile(_1744158, _1744162, hAPP(hAPP(c_List_Oappend(_1744158), _1744160), _1744164)) = hAPP(hAPP(c_List_Oappend(_1744158), _1744160), c_List_OtakeWhile(_1744158, _1744162, _1744164)))], (47974 ^ _779530) ^ [_1744392, _1744394, _1744396, _1744398, _1744400] : [class_Orderings_Olinorder(_1744392), 47980 ^ _779530 : [(47981 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744394), 47979 ^ [_1744392, _1744394, _1744396, _1744398, _1744400]), hAPP(c_List_Oset(_1744394), _1744396))))], (47983 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1744392), hAPP(_1744398, _1744400)), hAPP(_1744398, 47979 ^ [_1744392, _1744394, _1744396, _1744398, _1744400])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744394, _1744392, _1744398), _1744400), _1744396) = hAPP(hAPP(c_List_Olist_OCons(_1744394), _1744400), _1744396))], (47987 ^ _779530) ^ [_1744711, _1744713] : [47989 ^ _779530 : [(47990 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1744711, tc_HOL_Obool)), 47988 ^ [_1744711, _1744713]), hAPP(c_Relation_OImage(_1744711, _1744711, _1744713), 47988 ^ [_1744711, _1744713]))))], (47992 ^ _779530) ^ [] : [47988 ^ [_1744711, _1744713] = c_Orderings_Obot__class_Obot(tc_fun(_1744711, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1744711, _1744713))], (47996 ^ _779530) ^ [_1744932, _1744934, _1744936, _1744938, _1744940] : [hAPP(hAPP(c_List_Olist_OCons(_1744932), _1744934), _1744936) = hAPP(c_List_Ofilter(_1744932, _1744938), _1744940), 48001 ^ _779530 : [(48002 ^ _779530) ^ [] : [-(_1744940 = hAPP(hAPP(c_List_Oappend(_1744932), 47999 ^ [_1744932, _1744934, _1744936, _1744938, _1744940]), hAPP(hAPP(c_List_Olist_OCons(_1744932), _1744934), 48000 ^ [_1744932, _1744934, _1744936, _1744938, _1744940])))], (48010 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1744938, _1744934)))], (48012 ^ _779530) ^ [] : [-(_1744936 = hAPP(c_List_Ofilter(_1744932, _1744938), 48000 ^ [_1744932, _1744934, _1744936, _1744938, _1744940]))], (48004 ^ _779530) ^ [_1745246] : [hBOOL(hAPP(hAPP(c_member(_1744932), _1745246), hAPP(c_List_Oset(_1744932), 47999 ^ [_1744932, _1744934, _1744936, _1744938, _1744940]))), hBOOL(hAPP(_1744938, _1745246))]]], (48014 ^ _779530) ^ [_1745450, _1745452, _1745454, _1745456, _1745458] : [-(hAPP(hAPP(c_List_Olist_OCons(_1745450), _1745452), _1745454) = hAPP(c_List_Ofilter(_1745450, _1745456), _1745458)), 48015 ^ _779530 : [(48016 ^ _779530) ^ [_1745578, _1745580] : [_1745458 = hAPP(hAPP(c_List_Oappend(_1745450), _1745580), hAPP(hAPP(c_List_Olist_OCons(_1745450), _1745452), _1745578)), 48022 ^ _779530 : [(48023 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745450), 48021 ^ [_1745450, _1745452, _1745454, _1745456, _1745458, _1745578, _1745580]), hAPP(c_List_Oset(_1745450), _1745580))))], (48025 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1745456, 48021 ^ [_1745450, _1745452, _1745454, _1745456, _1745458, _1745578, _1745580])))]], hBOOL(hAPP(_1745456, _1745452)), _1745454 = hAPP(c_List_Ofilter(_1745450, _1745456), _1745578)]]], (48035 ^ _779530) ^ [_1746000, _1746002, _1746004, _1746006, _1746008] : [hAPP(c_List_Ofilter(_1746000, _1746002), _1746004) = hAPP(hAPP(c_List_Olist_OCons(_1746000), _1746006), _1746008), 48040 ^ _779530 : [(48041 ^ _779530) ^ [] : [-(_1746004 = hAPP(hAPP(c_List_Oappend(_1746000), 48038 ^ [_1746000, _1746002, _1746004, _1746006, _1746008]), hAPP(hAPP(c_List_Olist_OCons(_1746000), _1746006), 48039 ^ [_1746000, _1746002, _1746004, _1746006, _1746008])))], (48049 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1746002, _1746006)))], (48051 ^ _779530) ^ [] : [-(_1746008 = hAPP(c_List_Ofilter(_1746000, _1746002), 48039 ^ [_1746000, _1746002, _1746004, _1746006, _1746008]))], (48043 ^ _779530) ^ [_1746314] : [hBOOL(hAPP(hAPP(c_member(_1746000), _1746314), hAPP(c_List_Oset(_1746000), 48038 ^ [_1746000, _1746002, _1746004, _1746006, _1746008]))), hBOOL(hAPP(_1746002, _1746314))]]], (48053 ^ _779530) ^ [_1746518, _1746520, _1746522, _1746524, _1746526] : [-(hAPP(c_List_Ofilter(_1746518, _1746520), _1746522) = hAPP(hAPP(c_List_Olist_OCons(_1746518), _1746524), _1746526)), 48054 ^ _779530 : [(48055 ^ _779530) ^ [_1746646, _1746648] : [_1746522 = hAPP(hAPP(c_List_Oappend(_1746518), _1746648), hAPP(hAPP(c_List_Olist_OCons(_1746518), _1746524), _1746646)), 48061 ^ _779530 : [(48062 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746518), 48060 ^ [_1746518, _1746520, _1746522, _1746524, _1746526, _1746646, _1746648]), hAPP(c_List_Oset(_1746518), _1746648))))], (48064 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1746520, 48060 ^ [_1746518, _1746520, _1746522, _1746524, _1746526, _1746646, _1746648])))]], hBOOL(hAPP(_1746520, _1746524)), _1746526 = hAPP(c_List_Ofilter(_1746518, _1746520), _1746646)]]], (48074 ^ _779530) ^ [_1747044, _1747046, _1747048, _1747050, _1747052, _1747054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747044, tc_HOL_Obool)), _1747046), _1747048)), 48080 ^ _779530 : [(48081 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747044), 48079 ^ [_1747044, _1747046, _1747048, _1747050, _1747052, _1747054]), _1747046)))], (48083 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1747050, tc_HOL_Obool)), hAPP(_1747052, 48079 ^ [_1747044, _1747046, _1747048, _1747050, _1747052, _1747054])), hAPP(_1747054, 48079 ^ [_1747044, _1747046, _1747048, _1747050, _1747052, _1747054])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1747044, _1747050), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1747044, _1747050), _1747046), _1747052)), hAPP(hAPP(c_Product__Type_OSigma(_1747044, _1747050), _1747048), _1747054))))], (48087 ^ _779530) ^ [_1747435, _1747437, _1747439] : [48089 ^ _779530 : [(48090 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1747435, _1747435)), hAPP(hAPP(c_Product__Type_OPair(_1747435, _1747435), 48088 ^ [_1747435, _1747437, _1747439]), _1747437)), _1747439)))], (48092 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1747435), 48088 ^ [_1747435, _1747437, _1747439]), c_Wellfounded_Oacc(_1747435, _1747439)))]], -(hBOOL(hAPP(hAPP(c_member(_1747435), _1747437), c_Wellfounded_Oacc(_1747435, _1747439))))], (48096 ^ _779530) ^ [_1747672, _1747674, _1747676] : [-(hBOOL(hAPP(hAPP(c_member(_1747672), _1747674), c_Wellfounded_Oacc(_1747672, _1747676)))), 48100 ^ _779530 : [(48101 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1747672, _1747672)), hAPP(hAPP(c_Product__Type_OPair(_1747672, _1747672), 48099 ^ [_1747672, _1747674, _1747676]), _1747674)), _1747676)))], (48103 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1747672), 48099 ^ [_1747672, _1747674, _1747676]), c_Wellfounded_Oacc(_1747672, _1747676)))]]], (48105 ^ _779530) ^ [_1747899, _1747901, _1747903, _1747905] : [class_Groups_Ocomm__monoid__mult(_1747899), hBOOL(hAPP(c_Finite__Set_Ofinite(_1747901), _1747903)), 48115 ^ _779530 : [(48116 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747901), 48114 ^ [_1747899, _1747901, _1747903, _1747905]), _1747903)))], (48118 ^ _779530) ^ [] : [hAPP(_1747905, 48114 ^ [_1747899, _1747901, _1747903, _1747905]) = c_Groups_Oone__class_Oone(_1747899)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1747899, _1747901, c_Groups_Otimes__class_Otimes(_1747899)), _1747905), c_Groups_Oone__class_Oone(_1747899)), _1747903) = c_Groups_Oone__class_Oone(_1747899))], (48122 ^ _779530) ^ [_1748240, _1748242] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1748240), _1748242)), 48128 ^ _779530 : [(48129 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748240), 48127 ^ [_1748240, _1748242]), _1748242)))], (48131 ^ _779530) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1748240), _1748242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48135 ^ _779530) ^ [_1748461, _1748463, _1748465, _1748467] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1748461, tc_HOL_Obool), tc_fun(_1748461, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1748461, tc_HOL_Obool), tc_fun(_1748461, tc_HOL_Obool)), _1748463), _1748465)), c_Wellfounded_Omax__ext(_1748461, _1748467))), 48138 ^ _779530 : [(48139 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1748461), _1748463)))], (48141 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1748461), _1748465)))], (48143 ^ _779530) ^ [] : [_1748465 = c_Orderings_Obot__class_Obot(tc_fun(_1748461, tc_HOL_Obool))], (48145 ^ _779530) ^ [_1748755] : [hBOOL(hAPP(hAPP(c_member(_1748461), _1748755), _1748463)), 48149 ^ _779530 : [(48150 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748461), 48148 ^ [_1748461, _1748463, _1748465, _1748467, _1748755]), _1748465)))], (48152 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748461, _1748461)), hAPP(hAPP(c_Product__Type_OPair(_1748461, _1748461), _1748755), 48148 ^ [_1748461, _1748463, _1748465, _1748467, _1748755])), _1748467)))]]]]], (48154 ^ _779530) ^ [_1748967, _1748969, _1748971, _1748973] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1748967, tc_HOL_Obool), tc_fun(_1748967, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1748967, tc_HOL_Obool), tc_fun(_1748967, tc_HOL_Obool)), _1748969), _1748971)), c_Wellfounded_Omax__ext(_1748967, _1748973)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748967), _1748969)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1748967), _1748971)), -(_1748971 = c_Orderings_Obot__class_Obot(tc_fun(_1748967, tc_HOL_Obool))), 48168 ^ _779530 : [(48169 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748967), 48167 ^ [_1748967, _1748969, _1748971, _1748973]), _1748969)))], (48171 ^ _779530) ^ [_1749372] : [hBOOL(hAPP(hAPP(c_member(_1748967), _1749372), _1748971)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1748967, _1748967)), hAPP(hAPP(c_Product__Type_OPair(_1748967, _1748967), 48167 ^ [_1748967, _1748969, _1748971, _1748973]), _1749372)), _1748973))]]], (48179 ^ _779530) ^ [_1749600, _1749602, _1749604, _1749606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749600), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749602)), _1749604))), 48185 ^ _779530 : [(48186 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749602), 48184 ^ [_1749600, _1749602, _1749604, _1749606]), hAPP(c_List_Oset(_1749602), _1749604))))], (48188 ^ _779530) ^ [] : [hBOOL(hAPP(_1749606, 48184 ^ [_1749600, _1749602, _1749604, _1749606]))]], -(hBOOL(hAPP(_1749606, hAPP(hAPP(c_List_Onth(_1749602), _1749604), _1749600))))], (48192 ^ _779530) ^ [_1749886, _1749888, _1749890] : [48194 ^ _779530 : [(48195 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48193 ^ [_1749886, _1749888, _1749890]), _1749886)))], (48197 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1749888, 48193 ^ [_1749886, _1749888, _1749890])))], (48199 ^ _779530) ^ [] : [hBOOL(hAPP(_1749888, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 48193 ^ [_1749886, _1749888, _1749890]), _1749886)))]], hBOOL(hAPP(_1749888, _1749890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749890), _1749886)), -(hBOOL(hAPP(_1749888, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48211 ^ _779530) ^ [_1750248, _1750250, _1750252] : [class_Orderings_Olinorder(_1750248), 48217 ^ _779530 : [(48218 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750248), 48216 ^ [_1750248, _1750250, _1750252]), hAPP(c_List_Oset(_1750248), _1750250))))], (48220 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1750248), _1750252), 48216 ^ [_1750248, _1750250, _1750252]))]], c_List_Olinorder__class_Osorted(_1750248, _1750250), -(c_List_Olinorder__class_Osorted(_1750248, hAPP(hAPP(c_List_Olist_OCons(_1750248), _1750252), _1750250)))], (48228 ^ _779530) ^ [_1750564, _1750566, _1750568] : [48230 ^ _779530 : [(48231 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1750564, tc_HOL_Obool)), 48229 ^ [_1750564, _1750566, _1750568]), _1750566)))], (48233 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1750564), _1750568), 48229 ^ [_1750564, _1750566, _1750568]))]], -(hBOOL(hAPP(hAPP(c_member(_1750564), _1750568), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1750564, tc_HOL_Obool), _1750566))))], (48237 ^ _779530) ^ [_1750780, _1750782, _1750784, _1750786, _1750788, _1750790] : [class_Groups_Oab__semigroup__mult(_1750780), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750782), _1750784)), 48247 ^ _779530 : [(48248 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750782), 48246 ^ [_1750780, _1750782, _1750784, _1750786, _1750788, _1750790]), _1750784)))], (48250 ^ _779530) ^ [] : [hAPP(_1750786, 48246 ^ [_1750780, _1750782, _1750784, _1750786, _1750788, _1750790]) = hAPP(_1750788, 48246 ^ [_1750780, _1750782, _1750784, _1750786, _1750788, _1750790])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1750780, _1750782, c_Groups_Otimes__class_Otimes(_1750780)), _1750786), _1750790), _1750784) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1750780, _1750782, c_Groups_Otimes__class_Otimes(_1750780)), _1750788), _1750790), _1750784))], (48254 ^ _779530) ^ [_1751185, _1751187, _1751189] : [class_Orderings_Olinorder(_1751185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751185), _1751187)), 48264 ^ _779530 : [(48265 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751185), 48263 ^ [_1751185, _1751187, _1751189]), _1751187)))], (48267 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1751185), 48263 ^ [_1751185, _1751187, _1751189]), _1751189))]], hBOOL(hAPP(hAPP(c_member(_1751185), _1751189), _1751187)), -(c_Big__Operators_Olinorder__class_OMax(_1751185, _1751187) = _1751189)], (48275 ^ _779530) ^ [_1751557, _1751559, _1751561] : [class_Orderings_Olinorder(_1751557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1751557), _1751559)), 48285 ^ _779530 : [(48286 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751557), 48284 ^ [_1751557, _1751559, _1751561]), _1751559)))], (48288 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1751557), _1751561), 48284 ^ [_1751557, _1751559, _1751561]))]], hBOOL(hAPP(hAPP(c_member(_1751557), _1751561), _1751559)), -(c_Big__Operators_Olinorder__class_OMin(_1751557, _1751559) = _1751561)], (48296 ^ _779530) ^ [_1751929, _1751931, _1751933] : [c_Wellfounded_Owf(_1751929, _1751931), hBOOL(hAPP(hAPP(c_member(tc_prod(_1751929, _1751929)), hAPP(hAPP(c_Product__Type_OPair(_1751929, _1751929), hAPP(_1751933, hAPP(c_Nat_OSuc, 48299 ^ [_1751929, _1751931, _1751933]))), hAPP(_1751933, 48299 ^ [_1751929, _1751931, _1751933]))), _1751931))], (48303 ^ _779530) ^ [_1752148, _1752150, _1752152] : [c_List_Olist__ex(_1752148, _1752150, _1752152), 48307 ^ _779530 : [(48308 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48306 ^ [_1752148, _1752150, _1752152]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752148)), _1752152))))], (48310 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1752150, hAPP(hAPP(c_List_Onth(_1752148), _1752152), 48306 ^ [_1752148, _1752150, _1752152]))))]]], (48312 ^ _779530) ^ [_1752318, _1752320, _1752322] : [-(c_List_Olist__ex(_1752318, _1752320, _1752322)), 48313 ^ _779530 : [(48314 ^ _779530) ^ [_1752383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752383), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752318)), _1752322))), hBOOL(hAPP(_1752320, hAPP(hAPP(c_List_Onth(_1752318), _1752322), _1752383)))]]], (48322 ^ _779530) ^ [_1752538, _1752540, _1752542, _1752544, _1752546, _1752548, _1752550] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1752538, _1752540, _1752542, _1752544), _1752546), _1752548), _1752550) = hAPP(hAPP(_1752548, hAPP(c_Product__Type_Ofst(_1752540, _1752542), hAPP(_1752546, _1752550))), hAPP(c_Product__Type_Osnd(_1752540, _1752542), hAPP(_1752546, _1752550))))], (48334 ^ _779530) ^ [_1752746, _1752748, _1752750, _1752752] : [48335 ^ _779530 : [(48336 ^ _779530) ^ [] : [hBOOL(hAPP(_1752748, _1752750))], (48338 ^ _779530) ^ [] : [c_List_Olist__ex(_1752746, _1752748, _1752752)]], -(c_List_Olist__ex(_1752746, _1752748, hAPP(hAPP(c_List_Olist_OCons(_1752746), _1752750), _1752752)))], (48324 ^ _779530) ^ [_1752632, _1752634, _1752636, _1752638] : [c_List_Olist__ex(_1752632, _1752634, hAPP(hAPP(c_List_Olist_OCons(_1752632), _1752636), _1752638)), -(hBOOL(hAPP(_1752634, _1752636))), -(c_List_Olist__ex(_1752632, _1752634, _1752638))], (48352 ^ _779530) ^ [_1753024, _1753026, _1753028, _1753030] : [48353 ^ _779530 : [(48354 ^ _779530) ^ [] : [c_List_Olist__ex(_1753024, _1753026, _1753028)], (48356 ^ _779530) ^ [] : [c_List_Olist__ex(_1753024, _1753026, _1753030)]], -(c_List_Olist__ex(_1753024, _1753026, hAPP(hAPP(c_List_Oappend(_1753024), _1753028), _1753030)))], (48342 ^ _779530) ^ [_1752912, _1752914, _1752916, _1752918] : [c_List_Olist__ex(_1752912, _1752914, hAPP(hAPP(c_List_Oappend(_1752912), _1752916), _1752918)), -(c_List_Olist__ex(_1752912, _1752914, _1752916)), -(c_List_Olist__ex(_1752912, _1752914, _1752918))], (48360 ^ _779530) ^ [_1753167, _1753169, _1753171, _1753173, _1753175, _1753177, _1753179, _1753181, _1753183] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1753167, _1753169, _1753171, _1753173), hAPP(hAPP(c_Product__Type_Oscomp(_1753167, _1753175, _1753177, tc_prod(_1753169, _1753171)), _1753179), _1753181)), _1753183) = hAPP(hAPP(c_Product__Type_Oscomp(_1753167, _1753175, _1753177, _1753173), _1753179), hAPP(hAPP(c_COMBC(_1753175, tc_fun(_1753169, tc_fun(_1753171, _1753173)), tc_fun(_1753177, _1753173)), hAPP(hAPP(c_COMBB(tc_fun(_1753177, tc_prod(_1753169, _1753171)), tc_fun(tc_fun(_1753169, tc_fun(_1753171, _1753173)), tc_fun(_1753177, _1753173)), _1753175), c_Product__Type_Oscomp(_1753177, _1753169, _1753171, _1753173)), _1753181)), _1753183)))], (48362 ^ _779530) ^ [_1753294, _1753296, _1753298, _1753300] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1753294, _1753296, _1753298, tc_prod(_1753296, _1753298)), _1753300), c_Product__Type_OPair(_1753296, _1753298)) = _1753300)], (48364 ^ _779530) ^ [_1753340, _1753342, _1753344, _1753346, _1753348] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1753340, _1753342, _1753340, _1753344), hAPP(c_Product__Type_OPair(_1753342, _1753340), _1753346)), _1753348) = hAPP(_1753348, _1753346))], (48366 ^ _779530) ^ [_1753409, _1753411, _1753413] : [c_List_Olist__ex(_1753409, _1753411, _1753413), 48370 ^ _779530 : [(48371 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753409), 48369 ^ [_1753409, _1753411, _1753413]), hAPP(c_List_Oset(_1753409), _1753413))))], (48373 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1753411, 48369 ^ [_1753409, _1753411, _1753413])))]]], (48375 ^ _779530) ^ [_1753563, _1753565, _1753567] : [-(c_List_Olist__ex(_1753563, _1753565, _1753567)), 48376 ^ _779530 : [(48377 ^ _779530) ^ [_1753620] : [hBOOL(hAPP(hAPP(c_member(_1753563), _1753620), hAPP(c_List_Oset(_1753563), _1753567))), hBOOL(hAPP(_1753565, _1753620))]]], (48385 ^ _779530) ^ [_1753759, _1753761, _1753763, _1753765, _1753767, _1753769, _1753771] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1753759, _1753761, _1753763, _1753765), _1753767), _1753769), _1753771) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1753761, _1753763, _1753765), _1753769), hAPP(_1753767, _1753771)))], (48387 ^ _779530) ^ [_1753821, _1753823, _1753825, _1753827, _1753829, _1753831, _1753833] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1753821, _1753823, _1753825, _1753827), _1753829), _1753831), _1753833) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1753823, _1753825, _1753827), _1753831), hAPP(_1753829, _1753833)))], (48389 ^ _779530) ^ [_1753901, _1753903, _1753905] : [c_List_Olist__ex(_1753901, _1753903, hAPP(c_List_Orev(_1753901), _1753905)), -(c_List_Olist__ex(_1753901, _1753903, _1753905))], (48395 ^ _779530) ^ [_1753990, _1753992, _1753994] : [c_List_Olist__ex(_1753990, _1753992, _1753994), -(c_List_Olist__ex(_1753990, _1753992, hAPP(c_List_Orev(_1753990), _1753994)))], (48401 ^ _779530) ^ [_1754097, _1754099] : [c_List_Olist__ex(_1754097, _1754099, c_List_Olist_ONil(_1754097))], (48403 ^ _779530) ^ [_1754143, _1754145, _1754147, _1754149, _1754151] : [_1754143 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1754145, _1754147, _1754143, _1754149), _1754151) = hAPP(c_Product__Type_OPair(_1754145, _1754147), _1754151))], (48409 ^ _779530) ^ [_1754248, _1754250, _1754252, _1754254, _1754256] : [-(_1754248 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1754250, _1754252, _1754248, _1754254), _1754256) = hAPP(hAPP(c_Product__Type_Oscomp(_1754252, _1754250, _1754252, tc_prod(_1754250, _1754252)), hAPP(_1754254, _1754256)), c_Random_Oiterate(_1754250, _1754252, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1754248), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1754254)))], (48415 ^ _779530) ^ [_1754328, _1754330, _1754332, _1754334, _1754336, _1754338, _1754340, _1754342] : [class_Groups_Ocomm__monoid__add(_1754328), class_Orderings_Oord(_1754330), _1754332 = _1754334, _1754336 = _1754338, 48433 ^ _779530 : [(48434 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754330), _1754334), 48432 ^ [_1754328, _1754330, _1754332, _1754334, _1754336, _1754338, _1754340, _1754342])))], (48436 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1754330), 48432 ^ [_1754328, _1754330, _1754332, _1754334, _1754336, _1754338, _1754340, _1754342]), _1754338)))], (48438 ^ _779530) ^ [] : [hAPP(_1754340, 48432 ^ [_1754328, _1754330, _1754332, _1754334, _1754336, _1754338, _1754340, _1754342]) = hAPP(_1754342, 48432 ^ [_1754328, _1754330, _1754332, _1754334, _1754336, _1754338, _1754340, _1754342])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1754330, _1754328), _1754340), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1754330, _1754332), _1754336)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1754330, _1754328), _1754342), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1754330, _1754334), _1754338)))], (48442 ^ _779530) ^ [_1754966, _1754968] : [48443 ^ _779530 : [(48444 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1754966), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48446 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1754968), _1754966))]], -(c_Random_Olog(_1754966, _1754968) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (48450 ^ _779530) ^ [_1755101, _1755103] : [-(c_Random_Olog(_1755101, _1755103) = 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(_1755101, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1755103), _1755101)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1755101), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1755103), _1755101)))], (48460 ^ _779530) ^ [_1755183, _1755185, _1755187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1755183), _1755185)), -(c_Random_Ominus__shift(_1755187, _1755183, _1755185) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1755187), _1755183)), _1755185))], (48466 ^ _779530) ^ [_1755298, _1755300, _1755302] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1755298), _1755300))), -(c_Random_Ominus__shift(_1755302, _1755298, _1755300) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1755298), _1755300))], (48472 ^ _779530) ^ [_1755362, _1755364] : [_1755362 = _1755364, -(c_Random_Oinc__shift(_1755362, _1755364) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (48478 ^ _779530) ^ [_1755439, _1755441] : [-(_1755439 = _1755441), -(c_Random_Oinc__shift(_1755439, _1755441) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1755441), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48484 ^ _779530) ^ [_1755482, _1755484, _1755486] : [-(_1755482 = c_List_Olist_ONil(_1755484)), -(hBOOL(hAPP(hAPP(c_member(_1755484), hAPP(c_Product__Type_Ofst(_1755484, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1755484, _1755482), _1755486))), hAPP(c_List_Oset(_1755484), _1755482))))], (48490 ^ _779530) ^ [_1755546, _1755548, _1755550] : [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, _1755546), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1755546)), _1755548)))), -(hBOOL(hAPP(hAPP(c_member(_1755546), hAPP(c_Product__Type_Ofst(_1755546, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1755546, _1755548), _1755550))), hAPP(c_List_Oset(_1755546), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755546), _1755546), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1755546)), _1755548)))))], (48496 ^ _779530) ^ [_1755739, _1755741] : [-(_1755739 = c_List_Olist_ONil(_1755741)), -(c_Random_Oselect__weight(_1755741, hAPP(hAPP(c_List_Omap(_1755741, tc_prod(tc_Code__Numeral_Ocode__numeral, _1755741)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1755741), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1755739)) = c_Random_Oselect(_1755741, _1755739))], (48502 ^ _779530) ^ [_1755801, _1755803, _1755805] : [-(c_Random_Oselect__weight(_1755801, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755801)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1755801), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1755803)), _1755805)) = c_Random_Oselect__weight(_1755801, _1755805))], (48504 ^ _779530) ^ [_1755854, _1755856] : [-(c_Random_Oselect__weight(_1755854, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755854), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1755854, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1755854, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1755854)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1755856)) = c_Random_Oselect__weight(_1755854, _1755856))], (48506 ^ _779530) ^ [_1755917, _1755919, _1755921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1755917), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755919), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1755919)), _1755921)))), -(hBOOL(hAPP(hAPP(c_member(_1755919), hAPP(c_Random_Opick(_1755919, _1755921), _1755917)), hAPP(c_List_Oset(_1755919), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1755919), _1755919), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1755919)), _1755921)))))], (48512 ^ _779530) ^ [_1756123, _1756125, _1756127, _1756129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1756123), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1756125), _1756127))), -(hAPP(c_Random_Opick(_1756125, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1756125)), _1756127), _1756129)), _1756123) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1756125), _1756127))], (48518 ^ _779530) ^ [_1756266, _1756268, _1756270, _1756272] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1756266), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1756268), _1756270)))), -(hAPP(c_Random_Opick(_1756268, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1756268)), _1756270), _1756272)), _1756266) = hAPP(c_Random_Opick(_1756268, _1756272), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1756266), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1756268), _1756270))))], (48524 ^ _779530) ^ [_1756354, _1756356] : [-(c_Random_Opick(_1756354, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1756354), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1756354, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1756354, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1756354)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1756356)) = c_Random_Opick(_1756354, _1756356))], (48526 ^ _779530) ^ [_1756417, _1756419] : [-(c_Random_Oselect__weight(_1756417, _1756419) = 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(_1756417, 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, _1756417), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1756417)), _1756419)))), hAPP(hAPP(c_COMBB(_1756417, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1756417, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1756417, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1756417, _1756419))))], (48528 ^ _779530) ^ [_1756501, _1756503, _1756505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756501), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756503)), _1756505))), -(hAPP(c_Random_Opick(_1756503, hAPP(hAPP(c_List_Omap(_1756503, tc_prod(tc_Code__Numeral_Ocode__numeral, _1756503)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1756503), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1756505)), hAPP(c_Code__Numeral_Oof__nat, _1756501)) = hAPP(hAPP(c_List_Onth(_1756503), _1756505), _1756501))], (48534 ^ _779530) ^ [] : [-(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))], (48536 ^ _779530) ^ [_1756692, _1756694] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1756692), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1756694), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 48543 ^ _779530 : [(48544 ^ _779530) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1756692) = hAPP(c_Code__Numeral_Oof__nat, _1756694), -(_1756692 = _1756694)], (48550 ^ _779530) ^ [] : [_1756692 = _1756694, -(hAPP(c_Code__Numeral_Oof__nat, _1756692) = hAPP(c_Code__Numeral_Oof__nat, _1756694))]]], (48556 ^ _779530) ^ [_1757004, _1757006] : [hAPP(c_Code__Numeral_Oof__nat, _1757004) = hAPP(c_Code__Numeral_Oof__nat, _1757006), -(_1757004 = _1757006)], (48562 ^ _779530) ^ [_1757089, _1757091] : [_1757089 = _1757091, -(hAPP(c_Code__Numeral_Oof__nat, _1757089) = hAPP(c_Code__Numeral_Oof__nat, _1757091))], (48568 ^ _779530) ^ [_1757180, _1757182] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757180)), hAPP(c_Code__Numeral_Oof__nat, _1757182)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1757180), _1757182)))], (48570 ^ _779530) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (48572 ^ _779530) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48574 ^ _779530) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48576 ^ _779530) ^ [_1757295, _1757297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757295)), hAPP(c_Code__Numeral_Oof__nat, _1757297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757295), _1757297)))], (48582 ^ _779530) ^ [_1757400, _1757402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1757400), _1757402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757400)), hAPP(c_Code__Numeral_Oof__nat, _1757402))))], (48588 ^ _779530) ^ [_1757511, _1757513] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757511)), hAPP(c_Code__Numeral_Oof__nat, _1757513)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1757511), _1757513)))], (48590 ^ _779530) ^ [_1757572, _1757574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757572)), hAPP(c_Code__Numeral_Oof__nat, _1757574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757572), _1757574)))], (48596 ^ _779530) ^ [_1757677, _1757679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1757677), _1757679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1757677)), hAPP(c_Code__Numeral_Oof__nat, _1757679))))], (48602 ^ _779530) ^ [_1757794] : [-(_1757794 = 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)), _1757794)))], (48608 ^ _779530) ^ [_1757826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1757826)), _1757826 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48614 ^ _779530) ^ [_1757908, _1757910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1757908)), -(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(_1757908), _1757910))), _1757908)))], (48620 ^ _779530) ^ [_1758015, _1758017] : [-(c_Random_Oselect(_1758015, _1758017) = 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(_1758015, 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(_1758015)), _1758017)))), hAPP(hAPP(c_COMBB(_1758015, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1758015, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1758015, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1758015, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1758015), _1758017)), c_Code__Numeral_Onat__of))))], (48622 ^ _779530) ^ [_1758103, _1758105] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1758103)), hAPP(c_Code__Numeral_Oof__nat, _1758105)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1758103), _1758105)))], (48624 ^ _779530) ^ [] : [-(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))))], (48626 ^ _779530) ^ [_1758167] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1758167)) = _1758167)], (48628 ^ _779530) ^ [_1758196] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1758196)) = _1758196)], (48630 ^ _779530) ^ [_1758225] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1758225)) = _1758225)], (48632 ^ _779530) ^ [_1758254, _1758256] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1758254), _1758256) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1758254)), hAPP(c_Code__Numeral_Onat__of, _1758256))))], (48634 ^ _779530) ^ [_1758315, _1758317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1758315), _1758317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1758315)), hAPP(c_Code__Numeral_Onat__of, _1758317))))], (48640 ^ _779530) ^ [_1758420, _1758422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1758420)), hAPP(c_Code__Numeral_Onat__of, _1758422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1758420), _1758422)))], (48646 ^ _779530) ^ [_1758546, _1758548] : [hAPP(c_Code__Numeral_Onat__of, _1758546) = hAPP(c_Code__Numeral_Onat__of, _1758548), -(_1758546 = _1758548)], (48652 ^ _779530) ^ [_1758631, _1758633] : [_1758631 = _1758633, -(hAPP(c_Code__Numeral_Onat__of, _1758631) = hAPP(c_Code__Numeral_Onat__of, _1758633))], (48658 ^ _779530) ^ [_1758737, _1758739] : [hAPP(c_Code__Numeral_Onat__of, _1758737) = hAPP(c_Code__Numeral_Onat__of, _1758739), -(_1758737 = _1758739)], (48664 ^ _779530) ^ [_1758822, _1758824] : [_1758822 = _1758824, -(hAPP(c_Code__Numeral_Onat__of, _1758822) = hAPP(c_Code__Numeral_Onat__of, _1758824))], (48670 ^ _779530) ^ [_1758913] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1758913)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (48672 ^ _779530) ^ [_1758944] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1758944)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1758944))], (48674 ^ _779530) ^ [] : [-(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))], (48676 ^ _779530) ^ [_1759009, _1759011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1759009), _1759011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759009)), hAPP(c_Code__Numeral_Onat__of, _1759011))))], (48682 ^ _779530) ^ [_1759114, _1759116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759114)), hAPP(c_Code__Numeral_Onat__of, _1759116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1759114), _1759116)))], (48688 ^ _779530) ^ [_1759225] : [-(hAPP(c_Code__Numeral_Onat__of, _1759225) = c_Code__Numeral_Onat__of__aux(_1759225, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48690 ^ _779530) ^ [_1759254, _1759256] : [-(c_Code__Numeral_Onat__of__aux(_1759254, _1759256) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759254)), _1759256))], (48692 ^ _779530) ^ [_1759291] : [-(c_Code__Numeral_OSuc__code__numeral(_1759291) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1759291))))], (48694 ^ _779530) ^ [_1759325, _1759327] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1759325), _1759327) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759325)), hAPP(c_Code__Numeral_Onat__of, _1759327))))], (48696 ^ _779530) ^ [_1759371] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1759371), 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, _1759371)) = _1759371)], (48702 ^ _779530) ^ [_1759468, _1759470] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1759468), _1759470) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759468)), hAPP(c_Code__Numeral_Onat__of, _1759470))))], (48704 ^ _779530) ^ [_1759514, _1759516] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1759514), _1759516) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1759514)), hAPP(c_Code__Numeral_Onat__of, _1759516))))], (48706 ^ _779530) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (48708 ^ _779530) ^ [_1759578, _1759580] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1759578), _1759580) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1759578), _1759580))], (48710 ^ _779530) ^ [_1759615, _1759617] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1759615, _1759617) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1759615), hAPP(c_Code__Numeral_Onat__of, _1759617))))], (48712 ^ _779530) ^ [_1759653] : [-(_1759653 = 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, _1759653)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1759653))))], (48718 ^ _779530) ^ [_1759704, _1759706] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1759704), _1759706) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1759704, 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)))), _1759706))))], (48720 ^ _779530) ^ [_1759757, _1759759] : [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), _1759757), _1759759)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759757), _1759759)))], (48726 ^ _779530) ^ [_1759862, _1759864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759862), _1759864)), -(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), _1759862), _1759864)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (48732 ^ _779530) ^ [_1759973, _1759975] : [c_Wellfounded_Owf(_1759973, _1759975), -(c_Wellfounded_Owf(_1759973, c_Transitive__Closure_Otrancl(_1759973, _1759975)))], (48738 ^ _779530) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (48740 ^ _779530) ^ [_1760089, _1760091] : [c_Wellfounded_Oacyclic(_1760089, _1760091), 48743 ^ _779530 : [(48744 ^ _779530) ^ [_1760174] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760089, _1760089)), hAPP(hAPP(c_Product__Type_OPair(_1760089, _1760089), _1760174), _1760174)), c_Transitive__Closure_Otrancl(_1760089, _1760091)))]]], (48746 ^ _779530) ^ [_1760217, _1760219] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760217, _1760217)), hAPP(hAPP(c_Product__Type_OPair(_1760217, _1760217), 48747 ^ [_1760217, _1760219]), 48747 ^ [_1760217, _1760219])), c_Transitive__Closure_Otrancl(_1760217, _1760219)))), -(c_Wellfounded_Oacyclic(_1760217, _1760219))], (48753 ^ _779530) ^ [_1760291, _1760293, _1760295, _1760297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760291, _1760291)), hAPP(hAPP(c_Product__Type_OPair(_1760291, _1760291), _1760293), _1760295)), _1760297)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760291, _1760291)), hAPP(hAPP(c_Product__Type_OPair(_1760291, _1760291), _1760293), _1760295)), c_Transitive__Closure_Otrancl(_1760291, _1760297))))], (48759 ^ _779530) ^ [_1760454, _1760456] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1760454, _1760454), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1760454, _1760456)), hAPP(hAPP(c_Product__Type_OSigma(_1760454, _1760454), hAPP(c_Relation_OField(_1760454), _1760456)), hAPP(c_COMBK(tc_fun(_1760454, tc_HOL_Obool), _1760454), hAPP(c_Relation_OField(_1760454), _1760456))))))], (48761 ^ _779530) ^ [_1760523, _1760525, _1760527] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760523, _1760523)), _1760525), _1760527)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760523, _1760523)), _1760525), c_Transitive__Closure_Otrancl(_1760523, _1760527))))], (48767 ^ _779530) ^ [_1760648] : [-(c_Transitive__Closure_Otrancl(_1760648, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1760648, _1760648), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1760648, _1760648), tc_HOL_Obool)))], (48769 ^ _779530) ^ [_1760690, _1760692] : [-(hAPP(c_Relation_ODomain(_1760690, _1760690), c_Transitive__Closure_Otrancl(_1760690, _1760692)) = hAPP(c_Relation_ODomain(_1760690, _1760690), _1760692))], (48771 ^ _779530) ^ [_1760730, _1760732] : [-(hAPP(c_Relation_ORange(_1760730, _1760730), c_Transitive__Closure_Otrancl(_1760730, _1760732)) = hAPP(c_Relation_ORange(_1760730, _1760730), _1760732))], (48773 ^ _779530) ^ [_1760785, _1760787] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1760785, _1760785)), c_Transitive__Closure_Otrancl(_1760785, _1760787))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1760785, _1760785)), _1760787)))], (48779 ^ _779530) ^ [_1760892, _1760894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1760892, _1760892)), _1760894)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1760892, _1760892)), c_Transitive__Closure_Otrancl(_1760892, _1760894))))], (48785 ^ _779530) ^ [_1761005, _1761007, _1761009, _1761011, _1761013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761005, _1761005)), hAPP(hAPP(c_Product__Type_OPair(_1761005, _1761005), _1761007), _1761009)), c_Transitive__Closure_Otrancl(_1761005, _1761011))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1761005, _1761005)), hAPP(hAPP(c_Product__Type_OPair(_1761005, _1761005), _1761009), _1761013)), c_Transitive__Closure_Otrancl(_1761005, _1761011))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761005, _1761005)), hAPP(hAPP(c_Product__Type_OPair(_1761005, _1761005), _1761007), _1761013)), c_Transitive__Closure_Otrancl(_1761005, _1761011))))], (48795 ^ _779530) ^ [_1761278, _1761280, _1761282, _1761284, _1761286] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761278, _1761278)), hAPP(hAPP(c_Product__Type_OPair(_1761278, _1761278), _1761280), _1761282)), c_Transitive__Closure_Otrancl(_1761278, _1761284))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1761278, _1761278)), hAPP(hAPP(c_Product__Type_OPair(_1761278, _1761278), _1761282), _1761286)), _1761284)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761278, _1761278)), hAPP(hAPP(c_Product__Type_OPair(_1761278, _1761278), _1761280), _1761286)), c_Transitive__Closure_Otrancl(_1761278, _1761284))))], (48805 ^ _779530) ^ [_1761545, _1761547, _1761549, _1761551, _1761553] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761545, _1761545)), hAPP(hAPP(c_Product__Type_OPair(_1761545, _1761545), _1761547), _1761549)), _1761551)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1761545, _1761545)), hAPP(hAPP(c_Product__Type_OPair(_1761545, _1761545), _1761549), _1761553)), c_Transitive__Closure_Otrancl(_1761545, _1761551))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761545, _1761545)), hAPP(hAPP(c_Product__Type_OPair(_1761545, _1761545), _1761547), _1761553)), c_Transitive__Closure_Otrancl(_1761545, _1761551))))], (48815 ^ _779530) ^ [_1761812, _1761814, _1761816, _1761818, _1761820] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761812, _1761812)), hAPP(hAPP(c_Product__Type_OPair(_1761812, _1761812), _1761814), _1761816)), _1761818)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1761812, _1761812)), hAPP(hAPP(c_Product__Type_OPair(_1761812, _1761812), _1761816), _1761820)), _1761818)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761812, _1761812)), hAPP(hAPP(c_Product__Type_OPair(_1761812, _1761812), _1761814), _1761820)), c_Transitive__Closure_Otrancl(_1761812, _1761818))))], (48825 ^ _779530) ^ [_1762073, _1762075, _1762077, _1762079] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762073, _1762073)), _1762075), c_Transitive__Closure_Otrancl(_1762073, _1762077))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762073, _1762073), tc_HOL_Obool)), _1762077), _1762079)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762073, _1762073)), _1762075), c_Transitive__Closure_Otrancl(_1762073, _1762079))))], (48835 ^ _779530) ^ [_1762288, _1762290] : [-(c_Transitive__Closure_Otrancl(_1762288, _1762290) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1762288, _1762288), tc_HOL_Obool)), _1762290), hAPP(hAPP(c_Relation_Orel__comp(_1762288, _1762288, _1762288), c_Transitive__Closure_Otrancl(_1762288, _1762290)), _1762290)))], (48837 ^ _779530) ^ [_1762343, _1762345, _1762347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762343, _1762343), tc_HOL_Obool)), _1762345), hAPP(hAPP(c_Product__Type_OSigma(_1762343, _1762343), _1762347), hAPP(c_COMBK(tc_fun(_1762343, tc_HOL_Obool), _1762343), _1762347)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762343, _1762343), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1762343, _1762345)), hAPP(hAPP(c_Product__Type_OSigma(_1762343, _1762343), _1762347), hAPP(c_COMBK(tc_fun(_1762343, tc_HOL_Obool), _1762343), _1762347)))))], (48843 ^ _779530) ^ [_1762552, _1762554, _1762556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762552, _1762552), tc_HOL_Obool)), _1762554), _1762556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762552, _1762552), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1762552, _1762552, _1762552), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1762552, _1762552), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1762552, _1762554)), _1762556)), _1762554)), _1762556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1762552, _1762552), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1762552, _1762554)), _1762556)))], (48853 ^ _779530) ^ [_1762823, _1762825, _1762827, _1762829] : [-(c_Transitive__Closure_Otrancl(_1762823, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1762823, _1762823)), hAPP(hAPP(c_Product__Type_OPair(_1762823, _1762823), _1762825), _1762827)), _1762829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1762823, _1762823), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1762823, _1762829)), hAPP(c_Set_OCollect(tc_prod(_1762823, _1762823)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762823, _1762823, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1762823, tc_fun(_1762823, tc_HOL_Obool), tc_fun(_1762823, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1762823, tc_HOL_Obool), tc_fun(_1762823, tc_HOL_Obool)), _1762823), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1762823)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762823), c_fconj), hAPP(hAPP(c_COMBC(_1762823, tc_fun(tc_prod(_1762823, _1762823), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1762823, _1762823), tc_fun(tc_fun(tc_prod(_1762823, _1762823), tc_HOL_Obool), tc_HOL_Obool), _1762823), c_member(tc_prod(_1762823, _1762823))), hAPP(hAPP(c_COMBC(_1762823, _1762823, tc_prod(_1762823, _1762823)), c_Product__Type_OPair(_1762823, _1762823)), _1762825))), c_Transitive__Closure_Ortrancl(_1762823, _1762829))))), hAPP(hAPP(c_COMBC(_1762823, tc_fun(tc_prod(_1762823, _1762823), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1762823, _1762823), tc_fun(tc_fun(tc_prod(_1762823, _1762823), tc_HOL_Obool), tc_HOL_Obool), _1762823), c_member(tc_prod(_1762823, _1762823))), hAPP(c_Product__Type_OPair(_1762823, _1762823), _1762827))), c_Transitive__Closure_Ortrancl(_1762823, _1762829)))))))], (48855 ^ _779530) ^ [_1763091, _1763093, _1763095, _1763097] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1763091, tc_fun(_1763091, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1763091, tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_fun(_1763091, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1763091, tc_fun(tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_fun(_1763091, tc_HOL_Obool)), _1763091), c_COMBC(_1763091, tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1763091, tc_prod(_1763091, _1763091)), tc_fun(_1763091, tc_fun(tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_HOL_Obool)), _1763091), hAPP(c_COMBB(tc_prod(_1763091, _1763091), tc_fun(tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool), tc_HOL_Obool), _1763091), c_member(tc_prod(_1763091, _1763091)))), c_Product__Type_OPair(_1763091, _1763091)))), _1763093)), c_fequal), _1763095), _1763097)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763091, _1763091)), hAPP(hAPP(c_Product__Type_OPair(_1763091, _1763091), _1763095), _1763097)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1763091, _1763091), tc_HOL_Obool)), _1763093), c_Relation_OId(_1763091)))))], (48861 ^ _779530) ^ [_1763512, _1763514, _1763516, _1763518] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763512, _1763512)), hAPP(hAPP(c_Product__Type_OPair(_1763512, _1763512), _1763516), _1763518)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool)), _1763514), c_Relation_OId(_1763512)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1763512, tc_fun(_1763512, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1763512, tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_fun(_1763512, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1763512, tc_fun(tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_fun(_1763512, tc_HOL_Obool)), _1763512), c_COMBC(_1763512, tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1763512, tc_prod(_1763512, _1763512)), tc_fun(_1763512, tc_fun(tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_HOL_Obool)), _1763512), hAPP(c_COMBB(tc_prod(_1763512, _1763512), tc_fun(tc_fun(tc_prod(_1763512, _1763512), tc_HOL_Obool), tc_HOL_Obool), _1763512), c_member(tc_prod(_1763512, _1763512)))), c_Product__Type_OPair(_1763512, _1763512)))), _1763514)), c_fequal), _1763516), _1763518)))], (48867 ^ _779530) ^ [_1763939, _1763941, _1763943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763939, _1763939)), _1763941), _1763943)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763939, _1763939)), _1763941), c_Transitive__Closure_Ortrancl(_1763939, _1763943))))], (48873 ^ _779530) ^ [_1764064, _1764066, _1764068] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764064, _1764064)), hAPP(hAPP(c_Product__Type_OPair(_1764064, _1764064), _1764066), _1764066)), c_Transitive__Closure_Ortrancl(_1764064, _1764068))))], (48875 ^ _779530) ^ [_1764113, _1764115] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764113, _1764113)), hAPP(hAPP(c_Product__Type_OPair(_1764113, _1764113), _1764115), _1764115)), c_Relation_OId(_1764113))))], (48877 ^ _779530) ^ [_1764159, _1764161, _1764163, _1764165] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764159, _1764159)), hAPP(hAPP(c_Product__Type_OPair(_1764159, _1764159), _1764161), _1764163)), c_Transitive__Closure_Otrancl(_1764159, _1764165))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764159, _1764159)), hAPP(hAPP(c_Product__Type_OPair(_1764159, _1764159), _1764161), _1764163)), c_Transitive__Closure_Ortrancl(_1764159, _1764165))))], (48883 ^ _779530) ^ [_1764328, _1764330, _1764332] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764328), tc_List_Olist(_1764328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764328), tc_List_Olist(_1764328)), _1764330), _1764330)), c_List_Olistrel(_1764328, c_Transitive__Closure_Ortrancl(_1764328, _1764332)))))], (48885 ^ _779530) ^ [_1764388, _1764390] : [-(c_Transitive__Closure_Otrancl(_1764388, _1764390) = hAPP(hAPP(c_Relation_Orel__comp(_1764388, _1764388, _1764388), c_Transitive__Closure_Ortrancl(_1764388, _1764390)), _1764390))], (48887 ^ _779530) ^ [_1764429, _1764431] : [-(c_Transitive__Closure_Otrancl(_1764429, _1764431) = hAPP(hAPP(c_Relation_Orel__comp(_1764429, _1764429, _1764429), _1764431), c_Transitive__Closure_Ortrancl(_1764429, _1764431)))], (48889 ^ _779530) ^ [_1764470, _1764472] : [-(c_Transitive__Closure_Otrancl(_1764470, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764470, _1764470), tc_HOL_Obool)), _1764472), c_Relation_OId(_1764470))) = c_Transitive__Closure_Ortrancl(_1764470, _1764472))], (48891 ^ _779530) ^ [_1764517, _1764519] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764517, _1764517), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1764517, _1764519)), c_Relation_OId(_1764517)) = c_Transitive__Closure_Ortrancl(_1764517, _1764519))], (48893 ^ _779530) ^ [_1764564, _1764566] : [-(c_Transitive__Closure_Ortrancl(_1764564, c_Transitive__Closure_Otrancl(_1764564, _1764566)) = c_Transitive__Closure_Ortrancl(_1764564, _1764566))], (48895 ^ _779530) ^ [_1764598, _1764600] : [-(c_Transitive__Closure_Otrancl(_1764598, c_Transitive__Closure_Ortrancl(_1764598, _1764600)) = c_Transitive__Closure_Ortrancl(_1764598, _1764600))], (48897 ^ _779530) ^ [_1764653, _1764655, _1764657, _1764659] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764653, _1764653)), hAPP(hAPP(c_Product__Type_OPair(_1764653, _1764653), _1764655), _1764657)), c_Transitive__Closure_Ortrancl(_1764653, _1764659))), -(_1764655 = _1764657), 48904 ^ _779530 : [(48905 ^ _779530) ^ [] : [_1764655 = _1764657], (48907 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764653, _1764653)), hAPP(hAPP(c_Product__Type_OPair(_1764653, _1764653), _1764655), _1764657)), c_Transitive__Closure_Otrancl(_1764653, _1764659))))]]], (48909 ^ _779530) ^ [_1764911, _1764913, _1764915, _1764917] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764911, _1764911)), hAPP(hAPP(c_Product__Type_OPair(_1764911, _1764911), _1764913), _1764915)), c_Transitive__Closure_Ortrancl(_1764911, _1764917)))), 48910 ^ _779530 : [(48911 ^ _779530) ^ [] : [_1764913 = _1764915], (48913 ^ _779530) ^ [] : [-(_1764913 = _1764915), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764911, _1764911)), hAPP(hAPP(c_Product__Type_OPair(_1764911, _1764911), _1764913), _1764915)), c_Transitive__Closure_Otrancl(_1764911, _1764917)))]]], (48921 ^ _779530) ^ [_1765177, _1765179, _1765181, _1765183, _1765185] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765177, _1765177)), hAPP(hAPP(c_Product__Type_OPair(_1765177, _1765177), _1765179), _1765181)), _1765183)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765177, _1765177)), hAPP(hAPP(c_Product__Type_OPair(_1765177, _1765177), _1765181), _1765185)), c_Transitive__Closure_Ortrancl(_1765177, _1765183))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765177, _1765177)), hAPP(hAPP(c_Product__Type_OPair(_1765177, _1765177), _1765179), _1765185)), c_Transitive__Closure_Otrancl(_1765177, _1765183))))], (48931 ^ _779530) ^ [_1765444, _1765446, _1765448, _1765450] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765444, _1765444)), hAPP(hAPP(c_Product__Type_OPair(_1765444, _1765444), _1765446), _1765448)), c_Transitive__Closure_Ortrancl(_1765444, _1765450))), -(_1765446 = _1765448), 48938 ^ _779530 : [(48939 ^ _779530) ^ [] : [_1765446 = _1765448], (48941 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765444, _1765444)), hAPP(hAPP(c_Product__Type_OPair(_1765444, _1765444), _1765446), _1765448)), c_Transitive__Closure_Otrancl(_1765444, _1765450))))]]], (48943 ^ _779530) ^ [_1765706, _1765708, _1765710, _1765712, _1765714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765706, _1765706)), hAPP(hAPP(c_Product__Type_OPair(_1765706, _1765706), _1765708), _1765710)), c_Transitive__Closure_Ortrancl(_1765706, _1765712))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765706, _1765706)), hAPP(hAPP(c_Product__Type_OPair(_1765706, _1765706), _1765710), _1765714)), _1765712)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765706, _1765706)), hAPP(hAPP(c_Product__Type_OPair(_1765706, _1765706), _1765708), _1765714)), c_Transitive__Closure_Otrancl(_1765706, _1765712))))], (48953 ^ _779530) ^ [_1765973, _1765975, _1765977, _1765979, _1765981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765973, _1765973)), hAPP(hAPP(c_Product__Type_OPair(_1765973, _1765973), _1765975), _1765977)), c_Transitive__Closure_Otrancl(_1765973, _1765979))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765973, _1765973)), hAPP(hAPP(c_Product__Type_OPair(_1765973, _1765973), _1765977), _1765981)), c_Transitive__Closure_Ortrancl(_1765973, _1765979))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765973, _1765973)), hAPP(hAPP(c_Product__Type_OPair(_1765973, _1765973), _1765975), _1765981)), c_Transitive__Closure_Otrancl(_1765973, _1765979))))], (48963 ^ _779530) ^ [_1766246, _1766248, _1766250, _1766252, _1766254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766246, _1766246)), hAPP(hAPP(c_Product__Type_OPair(_1766246, _1766246), _1766248), _1766250)), c_Transitive__Closure_Ortrancl(_1766246, _1766252))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1766246, _1766246)), hAPP(hAPP(c_Product__Type_OPair(_1766246, _1766246), _1766250), _1766254)), c_Transitive__Closure_Otrancl(_1766246, _1766252))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766246, _1766246)), hAPP(hAPP(c_Product__Type_OPair(_1766246, _1766246), _1766248), _1766254)), c_Transitive__Closure_Otrancl(_1766246, _1766252))))], (48973 ^ _779530) ^ [_1766519, _1766521, _1766523, _1766525, _1766527] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766519, _1766519)), hAPP(hAPP(c_Product__Type_OPair(_1766519, _1766519), _1766521), _1766523)), c_Transitive__Closure_Ortrancl(_1766519, _1766525))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1766519, _1766519)), hAPP(hAPP(c_Product__Type_OPair(_1766519, _1766519), _1766523), _1766527)), c_Transitive__Closure_Ortrancl(_1766519, _1766525))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766519, _1766519)), hAPP(hAPP(c_Product__Type_OPair(_1766519, _1766519), _1766521), _1766527)), c_Transitive__Closure_Ortrancl(_1766519, _1766525))))], (48983 ^ _779530) ^ [_1766792, _1766794, _1766796, _1766798, _1766800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766792, _1766792)), hAPP(hAPP(c_Product__Type_OPair(_1766792, _1766792), _1766794), _1766796)), c_Transitive__Closure_Ortrancl(_1766792, _1766798))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1766792, _1766792)), hAPP(hAPP(c_Product__Type_OPair(_1766792, _1766792), _1766796), _1766800)), _1766798)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766792, _1766792)), hAPP(hAPP(c_Product__Type_OPair(_1766792, _1766792), _1766794), _1766800)), c_Transitive__Closure_Ortrancl(_1766792, _1766798))))], (48993 ^ _779530) ^ [_1767059, _1767061, _1767063, _1767065, _1767067] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1767059, _1767059)), hAPP(hAPP(c_Product__Type_OPair(_1767059, _1767059), _1767061), _1767063)), _1767065)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1767059, _1767059)), hAPP(hAPP(c_Product__Type_OPair(_1767059, _1767059), _1767063), _1767067)), c_Transitive__Closure_Ortrancl(_1767059, _1767065))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767059, _1767059)), hAPP(hAPP(c_Product__Type_OPair(_1767059, _1767059), _1767061), _1767067)), c_Transitive__Closure_Ortrancl(_1767059, _1767065))))], (49003 ^ _779530) ^ [_1767326, _1767328, _1767330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1767326, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1767326, _1767326, _1767328), _1767330)), _1767330)), -(hAPP(c_Relation_OImage(_1767326, _1767326, c_Transitive__Closure_Ortrancl(_1767326, _1767328)), _1767330) = _1767330)], (49009 ^ _779530) ^ [_1767459, _1767461, _1767463] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767459, _1767459), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767459, _1767459), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1767459, _1767461)), c_Transitive__Closure_Ortrancl(_1767459, _1767463))), c_Transitive__Closure_Ortrancl(_1767459, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767459, _1767459), tc_HOL_Obool)), _1767461), _1767463)))))], (49011 ^ _779530) ^ [_1767536, _1767538, _1767540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767536, _1767536), tc_HOL_Obool)), _1767538), _1767540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767536, _1767536), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1767536, _1767538)), c_Transitive__Closure_Ortrancl(_1767536, _1767540))))], (49017 ^ _779530) ^ [_1767679, _1767681, _1767683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767679, _1767679), tc_HOL_Obool)), _1767681), _1767683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767679, _1767679), tc_HOL_Obool)), _1767683), c_Transitive__Closure_Ortrancl(_1767679, _1767681))), -(c_Transitive__Closure_Ortrancl(_1767679, _1767683) = c_Transitive__Closure_Ortrancl(_1767679, _1767681))], (49027 ^ _779530) ^ [_1767882, _1767884, _1767886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767882, _1767882), tc_HOL_Obool)), _1767884), c_Transitive__Closure_Ortrancl(_1767882, _1767886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767882, _1767882), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1767882, _1767884)), c_Transitive__Closure_Ortrancl(_1767882, _1767886))))], (49033 ^ _779530) ^ [_1768031, _1768033, _1768035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1768031, _1768031), tc_HOL_Obool)), c_Relation_OId(_1768031)), _1768033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1768031, _1768031), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1768031, _1768031, _1768031), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1768031, _1768031), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1768031, _1768035)), _1768033)), _1768035)), _1768033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1768031, _1768031), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1768031, _1768035)), _1768033)))], (49043 ^ _779530) ^ [_1768306, _1768308] : [-(c_Relation_Orefl__on(_1768306, c_Orderings_Otop__class_Otop(tc_fun(_1768306, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1768306, _1768308)))], (49045 ^ _779530) ^ [_1768340, _1768342] : [-(c_Transitive__Closure_Ortrancl(_1768340, c_Transitive__Closure_Ortrancl(_1768340, _1768342)) = c_Transitive__Closure_Ortrancl(_1768340, _1768342))], (49047 ^ _779530) ^ [_1768374, _1768376] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768374, _1768374), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1768374, _1768376)), c_Relation_OId(_1768374)) = c_Transitive__Closure_Ortrancl(_1768374, _1768376))], (49049 ^ _779530) ^ [_1768421, _1768423, _1768425] : [-(c_Transitive__Closure_Ortrancl(_1768421, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768421, _1768421), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1768421, _1768423)), c_Transitive__Closure_Ortrancl(_1768421, _1768425))) = c_Transitive__Closure_Ortrancl(_1768421, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768421, _1768421), tc_HOL_Obool)), _1768423), _1768425)))], (49051 ^ _779530) ^ [_1768488, _1768490] : [-(c_Transitive__Closure_Ortrancl(_1768488, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768488, _1768488), tc_HOL_Obool)), _1768490), c_Relation_OId(_1768488))) = c_Transitive__Closure_Ortrancl(_1768488, _1768490))], (49053 ^ _779530) ^ [_1768535, _1768537] : [-(c_Transitive__Closure_Ortrancl(_1768535, _1768537) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768535, _1768535), tc_HOL_Obool)), c_Relation_OId(_1768535)), hAPP(hAPP(c_Relation_Orel__comp(_1768535, _1768535, _1768535), c_Transitive__Closure_Ortrancl(_1768535, _1768537)), _1768537)))], (49055 ^ _779530) ^ [_1768592, _1768594] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1768592, _1768592, _1768592), _1768594), c_Transitive__Closure_Ortrancl(_1768592, _1768594)) = hAPP(hAPP(c_Relation_Orel__comp(_1768592, _1768592, _1768592), c_Transitive__Closure_Ortrancl(_1768592, _1768594)), _1768594))], (49057 ^ _779530) ^ [_1768643, _1768645] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1768643, _1768643, _1768643), c_Transitive__Closure_Ortrancl(_1768643, _1768645)), c_Transitive__Closure_Ortrancl(_1768643, _1768645)) = c_Transitive__Closure_Ortrancl(_1768643, _1768645))], (49059 ^ _779530) ^ [_1768687, _1768689] : [-(c_Transitive__Closure_Ortrancl(_1768687, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1768687, _1768687), tc_HOL_Obool)), _1768689), c_Relation_OId(_1768687))) = c_Transitive__Closure_Ortrancl(_1768687, _1768689))], (49061 ^ _779530) ^ [_1768734, _1768736] : [-(hAPP(c_Relation_ORange(_1768734, _1768734), c_Transitive__Closure_Ortrancl(_1768734, _1768736)) = c_Orderings_Otop__class_Otop(tc_fun(_1768734, tc_HOL_Obool)))], (49063 ^ _779530) ^ [_1768773, _1768775] : [-(hAPP(c_Relation_ODomain(_1768773, _1768773), c_Transitive__Closure_Ortrancl(_1768773, _1768775)) = c_Orderings_Otop__class_Otop(tc_fun(_1768773, tc_HOL_Obool)))], (49065 ^ _779530) ^ [_1768812, _1768814, _1768816, _1768818] : [49066 ^ _779530 : [(49067 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768812, _1768812)), _1768814), c_Transitive__Closure_Ortrancl(_1768812, _1768816)))], (49069 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768812, _1768812)), _1768814), c_Transitive__Closure_Ortrancl(_1768812, _1768818)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768812, _1768812)), _1768814), c_Transitive__Closure_Ortrancl(_1768812, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1768812, _1768812), tc_HOL_Obool)), _1768816), _1768818)))))], (49073 ^ _779530) ^ [_1769037] : [-(c_Transitive__Closure_Ortrancl(_1769037, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1769037, _1769037), tc_HOL_Obool))) = c_Relation_OId(_1769037))], (49075 ^ _779530) ^ [_1769073] : [-(hAPP(c_Relation_ODomain(_1769073, _1769073), c_Relation_OId(_1769073)) = c_Orderings_Otop__class_Otop(tc_fun(_1769073, tc_HOL_Obool)))], (49077 ^ _779530) ^ [_1769109, _1769111] : [-(c_List_Olistrel(_1769109, c_Transitive__Closure_Ortrancl(_1769109, _1769111)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1769109), c_List_Olistrel1(_1769109, _1769111)))], (49079 ^ _779530) ^ [_1769148, _1769150] : [-(hAPP(c_Relation_OImage(_1769148, _1769148, c_Relation_OId(_1769148)), _1769150) = _1769150)], (49081 ^ _779530) ^ [_1769182, _1769184, _1769186] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1769182, _1769182, _1769184), c_Relation_OId(_1769182)), _1769186) = _1769186)], (49083 ^ _779530) ^ [_1769221, _1769223, _1769225] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1769221, _1769223, _1769223), _1769225), c_Relation_OId(_1769223)) = _1769225)], (49085 ^ _779530) ^ [_1769260] : [-(hAPP(c_Relation_ORange(_1769260, _1769260), c_Relation_OId(_1769260)) = c_Orderings_Otop__class_Otop(tc_fun(_1769260, tc_HOL_Obool)))], (49087 ^ _779530) ^ [_1769296] : [-(c_Relation_Orefl__on(_1769296, c_Orderings_Otop__class_Otop(tc_fun(_1769296, tc_HOL_Obool)), c_Relation_OId(_1769296)))], (49089 ^ _779530) ^ [_1769327, _1769329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1769327), tc_List_Olist(_1769327)), tc_HOL_Obool)), c_List_Olistrel1(_1769327, c_Transitive__Closure_Ortrancl(_1769327, _1769329))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1769327), c_List_Olistrel1(_1769327, _1769329)))))], (49091 ^ _779530) ^ [_1769401, _1769403, _1769405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769401, _1769401)), hAPP(hAPP(c_Product__Type_OPair(_1769401, _1769401), _1769403), _1769405)), c_Relation_OId(_1769401))), -(_1769403 = _1769405)], (49097 ^ _779530) ^ [_1769518, _1769520, _1769522] : [_1769520 = _1769522, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769518, _1769518)), hAPP(hAPP(c_Product__Type_OPair(_1769518, _1769518), _1769520), _1769522)), c_Relation_OId(_1769518))))], (49103 ^ _779530) ^ [_1769641, _1769643, _1769645, _1769647, _1769649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769641), tc_List_Olist(_1769641))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769641), tc_List_Olist(_1769641)), _1769643), _1769645)), c_List_Olistrel(_1769641, c_Transitive__Closure_Ortrancl(_1769641, _1769647)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769641), tc_List_Olist(_1769641))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769641), tc_List_Olist(_1769641)), _1769645), _1769649)), c_List_Olistrel(_1769641, c_Transitive__Closure_Ortrancl(_1769641, _1769647)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769641), tc_List_Olist(_1769641))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769641), tc_List_Olist(_1769641)), _1769643), _1769649)), c_List_Olistrel(_1769641, c_Transitive__Closure_Ortrancl(_1769641, _1769647)))))], (49113 ^ _779530) ^ [_1769980, _1769982, _1769984, _1769986, _1769988, _1769990] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769980, _1769980)), hAPP(hAPP(c_Product__Type_OPair(_1769980, _1769980), _1769982), _1769984)), c_Transitive__Closure_Ortrancl(_1769980, _1769986))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769980), tc_List_Olist(_1769980))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769980), tc_List_Olist(_1769980)), _1769988), _1769990)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1769980), c_List_Olistrel1(_1769980, _1769986)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1769980), tc_List_Olist(_1769980))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1769980), tc_List_Olist(_1769980)), hAPP(hAPP(c_List_Olist_OCons(_1769980), _1769982), _1769988)), hAPP(hAPP(c_List_Olist_OCons(_1769980), _1769984), _1769990))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1769980), c_List_Olistrel1(_1769980, _1769986)))))], (49123 ^ _779530) ^ [_1770341, _1770343] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1770341), tc_List_Olist(_1770341)), tc_HOL_Obool)), c_List_Olistrel(_1770341, _1770343)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1770341), c_List_Olistrel1(_1770341, _1770343)))))], (49125 ^ _779530) ^ [] : [-(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))))], (49127 ^ _779530) ^ [_1770411, _1770413, _1770415, _1770417] : [-(hBOOL(hAPP(hAPP(c_member(_1770411), _1770413), hAPP(c_Relation_ODomain(_1770411, _1770411), _1770415)))), 49130 ^ _779530 : [(49131 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1770411, _1770411)), hAPP(hAPP(c_Product__Type_OPair(_1770411, _1770411), _1770413), _1770417)), c_Transitive__Closure_Ortrancl(_1770411, _1770415))), -(_1770413 = _1770417)], (49137 ^ _779530) ^ [] : [_1770413 = _1770417, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1770411, _1770411)), hAPP(hAPP(c_Product__Type_OPair(_1770411, _1770411), _1770413), _1770417)), c_Transitive__Closure_Ortrancl(_1770411, _1770415))))]]], (49143 ^ _779530) ^ [_1770707, _1770709, _1770711, _1770713] : [hBOOL(hAPP(hAPP(c_member(_1770707), _1770709), c_Wellfounded_Oacc(_1770707, _1770711))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1770707, _1770707)), hAPP(hAPP(c_Product__Type_OPair(_1770707, _1770707), _1770713), _1770709)), c_Transitive__Closure_Ortrancl(_1770707, _1770711))), -(hBOOL(hAPP(hAPP(c_member(_1770707), _1770713), c_Wellfounded_Oacc(_1770707, _1770711))))], (49153 ^ _779530) ^ [_1770928, _1770930, _1770932, _1770934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1770928, _1770928)), hAPP(hAPP(c_Product__Type_OPair(_1770928, _1770928), _1770930), _1770932)), c_Transitive__Closure_Ortrancl(_1770928, _1770934))), hBOOL(hAPP(hAPP(c_member(_1770928), _1770932), c_Wellfounded_Oacc(_1770928, _1770934))), -(hBOOL(hAPP(hAPP(c_member(_1770928), _1770930), c_Wellfounded_Oacc(_1770928, _1770934))))], (49163 ^ _779530) ^ [_1771170, _1771172, _1771174, _1771176] : [c_Wellfounded_Owf(_1771170, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1771170, _1771170)), hAPP(hAPP(c_Product__Type_OPair(_1771170, _1771170), _1771172), _1771174)), _1771176)), 49166 ^ _779530 : [(49167 ^ _779530) ^ [] : [-(c_Wellfounded_Owf(_1771170, _1771176))], (49169 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771170, _1771170)), hAPP(hAPP(c_Product__Type_OPair(_1771170, _1771170), _1771174), _1771172)), c_Transitive__Closure_Ortrancl(_1771170, _1771176)))]]], (49171 ^ _779530) ^ [_1771365, _1771367, _1771369, _1771371] : [-(c_Wellfounded_Owf(_1771365, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1771365, _1771365)), hAPP(hAPP(c_Product__Type_OPair(_1771365, _1771365), _1771367), _1771369)), _1771371))), c_Wellfounded_Owf(_1771365, _1771371), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771365, _1771365)), hAPP(hAPP(c_Product__Type_OPair(_1771365, _1771365), _1771369), _1771367)), c_Transitive__Closure_Ortrancl(_1771365, _1771371))))], (49181 ^ _779530) ^ [_1771591, _1771593, _1771595, _1771597, _1771599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1771591), tc_List_Olist(_1771591))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771591), tc_List_Olist(_1771591)), _1771593), _1771595)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1771591), c_List_Olistrel1(_1771591, _1771597)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1771591), tc_List_Olist(_1771591))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771591), tc_List_Olist(_1771591)), hAPP(hAPP(c_List_Olist_OCons(_1771591), _1771599), _1771593)), hAPP(hAPP(c_List_Olist_OCons(_1771591), _1771599), _1771595))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1771591), c_List_Olistrel1(_1771591, _1771597)))))], (49187 ^ _779530) ^ [_1771846, _1771848, _1771850, _1771852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1771846), tc_List_Olist(_1771846))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1771846), tc_List_Olist(_1771846)), _1771848), _1771850)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1771846), c_List_Olistrel1(_1771846, _1771852)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771846)), _1771848) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771846)), _1771850))], (49193 ^ _779530) ^ [_1772046, _1772048, _1772050, _1772052] : [c_Wellfounded_Oacyclic(_1772046, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1772046, _1772046)), hAPP(hAPP(c_Product__Type_OPair(_1772046, _1772046), _1772048), _1772050)), _1772052)), 49196 ^ _779530 : [(49197 ^ _779530) ^ [] : [-(c_Wellfounded_Oacyclic(_1772046, _1772052))], (49199 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772046, _1772046)), hAPP(hAPP(c_Product__Type_OPair(_1772046, _1772046), _1772050), _1772048)), c_Transitive__Closure_Ortrancl(_1772046, _1772052)))]]], (49201 ^ _779530) ^ [_1772241, _1772243, _1772245, _1772247] : [-(c_Wellfounded_Oacyclic(_1772241, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1772241, _1772241)), hAPP(hAPP(c_Product__Type_OPair(_1772241, _1772241), _1772243), _1772245)), _1772247))), c_Wellfounded_Oacyclic(_1772241, _1772247), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772241, _1772241)), hAPP(hAPP(c_Product__Type_OPair(_1772241, _1772241), _1772245), _1772243)), c_Transitive__Closure_Ortrancl(_1772241, _1772247))))], (49211 ^ _779530) ^ [_1772467, _1772469, _1772471, _1772473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772467), tc_List_Olist(_1772467))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772467), tc_List_Olist(_1772467)), _1772469), _1772471)), c_List_Olistrel1(_1772467, _1772473))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772467), tc_List_Olist(_1772467))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772467), tc_List_Olist(_1772467)), _1772469), _1772471)), c_List_Olistrel(_1772467, c_Transitive__Closure_Ortrancl(_1772467, _1772473)))))], (49217 ^ _779530) ^ [_1772674, _1772676, _1772678, _1772680] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772674), tc_List_Olist(_1772674))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772674), tc_List_Olist(_1772674)), _1772676), _1772678)), c_List_Olistrel(_1772674, _1772680))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1772674), tc_List_Olist(_1772674))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1772674), tc_List_Olist(_1772674)), _1772676), _1772678)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1772674), c_List_Olistrel1(_1772674, _1772680)))))], (49223 ^ _779530) ^ [_1772885, _1772887] : [-(c_Relation_Orefl__on(_1772885, c_Orderings_Otop__class_Otop(tc_fun(_1772885, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1772885, _1772885), tc_HOL_Obool)), _1772887), c_Relation_OId(_1772885))))], (49225 ^ _779530) ^ [_1772932] : [-(c_Relation_OId(_1772932) = hAPP(c_Set_OCollect(tc_prod(_1772932, _1772932)), hAPP(hAPP(c_COMBB(tc_fun(_1772932, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1772932, _1772932)), c_HOL_OEx(_1772932)), hAPP(hAPP(c_COMBC(tc_prod(_1772932, _1772932), tc_fun(_1772932, tc_prod(_1772932, _1772932)), tc_fun(_1772932, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1772932, _1772932), tc_HOL_Obool), tc_fun(tc_fun(_1772932, tc_prod(_1772932, _1772932)), tc_fun(_1772932, tc_HOL_Obool)), tc_prod(_1772932, _1772932)), c_COMBB(tc_prod(_1772932, _1772932), tc_HOL_Obool, _1772932)), c_fequal)), hAPP(hAPP(c_COMBS(_1772932, _1772932, tc_prod(_1772932, _1772932)), c_Product__Type_OPair(_1772932, _1772932)), c_COMBI(_1772932))))))], (49227 ^ _779530) ^ [_1773061, _1773063] : [-(c_Relation_Oirrefl(_1773061, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1773061, _1773061), tc_HOL_Obool)), _1773063), c_Relation_OId(_1773061))))], (49229 ^ _779530) ^ [_1773117, _1773119] : [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), _1773117), _1773119)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1773117), _1773119)))], (49235 ^ _779530) ^ [_1773222, _1773224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1773222), _1773224)), -(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), _1773222), _1773224)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (49241 ^ _779530) ^ [_1773333, _1773335, _1773337, _1773339, _1773341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773333, _1773333)), hAPP(hAPP(c_Product__Type_OPair(_1773333, _1773333), _1773335), _1773337)), c_Transitive__Closure_Ortrancl(_1773333, _1773339))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1773333, _1773333), tc_HOL_Obool)), _1773339), hAPP(hAPP(c_Product__Type_OSigma(_1773333, _1773333), _1773341), hAPP(c_COMBK(tc_fun(_1773333, tc_HOL_Obool), _1773333), _1773341)))), -(_1773335 = _1773337), -(hBOOL(hAPP(hAPP(c_member(_1773333), _1773335), _1773341)))], (49255 ^ _779530) ^ [_1773607, _1773609, _1773611] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1773607, _1773607), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1773607, _1773607), _1773609)), c_Transitive__Closure_Ortrancl(_1773607, _1773609)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1773607, _1773607), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773607, _1773607)), hAPP(hAPP(c_Product__Type_OPair(_1773607, _1773607), _1773611), _1773611)), c_Transitive__Closure_Otrancl(_1773607, _1773609)))], (49261 ^ _779530) ^ [_1773793, _1773795, _1773797, _1773799, _1773801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773793, _1773793)), hAPP(hAPP(c_Product__Type_OPair(_1773793, _1773793), hAPP(_1773795, hAPP(c_Nat_OSuc, 49262 ^ [_1773793, _1773795, _1773797, _1773799, _1773801]))), hAPP(_1773795, 49262 ^ [_1773793, _1773795, _1773797, _1773799, _1773801]))), c_Transitive__Closure_Ortrancl(_1773793, _1773797))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773793, _1773793)), hAPP(hAPP(c_Product__Type_OPair(_1773793, _1773793), hAPP(_1773795, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1773799), _1773801))), hAPP(_1773795, _1773799))), c_Transitive__Closure_Ortrancl(_1773793, _1773797))))], (49268 ^ _779530) ^ [_1774086, _1774088, _1774090, _1774092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774086, _1774086)), hAPP(hAPP(c_Product__Type_OPair(_1774086, _1774086), _1774088), _1774090)), c_Transitive__Closure_Ortrancl(_1774086, hAPP(c_Relation_Oconverse(_1774086, _1774086), _1774092)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774086, _1774086)), hAPP(hAPP(c_Product__Type_OPair(_1774086, _1774086), _1774090), _1774088)), c_Transitive__Closure_Ortrancl(_1774086, _1774092))))], (49274 ^ _779530) ^ [_1774267, _1774269, _1774271, _1774273] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774267, _1774267)), hAPP(hAPP(c_Product__Type_OPair(_1774267, _1774267), _1774269), _1774271)), c_Transitive__Closure_Ortrancl(_1774267, _1774273))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774267, _1774267)), hAPP(hAPP(c_Product__Type_OPair(_1774267, _1774267), _1774271), _1774269)), c_Transitive__Closure_Ortrancl(_1774267, hAPP(c_Relation_Oconverse(_1774267, _1774267), _1774273)))))], (49280 ^ _779530) ^ [_1774448, _1774450] : [-(c_Transitive__Closure_Ortrancl(_1774448, hAPP(c_Relation_Oconverse(_1774448, _1774448), _1774450)) = hAPP(c_Relation_Oconverse(_1774448, _1774448), c_Transitive__Closure_Ortrancl(_1774448, _1774450)))], (49282 ^ _779530) ^ [_1774491] : [-(hAPP(c_Relation_Oconverse(_1774491, _1774491), c_Relation_OId(_1774491)) = c_Relation_OId(_1774491))], (49284 ^ _779530) ^ [_1774545, _1774547, _1774549, _1774551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774545), tc_List_Olist(_1774545))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774545), tc_List_Olist(_1774545)), _1774547), _1774549)), c_List_Olistrel1(_1774545, hAPP(c_Relation_Oconverse(_1774545, _1774545), _1774551)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774545), tc_List_Olist(_1774545))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774545), tc_List_Olist(_1774545)), _1774547), _1774549)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1774545), tc_List_Olist(_1774545)), c_List_Olistrel1(_1774545, _1774551)))))], (49290 ^ _779530) ^ [_1774774, _1774776, _1774778, _1774780] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774774), tc_List_Olist(_1774774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774774), tc_List_Olist(_1774774)), _1774776), _1774778)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1774774), tc_List_Olist(_1774774)), c_List_Olistrel1(_1774774, _1774780)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1774774), tc_List_Olist(_1774774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1774774), tc_List_Olist(_1774774)), _1774776), _1774778)), c_List_Olistrel1(_1774774, hAPP(c_Relation_Oconverse(_1774774, _1774774), _1774780)))))], (49296 ^ _779530) ^ [_1775033, _1775035, _1775037, _1775039, _1775041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775033, _1775035)), hAPP(hAPP(c_Product__Type_OPair(_1775033, _1775035), _1775037), _1775039)), hAPP(c_Relation_Oconverse(_1775035, _1775033), _1775041))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775035, _1775033)), hAPP(hAPP(c_Product__Type_OPair(_1775035, _1775033), _1775039), _1775037)), _1775041)))], (49302 ^ _779530) ^ [_1775200, _1775202, _1775204, _1775206, _1775208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775202, _1775200)), hAPP(hAPP(c_Product__Type_OPair(_1775202, _1775200), _1775206), _1775204)), _1775208)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775200, _1775202)), hAPP(hAPP(c_Product__Type_OPair(_1775200, _1775202), _1775204), _1775206)), hAPP(c_Relation_Oconverse(_1775202, _1775200), _1775208))))], (49308 ^ _779530) ^ [_1775373, _1775375, _1775377, _1775379, _1775381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775373, _1775375)), hAPP(hAPP(c_Product__Type_OPair(_1775373, _1775375), _1775377), _1775379)), _1775381)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775375, _1775373)), hAPP(hAPP(c_Product__Type_OPair(_1775375, _1775373), _1775379), _1775377)), hAPP(c_Relation_Oconverse(_1775373, _1775375), _1775381))))], (49314 ^ _779530) ^ [_1775544, _1775546, _1775548, _1775550, _1775552] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775544, _1775546)), hAPP(hAPP(c_Product__Type_OPair(_1775544, _1775546), _1775548), _1775550)), hAPP(c_Relation_Oconverse(_1775546, _1775544), _1775552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775546, _1775544)), hAPP(hAPP(c_Product__Type_OPair(_1775546, _1775544), _1775550), _1775548)), _1775552)))], (49320 ^ _779530) ^ [_1775715, _1775717, _1775719, _1775721] : [-(hAPP(c_Relation_Oconverse(_1775715, _1775715), hAPP(hAPP(c_Relation_Oinv__image(_1775717, _1775715), _1775719), _1775721)) = hAPP(hAPP(c_Relation_Oinv__image(_1775717, _1775715), hAPP(c_Relation_Oconverse(_1775717, _1775717), _1775719)), _1775721))], (49322 ^ _779530) ^ [_1775774, _1775776, _1775778, _1775780, _1775782] : [-(hAPP(c_Relation_Oconverse(_1775774, _1775776), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1775778, tc_fun(tc_prod(_1775774, _1775776), tc_HOL_Obool)), _1775780), _1775782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1775778, tc_fun(tc_prod(_1775776, _1775774), tc_HOL_Obool)), _1775780), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1775774, _1775776), tc_HOL_Obool), tc_fun(tc_prod(_1775776, _1775774), tc_HOL_Obool), _1775778), c_Relation_Oconverse(_1775774, _1775776)), _1775782)))], (49324 ^ _779530) ^ [_1775866, _1775868, _1775870, _1775872] : [-(hAPP(c_Relation_Oconverse(_1775866, _1775868), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775866, _1775868), tc_HOL_Obool)), _1775870), _1775872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775868, _1775866), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1775866, _1775868), _1775870)), hAPP(c_Relation_Oconverse(_1775866, _1775868), _1775872)))], (49326 ^ _779530) ^ [_1775941, _1775943, _1775945, _1775947, _1775949] : [-(hAPP(c_Relation_Oconverse(_1775941, _1775943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1775945, tc_fun(tc_prod(_1775941, _1775943), tc_HOL_Obool)), _1775947), _1775949)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1775945, tc_fun(tc_prod(_1775943, _1775941), tc_HOL_Obool)), _1775947), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1775941, _1775943), tc_HOL_Obool), tc_fun(tc_prod(_1775943, _1775941), tc_HOL_Obool), _1775945), c_Relation_Oconverse(_1775941, _1775943)), _1775949)))], (49328 ^ _779530) ^ [_1776051, _1776053, _1776055] : [c_Relation_Orefl__on(_1776051, _1776053, hAPP(c_Relation_Oconverse(_1776051, _1776051), _1776055)), -(c_Relation_Orefl__on(_1776051, _1776053, _1776055))], (49334 ^ _779530) ^ [_1776142, _1776144, _1776146] : [c_Relation_Orefl__on(_1776142, _1776144, _1776146), -(c_Relation_Orefl__on(_1776142, _1776144, hAPP(c_Relation_Oconverse(_1776142, _1776142), _1776146)))], (49340 ^ _779530) ^ [_1776257, _1776259, _1776261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1776257, _1776259)), hAPP(c_Relation_Oconverse(_1776259, _1776257), _1776261))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1776259, _1776257)), _1776261)))], (49346 ^ _779530) ^ [_1776372, _1776374, _1776376] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1776374, _1776372)), _1776376)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1776372, _1776374)), hAPP(c_Relation_Oconverse(_1776374, _1776372), _1776376))))], (49352 ^ _779530) ^ [_1776508, _1776510] : [c_Wellfounded_Oacyclic(_1776508, hAPP(c_Relation_Oconverse(_1776508, _1776508), _1776510)), -(c_Wellfounded_Oacyclic(_1776508, _1776510))], (49358 ^ _779530) ^ [_1776593, _1776595] : [c_Wellfounded_Oacyclic(_1776593, _1776595), -(c_Wellfounded_Oacyclic(_1776593, hAPP(c_Relation_Oconverse(_1776593, _1776593), _1776595)))], (49364 ^ _779530) ^ [_1776684, _1776686] : [-(hAPP(c_Relation_Oconverse(_1776684, _1776684), c_Relation_OId__on(_1776684, _1776686)) = c_Relation_OId__on(_1776684, _1776686))], (49366 ^ _779530) ^ [_1776721, _1776723] : [-(hAPP(c_Relation_OField(_1776721), hAPP(c_Relation_Oconverse(_1776721, _1776721), _1776723)) = hAPP(c_Relation_OField(_1776721), _1776723))], (49368 ^ _779530) ^ [_1776762, _1776764, _1776766] : [-(hAPP(c_Relation_Oconverse(_1776762, _1776764), hAPP(c_Relation_Oconverse(_1776764, _1776762), _1776766)) = _1776766)], (49370 ^ _779530) ^ [_1776801, _1776803, _1776805, _1776807] : [-(hAPP(c_Relation_Oconverse(_1776801, _1776803), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776801, _1776803), tc_HOL_Obool)), _1776805), _1776807)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776803, _1776801), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1776801, _1776803), _1776805)), hAPP(c_Relation_Oconverse(_1776801, _1776803), _1776807)))], (49372 ^ _779530) ^ [_1776876, _1776878, _1776880, _1776882, _1776884] : [-(hAPP(c_Relation_Oconverse(_1776876, _1776878), hAPP(hAPP(c_Relation_Orel__comp(_1776876, _1776880, _1776878), _1776882), _1776884)) = hAPP(hAPP(c_Relation_Orel__comp(_1776878, _1776880, _1776876), hAPP(c_Relation_Oconverse(_1776880, _1776878), _1776884)), hAPP(c_Relation_Oconverse(_1776876, _1776880), _1776882)))], (49374 ^ _779530) ^ [_1776945, _1776947] : [-(c_List_Olistrel1(_1776945, hAPP(c_Relation_Oconverse(_1776945, _1776945), _1776947)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1776945), tc_List_Olist(_1776945)), c_List_Olistrel1(_1776945, _1776947)))], (49376 ^ _779530) ^ [_1776992, _1776994, _1776996] : [c_Equiv__Relations_Oequiv(_1776992, _1776994, _1776996), -(hAPP(hAPP(c_Relation_Orel__comp(_1776992, _1776992, _1776992), hAPP(c_Relation_Oconverse(_1776992, _1776992), _1776996)), _1776996) = _1776996)], (49382 ^ _779530) ^ [_1777105, _1777107, _1777109] : [-(hAPP(c_Relation_ORange(_1777105, _1777107), _1777109) = hAPP(c_Relation_ODomain(_1777107, _1777105), hAPP(c_Relation_Oconverse(_1777105, _1777107), _1777109)))], (49384 ^ _779530) ^ [_1777150, _1777152, _1777154] : [-(hAPP(c_Relation_ODomain(_1777150, _1777152), hAPP(c_Relation_Oconverse(_1777152, _1777150), _1777154)) = hAPP(c_Relation_ORange(_1777152, _1777150), _1777154))], (49386 ^ _779530) ^ [_1777195, _1777197, _1777199] : [-(hAPP(c_Relation_ORange(_1777195, _1777197), hAPP(c_Relation_Oconverse(_1777197, _1777195), _1777199)) = hAPP(c_Relation_ODomain(_1777197, _1777195), _1777199))], (49388 ^ _779530) ^ [_1777240, _1777242, _1777244, _1777246] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777240, _1777240)), hAPP(hAPP(c_Product__Type_OPair(_1777240, _1777240), _1777242), _1777244)), c_Transitive__Closure_Otrancl(_1777240, hAPP(c_Relation_Oconverse(_1777240, _1777240), _1777246)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777240, _1777240)), hAPP(hAPP(c_Product__Type_OPair(_1777240, _1777240), _1777242), _1777244)), hAPP(c_Relation_Oconverse(_1777240, _1777240), c_Transitive__Closure_Otrancl(_1777240, _1777246)))))], (49394 ^ _779530) ^ [_1777433, _1777435, _1777437, _1777439] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777433, _1777433)), hAPP(hAPP(c_Product__Type_OPair(_1777433, _1777433), _1777435), _1777437)), hAPP(c_Relation_Oconverse(_1777433, _1777433), c_Transitive__Closure_Otrancl(_1777433, _1777439)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777433, _1777433)), hAPP(hAPP(c_Product__Type_OPair(_1777433, _1777433), _1777435), _1777437)), c_Transitive__Closure_Otrancl(_1777433, hAPP(c_Relation_Oconverse(_1777433, _1777433), _1777439)))))], (49400 ^ _779530) ^ [_1777626, _1777628] : [c_Wellfounded_Owf(_1777626, hAPP(c_Relation_Oconverse(_1777626, _1777626), _1777628)), -(c_Wellfounded_Owf(_1777626, hAPP(c_Relation_Oconverse(_1777626, _1777626), c_Transitive__Closure_Otrancl(_1777626, _1777628))))], (49406 ^ _779530) ^ [_1777733, _1777735] : [-(c_Transitive__Closure_Otrancl(_1777733, hAPP(c_Relation_Oconverse(_1777733, _1777733), _1777735)) = hAPP(c_Relation_Oconverse(_1777733, _1777733), c_Transitive__Closure_Otrancl(_1777733, _1777735)))], (49408 ^ _779530) ^ [_1777800, _1777802, _1777804, _1777806, _1777808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1777800, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1777802, _1777800, _1777804), _1777806)), _1777808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1777802, tc_HOL_Obool)), _1777806), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1777802, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1777800, _1777802, hAPP(c_Relation_Oconverse(_1777802, _1777800), _1777804)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1777800, tc_HOL_Obool)), _1777808))))))], (49414 ^ _779530) ^ [_1777991, _1777993, _1777995, _1777997, _1777999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1777993, tc_HOL_Obool)), _1777997), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1777993, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1777991, _1777993, hAPP(c_Relation_Oconverse(_1777993, _1777991), _1777995)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1777991, tc_HOL_Obool)), _1777999))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1777991, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1777993, _1777991, _1777995), _1777997)), _1777999)))], (49420 ^ _779530) ^ [_1778188, _1778190, _1778192] : [c_Relation_Orefl__on(_1778188, _1778190, _1778192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1778188, _1778188), tc_HOL_Obool)), _1778192), hAPP(hAPP(c_Relation_Orel__comp(_1778188, _1778188, _1778188), hAPP(c_Relation_Oconverse(_1778188, _1778188), _1778192)), _1778192))))], (49426 ^ _779530) ^ [_1778327, _1778329, _1778331] : [hAPP(hAPP(c_Relation_Orel__comp(_1778327, _1778327, _1778327), hAPP(c_Relation_Oconverse(_1778327, _1778327), _1778329)), _1778329) = _1778329, hAPP(c_Relation_ODomain(_1778327, _1778327), _1778329) = _1778331, -(c_Equiv__Relations_Oequiv(_1778327, _1778331, _1778329))], (49436 ^ _779530) ^ [_1778506, _1778508] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1778506, _1778506)), _1778508)), c_Wellfounded_Oacyclic(_1778506, _1778508), -(c_Wellfounded_Owf(_1778506, hAPP(c_Relation_Oconverse(_1778506, _1778506), _1778508)))], (49446 ^ _779530) ^ [_1778661, _1778663, _1778665] : [-(hAPP(c_Relation_Oconverse(_1778661, _1778663), _1778665) = hAPP(c_Set_OCollect(tc_prod(_1778663, _1778661)), hAPP(c_Product__Type_Oprod_Oprod__case(_1778663, _1778661, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1778663, tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_fun(_1778661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778661, tc_fun(tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_fun(_1778661, tc_HOL_Obool)), _1778663), c_COMBC(_1778661, tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778661, tc_prod(_1778661, _1778663)), tc_fun(_1778661, tc_fun(tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_HOL_Obool)), _1778663), hAPP(c_COMBB(tc_prod(_1778661, _1778663), tc_fun(tc_fun(tc_prod(_1778661, _1778663), tc_HOL_Obool), tc_HOL_Obool), _1778661), c_member(tc_prod(_1778661, _1778663)))), hAPP(c_COMBC(_1778661, _1778663, tc_prod(_1778661, _1778663)), c_Product__Type_OPair(_1778661, _1778663))))), _1778665))))], (49448 ^ _779530) ^ [_1778837, _1778839, _1778841, _1778843, _1778845, _1778847] : [c_Relation_Osingle__valued(_1778837, _1778839, hAPP(c_Relation_Oconverse(_1778839, _1778837), _1778841)), -(_1778843 = c_Orderings_Obot__class_Obot(tc_fun(_1778845, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1778839, _1778837, _1778841), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1778845, tc_fun(_1778839, tc_HOL_Obool)), _1778843), _1778847)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1778845, tc_fun(_1778837, tc_HOL_Obool)), _1778843), hAPP(hAPP(c_COMBB(tc_fun(_1778839, tc_HOL_Obool), tc_fun(_1778837, tc_HOL_Obool), _1778845), c_Relation_OImage(_1778839, _1778837, _1778841)), _1778847)))], (49458 ^ _779530) ^ [_1779081, _1779083, _1779085] : [c_Relation_Ototal__on(_1779081, _1779083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1779081, _1779081), tc_HOL_Obool)), _1779085), c_Relation_OId(_1779081))), -(c_Relation_Ototal__on(_1779081, _1779083, _1779085))], (49464 ^ _779530) ^ [_1779192, _1779194, _1779196] : [c_Relation_Ototal__on(_1779192, _1779194, _1779196), -(c_Relation_Ototal__on(_1779192, _1779194, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1779192, _1779192), tc_HOL_Obool)), _1779196), c_Relation_OId(_1779192))))], (49470 ^ _779530) ^ [_1779309] : [-(c_Relation_Osingle__valued(_1779309, _1779309, c_Relation_OId(_1779309)))], (49472 ^ _779530) ^ [_1779353, _1779355, _1779357] : [c_Relation_Ototal__on(_1779353, _1779355, hAPP(c_Relation_Oconverse(_1779353, _1779353), _1779357)), -(c_Relation_Ototal__on(_1779353, _1779355, _1779357))], (49478 ^ _779530) ^ [_1779444, _1779446, _1779448] : [c_Relation_Ototal__on(_1779444, _1779446, _1779448), -(c_Relation_Ototal__on(_1779444, _1779446, hAPP(c_Relation_Oconverse(_1779444, _1779444), _1779448)))], (49484 ^ _779530) ^ [_1779541, _1779543, _1779545, _1779547, _1779549] : [c_Relation_Osingle__valued(_1779541, _1779543, _1779545), c_Relation_Osingle__valued(_1779543, _1779547, _1779549), -(c_Relation_Osingle__valued(_1779541, _1779547, hAPP(hAPP(c_Relation_Orel__comp(_1779541, _1779543, _1779547), _1779545), _1779549)))], (49494 ^ _779530) ^ [_1779708, _1779710] : [-(c_Relation_Osingle__valued(_1779708, _1779708, c_Relation_OId__on(_1779708, _1779710)))], (49496 ^ _779530) ^ [_1779737, _1779739] : [-(c_Relation_Ototal__on(_1779737, c_Orderings_Obot__class_Obot(tc_fun(_1779737, tc_HOL_Obool)), _1779739))], (49498 ^ _779530) ^ [_1779768, _1779770, _1779772, _1779774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1779768, _1779770), tc_HOL_Obool)), _1779772), _1779774)), c_Relation_Osingle__valued(_1779768, _1779770, _1779774), -(c_Relation_Osingle__valued(_1779768, _1779770, _1779772))], (49508 ^ _779530) ^ [_1779935, _1779937, _1779939, _1779941, _1779943, _1779945] : [c_Relation_Osingle__valued(_1779935, _1779937, _1779939), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779935, _1779937)), hAPP(hAPP(c_Product__Type_OPair(_1779935, _1779937), _1779941), _1779943)), _1779939)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779935, _1779937)), hAPP(hAPP(c_Product__Type_OPair(_1779935, _1779937), _1779941), _1779945)), _1779939)), -(_1779943 = _1779945)], (49536 ^ _779530) ^ [_1780610, _1780612, _1780614] : [49539 ^ _779530 : [(49540 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780610, _1780612)), hAPP(hAPP(c_Product__Type_OPair(_1780610, _1780612), 49537 ^ [_1780610, _1780612, _1780614]), 49538 ^ [_1780610, _1780612, _1780614])), _1780614)))], (49543 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780610, _1780612)), hAPP(hAPP(c_Product__Type_OPair(_1780610, _1780612), 49537 ^ [_1780610, _1780612, _1780614]), 49541 ^ [_1780610, _1780612, _1780614])), _1780614)))], (49545 ^ _779530) ^ [] : [49538 ^ [_1780610, _1780612, _1780614] = 49541 ^ [_1780610, _1780612, _1780614]]], -(c_Relation_Osingle__valued(_1780610, _1780612, _1780614))], (49522 ^ _779530) ^ [_1780236, _1780238, _1780240] : [c_Relation_Osingle__valued(_1780236, _1780238, _1780240), 49525 ^ _779530 : [(49526 ^ _779530) ^ [_1780357, _1780359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780236, _1780238)), hAPP(hAPP(c_Product__Type_OPair(_1780236, _1780238), _1780359), _1780357)), _1780240)), 49529 ^ _779530 : [(49530 ^ _779530) ^ [_1780483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780236, _1780238)), hAPP(hAPP(c_Product__Type_OPair(_1780236, _1780238), _1780359), _1780483)), _1780240)), -(_1780357 = _1780483)]]]]], (49571 ^ _779530) ^ [_1781487, _1781489, _1781491] : [49573 ^ _779530 : [(49574 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781487), 49572 ^ [_1781487, _1781489, _1781491]), _1781489)))], (49577 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781487), 49575 ^ [_1781487, _1781489, _1781491]), _1781489)))], (49579 ^ _779530) ^ [] : [49572 ^ [_1781487, _1781489, _1781491] = 49575 ^ [_1781487, _1781489, _1781491]], (49581 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781487, _1781487)), hAPP(hAPP(c_Product__Type_OPair(_1781487, _1781487), 49572 ^ [_1781487, _1781489, _1781491]), 49575 ^ [_1781487, _1781489, _1781491])), _1781491))], (49583 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781487, _1781487)), hAPP(hAPP(c_Product__Type_OPair(_1781487, _1781487), 49575 ^ [_1781487, _1781489, _1781491]), 49572 ^ [_1781487, _1781489, _1781491])), _1781491))]], -(c_Relation_Ototal__on(_1781487, _1781489, _1781491))], (49549 ^ _779530) ^ [_1780998, _1781000, _1781002] : [c_Relation_Ototal__on(_1780998, _1781000, _1781002), 49552 ^ _779530 : [(49553 ^ _779530) ^ [_1781142] : [hBOOL(hAPP(hAPP(c_member(_1780998), _1781142), _1781000)), 49556 ^ _779530 : [(49557 ^ _779530) ^ [_1781282] : [hBOOL(hAPP(hAPP(c_member(_1780998), _1781282), _1781000)), -(_1781142 = _1781282), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780998, _1780998)), hAPP(hAPP(c_Product__Type_OPair(_1780998, _1780998), _1781142), _1781282)), _1781002))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780998, _1780998)), hAPP(hAPP(c_Product__Type_OPair(_1780998, _1780998), _1781282), _1781142)), _1781002)))]]]]], (49587 ^ _779530) ^ [_1782069, _1782071, _1782073, _1782075, _1782077] : [c_Relation_Osingle__valued(_1782069, _1782069, _1782071), hBOOL(hAPP(hAPP(c_member(tc_prod(_1782069, _1782069)), hAPP(hAPP(c_Product__Type_OPair(_1782069, _1782069), _1782073), _1782075)), c_Transitive__Closure_Ortrancl(_1782069, _1782071))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1782069, _1782069)), hAPP(hAPP(c_Product__Type_OPair(_1782069, _1782069), _1782073), _1782077)), c_Transitive__Closure_Ortrancl(_1782069, _1782071))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782069, _1782069)), hAPP(hAPP(c_Product__Type_OPair(_1782069, _1782069), _1782075), _1782077)), c_Transitive__Closure_Ortrancl(_1782069, _1782071)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782069, _1782069)), hAPP(hAPP(c_Product__Type_OPair(_1782069, _1782069), _1782077), _1782075)), c_Transitive__Closure_Ortrancl(_1782069, _1782071))))], (49605 ^ _779530) ^ [_1782459, _1782461, _1782463, _1782465, _1782467] : [c_Relation_Osingle__valued(_1782459, _1782461, hAPP(c_Relation_Oconverse(_1782461, _1782459), _1782463)), -(hAPP(c_Relation_OImage(_1782461, _1782459, _1782463), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1782461, tc_HOL_Obool)), _1782465), _1782467)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1782459, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1782461, _1782459, _1782463), _1782465)), hAPP(c_Relation_OImage(_1782461, _1782459, _1782463), _1782467)))], (49611 ^ _779530) ^ [_1782642, _1782644, _1782646] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782642, _1782642)), _1782644), c_Transitive__Closure_Ortrancl(_1782642, _1782646))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782642, _1782642)), _1782644), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1782642, _1782642), 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(_1782642, _1782642), tc_HOL_Obool), tc_fun(tc_prod(_1782642, _1782642), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1782642, _1782642), tc_HOL_Obool)), _1782646)))))], (49617 ^ _779530) ^ [_1782849, _1782851] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782849, _1782849)), hAPP(hAPP(c_Product__Type_OPair(_1782849, _1782849), 