%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW365+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n025.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 12:26:02 EDT 2023

% Result   : Theorem 142.73s 137.44s
% Output   : Proof 142.73s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW365+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:37:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 142.73/137.44  
% 142.73/137.44  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 142.73/137.44  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 142.73/137.44  %-----------------------------------------------------
% 142.73/137.44  ncf(matrix, plain, [(52825 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), v_G))], (2 ^ _779448) ^ [_779478] : [-(_779478 = _779478)], (4 ^ _779448) ^ [_779501, _779503] : [_779503 = _779501, -(_779501 = _779503)], (10 ^ _779448) ^ [_779574, _779576, _779578] : [-(_779578 = _779574), _779578 = _779576, _779576 = _779574], (20 ^ _779448) ^ [_779711, _779713, _779715, _779717, _779719, _779721, _779723, _779725, _779727, _779729, _779731, _779733] : [-(c_Nitpick_Ofold__graph_H(_779731, _779727, _779723, _779719, _779715, _779711)), c_Nitpick_Ofold__graph_H(_779733, _779729, _779725, _779721, _779717, _779713), _779733 = _779731, _779729 = _779727, _779725 = _779723, _779721 = _779719, _779717 = _779715, _779713 = _779711], (50 ^ _779448) ^ [_780256, _780258, _780260, _780262] : [-(c_Int_Oiszero(_780260, _780256)), c_Int_Oiszero(_780262, _780258), _780262 = _780260, _780258 = _780256], (64 ^ _779448) ^ [_780449, _780451, _780453, _780455, _780457, _780459] : [-(c_Big__Operators_Osemilattice__big(_780457, _780453, _780449)), c_Big__Operators_Osemilattice__big(_780459, _780455, _780451), _780459 = _780457, _780455 = _780453, _780451 = _780449], (82 ^ _779448) ^ [_780718, _780720, _780722, _780724, _780726, _780728, _780730, _780732, _780734, _780736] : [-(c_Big__Operators_Ocomm__monoid__big(_780734, _780730, _780726, _780722, _780718)), c_Big__Operators_Ocomm__monoid__big(_780736, _780732, _780728, _780724, _780720), _780736 = _780734, _780732 = _780730, _780728 = _780726, _780724 = _780722, _780720 = _780718], (108 ^ _779448) ^ [_781163, _781165, _781167, _781169] : [-(c_Nitpick_Orefl_H(_781167, _781163)), c_Nitpick_Orefl_H(_781169, _781165), _781169 = _781167, _781165 = _781163], (122 ^ _779448) ^ [_781356, _781358] : [-(class_Rings_Odivision__ring__inverse__zero(_781356)), _781358 = _781356, class_Rings_Odivision__ring__inverse__zero(_781358)], (132 ^ _779448) ^ [_781481, _781483] : [-(class_Rings_Odivision__ring(_781481)), _781483 = _781481, class_Rings_Odivision__ring(_781483)], (142 ^ _779448) ^ [_781606, _781608] : [-(class_Fields_Ofield__inverse__zero(_781606)), _781608 = _781606, class_Fields_Ofield__inverse__zero(_781608)], (152 ^ _779448) ^ [_781731, _781733, _781735, _781737, _781739, _781741, _781743, _781745, _781747, _781749, _781751, _781753] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781751, _781747, _781743, _781739, _781735, _781731)), c_Finite__Set_Ofolding__image__simple__idem(_781753, _781749, _781745, _781741, _781737, _781733), _781753 = _781751, _781749 = _781747, _781745 = _781743, _781741 = _781739, _781737 = _781735, _781733 = _781731], (182 ^ _779448) ^ [_782276, _782278, _782280, _782282, _782284, _782286] : [-(c_Finite__Set_Ofolding__one__idem(_782284, _782280, _782276)), c_Finite__Set_Ofolding__one__idem(_782286, _782282, _782278), _782286 = _782284, _782282 = _782280, _782278 = _782276], (200 ^ _779448) ^ [_782545, _782547, _782549, _782551, _782553, _782555, _782557, _782559] : [-(c_Finite__Set_Ofolding__idem(_782557, _782553, _782549, _782545)), c_Finite__Set_Ofolding__idem(_782559, _782555, _782551, _782547), _782559 = _782557, _782555 = _782553, _782551 = _782549, _782547 = _782545], (222 ^ _779448) ^ [_782898, _782900] : [-(c_Nat__Transfer_Ois__nat(_782898)), _782900 = _782898, c_Nat__Transfer_Ois__nat(_782900)], (232 ^ _779448) ^ [_783023, _783025, _783027, _783029, _783031, _783033] : [-(c_Finite__Set_Ofolding__one(_783031, _783027, _783023)), c_Finite__Set_Ofolding__one(_783033, _783029, _783025), _783033 = _783031, _783029 = _783027, _783025 = _783023], (250 ^ _779448) ^ [_783292, _783294] : [-(class_Fields_Ofield(_783292)), _783294 = _783292, class_Fields_Ofield(_783294)], (260 ^ _779448) ^ [_783417, _783419] : [-(class_Fields_Olinordered__field__inverse__zero(_783417)), _783419 = _783417, class_Fields_Olinordered__field__inverse__zero(_783419)], (270 ^ _779448) ^ [_783542, _783544, _783546, _783548, _783550, _783552, _783554, _783556, _783558, _783560, _783562, _783564] : [-(c_Finite__Set_Ofolding__image__simple(_783562, _783558, _783554, _783550, _783546, _783542)), c_Finite__Set_Ofolding__image__simple(_783564, _783560, _783556, _783552, _783548, _783544), _783564 = _783562, _783560 = _783558, _783556 = _783554, _783552 = _783550, _783548 = _783546, _783544 = _783542], (300 ^ _779448) ^ [_784087, _784089, _784091, _784093, _784095, _784097, _784099, _784101] : [-(c_Finite__Set_Ofolding(_784099, _784095, _784091, _784087)), c_Finite__Set_Ofolding(_784101, _784097, _784093, _784089), _784101 = _784099, _784097 = _784095, _784093 = _784091, _784089 = _784087], (322 ^ _779448) ^ [_784440, _784442, _784444, _784446] : [-(c_FunDef_Oreduction__pair(_784444, _784440)), c_FunDef_Oreduction__pair(_784446, _784442), _784446 = _784444, _784442 = _784440], (336 ^ _779448) ^ [_784633, _784635, _784637, _784639] : [-(c_Nitpick_Owf_H(_784637, _784633)), c_Nitpick_Owf_H(_784639, _784635), _784639 = _784637, _784635 = _784633], (350 ^ _779448) ^ [_784826, _784828] : [-(c_Nitpick_Ounknown(_784826)), _784828 = _784826, c_Nitpick_Ounknown(_784828)], (360 ^ _779448) ^ [_784951, _784953, _784955, _784957] : [-(c_Wellfounded_OwfP(_784955, _784951)), c_Wellfounded_OwfP(_784957, _784953), _784957 = _784955, _784953 = _784951], (374 ^ _779448) ^ [_785144, _785146, _785148, _785150] : [-(c_Relation_Oirrefl(_785148, _785144)), c_Relation_Oirrefl(_785150, _785146), _785150 = _785148, _785146 = _785144], (388 ^ _779448) ^ [_785337, _785339, _785341, _785343, _785345, _785347] : [-(c_Relation_Osingle__valued(_785345, _785341, _785337)), c_Relation_Osingle__valued(_785347, _785343, _785339), _785347 = _785345, _785343 = _785341, _785339 = _785337], (406 ^ _779448) ^ [_785606, _785608, _785610, _785612, _785614, _785616] : [-(c_Relation_Ototal__on(_785614, _785610, _785606)), c_Relation_Ototal__on(_785616, _785612, _785608), _785616 = _785614, _785612 = _785610, _785608 = _785606], (424 ^ _779448) ^ [_785875, _785877] : [-(class_Rings_Oinverse(_785875)), _785877 = _785875, class_Rings_Oinverse(_785877)], (434 ^ _779448) ^ [_786000, _786002, _786004, _786006, _786008, _786010] : [-(c_Nitpick_Oless__frac(_786008, _786004, _786000)), c_Nitpick_Oless__frac(_786010, _786006, _786002), _786010 = _786008, _786006 = _786004, _786002 = _786000], (452 ^ _779448) ^ [_786269, _786271, _786273, _786275, _786277, _786279] : [-(c_Nitpick_Oless__eq__frac(_786277, _786273, _786269)), c_Nitpick_Oless__eq__frac(_786279, _786275, _786271), _786279 = _786277, _786275 = _786273, _786271 = _786269], (470 ^ _779448) ^ [_786538, _786540] : [-(c_Nat__Transfer_Onat__set(_786538)), _786540 = _786538, c_Nat__Transfer_Onat__set(_786540)], (480 ^ _779448) ^ [_786663, _786665, _786667, _786669, _786671, _786673, _786675, _786677] : [-(c_List_Olistrelp(_786675, _786671, _786667, _786663)), c_List_Olistrelp(_786677, _786673, _786669, _786665), _786677 = _786675, _786673 = _786671, _786669 = _786667, _786665 = _786663], (502 ^ _779448) ^ [_787016, _787018] : [-(class_Lattices_Oab__semigroup__idem__mult(_787016)), _787018 = _787016, class_Lattices_Oab__semigroup__idem__mult(_787018)], (512 ^ _779448) ^ [_787141, _787143, _787145, _787147, _787149, _787151] : [-(c_Finite__Set_Ofun__left__comm__idem(_787149, _787145, _787141)), c_Finite__Set_Ofun__left__comm__idem(_787151, _787147, _787143), _787151 = _787149, _787147 = _787145, _787143 = _787141], (530 ^ _779448) ^ [_787410, _787412, _787414, _787416, _787418, _787420, _787422, _787424, _787426, _787428] : [-(c_Typedef_Otype__definition(_787426, _787422, _787418, _787414, _787410)), c_Typedef_Otype__definition(_787428, _787424, _787420, _787416, _787412), _787428 = _787426, _787424 = _787422, _787420 = _787418, _787416 = _787414, _787412 = _787410], (556 ^ _779448) ^ [_787855, _787857, _787859, _787861, _787863, _787865] : [-(c_Finite__Set_Ofun__left__comm(_787863, _787859, _787855)), c_Finite__Set_Ofun__left__comm(_787865, _787861, _787857), _787865 = _787863, _787861 = _787859, _787857 = _787855], (574 ^ _779448) ^ [_788124, _788126] : [-(c_List_Onat__list(_788124)), _788126 = _788124, c_List_Onat__list(_788126)], (584 ^ _779448) ^ [_788249, _788251, _788253, _788255, _788257, _788259, _788261, _788263, _788265, _788267] : [-(c_List_Olist__all2(_788265, _788261, _788257, _788253, _788249)), c_List_Olist__all2(_788267, _788263, _788259, _788255, _788251), _788267 = _788265, _788263 = _788261, _788259 = _788257, _788255 = _788253, _788251 = _788249], (610 ^ _779448) ^ [_788694, _788696, _788698, _788700] : [-(c_List_Olinorder__class_Osorted(_788698, _788694)), c_List_Olinorder__class_Osorted(_788700, _788696), _788700 = _788698, _788696 = _788694], (624 ^ _779448) ^ [_788887, _788889, _788891, _788893] : [-(c_FunDef_Ois__measure(_788891, _788887)), c_FunDef_Ois__measure(_788893, _788889), _788893 = _788891, _788889 = _788887], (638 ^ _779448) ^ [_789080, _789082, _789084, _789086, _789088, _789090, _789092, _789094] : [-(c_Nat__Transfer_Otransfer__morphism(_789092, _789088, _789084, _789080)), c_Nat__Transfer_Otransfer__morphism(_789094, _789090, _789086, _789082), _789094 = _789092, _789090 = _789088, _789086 = _789084, _789082 = _789080], (660 ^ _779448) ^ [_789433, _789435] : [-(class_Fields_Olinordered__field(_789433)), _789435 = _789433, class_Fields_Olinordered__field(_789435)], (670 ^ _779448) ^ [_789558, _789560, _789562, _789564, _789566, _789568] : [-(c_List_Olist__ex1(_789566, _789562, _789558)), c_List_Olist__ex1(_789568, _789564, _789560), _789568 = _789566, _789564 = _789562, _789560 = _789558], (688 ^ _779448) ^ [_789827, _789829, _789831, _789833, _789835, _789837] : [-(c_List_Oall__interval__int(_789835, _789831, _789827)), c_List_Oall__interval__int(_789837, _789833, _789829), _789837 = _789835, _789833 = _789831, _789829 = _789827], (706 ^ _779448) ^ [_790096, _790098, _790100, _790102] : [-(c_Predicate_Oreflp(_790100, _790096)), c_Predicate_Oreflp(_790102, _790098), _790102 = _790100, _790098 = _790096], (720 ^ _779448) ^ [_790289, _790291, _790293, _790295, _790297, _790299, _790301, _790303] : [-(c_Wellfounded_Omax__extp(_790301, _790297, _790293, _790289)), c_Wellfounded_Omax__extp(_790303, _790299, _790295, _790291), _790303 = _790301, _790299 = _790297, _790295 = _790293, _790291 = _790289], (742 ^ _779448) ^ [_790642, _790644, _790646, _790648] : [-(c_Wellfounded_Oacyclic(_790646, _790642)), c_Wellfounded_Oacyclic(_790648, _790644), _790648 = _790646, _790644 = _790642], (756 ^ _779448) ^ [_790835, _790837, _790839, _790841] : [-(c_Relation_Oantisym(_790839, _790835)), c_Relation_Oantisym(_790841, _790837), _790841 = _790839, _790837 = _790835], (770 ^ _779448) ^ [_791028, _791030, _791032, _791034] : [-(c_Relation_Otrans(_791032, _791028)), c_Relation_Otrans(_791034, _791030), _791034 = _791032, _791030 = _791028], (784 ^ _779448) ^ [_791221, _791223, _791225, _791227] : [-(c_Relation_Osym(_791225, _791221)), c_Relation_Osym(_791227, _791223), _791227 = _791225, _791223 = _791221], (798 ^ _779448) ^ [_791414, _791416, _791418, _791420] : [-(c_Predicate_Osymp(_791418, _791414)), c_Predicate_Osymp(_791420, _791416), _791420 = _791418, _791416 = _791414], (812 ^ _779448) ^ [_791607, _791609, _791611, _791613] : [-(c_Predicate_Otransp(_791611, _791607)), c_Predicate_Otransp(_791613, _791609), _791613 = _791611, _791609 = _791607], (826 ^ _779448) ^ [_791800, _791802, _791804, _791806] : [-(c_Equiv__Relations_Opart__equivp(_791804, _791800)), c_Equiv__Relations_Opart__equivp(_791806, _791802), _791806 = _791804, _791802 = _791800], (840 ^ _779448) ^ [_791993, _791995, _791997, _791999, _792001, _792003, _792005, _792007] : [-(c_Fun_Oinj__on(_792005, _792001, _791997, _791993)), c_Fun_Oinj__on(_792007, _792003, _791999, _791995), _792007 = _792005, _792003 = _792001, _791999 = _791997, _791995 = _791993], (862 ^ _779448) ^ [_792346, _792348, _792350, _792352, _792354, _792356, _792358, _792360, _792362, _792364] : [-(c_Fun_Obij__betw(_792362, _792358, _792354, _792350, _792346)), c_Fun_Obij__betw(_792364, _792360, _792356, _792352, _792348), _792364 = _792362, _792360 = _792358, _792356 = _792354, _792352 = _792350, _792348 = _792346], (888 ^ _779448) ^ [_792791, _792793, _792795, _792797, _792799, _792801] : [-(c_Relation_Orefl__on(_792799, _792795, _792791)), c_Relation_Orefl__on(_792801, _792797, _792793), _792801 = _792799, _792797 = _792795, _792793 = _792791], (906 ^ _779448) ^ [_793060, _793062, _793064, _793066] : [-(c_Equiv__Relations_Oequivp(_793064, _793060)), c_Equiv__Relations_Oequivp(_793066, _793062), _793066 = _793064, _793062 = _793060], (920 ^ _779448) ^ [_793253, _793255, _793257, _793259] : [-(c_Wellfounded_Owf(_793257, _793253)), c_Wellfounded_Owf(_793259, _793255), _793259 = _793257, _793255 = _793253], (934 ^ _779448) ^ [_793446, _793448, _793450, _793452, _793454, _793456, _793458, _793460] : [-(c_Equiv__Relations_Ocongruent(_793458, _793454, _793450, _793446)), c_Equiv__Relations_Ocongruent(_793460, _793456, _793452, _793448), _793460 = _793458, _793456 = _793454, _793452 = _793450, _793448 = _793446], (956 ^ _779448) ^ [_793799, _793801, _793803, _793805, _793807, _793809, _793811, _793813, _793815, _793817, _793819, _793821] : [-(c_Equiv__Relations_Ocongruent2(_793819, _793815, _793811, _793807, _793803, _793799)), c_Equiv__Relations_Ocongruent2(_793821, _793817, _793813, _793809, _793805, _793801), _793821 = _793819, _793817 = _793815, _793813 = _793811, _793809 = _793807, _793805 = _793803, _793801 = _793799], (986 ^ _779448) ^ [_794344, _794346, _794348, _794350, _794352, _794354] : [-(c_List_Olist__all(_794352, _794348, _794344)), c_List_Olist__all(_794354, _794350, _794346), _794354 = _794352, _794350 = _794348, _794346 = _794344], (1004 ^ _779448) ^ [_794613, _794615, _794617, _794619, _794621, _794623] : [-(c_List_Olist__ex(_794621, _794617, _794613)), c_List_Olist__ex(_794623, _794619, _794615), _794623 = _794621, _794619 = _794617, _794615 = _794613], (1022 ^ _779448) ^ [_794882, _794884, _794886, _794888, _794890, _794892] : [-(c_List_Oall__interval__nat(_794890, _794886, _794882)), c_List_Oall__interval__nat(_794892, _794888, _794884), _794892 = _794890, _794888 = _794886, _794884 = _794882], (1040 ^ _779448) ^ [_795151, _795153, _795155, _795157, _795159, _795161, _795163, _795165, _795167, _795169] : [-(c_Finite__Set_Ofolding__image(_795167, _795163, _795159, _795155, _795151)), c_Finite__Set_Ofolding__image(_795169, _795165, _795161, _795157, _795153), _795169 = _795167, _795165 = _795163, _795161 = _795159, _795157 = _795155, _795153 = _795151], (1066 ^ _779448) ^ [_795596, _795598, _795600, _795602, _795604, _795606, _795608, _795610] : [-(c_Orderings_Oorder_Ostrict__mono(_795608, _795604, _795600, _795596)), c_Orderings_Oorder_Ostrict__mono(_795610, _795606, _795602, _795598), _795610 = _795608, _795606 = _795604, _795602 = _795600, _795598 = _795596], (1088 ^ _779448) ^ [_795949, _795951, _795953, _795955, _795957, _795959] : [-(c_Equiv__Relations_Oequiv(_795957, _795953, _795949)), c_Equiv__Relations_Oequiv(_795959, _795955, _795951), _795959 = _795957, _795955 = _795953, _795951 = _795949], (1106 ^ _779448) ^ [_796218, _796220] : [-(class_Lattices_Obounded__lattice(_796218)), _796220 = _796218, class_Lattices_Obounded__lattice(_796220)], (1116 ^ _779448) ^ [_796343, _796345] : [-(class_Rings_Olinordered__semiring__1__strict(_796343)), _796345 = _796343, class_Rings_Olinordered__semiring__1__strict(_796345)], (1126 ^ _779448) ^ [_796468, _796470] : [-(class_Groups_Oordered__ab__group__add__abs(_796468)), _796470 = _796468, class_Groups_Oordered__ab__group__add__abs(_796470)], (1136 ^ _779448) ^ [_796593, _796595] : [-(class_Groups_Olinordered__ab__group__add(_796593)), _796595 = _796593, class_Groups_Olinordered__ab__group__add(_796595)], (1146 ^ _779448) ^ [_796718, _796720] : [-(class_Rings_Oring__1__no__zero__divisors(_796718)), _796720 = _796718, class_Rings_Oring__1__no__zero__divisors(_796720)], (1156 ^ _779448) ^ [_796843, _796845] : [-(class_Rings_Olinordered__ring__strict(_796843)), _796845 = _796843, class_Rings_Olinordered__ring__strict(_796845)], (1166 ^ _779448) ^ [_796968, _796970] : [-(class_Rings_Oring__no__zero__divisors(_796968)), _796970 = _796968, class_Rings_Oring__no__zero__divisors(_796970)], (1176 ^ _779448) ^ [_797093, _797095] : [-(class_Rings_Olinordered__semiring__1(_797093)), _797095 = _797093, class_Rings_Olinordered__semiring__1(_797095)], (1186 ^ _779448) ^ [_797218, _797220] : [-(class_Groups_Oordered__ab__group__add(_797218)), _797220 = _797218, class_Groups_Oordered__ab__group__add(_797220)], (1196 ^ _779448) ^ [_797343, _797345] : [-(class_Rings_Oordered__ring__abs(_797343)), _797345 = _797343, class_Rings_Oordered__ring__abs(_797345)], (1206 ^ _779448) ^ [_797468, _797470] : [-(class_Rings_Olinordered__ring(_797468)), _797470 = _797468, class_Rings_Olinordered__ring(_797470)], (1216 ^ _779448) ^ [_797593, _797595] : [-(class_Rings_Olinordered__idom(_797593)), _797595 = _797593, class_Rings_Olinordered__idom(_797595)], (1226 ^ _779448) ^ [_797718, _797720] : [-(class_Groups_Oab__group__add(_797718)), _797720 = _797718, class_Groups_Oab__group__add(_797720)], (1236 ^ _779448) ^ [_797843, _797845] : [-(class_Rings_Oordered__ring(_797843)), _797845 = _797843, class_Rings_Oordered__ring(_797845)], (1246 ^ _779448) ^ [_797968, _797970] : [-(class_Rings_Ocomm__ring__1(_797968)), _797970 = _797968, class_Rings_Ocomm__ring__1(_797970)], (1256 ^ _779448) ^ [_798093, _798095] : [-(class_Groups_Ogroup__add(_798093)), _798095 = _798093, class_Groups_Ogroup__add(_798095)], (1266 ^ _779448) ^ [_798218, _798220] : [-(class_Divides_Oring__div(_798218)), _798220 = _798218, class_Divides_Oring__div(_798220)], (1276 ^ _779448) ^ [_798343, _798345] : [-(class_Rings_Ocomm__ring(_798343)), _798345 = _798343, class_Rings_Ocomm__ring(_798345)], (1286 ^ _779448) ^ [_798468, _798470] : [-(class_Int_Oring__char__0(_798468)), _798470 = _798468, class_Int_Oring__char__0(_798470)], (1296 ^ _779448) ^ [_798593, _798595] : [-(class_Int_Onumber__ring(_798593)), _798595 = _798593, class_Int_Onumber__ring(_798595)], (1306 ^ _779448) ^ [_798718, _798720] : [-(class_Groups_Osgn__if(_798718)), _798720 = _798718, class_Groups_Osgn__if(_798720)], (1316 ^ _779448) ^ [_798843, _798845] : [-(class_Groups_Oabs__if(_798843)), _798845 = _798843, class_Groups_Oabs__if(_798845)], (1326 ^ _779448) ^ [_798968, _798970] : [-(class_Rings_Oring__1(_798968)), _798970 = _798968, class_Rings_Oring__1(_798970)], (1336 ^ _779448) ^ [_799093, _799095] : [-(class_Rings_Oring(_799093)), _799095 = _799093, class_Rings_Oring(_799095)], (1346 ^ _779448) ^ [_799218, _799220] : [-(class_Rings_Oidom(_799218)), _799220 = _799218, class_Rings_Oidom(_799220)], (1356 ^ _779448) ^ [_799343, _799345] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799343)), _799345 = _799343, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799345)], (1366 ^ _779448) ^ [_799468, _799470] : [-(class_Orderings_Owellorder(_799468)), _799470 = _799468, class_Orderings_Owellorder(_799470)], (1376 ^ _779448) ^ [_799593, _799595] : [-(class_Complete__Lattice_Ocomplete__lattice(_799593)), _799595 = _799593, class_Complete__Lattice_Ocomplete__lattice(_799595)], (1386 ^ _779448) ^ [_799718, _799720] : [-(class_Lattices_Obounded__lattice__top(_799718)), _799720 = _799718, class_Lattices_Obounded__lattice__top(_799720)], (1396 ^ _779448) ^ [_799843, _799845] : [-(class_Lattices_Obounded__lattice__bot(_799843)), _799845 = _799843, class_Lattices_Obounded__lattice__bot(_799845)], (1406 ^ _779448) ^ [_799968, _799970] : [-(class_Lattices_Osemilattice__sup(_799968)), _799970 = _799968, class_Lattices_Osemilattice__sup(_799970)], (1416 ^ _779448) ^ [_800093, _800095] : [-(class_Lattices_Osemilattice__inf(_800093)), _800095 = _800093, class_Lattices_Osemilattice__inf(_800095)], (1426 ^ _779448) ^ [_800218, _800220] : [-(class_Lattices_Odistrib__lattice(_800218)), _800220 = _800218, class_Lattices_Odistrib__lattice(_800220)], (1436 ^ _779448) ^ [_800343, _800345] : [-(class_Lattices_Oboolean__algebra(_800343)), _800345 = _800343, class_Lattices_Oboolean__algebra(_800345)], (1446 ^ _779448) ^ [_800468, _800470] : [-(class_Lattices_Olattice(_800468)), _800470 = _800468, class_Lattices_Olattice(_800470)], (1456 ^ _779448) ^ [_800593, _800595] : [-(class_Orderings_Otop(_800593)), _800595 = _800593, class_Orderings_Otop(_800595)], (1466 ^ _779448) ^ [_800718, _800720] : [-(class_Orderings_Obot(_800718)), _800720 = _800718, class_Orderings_Obot(_800720)], (1476 ^ _779448) ^ [_800843, _800845] : [-(class_Groups_Ouminus(_800843)), _800845 = _800843, class_Groups_Ouminus(_800845)], (1486 ^ _779448) ^ [_800968, _800970] : [-(class_Lazy__Sequence_Osmall__lazy(_800968)), _800970 = _800968, class_Lazy__Sequence_Osmall__lazy(_800970)], (1496 ^ _779448) ^ [_801093, _801095] : [-(class_Finite__Set_Ofinite(_801093)), _801095 = _801093, class_Finite__Set_Ofinite(_801095)], (1506 ^ _779448) ^ [_801218, _801220] : [-(class_Enum_Oenum(_801218)), _801220 = _801218, class_Enum_Oenum(_801220)], (1516 ^ _779448) ^ [_801343, _801345] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801343)), _801345 = _801343, class_Groups_Oordered__cancel__ab__semigroup__add(_801345)], (1526 ^ _779448) ^ [_801468, _801470] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801468)), _801470 = _801468, class_Groups_Oordered__ab__semigroup__add__imp__le(_801470)], (1536 ^ _779448) ^ [_801593, _801595] : [-(class_Rings_Olinordered__comm__semiring__strict(_801593)), _801595 = _801593, class_Rings_Olinordered__comm__semiring__strict(_801595)], (1546 ^ _779448) ^ [_801718, _801720] : [-(class_Groups_Olinordered__ab__semigroup__add(_801718)), _801720 = _801718, class_Groups_Olinordered__ab__semigroup__add(_801720)], (1556 ^ _779448) ^ [_801843, _801845] : [-(class_Rings_Olinordered__semiring__strict(_801843)), _801845 = _801843, class_Rings_Olinordered__semiring__strict(_801845)], (1566 ^ _779448) ^ [_801968, _801970] : [-(class_Groups_Oordered__ab__semigroup__add(_801968)), _801970 = _801968, class_Groups_Oordered__ab__semigroup__add(_801970)], (1576 ^ _779448) ^ [_802093, _802095] : [-(class_Groups_Oordered__comm__monoid__add(_802093)), _802095 = _802093, class_Groups_Oordered__comm__monoid__add(_802095)], (1586 ^ _779448) ^ [_802218, _802220] : [-(class_Groups_Ocancel__ab__semigroup__add(_802218)), _802220 = _802218, class_Groups_Ocancel__ab__semigroup__add(_802220)], (1596 ^ _779448) ^ [_802343, _802345] : [-(class_Rings_Oordered__cancel__semiring(_802343)), _802345 = _802343, class_Rings_Oordered__cancel__semiring(_802345)], (1606 ^ _779448) ^ [_802468, _802470] : [-(class_Rings_Oordered__comm__semiring(_802468)), _802470 = _802468, class_Rings_Oordered__comm__semiring(_802470)], (1616 ^ _779448) ^ [_802593, _802595] : [-(class_Groups_Ocancel__semigroup__add(_802593)), _802595 = _802593, class_Groups_Ocancel__semigroup__add(_802595)], (1626 ^ _779448) ^ [_802718, _802720] : [-(class_Rings_Olinordered__semiring(_802718)), _802720 = _802718, class_Rings_Olinordered__semiring(_802720)], (1636 ^ _779448) ^ [_802843, _802845] : [-(class_Rings_Olinordered__semidom(_802843)), _802845 = _802843, class_Rings_Olinordered__semidom(_802845)], (1646 ^ _779448) ^ [_802968, _802970] : [-(class_Groups_Oab__semigroup__mult(_802968)), _802970 = _802968, class_Groups_Oab__semigroup__mult(_802970)], (1656 ^ _779448) ^ [_803093, _803095] : [-(class_Groups_Ocomm__monoid__mult(_803093)), _803095 = _803093, class_Groups_Ocomm__monoid__mult(_803095)], (1666 ^ _779448) ^ [_803218, _803220] : [-(class_Groups_Oab__semigroup__add(_803218)), _803220 = _803218, class_Groups_Oab__semigroup__add(_803220)], (1676 ^ _779448) ^ [_803343, _803345] : [-(class_Rings_Oordered__semiring(_803343)), _803345 = _803343, class_Rings_Oordered__semiring(_803345)], (1686 ^ _779448) ^ [_803468, _803470] : [-(class_Rings_Ono__zero__divisors(_803468)), _803470 = _803468, class_Rings_Ono__zero__divisors(_803470)], (1696 ^ _779448) ^ [_803593, _803595] : [-(class_Groups_Ocomm__monoid__add(_803593)), _803595 = _803593, class_Groups_Ocomm__monoid__add(_803595)], (1706 ^ _779448) ^ [_803718, _803720] : [-(class_Rings_Ocomm__semiring__1(_803718)), _803720 = _803718, class_Rings_Ocomm__semiring__1(_803720)], (1716 ^ _779448) ^ [_803843, _803845] : [-(class_Groups_Osemigroup__add(_803843)), _803845 = _803843, class_Groups_Osemigroup__add(_803845)], (1726 ^ _779448) ^ [_803968, _803970] : [-(class_Divides_Osemiring__div(_803968)), _803970 = _803968, class_Divides_Osemiring__div(_803970)], (1736 ^ _779448) ^ [_804093, _804095] : [-(class_Rings_Ocomm__semiring(_804093)), _804095 = _804093, class_Rings_Ocomm__semiring(_804095)], (1746 ^ _779448) ^ [_804218, _804220] : [-(class_Nat_Osemiring__char__0(_804218)), _804220 = _804218, class_Nat_Osemiring__char__0(_804220)], (1756 ^ _779448) ^ [_804343, _804345] : [-(class_Rings_Ozero__neq__one(_804343)), _804345 = _804343, class_Rings_Ozero__neq__one(_804345)], (1766 ^ _779448) ^ [_804468, _804470] : [-(class_Orderings_Opreorder(_804468)), _804470 = _804468, class_Orderings_Opreorder(_804470)], (1776 ^ _779448) ^ [_804593, _804595] : [-(class_Orderings_Olinorder(_804593)), _804595 = _804593, class_Orderings_Olinorder(_804595)], (1786 ^ _779448) ^ [_804718, _804720] : [-(class_Groups_Omonoid__mult(_804718)), _804720 = _804718, class_Groups_Omonoid__mult(_804720)], (1796 ^ _779448) ^ [_804843, _804845] : [-(class_Groups_Omonoid__add(_804843)), _804845 = _804843, class_Groups_Omonoid__add(_804845)], (1806 ^ _779448) ^ [_804968, _804970] : [-(class_Rings_Osemiring__1(_804968)), _804970 = _804968, class_Rings_Osemiring__1(_804970)], (1816 ^ _779448) ^ [_805093, _805095] : [-(class_Rings_Osemiring__0(_805093)), _805095 = _805093, class_Rings_Osemiring__0(_805095)], (1826 ^ _779448) ^ [_805218, _805220] : [-(class_Rings_Omult__zero(_805218)), _805220 = _805218, class_Rings_Omult__zero(_805220)], (1836 ^ _779448) ^ [_805343, _805345] : [-(class_Orderings_Oorder(_805343)), _805345 = _805343, class_Orderings_Oorder(_805345)], (1846 ^ _779448) ^ [_805468, _805470] : [-(class_Rings_Osemiring(_805468)), _805470 = _805468, class_Rings_Osemiring(_805470)], (1856 ^ _779448) ^ [_805593, _805595] : [-(class_Orderings_Oord(_805593)), _805595 = _805593, class_Orderings_Oord(_805595)], (1866 ^ _779448) ^ [_805718, _805720] : [-(class_Groups_Ominus(_805718)), _805720 = _805718, class_Groups_Ominus(_805720)], (1876 ^ _779448) ^ [_805843, _805845] : [-(class_Power_Opower(_805843)), _805845 = _805843, class_Power_Opower(_805845)], (1886 ^ _779448) ^ [_805968, _805970] : [-(class_Groups_Ozero(_805968)), _805970 = _805968, class_Groups_Ozero(_805970)], (1896 ^ _779448) ^ [_806093, _806095] : [-(class_Int_Onumber(_806093)), _806095 = _806093, class_Int_Onumber(_806095)], (1906 ^ _779448) ^ [_806218, _806220] : [-(class_Groups_Oone(_806218)), _806220 = _806218, class_Groups_Oone(_806220)], (1916 ^ _779448) ^ [_806343, _806345] : [-(class_Rings_Odvd(_806343)), _806345 = _806343, class_Rings_Odvd(_806345)], (1926 ^ _779448) ^ [_806468, _806470] : [-(class_Nat_Osize(_806468)), _806470 = _806468, class_Nat_Osize(_806470)], (1936 ^ _779448) ^ [_806593, _806595] : [-(v_wt(_806593)), _806595 = _806593, v_wt(_806595)], (1960 ^ _779448) ^ [_806907, _806909] : [-(hBOOL(_806907)), _806909 = _806907, hBOOL(_806909)], (1946 ^ _779448) ^ [_806718, _806720, _806722, _806724] : [-(v_P(_806722, _806718)), v_P(_806724, _806720), _806724 = _806722, _806720 = _806718], (1970 ^ _779448) ^ [_807828, _807830, _807832, _807834] : [-(c_Option_Othe(_807834, _807830) = c_Option_Othe(_807832, _807828)), _807834 = _807832, _807830 = _807828], (1980 ^ _779448) ^ [_807977, _807979] : [_807979 = _807977, -(c_Com_Obody(_807979) = c_Com_Obody(_807977))], (1986 ^ _779448) ^ [_808062, _808064, _808066, _808068, _808070, _808072] : [-(c_Partial__Function_Oflat__lub(_808072, _808068, _808064) = c_Partial__Function_Oflat__lub(_808070, _808066, _808062)), _808072 = _808070, _808068 = _808066, _808064 = _808062], (2000 ^ _779448) ^ [_808283, _808285, _808287, _808289, _808291, _808293] : [-(c_Finite__Set_Ofold1Set(_808293, _808289, _808285) = c_Finite__Set_Ofold1Set(_808291, _808287, _808283)), _808293 = _808291, _808289 = _808287, _808285 = _808283], (2014 ^ _779448) ^ [_808504, _808506, _808508, _808510, _808512, _808514, _808516, _808518, _808520, _808522] : [-(c_Nitpick_Opair__box_Opair__box__size(_808522, _808518, _808514, _808510, _808506) = c_Nitpick_Opair__box_Opair__box__size(_808520, _808516, _808512, _808508, _808504)), _808522 = _808520, _808518 = _808516, _808514 = _808512, _808510 = _808508, _808506 = _808504], (2036 ^ _779448) ^ [_808893, _808895] : [_808895 = _808893, -(c_Nat_Onat_Onat__size(_808895) = c_Nat_Onat_Onat__size(_808893))], (2042 ^ _779448) ^ [_808978, _808980, _808982, _808984, _808986, _808988, _808990, _808992, _808994, _808996] : [-(c_Nitpick_Opair__box_Opair__box__rec(_808996, _808992, _808988, _808984, _808980) = c_Nitpick_Opair__box_Opair__box__rec(_808994, _808990, _808986, _808982, _808978)), _808996 = _808994, _808992 = _808990, _808988 = _808986, _808984 = _808982, _808980 = _808978], (2064 ^ _779448) ^ [_809367, _809369, _809371, _809373, _809375, _809377, _809379, _809381, _809383, _809385] : [-(c_Nitpick_Opair__box_Opair__box__case(_809385, _809381, _809377, _809373, _809369) = c_Nitpick_Opair__box_Opair__box__case(_809383, _809379, _809375, _809371, _809367)), _809385 = _809383, _809381 = _809379, _809377 = _809375, _809373 = _809371, _809369 = _809367], (2086 ^ _779448) ^ [_809756, _809758, _809760, _809762, _809764, _809766, _809768, _809770] : [-(c_Nitpick_Opair__box_OPairBox(_809770, _809766, _809762, _809758) = c_Nitpick_Opair__box_OPairBox(_809768, _809764, _809760, _809756)), _809770 = _809768, _809766 = _809764, _809762 = _809760, _809758 = _809756], (2104 ^ _779448) ^ [_810057, _810059, _810061, _810063, _810065, _810067, _810069, _810071, _810073, _810075] : [-(c_Finite__Set_Ofold__graph(_810075, _810071, _810067, _810063, _810059) = c_Finite__Set_Ofold__graph(_810073, _810069, _810065, _810061, _810057)), _810075 = _810073, _810071 = _810069, _810067 = _810065, _810063 = _810061, _810059 = _810057], (2126 ^ _779448) ^ [_810446, _810448, _810450, _810452, _810454, _810456, _810458, _810460] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810460, _810456, _810452, _810448) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810458, _810454, _810450, _810446)), _810460 = _810458, _810456 = _810454, _810452 = _810450, _810448 = _810446], (2144 ^ _779448) ^ [_810747, _810749] : [_810749 = _810747, -(c_Nat_Osemiring__1__class_ONats(_810749) = c_Nat_Osemiring__1__class_ONats(_810747))], (2150 ^ _779448) ^ [_810832, _810834, _810836, _810838, _810840, _810842] : [-(c_Power_Opower_Opower(_810842, _810838, _810834) = c_Power_Opower_Opower(_810840, _810836, _810832)), _810842 = _810840, _810838 = _810