49618 ^ [_1782849, _1782851]), 49618 ^ [_1782849, _1782851])), c_Transitive__Closure_Otrancl(_1782849, _1782851)))), -(c_Wellfounded_Oacyclic(_1782849, _1782851))], (49624 ^ _779530) ^ [_1782921, _1782923, _1782925] : [c_Relation_Osingle__valued(_1782921, _1782921, _1782923), -(c_Relation_Osingle__valued(_1782921, _1782921, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1782921, _1782921), tc_HOL_Obool), _1782925), _1782923)))], (49630 ^ _779530) ^ [_1783028, _1783030, _1783032] : [-(hAPP(hAPP(c_Nat_Ocompow(_1783028, _1783028), hAPP(c_Nat_OSuc, _1783030)), _1783032) = hAPP(c_Fun_Ocomp(_1783028, _1783028, _1783028, _1783032), hAPP(hAPP(c_Nat_Ocompow(_1783028, _1783028), _1783030), _1783032)))], (49632 ^ _779530) ^ [_1783084, _1783086, _1783088, _1783090] : [-(hAPP(hAPP(c_Nat_Ocompow(_1783084, _1783084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1783086), _1783088)), _1783090) = hAPP(c_Fun_Ocomp(_1783084, _1783084, _1783084, hAPP(hAPP(c_Nat_Ocompow(_1783084, _1783084), _1783086), _1783090)), hAPP(hAPP(c_Nat_Ocompow(_1783084, _1783084), _1783088), _1783090)))], (49634 ^ _779530) ^ [_1783154, _1783156, _1783158, _1783160] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1783154, _1783156), tc_fun(_1783154, _1783156)), _1783158), c_Fun_Ocomp(_1783156, _1783156, _1783154, _1783160)) = c_Fun_Ocomp(_1783156, _1783156, _1783154, hAPP(hAPP(c_Nat_Ocompow(_1783156, _1783156), _1783158), _1783160)))], (49636 ^ _779530) ^ [_1783217, _1783219, _1783221] : [c_Wellfounded_Owf(_1783217, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783217, _1783217), tc_HOL_Obool), _1783219), _1783221)), -(c_Wellfounded_Owf(_1783217, _1783221))], (49642 ^ _779530) ^ [_1783320, _1783322, _1783324, _1783326] : [-(hAPP(_1783320, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1783322, _1783322), _1783324), _1783320), _1783326)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1783322, _1783322), _1783324), _1783320), hAPP(_1783320, _1783326)))], (49644 ^ _779530) ^ [_1783379, _1783381, _1783383, _1783385] : [-(hAPP(hAPP(c_Nat_Ocompow(_1783379, _1783379), _1783381), hAPP(hAPP(c_Nat_Ocompow(_1783379, _1783379), _1783383), _1783385)) = hAPP(hAPP(c_Nat_Ocompow(_1783379, _1783379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1783383), _1783381)), _1783385))], (49646 ^ _779530) ^ [_1783441, _1783443, _1783445] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1783441, _1783441, _1783441), _1783443), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783441, _1783441), tc_HOL_Obool), _1783445), _1783443)) = hAPP(hAPP(c_Relation_Orel__comp(_1783441, _1783441, _1783441), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783441, _1783441), tc_HOL_Obool), _1783445), _1783443)), _1783443))], (49648 ^ _779530) ^ [_1783512, _1783514, _1783516] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783512, _1783512), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1783514)), _1783516) = hAPP(hAPP(c_Relation_Orel__comp(_1783512, _1783512, _1783512), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783512, _1783512), tc_HOL_Obool), _1783514), _1783516)), _1783516))], (49650 ^ _779530) ^ [_1783576, _1783578] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783576, _1783576), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1783578) = _1783578)], (49652 ^ _779530) ^ [_1783613, _1783615, _1783617, _1783619] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783613, _1783613), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1783615), _1783617)), _1783619) = hAPP(hAPP(c_Relation_Orel__comp(_1783613, _1783613, _1783613), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783613, _1783613), tc_HOL_Obool), _1783615), _1783619)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783613, _1783613), tc_HOL_Obool), _1783617), _1783619)))], (49654 ^ _779530) ^ [_1783694, _1783696, _1783698, _1783700, _1783702, _1783704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783694, _1783694)), hAPP(hAPP(c_Product__Type_OPair(_1783694, _1783694), _1783696), _1783698)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783694, _1783694), tc_HOL_Obool), _1783700), _1783702))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783694, _1783694)), hAPP(hAPP(c_Product__Type_OPair(_1783694, _1783694), _1783698), _1783704)), _1783702)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783694, _1783694)), hAPP(hAPP(c_Product__Type_OPair(_1783694, _1783694), _1783696), _1783704)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1783694, _1783694), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1783700)), _1783702))))], (49664 ^ _779530) ^ [_1784007, _1784009, _1784011, _1784013, _1784015, _1784017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784007, _1784007)), hAPP(hAPP(c_Product__Type_OPair(_1784007, _1784007), _1784009), _1784011)), _1784013)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784007, _1784007)), hAPP(hAPP(c_Product__Type_OPair(_1784007, _1784007), _1784011), _1784015)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784007, _1784007), tc_HOL_Obool), _1784017), _1784013))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784007, _1784007)), hAPP(hAPP(c_Product__Type_OPair(_1784007, _1784007), _1784009), _1784015)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784007, _1784007), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1784017)), _1784013))))], (49674 ^ _779530) ^ [_1784320, _1784322, _1784324, _1784326] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784320, _1784320)), hAPP(hAPP(c_Product__Type_OPair(_1784320, _1784320), _1784322), _1784324)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784320, _1784320), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1784326))), -(_1784322 = _1784324)], (49680 ^ _779530) ^ [_1784463, _1784465, _1784467] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784463, _1784463)), hAPP(hAPP(c_Product__Type_OPair(_1784463, _1784463), _1784465), _1784465)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784463, _1784463), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1784467))))], (49682 ^ _779530) ^ [_1784539, _1784541, _1784543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784539, _1784539)), _1784541), c_Transitive__Closure_Ortrancl(_1784539, _1784543))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784539, _1784539)), _1784541), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784539, _1784539), tc_HOL_Obool), 49685 ^ [_1784539, _1784541, _1784543]), _1784543))))], (49689 ^ _779530) ^ [_1784698, _1784700, _1784702] : [49690 ^ _779530 : [(49691 ^ _779530) ^ [_1784774] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784698, _1784698)), _1784700), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784698, _1784698), tc_HOL_Obool), _1784774), _1784702)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784698, _1784698)), _1784700), c_Transitive__Closure_Ortrancl(_1784698, _1784702))))], (49695 ^ _779530) ^ [_1784862, _1784864, _1784866, _1784868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1784862, _1784862)), _1784864), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1784862, _1784862), tc_HOL_Obool), _1784866), _1784868))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1784862, _1784862)), _1784864), c_Transitive__Closure_Ortrancl(_1784862, _1784868))))], (49701 ^ _779530) ^ [_1785013, _1785015] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1785013, _1785013), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1785015) = c_Relation_OId(_1785013))], (49703 ^ _779530) ^ [_1785052, _1785054] : [-(hAPP(hAPP(c_Nat_Ocompow(_1785052, _1785052), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1785054) = c_Fun_Oid(_1785052))], (49705 ^ _779530) ^ [_1785106, _1785108, _1785110] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785106, _1785106)), _1785108), c_Transitive__Closure_Otrancl(_1785106, _1785110))), 49709 ^ _779530 : [(49710 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 49708 ^ [_1785106, _1785108, _1785110])))], (49712 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785106, _1785106)), _1785108), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1785106, _1785106), tc_HOL_Obool), 49708 ^ [_1785106, _1785108, _1785110]), _1785110))))]]], (49714 ^ _779530) ^ [_1785304, _1785306, _1785308] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785304, _1785304)), _1785306), c_Transitive__Closure_Otrancl(_1785304, _1785308)))), 49715 ^ _779530 : [(49716 ^ _779530) ^ [_1785383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1785383)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1785304, _1785304)), _1785306), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1785304, _1785304), tc_HOL_Obool), _1785383), _1785308)))]]], (49724 ^ _779530) ^ [_1785554, _1785556] : [-(c_Transitive__Closure_Ortrancl(_1785554, _1785556) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1785554, _1785554), 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(_1785554, _1785554), tc_HOL_Obool), tc_fun(tc_prod(_1785554, _1785554), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1785554, _1785554), tc_HOL_Obool)), _1785556)))], (49726 ^ _779530) ^ [_1785625] : [-(c_Nat_Ofunpow(_1785625) = c_Nat_Ocompow(_1785625, _1785625))], (49728 ^ _779530) ^ [_1785653, _1785655, _1785657, _1785659, _1785661] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785653, _1785653)), hAPP(hAPP(c_Product__Type_OPair(_1785653, _1785653), _1785655), _1785657)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1785653, _1785653), tc_HOL_Obool), _1785659), _1785661))), 49733 ^ _779530 : [(49734 ^ _779530) ^ [] : [-(_1785659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49736 ^ _779530) ^ [] : [-(_1785655 = _1785657)]], 49739 ^ _779530 : [(49740 ^ _779530) ^ [] : [-(_1785659 = hAPP(c_Nat_OSuc, 49738 ^ [_1785653, _1785655, _1785657, _1785659, _1785661]))], (49742 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785653, _1785653)), hAPP(hAPP(c_Product__Type_OPair(_1785653, _1785653), _1785655), 49737 ^ [_1785653, _1785655, _1785657, _1785659, _1785661])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1785653, _1785653), tc_HOL_Obool), 49738 ^ [_1785653, _1785655, _1785657, _1785659, _1785661]), _1785661))))], (49744 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785653, _1785653)), hAPP(hAPP(c_Product__Type_OPair(_1785653, _1785653), 49737 ^ [_1785653, _1785655, _1785657, _1785659, _1785661]), _1785657)), _1785661)))]]], (49746 ^ _779530) ^ [_1786095, _1786097] : [-(c_List_Orotate(_1786095, _1786097) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1786095), tc_List_Olist(_1786095)), _1786097), c_List_Orotate1(_1786095)))], (49748 ^ _779530) ^ [_1786138, _1786140, _1786142, _1786144, _1786146] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786138, _1786138)), hAPP(hAPP(c_Product__Type_OPair(_1786138, _1786138), _1786140), _1786142)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1786138, _1786138), tc_HOL_Obool), _1786144), _1786146))), 49753 ^ _779530 : [(49754 ^ _779530) ^ [] : [-(_1786144 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49756 ^ _779530) ^ [] : [-(_1786140 = _1786142)]], 49759 ^ _779530 : [(49760 ^ _779530) ^ [] : [-(_1786144 = hAPP(c_Nat_OSuc, 49758 ^ [_1786138, _1786140, _1786142, _1786144, _1786146]))], (49762 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786138, _1786138)), hAPP(hAPP(c_Product__Type_OPair(_1786138, _1786138), _1786140), 49757 ^ [_1786138, _1786140, _1786142, _1786144, _1786146])), _1786146)))], (49764 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786138, _1786138)), hAPP(hAPP(c_Product__Type_OPair(_1786138, _1786138), 49757 ^ [_1786138, _1786140, _1786142, _1786144, _1786146]), _1786142)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1786138, _1786138), tc_HOL_Obool), 49758 ^ [_1786138, _1786140, _1786142, _1786144, _1786146]), _1786146))))]]], (49766 ^ _779530) ^ [_1786580, _1786582, _1786584, _1786586] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1786580, _1786582, _1786584, _1786586) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1786580, _1786582), _1786584), _1786586)))], (49768 ^ _779530) ^ [_1786625, _1786627, _1786629, _1786631, _1786633] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1786625, _1786625)), hAPP(hAPP(c_Product__Type_OPair(_1786625, _1786625), _1786627), _1786629)), c_Transitive__Closure_Ortrancl(_1786625, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1786625, _1786625), tc_HOL_Obool)), _1786631), _1786633)))), 49774 ^ _779530 : [(49775 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786625, _1786625)), hAPP(hAPP(c_Product__Type_OPair(_1786625, _1786625), _1786627), 49773 ^ [_1786625, _1786627, _1786629, _1786631, _1786633])), c_Transitive__Closure_Ortrancl(_1786625, _1786631))))], (49778 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786625, _1786625)), hAPP(hAPP(c_Product__Type_OPair(_1786625, _1786625), 49773 ^ [_1786625, _1786627, _1786629, _1786631, _1786633]), 49776 ^ [_1786625, _1786627, _1786629, _1786631, _1786633])), _1786633)))], (49780 ^ _779530) ^ [] : [49773 ^ [_1786625, _1786627, _1786629, _1786631, _1786633] = 49776 ^ [_1786625, _1786627, _1786629, _1786631, _1786633]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786625, _1786625)), hAPP(hAPP(c_Product__Type_OPair(_1786625, _1786625), _1786627), _1786629)), c_Transitive__Closure_Ortrancl(_1786625, _1786631))))], (49784 ^ _779530) ^ [_1787184, _1787186, _1787188, _1787190, _1787192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787184, _1787184)), hAPP(hAPP(c_Product__Type_OPair(_1787184, _1787184), _1787186), _1787188)), c_Transitive__Closure_Ortrancl(_1787184, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787184, _1787184), tc_HOL_Obool)), _1787190), _1787192)))), 49790 ^ _779530 : [(49791 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787184, _1787184)), hAPP(hAPP(c_Product__Type_OPair(_1787184, _1787184), 49789 ^ [_1787184, _1787186, _1787188, _1787190, _1787192]), _1787188)), c_Transitive__Closure_Ortrancl(_1787184, _1787190))))], (49794 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787184, _1787184)), hAPP(hAPP(c_Product__Type_OPair(_1787184, _1787184), 49792 ^ [_1787184, _1787186, _1787188, _1787190, _1787192]), 49789 ^ [_1787184, _1787186, _1787188, _1787190, _1787192])), _1787192)))], (49796 ^ _779530) ^ [] : [49792 ^ [_1787184, _1787186, _1787188, _1787190, _1787192] = 49789 ^ [_1787184, _1787186, _1787188, _1787190, _1787192]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787184, _1787184)), hAPP(hAPP(c_Product__Type_OPair(_1787184, _1787184), _1787186), _1787188)), c_Transitive__Closure_Ortrancl(_1787184, _1787190))))], (49800 ^ _779530) ^ [_1787743, _1787745, _1787747, _1787749, _1787751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787743, _1787743)), hAPP(hAPP(c_Product__Type_OPair(_1787743, _1787743), _1787745), _1787747)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1787743, _1787743), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1787749)), _1787751))), 49804 ^ _779530 : [(49805 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787743, _1787743)), hAPP(hAPP(c_Product__Type_OPair(_1787743, _1787743), _1787745), 49803 ^ [_1787743, _1787745, _1787747, _1787749, _1787751])), _1787751)))], (49807 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787743, _1787743)), hAPP(hAPP(c_Product__Type_OPair(_1787743, _1787743), 49803 ^ [_1787743, _1787745, _1787747, _1787749, _1787751]), _1787747)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1787743, _1787743), tc_HOL_Obool), _1787749), _1787751))))]]], (49809 ^ _779530) ^ [_1788051, _1788053, _1788055, _1788057, _1788059] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788051, _1788051)), hAPP(hAPP(c_Product__Type_OPair(_1788051, _1788051), _1788053), _1788055)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1788051, _1788051), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1788057)), _1788059))), 49813 ^ _779530 : [(49814 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788051, _1788051)), hAPP(hAPP(c_Product__Type_OPair(_1788051, _1788051), _1788053), 49812 ^ [_1788051, _1788053, _1788055, _1788057, _1788059])), _1788059)))], (49816 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788051, _1788051)), hAPP(hAPP(c_Product__Type_OPair(_1788051, _1788051), 49812 ^ [_1788051, _1788053, _1788055, _1788057, _1788059]), _1788055)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1788051, _1788051), tc_HOL_Obool), _1788057), _1788059))))]]], (49818 ^ _779530) ^ [_1788363, _1788365, _1788367, _1788369, _1788371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788363, _1788363)), hAPP(hAPP(c_Product__Type_OPair(_1788363, _1788363), _1788365), _1788367)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1788363, _1788363), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1788369)), _1788371))), 49822 ^ _779530 : [(49823 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788363, _1788363)), hAPP(hAPP(c_Product__Type_OPair(_1788363, _1788363), _1788365), 49821 ^ [_1788363, _1788365, _1788367, _1788369, _1788371])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1788363, _1788363), tc_HOL_Obool), _1788369), _1788371))))], (49825 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788363, _1788363)), hAPP(hAPP(c_Product__Type_OPair(_1788363, _1788363), 49821 ^ [_1788363, _1788365, _1788367, _1788369, _1788371]), _1788367)), _1788371)))]]], (49827 ^ _779530) ^ [_1788675, _1788677, _1788679, _1788681] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788675, _1788675)), hAPP(hAPP(c_Product__Type_OPair(_1788675, _1788675), _1788677), _1788679)), c_Transitive__Closure_Otrancl(_1788675, _1788681))), 49831 ^ _779530 : [(49832 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788675, _1788675)), hAPP(hAPP(c_Product__Type_OPair(_1788675, _1788675), _1788677), 49830 ^ [_1788675, _1788677, _1788679, _1788681])), c_Transitive__Closure_Ortrancl(_1788675, _1788681))))], (49834 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788675, _1788675)), hAPP(hAPP(c_Product__Type_OPair(_1788675, _1788675), 49830 ^ [_1788675, _1788677, _1788679, _1788681]), _1788679)), _1788681)))]]], (49836 ^ _779530) ^ [_1788935, _1788937, _1788939, _1788941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788935, _1788935)), hAPP(hAPP(c_Product__Type_OPair(_1788935, _1788935), _1788937), _1788939)), c_Transitive__Closure_Otrancl(_1788935, _1788941))), 49840 ^ _779530 : [(49841 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788935, _1788935)), hAPP(hAPP(c_Product__Type_OPair(_1788935, _1788935), _1788937), 49839 ^ [_1788935, _1788937, _1788939, _1788941])), _1788941)))], (49843 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788935, _1788935)), hAPP(hAPP(c_Product__Type_OPair(_1788935, _1788935), 49839 ^ [_1788935, _1788937, _1788939, _1788941]), _1788939)), c_Transitive__Closure_Ortrancl(_1788935, _1788941))))]]], (49845 ^ _779530) ^ [_1789195, _1789197] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1789195, _1789195)), _1789197), c_Relation_OId(_1789195))), -(_1789197 = hAPP(hAPP(c_Product__Type_OPair(_1789195, _1789195), 49848 ^ [_1789195, _1789197]), 49848 ^ [_1789195, _1789197]))], (49852 ^ _779530) ^ [_1789337, _1789339, _1789341, _1789343] : [49854 ^ _779530 : [(49855 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1789337), 49853 ^ [_1789337, _1789339, _1789341, _1789343])))], (49857 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49853 ^ [_1789337, _1789339, _1789341, _1789343]), _1789339)))], (49859 ^ _779530) ^ [] : [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(_1789341, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 49853 ^ [_1789337, _1789339, _1789341, _1789343]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1789341, 49853 ^ [_1789337, _1789339, _1789341, _1789343])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1789337), _1789339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1789341, _1789337)), _1789343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1789343), hAPP(_1789341, _1789339))), 49873 ^ _779530 : [(49874 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1789337), 49872 ^ [_1789337, _1789339, _1789341, _1789343])))], (49876 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49872 ^ [_1789337, _1789339, _1789341, _1789343]), _1789339)))], (49878 ^ _779530) ^ [] : [-(hAPP(_1789341, 49872 ^ [_1789337, _1789339, _1789341, _1789343]) = _1789343)]]], (49880 ^ _779530) ^ [_1789981, _1789983, _1789985] : [hBOOL(hAPP(hAPP(c_member(_1789981), _1789983), hAPP(c_List_Oset(_1789981), _1789985))), -(_1789985 = hAPP(hAPP(c_List_Oappend(_1789981), 49883 ^ [_1789981, _1789983, _1789985]), hAPP(hAPP(c_List_Olist_OCons(_1789981), _1789983), 49884 ^ [_1789981, _1789983, _1789985])))], (49888 ^ _779530) ^ [_1790140, _1790142, _1790144] : [49889 ^ _779530 : [(49890 ^ _779530) ^ [_1790217, _1790219] : [_1790144 = hAPP(hAPP(c_List_Oappend(_1790140), _1790219), hAPP(hAPP(c_List_Olist_OCons(_1790140), _1790142), _1790217))]], -(hBOOL(hAPP(hAPP(c_member(_1790140), _1790142), hAPP(c_List_Oset(_1790140), _1790144))))], (49894 ^ _779530) ^ [_1790318, _1790320, _1790322] : [hBOOL(hAPP(hAPP(c_member(_1790318), _1790320), hAPP(c_List_Oset(_1790318), _1790322))), 49899 ^ _779530 : [(49900 ^ _779530) ^ [] : [-(_1790322 = hAPP(hAPP(c_List_Oappend(_1790318), 49897 ^ [_1790318, _1790320, _1790322]), hAPP(hAPP(c_List_Olist_OCons(_1790318), _1790320), 49898 ^ [_1790318, _1790320, _1790322])))], (49902 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1790318), _1790320), hAPP(c_List_Oset(_1790318), 49897 ^ [_1790318, _1790320, _1790322])))]]], (49904 ^ _779530) ^ [_1790573, _1790575, _1790577] : [-(hBOOL(hAPP(hAPP(c_member(_1790573), _1790575), hAPP(c_List_Oset(_1790573), _1790577)))), 49905 ^ _779530 : [(49906 ^ _779530) ^ [_1790662] : [49907 ^ _779530 : [(49908 ^ _779530) ^ [_1790735] : [_1790577 = hAPP(hAPP(c_List_Oappend(_1790573), _1790662), hAPP(hAPP(c_List_Olist_OCons(_1790573), _1790575), _1790735))]], -(hBOOL(hAPP(hAPP(c_member(_1790573), _1790575), hAPP(c_List_Oset(_1790573), _1790662))))]]], (49914 ^ _779530) ^ [_1790874, _1790876, _1790878] : [hBOOL(hAPP(hAPP(c_member(_1790874), _1790876), hAPP(c_List_Oset(_1790874), _1790878))), 49919 ^ _779530 : [(49920 ^ _779530) ^ [] : [-(_1790878 = hAPP(hAPP(c_List_Oappend(_1790874), 49917 ^ [_1790874, _1790876, _1790878]), hAPP(hAPP(c_List_Olist_OCons(_1790874), _1790876), 49918 ^ [_1790874, _1790876, _1790878])))], (49922 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1790874), _1790876), hAPP(c_List_Oset(_1790874), 49918 ^ [_1790874, _1790876, _1790878])))]]], (49924 ^ _779530) ^ [_1791129, _1791131, _1791133] : [-(hBOOL(hAPP(hAPP(c_member(_1791129), _1791131), hAPP(c_List_Oset(_1791129), _1791133)))), 49925 ^ _779530 : [(49926 ^ _779530) ^ [_1791218, _1791220] : [_1791133 = hAPP(hAPP(c_List_Oappend(_1791129), _1791220), hAPP(hAPP(c_List_Olist_OCons(_1791129), _1791131), _1791218)), -(hBOOL(hAPP(hAPP(c_member(_1791129), _1791131), hAPP(c_List_Oset(_1791129), _1791218))))]]], (49934 ^ _779530) ^ [_1791401, _1791403, _1791405] : [class_Orderings_Olinorder(_1791401), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791401), _1791403)), -(hBOOL(hAPP(hAPP(c_member(_1791401), _1791405), _1791403))), -(c_Big__Operators_Olattice_OSup__fin(_1791401, c_Orderings_Oord__class_Omax(_1791401), hAPP(hAPP(c_Set_Oinsert(_1791401), _1791405), _1791403)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791401, _1791401, c_Orderings_Oord__class_Omax(_1791401)), _1791405), _1791403))], (49948 ^ _779530) ^ [_1791621, _1791623, _1791625] : [class_Orderings_Olinorder(_1791621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791621), _1791623)), -(hBOOL(hAPP(hAPP(c_member(_1791621), _1791625), _1791623))), -(c_Big__Operators_Olattice_OInf__fin(_1791621, c_Orderings_Oord__class_Omin(_1791621), hAPP(hAPP(c_Set_Oinsert(_1791621), _1791625), _1791623)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791621, _1791621, c_Orderings_Oord__class_Omin(_1791621)), _1791625), _1791623))], (49962 ^ _779530) ^ [_1791841, _1791843, _1791845, _1791847, _1791849] : [class_Complete__Lattice_Ocomplete__lattice(_1791841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791843), _1791845)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1791841), _1791847), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1791843, _1791841), _1791845), _1791849)) = hAPP(hAPP(c_Finite__Set_Ofold(_1791843, _1791841, hAPP(hAPP(c_COMBB(_1791841, tc_fun(_1791841, _1791841), _1791843), c_Lattices_Osemilattice__sup__class_Osup(_1791841)), _1791849)), _1791847), _1791845))], (49972 ^ _779530) ^ [_1792072, _1792074, _1792076, _1792078, _1792080] : [class_Complete__Lattice_Ocomplete__lattice(_1792072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792074), _1792076)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1792072), _1792078), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1792074, _1792072), _1792076), _1792080)) = hAPP(hAPP(c_Finite__Set_Ofold(_1792074, _1792072, hAPP(hAPP(c_COMBB(_1792072, tc_fun(_1792072, _1792072), _1792074), c_Lattices_Osemilattice__inf__class_Oinf(_1792072)), _1792080)), _1792078), _1792076))], (49982 ^ _779530) ^ [_1792303, _1792305, _1792307] : [class_Complete__Lattice_Ocomplete__lattice(_1792303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792303), _1792305)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1792303), _1792307), c_Complete__Lattice_OSup__class_OSup(_1792303, _1792305)) = hAPP(hAPP(c_Finite__Set_Ofold(_1792303, _1792303, c_Lattices_Osemilattice__sup__class_Osup(_1792303)), _1792307), _1792305))], (49992 ^ _779530) ^ [_1792488, _1792490, _1792492] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792488), _1792490)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1792488, tc_HOL_Obool)), _1792490), _1792492) = hAPP(hAPP(c_Finite__Set_Ofold(_1792488, tc_fun(_1792488, tc_HOL_Obool), c_Set_Oinsert(_1792488)), _1792492), _1792490))], (49998 ^ _779530) ^ [_1792627, _1792629, _1792631, _1792633] : [class_Lattices_Osemilattice__sup(_1792627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792627), _1792629)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1792627, _1792627, c_Lattices_Osemilattice__sup__class_Osup(_1792627)), _1792631), hAPP(hAPP(c_Set_Oinsert(_1792627), _1792633), _1792629)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1792627), _1792633), hAPP(hAPP(c_Finite__Set_Ofold(_1792627, _1792627, c_Lattices_Osemilattice__sup__class_Osup(_1792627)), _1792631), _1792629)))], (50008 ^ _779530) ^ [_1792850, _1792852, _1792854] : [class_Complete__Lattice_Ocomplete__lattice(_1792850), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792850), _1792852)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1792850), _1792854), c_Complete__Lattice_OInf__class_OInf(_1792850, _1792852)) = hAPP(hAPP(c_Finite__Set_Ofold(_1792850, _1792850, c_Lattices_Osemilattice__inf__class_Oinf(_1792850)), _1792854), _1792852))], (50018 ^ _779530) ^ [_1793035, _1793037, _1793039, _1793041, _1793043] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1793035, _1793037, _1793039), _1793041), _1793043) = c_HOL_OThe(_1793037, c_Finite__Set_Ofold__graph(_1793035, _1793037, _1793039, _1793041, _1793043)))], (50020 ^ _779530) ^ [_1793085, _1793087, _1793089, _1793091] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1793085, _1793087, _1793089), _1793091), c_Orderings_Obot__class_Obot(tc_fun(_1793085, tc_HOL_Obool))) = _1793091)], (50022 ^ _779530) ^ [_1793129, _1793131, _1793133, _1793135] : [-(hAPP(c_Finite__Set_Ofold__image(_1793129, _1793131, _1793133), _1793135) = c_Finite__Set_Ofold(_1793131, _1793129, hAPP(hAPP(c_COMBB(_1793129, tc_fun(_1793129, _1793129), _1793131), _1793133), _1793135)))], (50024 ^ _779530) ^ [_1793182, _1793184, _1793186, _1793188, _1793190, _1793192] : [c_Finite__Set_Ofolding(_1793182, _1793184, _1793186, _1793188), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793182), _1793190)), -(hAPP(hAPP(_1793188, _1793190), _1793192) = hAPP(hAPP(c_Finite__Set_Ofold(_1793182, _1793184, _1793186), _1793192), _1793190))], (50034 ^ _779530) ^ [_1793371, _1793373, _1793375, _1793377] : [class_Orderings_Olinorder(_1793371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793371), _1793373)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1793371, _1793371, c_Orderings_Oord__class_Omax(_1793371)), _1793375), hAPP(hAPP(c_Set_Oinsert(_1793371), _1793377), _1793373)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1793371), _1793377), hAPP(hAPP(c_Finite__Set_Ofold(_1793371, _1793371, c_Orderings_Oord__class_Omax(_1793371)), _1793375), _1793373)))], (50044 ^ _779530) ^ [_1793594, _1793596, _1793598, _1793600] : [class_Orderings_Olinorder(_1793594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793594), _1793596)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1793594, _1793594, c_Orderings_Oord__class_Omin(_1793594)), _1793598), hAPP(hAPP(c_Set_Oinsert(_1793594), _1793600), _1793596)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1793594), _1793600), hAPP(hAPP(c_Finite__Set_Ofold(_1793594, _1793594, c_Orderings_Oord__class_Omin(_1793594)), _1793598), _1793596)))], (50054 ^ _779530) ^ [_1793817, _1793819, _1793821, _1793823] : [class_Lattices_Osemilattice__inf(_1793817), hBOOL(hAPP(c_Finite__Set_Ofinite(_1793817), _1793819)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1793817, _1793817, c_Lattices_Osemilattice__inf__class_Oinf(_1793817)), _1793821), hAPP(hAPP(c_Set_Oinsert(_1793817), _1793823), _1793819)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1793817), _1793823), hAPP(hAPP(c_Finite__Set_Ofold(_1793817, _1793817, c_Lattices_Osemilattice__inf__class_Oinf(_1793817)), _1793821), _1793819)))], (50064 ^ _779530) ^ [_1794040, _1794042, _1794044, _1794046, _1794048, _1794050] : [c_Finite__Set_Ofun__left__comm__idem(_1794040, _1794042, _1794044), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794040), _1794046)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1794040, _1794042, _1794044), _1794048), hAPP(hAPP(c_Set_Oinsert(_1794040), _1794050), _1794046)) = hAPP(hAPP(_1794044, _1794050), hAPP(hAPP(c_Finite__Set_Ofold(_1794040, _1794042, _1794044), _1794048), _1794046)))], (50074 ^ _779530) ^ [_1794263, _1794265, _1794267, _1794269, _1794271, _1794273] : [c_Finite__Set_Ofun__left__comm__idem(_1794263, _1794265, _1794267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794263), _1794269)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1794263, _1794265, _1794267), _1794271), hAPP(hAPP(c_Set_Oinsert(_1794263), _1794273), _1794269)) = hAPP(hAPP(c_Finite__Set_Ofold(_1794263, _1794265, _1794267), hAPP(hAPP(_1794267, _1794273), _1794271)), _1794269))], (50084 ^ _779530) ^ [_1794486, _1794488, _1794490, _1794492, _1794494] : [c_Finite__Set_Ofolding__one__idem(_1794486, _1794488, _1794490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794486), _1794492)), -(hAPP(_1794490, hAPP(hAPP(c_Set_Oinsert(_1794486), _1794494), _1794492)) = hAPP(hAPP(c_Finite__Set_Ofold(_1794486, _1794486, _1794488), _1794494), _1794492))], (50094 ^ _779530) ^ [_1794679, _1794681, _1794683, _1794685, _1794687] : [c_Finite__Set_Ofun__left__comm__idem(_1794679, _1794681, _1794683), -(hAPP(hAPP(c_Finite__Set_Ofold(_1794679, _1794681, _1794683), _1794685), hAPP(c_List_Oset(_1794679), _1794687)) = hAPP(c_List_Ofoldl(_1794681, _1794679, hAPP(c_COMBC(_1794679, _1794681, _1794681), _1794683), _1794685), _1794687))], (50100 ^ _779530) ^ [_1794824, _1794826, _1794828, _1794830] : [class_Lattices_Osemilattice__sup(_1794824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1794824), _1794826)), hBOOL(hAPP(hAPP(c_member(_1794824), _1794828), _1794826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1794824), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1794824), _1794828), _1794830)), hAPP(hAPP(c_Finite__Set_Ofold(_1794824, _1794824, c_Lattices_Osemilattice__sup__class_Osup(_1794824)), _1794830), _1794826))))], (50114 ^ _779530) ^ [_1795091, _1795093, _1795095, _1795097] : [class_Lattices_Osemilattice__inf(_1795091), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795091), _1795093)), hBOOL(hAPP(hAPP(c_member(_1795091), _1795095), _1795093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795091), hAPP(hAPP(c_Finite__Set_Ofold(_1795091, _1795091, c_Lattices_Osemilattice__inf__class_Oinf(_1795091)), _1795097), _1795093)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1795091), _1795095), _1795097))))], (50128 ^ _779530) ^ [_1795358, _1795360, _1795362, _1795364] : [class_Orderings_Olinorder(_1795358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795358), _1795360)), hBOOL(hAPP(hAPP(c_member(_1795358), _1795362), _1795360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795358), hAPP(hAPP(c_Finite__Set_Ofold(_1795358, _1795358, c_Orderings_Oord__class_Omin(_1795358)), _1795364), _1795360)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1795358), _1795362), _1795364))))], (50142 ^ _779530) ^ [_1795625, _1795627, _1795629, _1795631] : [class_Orderings_Olinorder(_1795625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795625), _1795627)), hBOOL(hAPP(hAPP(c_member(_1795625), _1795629), _1795627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1795625), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1795625), _1795629), _1795631)), hAPP(hAPP(c_Finite__Set_Ofold(_1795625, _1795625, c_Orderings_Oord__class_Omax(_1795625)), _1795631), _1795627))))], (50156 ^ _779530) ^ [_1795892, _1795894] : [class_Complete__Lattice_Ocomplete__lattice(_1795892), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795892), _1795894)), -(c_Complete__Lattice_OSup__class_OSup(_1795892, _1795894) = hAPP(hAPP(c_Finite__Set_Ofold(_1795892, _1795892, c_Lattices_Osemilattice__sup__class_Osup(_1795892)), c_Orderings_Obot__class_Obot(_1795892)), _1795894))], (50166 ^ _779530) ^ [_1796061, _1796063] : [class_Complete__Lattice_Ocomplete__lattice(_1796061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796061), _1796063)), -(c_Complete__Lattice_OInf__class_OInf(_1796061, _1796063) = hAPP(hAPP(c_Finite__Set_Ofold(_1796061, _1796061, c_Lattices_Osemilattice__inf__class_Oinf(_1796061)), c_Orderings_Otop__class_Otop(_1796061)), _1796063))], (50176 ^ _779530) ^ [_1796230, _1796232, _1796234] : [class_Lattices_Oab__semigroup__idem__mult(_1796230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796230), _1796232)), -(hAPP(c_Finite__Set_Ofold1(_1796230, c_Groups_Otimes__class_Otimes(_1796230)), hAPP(hAPP(c_Set_Oinsert(_1796230), _1796234), _1796232)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796230, _1796230, c_Groups_Otimes__class_Otimes(_1796230)), _1796234), _1796232))], (50186 ^ _779530) ^ [_1796425, _1796427, _1796429] : [class_Lattices_Olattice(_1796425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796425), _1796427)), -(c_Big__Operators_Olattice__class_OSup__fin(_1796425, hAPP(hAPP(c_Set_Oinsert(_1796425), _1796429), _1796427)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796425, _1796425, c_Lattices_Osemilattice__sup__class_Osup(_1796425)), _1796429), _1796427))], (50196 ^ _779530) ^ [_1796610, _1796612, _1796614] : [class_Lattices_Olattice(_1796610), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796610), _1796612)), -(c_Big__Operators_Olattice__class_OInf__fin(_1796610, hAPP(hAPP(c_Set_Oinsert(_1796610), _1796614), _1796612)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796610, _1796610, c_Lattices_Osemilattice__inf__class_Oinf(_1796610)), _1796614), _1796612))], (50206 ^ _779530) ^ [_1796795, _1796797, _1796799] : [class_Orderings_Olinorder(_1796795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796795), _1796797)), -(c_Big__Operators_Olinorder__class_OMin(_1796795, hAPP(hAPP(c_Set_Oinsert(_1796795), _1796799), _1796797)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796795, _1796795, c_Orderings_Oord__class_Omin(_1796795)), _1796799), _1796797))], (50216 ^ _779530) ^ [_1796980, _1796982, _1796984] : [class_Orderings_Olinorder(_1796980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1796980), _1796982)), -(c_Big__Operators_Olinorder__class_OMax(_1796980, hAPP(hAPP(c_Set_Oinsert(_1796980), _1796984), _1796982)) = hAPP(hAPP(c_Finite__Set_Ofold(_1796980, _1796980, c_Orderings_Oord__class_Omax(_1796980)), _1796984), _1796982))], (50226 ^ _779530) ^ [_1797165, _1797167, _1797169] : [class_Orderings_Olinorder(_1797165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797165), _1797167)), -(c_Big__Operators_Olattice_OInf__fin(_1797165, c_Orderings_Oord__class_Omin(_1797165), hAPP(hAPP(c_Set_Oinsert(_1797165), _1797169), _1797167)) = hAPP(hAPP(c_Finite__Set_Ofold(_1797165, _1797165, c_Orderings_Oord__class_Omin(_1797165)), _1797169), _1797167))], (50236 ^ _779530) ^ [_1797356, _1797358, _1797360] : [class_Orderings_Olinorder(_1797356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797356), _1797358)), -(c_Big__Operators_Olattice_OSup__fin(_1797356, c_Orderings_Oord__class_Omax(_1797356), hAPP(hAPP(c_Set_Oinsert(_1797356), _1797360), _1797358)) = hAPP(hAPP(c_Finite__Set_Ofold(_1797356, _1797356, c_Orderings_Oord__class_Omax(_1797356)), _1797360), _1797358))], (50246 ^ _779530) ^ [_1797547, _1797549, _1797551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1797547), _1797549)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1797547, tc_HOL_Obool)), _1797551), _1797549) = hAPP(hAPP(c_Finite__Set_Ofold(_1797547, tc_fun(_1797547, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1797547, tc_HOL_Obool), tc_fun(tc_fun(_1797547, tc_HOL_Obool), tc_fun(_1797547, tc_HOL_Obool)), _1797547), hAPP(c_COMBC(tc_fun(_1797547, tc_HOL_Obool), tc_fun(_1797547, tc_HOL_Obool), tc_fun(_1797547, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1797547, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1797547, tc_fun(_1797547, tc_HOL_Obool), tc_fun(_1797547, tc_HOL_Obool)), c_Set_Oinsert(_1797547)), c_Orderings_Obot__class_Obot(tc_fun(_1797547, tc_HOL_Obool))))), _1797551), _1797549))], (50252 ^ _779530) ^ [_1797814, _1797816, _1797818, _1797820, _1797822] : [c_Finite__Set_Ofolding__one(_1797814, _1797816, _1797818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1797814), _1797820)), -(hBOOL(hAPP(hAPP(c_member(_1797814), _1797822), _1797820))), -(hAPP(_1797818, hAPP(hAPP(c_Set_Oinsert(_1797814), _1797822), _1797820)) = hAPP(hAPP(c_Finite__Set_Ofold(_1797814, _1797814, _1797816), _1797822), _1797820))], (50266 ^ _779530) ^ [_1798036, _1798038, _1798040, _1798042] : [class_Complete__Lattice_Ocomplete__lattice(_1798036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798038), _1798040)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1798038, _1798036), _1798040), _1798042) = hAPP(hAPP(c_Finite__Set_Ofold(_1798038, _1798036, hAPP(hAPP(c_COMBB(_1798036, tc_fun(_1798036, _1798036), _1798038), c_Lattices_Osemilattice__sup__class_Osup(_1798036)), _1798042)), c_Orderings_Obot__class_Obot(_1798036)), _1798040))], (50276 ^ _779530) ^ [_1798251, _1798253, _1798255, _1798257] : [class_Complete__Lattice_Ocomplete__lattice(_1798251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798253), _1798255)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798253, _1798251), _1798255), _1798257) = hAPP(hAPP(c_Finite__Set_Ofold(_1798253, _1798251, hAPP(hAPP(c_COMBB(_1798251, tc_fun(_1798251, _1798251), _1798253), c_Lattices_Osemilattice__inf__class_Oinf(_1798251)), _1798257)), c_Orderings_Otop__class_Otop(_1798251)), _1798255))], (50286 ^ _779530) ^ [_1798466, _1798468, _1798470] : [class_Groups_Oab__semigroup__mult(_1798466), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798466), _1798468)), -(hBOOL(hAPP(hAPP(c_member(_1798466), _1798470), _1798468))), -(hAPP(c_Finite__Set_Ofold1(_1798466, c_Groups_Otimes__class_Otimes(_1798466)), hAPP(hAPP(c_Set_Oinsert(_1798466), _1798470), _1798468)) = hAPP(hAPP(c_Finite__Set_Ofold(_1798466, _1798466, c_Groups_Otimes__class_Otimes(_1798466)), _1798470), _1798468))], (50300 ^ _779530) ^ [_1798690, _1798692, _1798694] : [class_Lattices_Olattice(_1798690), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798690), _1798692)), -(hBOOL(hAPP(hAPP(c_member(_1798690), _1798694), _1798692))), -(c_Big__Operators_Olattice__class_OSup__fin(_1798690, hAPP(hAPP(c_Set_Oinsert(_1798690), _1798694), _1798692)) = hAPP(hAPP(c_Finite__Set_Ofold(_1798690, _1798690, c_Lattices_Osemilattice__sup__class_Osup(_1798690)), _1798694), _1798692))], (50314 ^ _779530) ^ [_1798904, _1798906, _1798908] : [class_Lattices_Olattice(_1798904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1798904), _1798906)), -(hBOOL(hAPP(hAPP(c_member(_1798904), _1798908), _1798906))), -(c_Big__Operators_Olattice__class_OInf__fin(_1798904, hAPP(hAPP(c_Set_Oinsert(_1798904), _1798908), _1798906)) = hAPP(hAPP(c_Finite__Set_Ofold(_1798904, _1798904, c_Lattices_Osemilattice__inf__class_Oinf(_1798904)), _1798908), _1798906))], (50328 ^ _779530) ^ [_1799118, _1799120, _1799122] : [class_Orderings_Olinorder(_1799118), hBOOL(hAPP(c_Finite__Set_Ofinite(_1799118), _1799120)), -(hBOOL(hAPP(hAPP(c_member(_1799118), _1799122), _1799120))), -(c_Big__Operators_Olinorder__class_OMin(_1799118, hAPP(hAPP(c_Set_Oinsert(_1799118), _1799122), _1799120)) = hAPP(hAPP(c_Finite__Set_Ofold(_1799118, _1799118, c_Orderings_Oord__class_Omin(_1799118)), _1799122), _1799120))], (50342 ^ _779530) ^ [_1799332, _1799334, _1799336] : [class_Orderings_Olinorder(_1799332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1799332), _1799334)), -(hBOOL(hAPP(hAPP(c_member(_1799332), _1799336), _1799334))), -(c_Big__Operators_Olinorder__class_OMax(_1799332, hAPP(hAPP(c_Set_Oinsert(_1799332), _1799336), _1799334)) = hAPP(hAPP(c_Finite__Set_Ofold(_1799332, _1799332, c_Orderings_Oord__class_Omax(_1799332)), _1799336), _1799334))], (50356 ^ _779530) ^ [_1799546, _1799548, _1799550, _1799552, _1799554, _1799556] : [c_Finite__Set_Ofun__left__comm(_1799546, _1799548, _1799550), hBOOL(hAPP(c_Finite__Set_Ofinite(_1799546), _1799552)), hBOOL(hAPP(hAPP(c_member(_1799546), _1799554), _1799552)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1799546, _1799548, _1799550), _1799556), _1799552) = hAPP(hAPP(_1799550, _1799554), hAPP(hAPP(c_Finite__Set_Ofold(_1799546, _1799548, _1799550), _1799556), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1799546, tc_HOL_Obool)), _1799552), hAPP(hAPP(c_Set_Oinsert(_1799546), _1799554), c_Orderings_Obot__class_Obot(tc_fun(_1799546, tc_HOL_Obool)))))))], (50370 ^ _779530) ^ [_1799875, _1799877, _1799879, _1799881, _1799883, _1799885] : [c_Finite__Set_Ofun__left__comm(_1799875, _1799877, _1799879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1799875), _1799881)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1799875, _1799877, _1799879), _1799883), hAPP(hAPP(c_Set_Oinsert(_1799875), _1799885), _1799881)) = hAPP(hAPP(_1799879, _1799885), hAPP(hAPP(c_Finite__Set_Ofold(_1799875, _1799877, _1799879), _1799883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1799875, tc_HOL_Obool)), _1799881), hAPP(hAPP(c_Set_Oinsert(_1799875), _1799885), c_Orderings_Obot__class_Obot(tc_fun(_1799875, tc_HOL_Obool)))))))], (50380 ^ _779530) ^ [_1800146, _1800148, _1800150, _1800152, _1800154, _1800156] : [c_Finite__Set_Ofun__left__comm(_1800146, _1800148, _1800150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1800146), _1800152)), -(hAPP(hAPP(_1800150, _1800154), hAPP(hAPP(c_Finite__Set_Ofold(_1800146, _1800148, _1800150), _1800156), _1800152)) = hAPP(hAPP(c_Finite__Set_Ofold(_1800146, _1800148, _1800150), hAPP(hAPP(_1800150, _1800154), _1800156)), _1800152))], (50390 ^ _779530) ^ [_1800365, _1800367, _1800369, _1800371, _1800373] : [c_Finite__Set_Ofun__left__comm(_1800365, _1800367, _1800369), -(hAPP(c_Fun_Ocomp(_1800367, _1800367, _1800367, hAPP(_1800369, _1800371)), hAPP(_1800369, _1800373)) = hAPP(c_Fun_Ocomp(_1800367, _1800367, _1800367, hAPP(_1800369, _1800373)), hAPP(_1800369, _1800371)))], (50396 ^ _779530) ^ [_1800506, _1800508, _1800510, _1800512, _1800514, _1800516, _1800518] : [c_Finite__Set_Ofun__left__comm(_1800506, _1800508, _1800510), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1800506, _1800508, _1800510, _1800512, _1800514), _1800516)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1800506, _1800508, _1800510, _1800512, _1800514), _1800518)), -(_1800518 = _1800516)], (50410 ^ _779530) ^ [_1800751, _1800753, _1800755, _1800757, _1800759, _1800761] : [c_Finite__Set_Ofun__left__comm(_1800751, _1800753, _1800755), -(hAPP(hAPP(_1800755, _1800757), hAPP(hAPP(_1800755, _1800759), _1800761)) = hAPP(hAPP(_1800755, _1800759), hAPP(hAPP(_1800755, _1800757), _1800761)))], (50416 ^ _779530) ^ [_1800886, _1800888, _1800890, _1800892, _1800894] : [c_Finite__Set_Ofun__left__comm(_1800886, _1800888, _1800890), -(c_Finite__Set_Ofun__left__comm(_1800892, _1800888, hAPP(hAPP(c_COMBB(_1800886, tc_fun(_1800888, _1800888), _1800892), _1800890), _1800894)))], (50422 ^ _779530) ^ [_1800999] : [class_Orderings_Olinorder(_1800999), -(c_Finite__Set_Ofun__left__comm(_1800999, tc_List_Olist(_1800999), c_List_Olinorder__class_Oinsort__key(_1800999, _1800999, c_COMBI(_1800999))))], (50428 ^ _779530) ^ [_1801090] : [class_Groups_Oab__semigroup__mult(_1801090), -(c_Finite__Set_Ofun__left__comm(_1801090, _1801090, c_Groups_Otimes__class_Otimes(_1801090)))], (50434 ^ _779530) ^ [_1801169, _1801171, _1801173, _1801175, _1801177, _1801179] : [c_Finite__Set_Ofun__left__comm(_1801169, _1801171, _1801173), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1801169, _1801171, _1801173, _1801175, _1801177), _1801179)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1801169, _1801171, _1801173), _1801175), _1801177) = _1801179)], (50444 ^ _779530) ^ [_1801352, _1801354, _1801356, _1801358, _1801360] : [c_Finite__Set_Ofun__left__comm(_1801352, _1801354, _1801356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1801352), _1801358)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1801352, _1801354, _1801356, _1801360, _1801358), hAPP(hAPP(c_Finite__Set_Ofold(_1801352, _1801354, _1801356), _1801360), _1801358))))], (50454 ^ _779530) ^ [_1801539, _1801541, _1801543, _1801545, _1801547, _1801549] : [c_Finite__Set_Ofun__left__comm(_1801539, _1801541, _1801543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1801539), _1801545)), -(hBOOL(hAPP(hAPP(c_member(_1801539), _1801547), _1801545))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1801539, _1801541, _1801543), _1801549), hAPP(hAPP(c_Set_Oinsert(_1801539), _1801547), _1801545)) = hAPP(hAPP(c_Finite__Set_Ofold(_1801539, _1801541, _1801543), hAPP(hAPP(_1801543, _1801547), _1801549)), _1801545))], (50468 ^ _779530) ^ [_1801791, _1801793, _1801795, _1801797, _1801799, _1801801] : [c_Finite__Set_Ofun__left__comm(_1801791, _1801793, _1801795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1801791), _1801797)), -(hBOOL(hAPP(hAPP(c_member(_1801791), _1801799), _1801797))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1801791, _1801793, _1801795), _1801801), hAPP(hAPP(c_Set_Oinsert(_1801791), _1801799), _1801797)) = hAPP(hAPP(_1801795, _1801799), hAPP(hAPP(c_Finite__Set_Ofold(_1801791, _1801793, _1801795), _1801801), _1801797)))], (50482 ^ _779530) ^ [_1802043, _1802045, _1802047, _1802049, _1802051] : [c_Finite__Set_Ofun__left__comm(_1802043, _1802045, _1802047), -(hAPP(hAPP(c_Finite__Set_Ofold(_1802043, _1802045, _1802047), _1802049), hAPP(c_List_Oset(_1802043), _1802051)) = hAPP(c_List_Ofoldl(_1802045, _1802043, hAPP(c_COMBC(_1802043, _1802045, _1802045), _1802047), _1802049), c_List_Oremdups(_1802043, _1802051)))], (50488 ^ _779530) ^ [_1802194, _1802196, _1802198, _1802200, _1802202, _1802204, _1802206] : [c_Finite__Set_Ofun__left__comm(_1802194, _1802196, _1802198), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1802194, _1802196, _1802198, _1802200, _1802202), _1802204)), hBOOL(hAPP(hAPP(c_member(_1802194), _1802206), _1802202)), 50500 ^ _779530 : [(50501 ^ _779530) ^ [] : [-(_1802204 = hAPP(hAPP(_1802198, _1802206), 50499 ^ [_1802194, _1802196, _1802198, _1802200, _1802202, _1802204, _1802206]))], (50503 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1802194, _1802196, _1802198, _1802200, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1802194, tc_HOL_Obool)), _1802202), hAPP(hAPP(c_Set_Oinsert(_1802194), _1802206), c_Orderings_Obot__class_Obot(tc_fun(_1802194, tc_HOL_Obool))))), 50499 ^ [_1802194, _1802196, _1802198, _1802200, _1802202, _1802204, _1802206])))]]], (50505 ^ _779530) ^ [_1802578, _1802580, _1802582, _1802584, _1802586, _1802588, _1802590] : [c_Finite__Set_Ofun__left__comm(_1802578, _1802580, _1802582), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1802578, _1802580, _1802582, _1802584, hAPP(hAPP(c_Set_Oinsert(_1802578), _1802586), _1802588)), _1802590)), -(hBOOL(hAPP(hAPP(c_member(_1802578), _1802586), _1802588))), 50517 ^ _779530 : [(50518 ^ _779530) ^ [] : [-(_1802590 = hAPP(hAPP(_1802582, _1802586), 50516 ^ [_1802578, _1802580, _1802582, _1802584, _1802586, _1802588, _1802590]))], (50520 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1802578, _1802580, _1802582, _1802584, _1802588), 50516 ^ [_1802578, _1802580, _1802582, _1802584, _1802586, _1802588, _1802590])))]]], (50522 ^ _779530) ^ [_1802904, _1802906, _1802908, _1802910] : [class_Orderings_Olinorder(_1802904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802904), _1802906)), 50532 ^ _779530 : [(50533 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802904), 50531 ^ [_1802904, _1802906, _1802908, _1802910]), _1802906)))], (50535 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1802904), 50531 ^ [_1802904, _1802906, _1802908, _1802910]), _1802908))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1802904), hAPP(hAPP(c_Finite__Set_Ofold(_1802904, _1802904, c_Orderings_Oord__class_Omax(_1802904)), _1802910), _1802906)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1802904), _1802908), _1802910))))], (50539 ^ _779530) ^ [_1803268, _1803270, _1803272, _1803274] : [class_Orderings_Olinorder(_1803268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803268), _1803270)), 50549 ^ _779530 : [(50550 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803268), 50548 ^ [_1803268, _1803270, _1803272, _1803274]), _1803270)))], (50552 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803268), _1803272), 50548 ^ [_1803268, _1803270, _1803272, _1803274]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803268), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1803268), _1803272), _1803274)), hAPP(hAPP(c_Finite__Set_Ofold(_1803268, _1803268, c_Orderings_Oord__class_Omin(_1803268)), _1803274), _1803270))))], (50556 ^ _779530) ^ [_1803632, _1803634, _1803636, _1803638] : [class_Lattices_Osemilattice__inf(_1803632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803632), _1803634)), 50566 ^ _779530 : [(50567 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803632), 50565 ^ [_1803632, _1803634, _1803636, _1803638]), _1803634)))], (50569 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803632), _1803636), 50565 ^ [_1803632, _1803634, _1803636, _1803638]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803632), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1803632), _1803636), _1803638)), hAPP(hAPP(c_Finite__Set_Ofold(_1803632, _1803632, c_Lattices_Osemilattice__inf__class_Oinf(_1803632)), _1803638), _1803634))))], (50573 ^ _779530) ^ [_1803996, _1803998, _1804000, _1804002] : [class_Lattices_Osemilattice__sup(_1803996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803996), _1803998)), 50583 ^ _779530 : [(50584 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803996), 50582 ^ [_1803996, _1803998, _1804000, _1804002]), _1803998)))], (50586 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803996), 50582 ^ [_1803996, _1803998, _1804000, _1804002]), _1804000))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1803996), hAPP(hAPP(c_Finite__Set_Ofold(_1803996, _1803996, c_Lattices_Osemilattice__sup__class_Osup(_1803996)), _1804002), _1803998)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1803996), _1804000), _1804002))))], (50590 ^ _779530) ^ [_1804360, _1804362, _1804364] : [class_Divides_Osemiring__div(_1804360), -(_1804362 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1804360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804360), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804360), _1804362), _1804364)), _1804364)), c_Divides_Odiv__class_Omod(_1804360, _1804362, _1804364)))], (50613 ^ _779530) ^ [_1805027, _1805029] : [-(c_Wellfounded_Owf(_1805027, _1805029)), 50616 ^ _779530 : [(50617 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805027), 50615 ^ [_1805027, _1805029]), 50614 ^ [_1805027, _1805029])))], (50619 ^ _779530) ^ [_1805247] : [hBOOL(hAPP(hAPP(c_member(_1805027), _1805247), 50614 ^ [_1805027, _1805029])), 50623 ^ _779530 : [(50624 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1805027, _1805027)), hAPP(hAPP(c_Product__Type_OPair(_1805027, _1805027), 50622 ^ [_1805027, _1805029, _1805247]), _1805247)), _1805029)))], (50626 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805027), 50622 ^ [_1805027, _1805029, _1805247]), 50614 ^ [_1805027, _1805029])))]]]]], (50596 ^ _779530) ^ [_1804508, _1804510] : [c_Wellfounded_Owf(_1804508, _1804510), 50599 ^ _779530 : [(50600 ^ _779530) ^ [_1804640] : [50601 ^ _779530 : [(50602 ^ _779530) ^ [_1804745] : [hBOOL(hAPP(hAPP(c_member(_1804508), _1804745), _1804640))]], 50604 ^ _779530 : [(50605 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804508), 50603 ^ [_1804508, _1804510, _1804640]), _1804640)))], (50607 ^ _779530) ^ [_1804867] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1804508, _1804508)), hAPP(hAPP(c_Product__Type_OPair(_1804508, _1804508), _1804867), 50603 ^ [_1804508, _1804510, _1804640])), _1804510)), hBOOL(hAPP(hAPP(c_member(_1804508), _1804867), _1804640))]]]]], (50630 ^ _779530) ^ [_1805503, _1805505, _1805507, _1805509, _1805511, _1805513, _1805515, _1805517] : [c_Finite__Set_Ofolding__image__simple__idem(_1805503, _1805505, _1805507, _1805509, _1805511, _1805513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1805505), _1805515)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1805505), _1805517)), -(hAPP(_1805513, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1805505, tc_HOL_Obool)), _1805515), _1805517)) = hAPP(hAPP(_1805507, hAPP(_1805513, _1805515)), hAPP(_1805513, _1805517)))], (50644 ^ _779530) ^ [_1805796, _1805798] : [-(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)))), _1805796)) = 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)))), _1805798))), 50646 ^ _779530 : [(50647 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 50645 ^ [_1805796, _1805798])))], (50649 ^ _779530) ^ [] : [50650 ^ _779530 : [(50651 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1805796, 50645 ^ [_1805796, _1805798])))], (50653 ^ _779530) ^ [] : [hBOOL(hAPP(_1805798, 50645 ^ [_1805796, _1805798]))]], 50654 ^ _779530 : [(50655 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1805798, 50645 ^ [_1805796, _1805798])))], (50657 ^ _779530) ^ [] : [hBOOL(hAPP(_1805796, 50645 ^ [_1805796, _1805798]))]]]]], (50661 ^ _779530) ^ [_1806117, _1806119, _1806121, _1806123, _1806125, _1806127, _1806129] : [c_Finite__Set_Ofolding__image__simple__idem(_1806117, _1806119, _1806121, _1806123, _1806125, _1806127), -(hAPP(hAPP(_1806121, _1806129), _1806129) = _1806129)], (50667 ^ _779530) ^ [_1806224, _1806226, _1806228, _1806230, _1806232, _1806234, _1806236, _1806238] : [c_Finite__Set_Ofolding__image__simple__idem(_1806224, _1806226, _1806228, _1806230, _1806232, _1806234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1806226), _1806236)), hBOOL(hAPP(hAPP(c_member(_1806226), _1806238), _1806236)), -(hAPP(hAPP(_1806228, hAPP(_1806232, _1806238)), hAPP(_1806234, _1806236)) = hAPP(_1806234, _1806236))], (50681 ^ _779530) ^ [_1806501, _1806503, _1806505, _1806507, _1806509, _1806511, _1806513, _1806515] : [c_Finite__Set_Ofolding__image__simple__idem(_1806501, _1806503, _1806505, _1806507, _1806509, _1806511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1806503), _1806513)), -(hAPP(_1806511, hAPP(hAPP(c_Set_Oinsert(_1806503), _1806515), _1806513)) = hAPP(hAPP(_1806505, hAPP(_1806509, _1806515)), hAPP(_1806511, _1806513)))], (50691 ^ _779530) ^ [_1806716, _1806718, _1806720, _1806722, _1806724, _1806726, _1806728, _1806730] : [c_Finite__Set_Ofolding__image__simple__idem(_1806716, _1806718, _1806720, _1806722, _1806724, _1806726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1806718), _1806728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1806718, tc_HOL_Obool)), _1806730), _1806728)), -(hAPP(hAPP(_1806720, hAPP(_1806726, _1806730)), hAPP(_1806726, _1806728)) = hAPP(_1806726, _1806728))], (50705 ^ _779530) ^ [_1806999, _1807001, _1807003] : [hBOOL(hAPP(hAPP(c_member(_1806999), _1807001), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1806999, tc_HOL_Obool), _1807003))), 50709 ^ _779530 : [(50710 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806999), _1807001), 50708 ^ [_1806999, _1807001, _1807003])))], (50712 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1806999, tc_HOL_Obool)), 50708 ^ [_1806999, _1807001, _1807003]), _1807003)))]]], (50714 ^ _779530) ^ [_1807191, _1807193, _1807195, _1807197, _1807199] : [-(c_Option_Ooption_Ooption__rec(_1807191, _1807193, _1807195, _1807197, hAPP(c_Option_Ooption_OSome(_1807193), _1807199)) = hAPP(_1807197, _1807199))], (50716 ^ _779530) ^ [_1807236, _1807238, _1807240, _1807242] : [-(c_Option_Ooption_Ooption__rec(_1807236, _1807238, _1807240, _1807242, c_Option_Ooption_ONone(_1807238)) = _1807240)], (50718 ^ _779530) ^ [_1807273, _1807275, _1807277, _1807279] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807273, _1807275)), _1807277), hAPP(c_Relation_Oconverse(_1807275, _1807273), _1807279))), 50723 ^ _779530 : [(50724 ^ _779530) ^ [] : [-(_1807277 = hAPP(hAPP(c_Product__Type_OPair(_1807273, _1807275), 50722 ^ [_1807273, _1807275, _1807277, _1807279]), 50721 ^ [_1807273, _1807275, _1807277, _1807279]))], (50726 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807275, _1807273)), hAPP(hAPP(c_Product__Type_OPair(_1807275, _1807273), 50721 ^ [_1807273, _1807275, _1807277, _1807279]), 50722 ^ [_1807273, _1807275, _1807277, _1807279])), _1807279)))]]], (50728 ^ _779530) ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807526, _1807528)), _1807530), hAPP(hAPP(c_Relation_Orel__comp(_1807526, _1807532, _1807528), _1807534), _1807536))), 50734 ^ _779530 : [(50735 ^ _779530) ^ [] : [-(_1807530 = hAPP(hAPP(c_Product__Type_OPair(_1807526, _1807528), 50731 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536]), 50733 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536]))], (50737 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807526, _1807532)), hAPP(hAPP(c_Product__Type_OPair(_1807526, _1807532), 50731 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536]), 50732 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536])), _1807534)))], (50739 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807532, _1807528)), hAPP(hAPP(c_Product__Type_OPair(_1807532, _1807528), 50732 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536]), 50733 ^ [_1807526, _1807528, _1807530, _1807532, _1807534, _1807536])), _1807536)))]]], (50741 ^ _779530) ^ [_1807904, _1807906, _1807908] : [-(c_Nitpick_Oplus__frac(_1807904, _1807906, _1807908) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1807904), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1807904), _1807906), hAPP(c_Nitpick_Odenom(_1807904), _1807908))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1807904), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1807904), tc_Int_Oint), c_Nitpick_Ofrac(_1807904)), 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(_1807904), _1807906))), 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(_1807904), _1807906))))), 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(_1807904), _1807908))), 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(_1807904), _1807908)))))), c_COMBI(tc_Int_Oint))))], (50743 ^ _779530) ^ [_1808035, _1808037, _1808039, _1808041] : [class_Rings_Olinordered__semidom(_1808035), 50749 ^ _779530 : [(50750 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808037), 50748 ^ [_1808035, _1808037, _1808039, _1808041]), _1808039)))], (50752 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1808035), c_Groups_Ozero__class_Ozero(_1808035)), hAPP(_1808041, 50748 ^ [_1808035, _1808037, _1808039, _1808041])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1808035), c_Groups_Ozero__class_Ozero(_1808035)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1808037, _1808035), _1808041), _1808039))))], (50756 ^ _779530) ^ [_1808331, _1808333, _1808335] : [-(c_Nitpick_Otimes__frac(_1808331, _1808333, _1808335) = hAPP(hAPP(c_Nitpick_Ofrac(_1808331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1808331), _1808333)), hAPP(c_Nitpick_Onum(_1808331), _1808335))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1808331), _1808333)), hAPP(c_Nitpick_Odenom(_1808331), _1808335))))], (50758 ^ _779530) ^ [_1808402, _1808404, _1808406] : [-(c_Nitpick_Oof__frac(_1808404, _1808402, _1808406) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1808402), hAPP(c_Int_Oring__1__class_Oof__int(_1808402), hAPP(c_Nitpick_Onum(_1808404), _1808406))), hAPP(c_Int_Oring__1__class_Oof__int(_1808402), hAPP(c_Nitpick_Odenom(_1808404), _1808406)))), class_Rings_Oinverse(_1808402), class_Rings_Oring__1(_1808402)], (50768 ^ _779530) ^ [_1808595, _1808597] : [-(c_Nitpick_Oinverse__frac(_1808595, _1808597) = hAPP(hAPP(c_Nitpick_Ofrac(_1808595), hAPP(c_Nitpick_Odenom(_1808595), _1808597)), hAPP(c_Nitpick_Onum(_1808595), _1808597)))], (50770 ^ _779530) ^ [_1808641, _1808643] : [-(c_Nitpick_Ouminus__frac(_1808641, _1808643) = c_Nitpick_OAbs__Frac(_1808641, 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(_1808641), _1808643))), hAPP(c_Nitpick_Odenom(_1808641), _1808643))))], (50772 ^ _779530) ^ [_1808709, _1808711, _1808713] : [c_Nitpick_Oless__frac(_1808709, _1808711, _1808713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1808709), c_Nitpick_Oplus__frac(_1808709, _1808711, c_Nitpick_Ouminus__frac(_1808709, _1808713)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50778 ^ _779530) ^ [_1808820, _1808822, _1808824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1808820), c_Nitpick_Oplus__frac(_1808820, _1808822, c_Nitpick_Ouminus__frac(_1808820, _1808824)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1808820, _1808822, _1808824))], (50784 ^ _779530) ^ [_1808955, _1808957, _1808959] : [c_Nitpick_Oless__eq__frac(_1808955, _1808957, _1808959), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1808955), c_Nitpick_Oplus__frac(_1808955, _1808957, c_Nitpick_Ouminus__frac(_1808955, _1808959)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50790 ^ _779530) ^ [_1809066, _1809068, _1809070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1809066), c_Nitpick_Oplus__frac(_1809066, _1809068, c_Nitpick_Ouminus__frac(_1809066, _1809070)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1809066, _1809068, _1809070))], (50796 ^ _779530) ^ [_1809183] : [-(c_Nitpick_Odenom(_1809183) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1809183, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1809183)))], (50798 ^ _779530) ^ [_1809218] : [-(c_Nitpick_Onum(_1809218) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1809218, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1809218)))], (50810 ^ _779530) ^ [_1809485, _1809487, _1809489] : [50812 ^ _779530 : [(50813 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50811 ^ [_1809485, _1809487, _1809489]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1809485)), _1809489))))], (50815 ^ _779530) ^ [] : [hBOOL(hAPP(_1809487, hAPP(hAPP(c_List_Onth(_1809485), _1809489), 50811 ^ [_1809485, _1809487, _1809489])))]], -(c_List_Olist__all(_1809485, _1809487, _1809489))], (50800 ^ _779530) ^ [_1809271, _1809273, _1809275] : [c_List_Olist__all(_1809271, _1809273, _1809275), 50803 ^ _779530 : [(50804 ^ _779530) ^ [_1809360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1809360), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1809271)), _1809275))), -(hBOOL(hAPP(_1809273, hAPP(hAPP(c_List_Onth(_1809271), _1809275), _1809360))))]]], (50819 ^ _779530) ^ [_1809693, _1809695, _1809697] : [-(c_Product__Type_Ointernal__split(_1809693, _1809695, _1809697) = c_Product__Type_Oprod_Oprod__case(_1809693, _1809695, _1809697))], (50821 ^ _779530) ^ [_1809749, _1809751, _1809753, _1809755] : [c_List_Olist__all(_1809749, _1809751, hAPP(hAPP(c_List_Olist_OCons(_1809749), _1809753), _1809755)), 50824 ^ _779530 : [(50825 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1809751, _1809753)))], (50827 ^ _779530) ^ [] : [-(c_List_Olist__all(_1809749, _1809751, _1809755))]]], (50829 ^ _779530) ^ [_1809876, _1809878, _1809880, _1809882] : [-(c_List_Olist__all(_1809876, _1809878, hAPP(hAPP(c_List_Olist_OCons(_1809876), _1809880), _1809882))), hBOOL(hAPP(_1809878, _1809880)), c_List_Olist__all(_1809876, _1809878, _1809882)], (50839 ^ _779530) ^ [_1810259, _1810261, _1810263, _1810265] : [c_List_Olist__all(_1810259, _1810261, hAPP(hAPP(c_List_Oappend(_1810259), _1810263), _1810265)), 50842 ^ _779530 : [(50843 ^ _779530) ^ [] : [-(c_List_Olist__all(_1810259, _1810261, _1810263))], (50845 ^ _779530) ^ [] : [-(c_List_Olist__all(_1810259, _1810261, _1810265))]]], (50847 ^ _779530) ^ [_1810534, _1810536, _1810538, _1810540] : [-(c_List_Olist__all(_1810534, _1810536, hAPP(hAPP(c_List_Oappend(_1810534), _1810538), _1810540))), c_List_Olist__all(_1810534, _1810536, _1810538), c_List_Olist__all(_1810534, _1810536, _1810540)], (50867 ^ _779530) ^ [_1811290, _1811292, _1811294] : [50869 ^ _779530 : [(50870 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811290), 50868 ^ [_1811290, _1811292, _1811294]), hAPP(c_List_Oset(_1811290), _1811294))))], (50872 ^ _779530) ^ [] : [hBOOL(hAPP(_1811292, 50868 ^ [_1811290, _1811292, _1811294]))]], -(c_List_Olist__all(_1811290, _1811292, _1811294))], (50857 ^ _779530) ^ [_1810920, _1810922, _1810924] : [c_List_Olist__all(_1810920, _1810922, _1810924), 50860 ^ _779530 : [(50861 ^ _779530) ^ [_1811077] : [hBOOL(hAPP(hAPP(c_member(_1810920), _1811077), hAPP(c_List_Oset(_1810920), _1810924))), -(hBOOL(hAPP(_1810922, _1811077)))]]], (50876 ^ _779530) ^ [_1811750, _1811752, _1811754] : [c_List_Olist__all(_1811750, _1811752, hAPP(c_List_Orev(_1811750), _1811754)), -(c_List_Olist__all(_1811750, _1811752, _1811754))], (50882 ^ _779530) ^ [_1811932, _1811934, _1811936] : [c_List_Olist__all(_1811932, _1811934, _1811936), -(c_List_Olist__all(_1811932, _1811934, hAPP(c_List_Orev(_1811932), _1811936)))], (50888 ^ _779530) ^ [_1812149, _1812151] : [-(c_List_Olist__all(_1812149, _1812151, c_List_Olist_ONil(_1812149)))], (50890 ^ _779530) ^ [_1812304, _1812306, _1812308] : [50892 ^ _779530 : [(50893 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812304), 50891 ^ [_1812304, _1812306, _1812308]), hAPP(c_List_Oset(_1812304), _1812306))))], (50895 ^ _779530) ^ [] : [hBOOL(hAPP(_1812308, 50891 ^ [_1812304, _1812306, _1812308]))]], -(c_List_Olist__all(_1812304, _1812308, _1812306))], (50899 ^ _779530) ^ [_1812671, _1812673, _1812675] : [c_List_Olist__all(_1812671, _1812675, _1812673), 50902 ^ _779530 : [(50903 ^ _779530) ^ [_1812828] : [hBOOL(hAPP(hAPP(c_member(_1812671), _1812828), hAPP(c_List_Oset(_1812671), _1812673))), -(hBOOL(hAPP(_1812675, _1812828)))]]], (50919 ^ _779530) ^ [_1813504, _1813506, _1813508] : [50921 ^ _779530 : [(50922 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1813504), 50920 ^ [_1813504, _1813506, _1813508]), hAPP(c_List_Oset(_1813504), _1813508))))], (50924 ^ _779530) ^ [] : [hBOOL(hAPP(_1813506, 50920 ^ [_1813504, _1813506, _1813508]))]], -(c_List_Olist__all(_1813504, _1813506, _1813508))], (50909 ^ _779530) ^ [_1813134, _1813136, _1813138] : [c_List_Olist__all(_1813134, _1813136, _1813138), 50912 ^ _779530 : [(50913 ^ _779530) ^ [_1813291] : [hBOOL(hAPP(hAPP(c_member(_1813134), _1813291), hAPP(c_List_Oset(_1813134), _1813138))), -(hBOOL(hAPP(_1813136, _1813291)))]]], (50928 ^ _779530) ^ [_1813962, _1813964, _1813966, _1813968, _1813970, _1813972] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1813962, _1813964, _1813966), _1813968), hAPP(hAPP(c_Product__Type_OPair(_1813962, _1813964), _1813970), _1813972)) = hAPP(hAPP(_1813968, _1813970), _1813972))], (50946 ^ _779530) ^ [_1814707, _1814709, _1814711, _1814713] : [-(c_List_Olist__ex1(_1814707, _1814709, hAPP(hAPP(c_List_Olist_OCons(_1814707), _1814711), _1814713))), 50949 ^ _779530 : [(50950 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1814709, _1814711)))], (50952 ^ _779530) ^ [] : [c_List_Olist__all(_1814707, hAPP(hAPP(c_COMBS(_1814707, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1814707), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1814707), c_fNot), _1814709))), hAPP(c_fequal, _1814711)), _1814713)]], 50953 ^ _779530 : [(50954 ^ _779530) ^ [] : [hBOOL(hAPP(_1814709, _1814711))], (50956 ^ _779530) ^ [] : [c_List_Olist__ex1(_1814707, _1814709, _1814713)]]], (50930 ^ _779530) ^ [_1814161, _1814163, _1814165, _1814167] : [c_List_Olist__ex1(_1814161, _1814163, hAPP(hAPP(c_List_Olist_OCons(_1814161), _1814165), _1814167)), 50933 ^ _779530 : [(50934 ^ _779530) ^ [] : [hBOOL(hAPP(_1814163, _1814165)), -(c_List_Olist__all(_1814161, hAPP(hAPP(c_COMBS(_1814161, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1814161), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1814161), c_fNot), _1814163))), hAPP(c_fequal, _1814165)), _1814167))], (50940 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1814163, _1814165))), -(c_List_Olist__ex1(_1814161, _1814163, _1814167))]]], (50960 ^ _779530) ^ [_1815311, _1815313, _1815315, _1815317] : [class_Rings_Olinordered__semidom(_1815311), 50966 ^ _779530 : [(50967 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1815313), 50965 ^ [_1815311, _1815313, _1815315, _1815317]), _1815315)))], (50969 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1815311), c_Groups_Ozero__class_Ozero(_1815311)), hAPP(_1815317, 50965 ^ [_1815311, _1815313, _1815315, _1815317])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1815311), c_Groups_Ozero__class_Ozero(_1815311)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1815313, _1815311), _1815317), _1815315))))], (50973 ^ _779530) ^ [_1815870, _1815872] : [c_List_Olist__ex1(_1815870, _1815872, c_List_Olist_ONil(_1815870))], (50975 ^ _779530) ^ [_1815982, _1815984] : [class_Enum_Oenum(_1815982), 50978 ^ _779530 : [(50979 ^ _779530) ^ [] : [-(c_List_Olist__ex1(_1815982, _1815984, c_Enum_Oenum__class_Oenum(_1815982))), 50980 ^ _779530 : [(50981 ^ _779530) ^ [_1816204] : [hBOOL(hAPP(_1815984, _1816204)), 50985 ^ _779530 : [(50986 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1815984, 50984 ^ [_1815982, _1815984, _1816204])))], (50988 ^ _779530) ^ [] : [50984 ^ [_1815982, _1815984, _1816204] = _1816204]]]]], (50992 ^ _779530) ^ [] : [c_List_Olist__ex1(_1815982, _1815984, c_Enum_Oenum__class_Oenum(_1815982)), 50996 ^ _779530 : [(50997 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1815984, 50995 ^ [_1815982, _1815984])))], (50999 ^ _779530) ^ [_1816831] : [hBOOL(hAPP(_1815984, _1816831)), -(_1816831 = 50995 ^ [_1815982, _1815984])]]]]], (51005 ^ _779530) ^ [_1817126, _1817128, _1817130] : [c_List_Olist__ex1(_1817126, _1817128, _1817130), 51009 ^ _779530 : [(51010 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1817126), 51008 ^ [_1817126, _1817128, _1817130]), hAPP(c_List_Oset(_1817126), _1817130))))], (51012 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1817128, 51008 ^ [_1817126, _1817128, _1817130])))], (51014 ^ _779530) ^ [_1817594] : [-(_1817594 = 51008 ^ [_1817126, _1817128, _1817130]), hBOOL(hAPP(hAPP(c_member(_1817126), _1817594), hAPP(c_List_Oset(_1817126), _1817130))), hBOOL(hAPP(_1817128, _1817594))]]], (51024 ^ _779530) ^ [_1817926, _1817928, _1817930] : [-(c_List_Olist__ex1(_1817926, _1817928, _1817930)), 51025 ^ _779530 : [(51026 ^ _779530) ^ [_1818072] : [hBOOL(hAPP(hAPP(c_member(_1817926), _1818072), hAPP(c_List_Oset(_1817926), _1817930))), hBOOL(hAPP(_1817928, _1818072)), 51034 ^ _779530 : [(51035 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1817926), 51033 ^ [_1817926, _1817928, _1817930, _1818072]), hAPP(c_List_Oset(_1817926), _1817930))))], (51037 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1817928, 51033 ^ [_1817926, _1817928, _1817930, _1818072])))], (51039 ^ _779530) ^ [] : [51033 ^ [_1817926, _1817928, _1817930, _1818072] = _1818072]]]]], (51043 ^ _779530) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51045 ^ _779530) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51047 ^ _779530) ^ [_1818890, _1818892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 51048 ^ [_1818890, _1818892]), hAPP(_1818890, 51048 ^ [_1818890, _1818892]))), -(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)), _1818890)), _1818892)))))], (51054 ^ _779530) ^ [_1819230, _1819232, _1819234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1819230), _1819232)), hBOOL(hAPP(_1819234, c_Orderings_Obot__class_Obot(tc_fun(_1819230, tc_HOL_Obool)))), 51065 ^ _779530 : [(51066 ^ _779530) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1819230), 51064 ^ [_1819230, _1819232, _1819234])))], (51068 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1819230), 51063 ^ [_1819230, _1819232, _1819234]), 51064 ^ [_1819230, _1819232, _1819234]))], (51070 ^ _779530) ^ [] : [-(hBOOL(hAPP(_1819234, 51064 ^ [_1819230, _1819232, _1819234])))], (51072 ^ _779530) ^ [] : [hBOOL(hAPP(_1819234, hAPP(hAPP(c_Set_Oinsert(_1819230), 51063 ^ [_1819230, _1819232, _1819234]), 51064 ^ [_1819230, _1819232, _1819234])))]], -(hBOOL(hAPP(_1819234, _1819232)))], (51076 ^ _779530) ^ [] : [-(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))))], (51078 ^ _779530) ^ [_1820286, _1820288, _1820290, _1820292] : [class_HOL_Oequal(_1820286), class_Enum_Oenum(_1820288), 51085 ^ _779530 : [(51096 ^ _779530) ^ [] : [51098 ^ _779530 : [(51099 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1820288), 51097 ^ [_1820286, _1820288, _1820290, _1820292]), hAPP(c_List_Oset(_1820288), c_Enum_Oenum__class_Oenum(_1820288)))))], (51101 ^ _779530) ^ [] : [hAPP(_1820290, 51097 ^ [_1820286, _1820288, _1820290, _1820292]) = hAPP(_1820292, 51097 ^ [_1820286, _1820288, _1820290, _1820292])]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1820288, _1820286)), _1820290), _1820292)))], (51086 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1820288, _1820286)), _1820290), _1820292)), 51089 ^ _779530 : [(51090 ^ _779530) ^ [_1820686] : [hBOOL(hAPP(hAPP(c_member(_1820288), _1820686), hAPP(c_List_Oset(_1820288), c_Enum_Oenum__class_Oenum(_1820288)))), -(hAPP(_1820290, _1820686) = hAPP(_1820292, _1820686))]]]]], (51105 ^ _779530) ^ [_1821346, _1821348, _1821350] : [c_FunDef_Ois__measure(_1821346, _1821348), -(c_FunDef_Ois__measure(tc_prod(_1821346, _1821350), hAPP(hAPP(c_COMBB(_1821346, tc_Nat_Onat, tc_prod(_1821346, _1821350)), _1821348), c_Product__Type_Ofst(_1821346, _1821350))))], (51111 ^ _779530) ^ [_1821585, _1821587] : [-(c_FunDef_Ois__measure(_1821585, _1821587))], (51113 ^ _779530) ^ [_1821679, _1821681] : [-(c_FunDef_Ois__measure(_1821679, _1821681))], (51115 ^ _779530) ^ [_1821773, _1821775] : [-(c_FunDef_Ois__measure(_1821773, _1821775))], (51117 ^ _779530) ^ [_1821868] : [class_HOL_Oequal(_1821868), -(c_HOL_Oequal__class_Oequal(_1821868) = c_fequal)], (51123 ^ _779530) ^ [_1822074, _1822076] : [class_HOL_Oequal(_1822074), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1822074), _1822076), _1822076)))], (51129 ^ _779530) ^ [_1822310, _1822312, _1822314] : [class_HOL_Oequal(_1822310), 51132 ^ _779530 : [(51133 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1822310), _1822312), _1822314)), -(_1822312 = _1822314)], (51139 ^ _779530) ^ [] : [_1822312 = _1822314, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1822310), _1822312), _1822314)))]]], (51145 ^ _779530) ^ [_1822791] : [class_HOL_Oequal(_1822791), -(c_fequal = c_HOL_Oequal__class_Oequal(_1822791))], (51151 ^ _779530) ^ [_1822983] : [class_Nat_Osize(_1822983), -(c_FunDef_Ois__measure(_1822983, c_Nat_Osize__class_Osize(_1822983)))], (51157 ^ _779530) ^ [_1823203, _1823205, _1823207] : [c_FunDef_Ois__measure(_1823203, _1823205), -(c_FunDef_Ois__measure(tc_prod(_1823207, _1823203), hAPP(hAPP(c_COMBB(_1823203, tc_Nat_Onat, tc_prod(_1823207, _1823203)), _1823205), c_Product__Type_Osnd(_1823207, _1823203))))], (51163 ^ _779530) ^ [] : [-(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)))], (51165 ^ _779530) ^ [_1823572, _1823574, _1823576, _1823578, _1823580] : [_1823572 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1823574, _1823576, _1823578, _1823580), _1823572) = c_Lazy__Sequence_Ohit__bound(_1823576))], (51171 ^ _779530) ^ [_1823772, _1823774, _1823776, _1823778, _1823780] : 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hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1824273))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1824271), _1824273)))], (51187 ^ _779530) ^ [_1824465, _1824467] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1824465), _1824467)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1824465)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1824467))))], (51193 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (51195 ^ _779530) ^ [_1824791, _1824793] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1824791)), c_Int_OBit1(_1824793))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1824791), _1824793)))], (51201 ^ _779530) ^ [_1824981, _1824983] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1824981), _1824983)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1824981)), c_Int_OBit1(_1824983))))], (51207 ^ _779530) ^ [_1825250, _1825252] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1825250)), c_Int_OBit0(_1825252))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1825250), _1825252)))], (51213 ^ _779530) ^ [_1825440, _1825442] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1825440), _1825442)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1825440)), c_Int_OBit0(_1825442))))], (51219 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (51221 ^ _779530) ^ [_1825703] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1825703)))], (51223 ^ _779530) ^ [_1825784] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1825784)), c_Int_OPls))], (51225 ^ _779530) ^ [_1825927, _1825929] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1825927), _1825929)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1825927), _1825929) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51231 ^ _779530) ^ [_1826111, _1826113] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1826111), _1826113) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1826111), _1826113)))], (51237 ^ _779530) ^ [_1826329, _1826331] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1826329)), c_Int_OBit1(_1826331)))], (51239 ^ _779530) ^ [_1826431, _1826433] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1826431)), c_Int_OBit0(_1826433)))], (51241 ^ _779530) ^ [_1826564] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1826564))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1826564)))], (51247 ^ _779530) ^ [_1826732] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1826732)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1826732))))], (51253 ^ _779530) ^ [_1826965] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1826965)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1826965), c_Int_OPls)))], (51259 ^ _779530) ^ [_1827145] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1827145), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1827145)), c_Int_OPls)))], (51265 ^ _779530) ^ [_1827390] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1827390))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1827390)))], (51271 ^ _779530) ^ [_1827558] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1827558)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1827558))))], (51277 ^ _779530) ^ [_1827791] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1827791)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1827791), c_Int_OMin)))], (51283 ^ _779530) ^ [_1827971] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1827971), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1827971)), c_Int_OMin)))], (51289 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (51291 ^ _779530) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (51293 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51295 ^ _779530) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51297 ^ _779530) ^ [_1828466, _1828468, _1828470, _1828472, _1828474, _1828476, _1828478] : 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_1828476)), _1828478)))], (51299 ^ _779530) ^ [_1828694, _1828696, _1828698, _1828700, _1828702] : [-(hAPP(c_New__DSequence_Oneg__bind(_1828694, _1828696, _1828698, _1828700), _1828702) = c_Lazy__Sequence_Ohb__bind(_1828694, _1828696, hAPP(_1828698, _1828702), hAPP(hAPP(c_COMBC(_1828694, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1828696))), _1828700), _1828702)))], (51301 ^ _779530) ^ [_1828810] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1828810), _1828810)))], (51303 ^ _779530) ^ [_1828977, _1828979, _1828981, _1828983, _1828985, _1828987, _1828989] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1828977, _1828979, _1828981, _1828983), _1828985), _1828987), _1828989) = c_New__DSequence_Oneg__bind(_1828977, _1828979, hAPP(hAPP(hAPP(_1828981, _1828985), _1828987), _1828989), hAPP(hAPP(c_COMBC(_1828977, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, 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_1830296, _1830298, _1830300, _1830302] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1830294, _1830296, _1830298) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1830294, _1830300, _1830302), 51320 ^ _779530 : [(51321 ^ _779530) ^ [] : [-(_1830296 = _1830300)], (51323 ^ _779530) ^ [] : [-(_1830298 = _1830302)]]], (51325 ^ _779530) ^ [_1830571, _1830573, _1830575, _1830577, _1830579] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1830571, _1830573, _1830575) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1830571, _1830577, _1830579)), _1830573 = _1830577, _1830575 = _1830579], (51335 ^ _779530) ^ [_1830917, _1830919, _1830921] : [-(hAPP(c_Lazy__Sequence_Oyield(_1830917), c_Lazy__Sequence_Olazy__sequence_OInsert(_1830917, _1830919, _1830921)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1830917, tc_Lazy__Sequence_Olazy__sequence(_1830917))), hAPP(hAPP(c_Product__Type_OPair(_1830917, tc_Lazy__Sequence_Olazy__sequence(_1830917)), _1830919), _1830921)))], (51337 ^ _779530) ^ [_1831057, _1831059, _1831061] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1831057)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1831057, _1831059, _1831061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1831057)), _1831061)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51339 ^ _779530) ^ [_1831205, _1831207, _1831209, _1831211] : [-(c_New__Random__Sequence_Oneg__map(_1831205, _1831207, _1831209, _1831211) = c_New__Random__Sequence_Oneg__bind(_1831205, _1831207, _1831211, hAPP(c_Fun_Ocomp(_1831207, 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(_1831207)))))), _1831205, c_New__Random__Sequence_Oneg__single(_1831207)), _1831209)))], (51341 ^ _779530) ^ [_1831416, _1831418, _1831420, _1831422, _1831424] : [_1831416 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1831418, _1831420, _1831422, _1831424), _1831416) = c_Lazy__Sequence_Oempty(_1831420))], (51347 ^ _779530) ^ [_1831616, _1831618, _1831620, _1831622, _1831624] : [-(_1831616 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1831618, _1831620, _1831622, _1831624), _1831616) = c_Lazy__Sequence_Obind(_1831618, _1831620, hAPP(_1831622, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1831616), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1831618, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1831620)), _1831624), _1831616)))], (51353 ^ _779530) ^ [_1831972, _1831974, _1831976, _1831978, _1831980, _1831982, _1831984] : [-(c_New__Random__Sequence_Opos__decr__bind(_1831972, _1831974, _1831976, _1831978, _1831980, 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[class_Lattices_Obounded__lattice(_1832220), -(class_Lattices_Obounded__lattice(tc_fun(_1832222, _1832220)))], (51363 ^ _779530) ^ [_1832432, _1832434] : [class_Complete__Lattice_Ocomplete__lattice(_1832432), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1832434, _1832432)))], (51369 ^ _779530) ^ [_1832644, _1832646] : [class_Lattices_Obounded__lattice(_1832644), -(class_Lattices_Obounded__lattice__top(tc_fun(_1832646, _1832644)))], (51375 ^ _779530) ^ [_1832856, _1832858] : [class_Lattices_Obounded__lattice(_1832856), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1832858, _1832856)))], (51381 ^ _779530) ^ [_1833068, _1833070] : [class_Lattices_Olattice(_1833068), -(class_Lattices_Osemilattice__sup(tc_fun(_1833070, _1833068)))], (51387 ^ _779530) ^ [_1833280, _1833282] : [class_Lattices_Olattice(_1833280), -(class_Lattices_Osemilattice__inf(tc_fun(_1833282, _1833280)))], (51393 ^ _779530) ^ [_1833492, _1833494] : [class_Lattices_Odistrib__lattice(_1833492), 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[-(class_Divides_Osemiring__div(tc_Int_Oint))], (51561 ^ _779530) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (51563 ^ _779530) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51565 ^ _779530) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (51567 ^ _779530) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (51569 ^ _779530) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (51571 ^ _779530) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51573 ^ _779530) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51575 ^ _779530) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (51577 ^ _779530) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (51579 ^ _779530) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (51581 ^ _779530) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (51583 ^ _779530) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (51585 ^ _779530) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (51587 ^ _779530) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (51589 ^ _779530) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (51591 ^ _779530) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (51593 ^ _779530) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51595 ^ _779530) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51597 ^ _779530) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (51599 ^ _779530) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51601 ^ _779530) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (51603 ^ _779530) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51605 ^ _779530) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51607 ^ _779530) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (51609 ^ _779530) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51611 ^ _779530) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51613 ^ _779530) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (51615 ^ _779530) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (51617 ^ _779530) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (51619 ^ _779530) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (51621 ^ _779530) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (51623 ^ _779530) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (51625 ^ _779530) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (51627 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (51629 ^ _779530) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (51631 ^ _779530) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (51633 ^ _779530) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (51635 ^ _779530) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (51637 ^ _779530) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (51639 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (51641 ^ _779530) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51643 ^ _779530) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (51645 ^ _779530) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (51647 ^ _779530) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (51649 ^ _779530) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (51651 ^ _779530) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (51653 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (51655 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (51657 ^ _779530) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (51659 ^ _779530) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (51661 ^ _779530) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (51663 ^ _779530) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (51665 ^ _779530) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (51667 ^ _779530) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (51669 ^ _779530) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (51671 ^ _779530) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51673 ^ _779530) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (51675 ^ _779530) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (51677 ^ _779530) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (51679 ^ _779530) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (51681 ^ _779530) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (51683 ^ _779530) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (51685 ^ _779530) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (51687 ^ _779530) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (51689 ^ _779530) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (51691 ^ _779530) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (51693 ^ _779530) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (51695 ^ _779530) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (51697 ^ _779530) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (51699 ^ _779530) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (51701 ^ _779530) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (51703 ^ _779530) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (51705 ^ _779530) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (51707 ^ _779530) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (51709 ^ _779530) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (51711 ^ _779530) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (51713 ^ _779530) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (51715 ^ _779530) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (51717 ^ _779530) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (51719 ^ _779530) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (51721 ^ _779530) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51723 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (51725 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (51727 ^ _779530) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (51729 ^ _779530) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (51731 ^ _779530) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (51733 ^ _779530) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (51735 ^ _779530) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (51737 ^ _779530) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (51739 ^ _779530) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (51741 ^ _779530) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (51743 ^ _779530) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (51745 ^ _779530) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (51747 ^ _779530) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51749 ^ _779530) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (51751 ^ _779530) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51753 ^ _779530) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (51755 ^ _779530) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (51757 ^ _779530) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (51759 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (51761 ^ _779530) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (51763 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (51765 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (51767 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (51769 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Com_Ovname))], (51771 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Com_Ovname))], (51773 ^ _779530) ^ [_1844165] : [-(class_HOL_Oequal(tc_List_Olist(_1844165)))], (51775 ^ _779530) ^ [_1844244] : [-(class_Nat_Osize(tc_List_Olist(_1844244)))], (51777 ^ _779530) ^ [_1844352, _1844354] : [-(class_Finite__Set_Ofinite(tc_sum(_1844352, _1844354))), class_Finite__Set_Ofinite(_1844352), class_Finite__Set_Ofinite(_1844354)], (51787 ^ _779530) ^ [_1844636, _1844638] : [-(class_HOL_Oequal(tc_sum(_1844636, _1844638)))], (51789 ^ _779530) ^ [_1844747, _1844749] : [-(class_Enum_Oenum(tc_sum(_1844747, _1844749))), class_Enum_Oenum(_1844747), class_Enum_Oenum(_1844749)], (51799 ^ _779530) ^ [_1845031, _1845033] : [-(class_Nat_Osize(tc_sum(_1845031, _1845033)))], (51801 ^ _779530) ^ [_1845128] : [class_Finite__Set_Ofinite(_1845128), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1845128)))], (51807 ^ _779530) ^ [_1845303] : [-(class_HOL_Oequal(tc_Option_Ooption(_1845303)))], (51809 ^ _779530) ^ [_1845397] : [class_Enum_Oenum(_1845397), -(class_Enum_Oenum(tc_Option_Ooption(_1845397)))], (51815 ^ _779530) ^ [_1845572] : [-(class_Nat_Osize(tc_Option_Ooption(_1845572)))], (51817 ^ _779530) ^ [_1845680, _1845682] : [-(class_Finite__Set_Ofinite(tc_prod(_1845680, _1845682))), class_Finite__Set_Ofinite(_1845680), class_Finite__Set_Ofinite(_1845682)], (51827 ^ _779530) ^ [_1845979, _1845981] : [-(class_Smallcheck_Osmall(tc_prod(_1845979, _1845981))), class_Smallcheck_Osmall(_1845979), class_Smallcheck_Osmall(_1845981)], (51837 ^ _779530) ^ [_1846263, _1846265] : [-(class_HOL_Oequal(tc_prod(_1846263, _1846265)))], (51839 ^ _779530) ^ [_1846374, _1846376] : [-(class_Enum_Oenum(tc_prod(_1846374, _1846376))), class_Enum_Oenum(_1846374), class_Enum_Oenum(_1846376)], (51849 ^ _779530) ^ [_1846658, _1846660] : [-(class_Nat_Osize(tc_prod(_1846658, _1846660)))], (51851 ^ _779530) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (51853 ^ _779530) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (51855 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (51857 ^ _779530) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (51859 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (51861 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (51863 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (51865 ^ _779530) ^ [_1847111] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1847111)))], (51867 ^ _779530) ^ [_1847190] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1847190)))], (51869 ^ _779530) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51871 ^ _779530) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (51873 ^ _779530) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51875 ^ _779530) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51877 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (51879 ^ _779530) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51881 ^ _779530) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51883 ^ _779530) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51885 ^ _779530) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (51887 ^ _779530) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (51889 ^ _779530) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51891 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51893 ^ _779530) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (51895 ^ _779530) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (51897 ^ _779530) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (51899 ^ _779530) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (51901 ^ _779530) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (51903 ^ _779530) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (51905 ^ _779530) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (51907 ^ _779530) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (51909 ^ _779530) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (51911 ^ _779530) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (51913 ^ _779530) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (51915 ^ _779530) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (51917 ^ _779530) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (51919 ^ _779530) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (51921 ^ _779530) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (51923 ^ _779530) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (51925 ^ _779530) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (51927 ^ _779530) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (51929 ^ _779530) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (51931 ^ _779530) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (51933 ^ _779530) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (51935 ^ _779530) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (51937 ^ _779530) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (51939 ^ _779530) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (51941 ^ _779530) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (51943 ^ _779530) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (51945 ^ _779530) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (51947 ^ _779530) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (51949 ^ _779530) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (51951 ^ _779530) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (51953 ^ _779530) ^ [_1849495] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1849495)))], (51955 ^ _779530) ^ [_1849574] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1849574)))], (51957 ^ _779530) ^ [_1849667, _1849669] : [-(hAPP(c_COMBI(_1849667), _1849669) = _1849669)], (51959 ^ _779530) ^ [_1849794, _1849796, _1849798, _1849800] : [-(hAPP(hAPP(c_COMBK(_1849794, _1849796), _1849798), _1849800) = _1849798)], (51961 ^ _779530) ^ [_1849957, _1849959, _1849961, _1849963, _1849965, _1849967] : [-(hAPP(hAPP(hAPP(c_COMBB(_1849957, _1849959, _1849961), _1849963), _1849965), _1849967) = hAPP(_1849963, hAPP(_1849965, _1849967)))], (51963 ^ _779530) ^ [_1850134, _1850136, _1850138, _1850140, _1850142, _1850144] : [-(hAPP(hAPP(hAPP(c_COMBC(_1850134, _1850136, _1850138), _1850140), _1850142), _1850144) = hAPP(hAPP(_1850140, _1850144), _1850142))], (51965 ^ _779530) ^ [_1850311, _1850313, _1850315, _1850317, _1850319, _1850321] : [-(hAPP(hAPP(hAPP(c_COMBS(_1850311, _1850313, _1850315), _1850317), _1850319), _1850321) = hAPP(hAPP(_1850317, _1850321), hAPP(_1850319, _1850321)))], (51967 ^ _779530) ^ [_1850450, _1850452] : [hBOOL(hAPP(hAPP(c_fequal, _1850450), _1850452)), -(_1850450 = _1850452)], (51973 ^ _779530) ^ [_1850672, _1850674] : [_1850672 = _1850674, -(hBOOL(hAPP(hAPP(c_fequal, _1850672), _1850674)))], (51979 ^ _779530) ^ [] : [hBOOL(c_fFalse)], (51981 ^ _779530) ^ [] : [-(hBOOL(c_fTrue))], (51983 ^ _779530) ^ [_1850985] : [hBOOL(hAPP(c_fNot, _1850985)), hBOOL(_1850985)], (51989 ^ _779530) ^ [_1851180] : [-(hBOOL(_1851180)), -(hBOOL(hAPP(c_fNot, _1851180)))], (51995 ^ _779530) ^ [_1851391, _1851393] : [hBOOL(_1851391), hBOOL(_1851393), -(hBOOL(hAPP(hAPP(c_fconj, _1851391), _1851393)))], (52005 ^ _779530) ^ [_1851700, _1851702] : [hBOOL(hAPP(hAPP(c_fconj, _1851700), _1851702)), -(hBOOL(_1851700))], (52011 ^ _779530) ^ [_1851920, _1851922] : [hBOOL(hAPP(hAPP(c_fconj, _1851920), _1851922)), -(hBOOL(_1851922))], (52017 ^ _779530) ^ [_1852140, _1852142] : [hBOOL(_1852140), -(hBOOL(hAPP(hAPP(c_fdisj, _1852140), _1852142)))], (52023 ^ _779530) ^ [_1852360, _1852362] : [hBOOL(_1852360), -(hBOOL(hAPP(hAPP(c_fdisj, _1852362), _1852360)))], (52029 ^ _779530) ^ [_1852580, _1852582] : [hBOOL(hAPP(hAPP(c_fdisj, _1852580), _1852582)), -(hBOOL(_1852580)), -(hBOOL(_1852582))], (52039 ^ _779530) ^ [_1852888, _1852890] : [-(hBOOL(_1852888)), -(hBOOL(hAPP(hAPP(c_fimplies, _1852888), _1852890)))], (52045 ^ _779530) ^ [_1853107, _1853109] : [hBOOL(_1853107), -(hBOOL(hAPP(hAPP(c_fimplies, _1853109), _1853107)))], (52061 ^ _779530) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (52051 ^ _779530) ^ [_1853327, _1853329] : [hBOOL(hAPP(hAPP(c_fimplies, _1853327), _1853329)), hBOOL(_1853327), -(hBOOL(_1853329))]], input).
% 1.61/2.47  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), c_Hoare__Mirabelle_Otriple_Otriple(t_a, v_P, c_Com_Ocom_OSKIP, v_P)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool))))],start(52063 ^ 0)).
% 1.61/2.47  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), c_Hoare__Mirabelle_Otriple_Otriple(t_a, v_P, c_Com_Ocom_OSKIP, v_P)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))],extension(5575 ^ 1,bind([[_867618, _867620, _867622], [t_a, v_Ga, v_P]]))).
% 1.61/2.47  %-----------------------------------------------------
% 1.61/2.47  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------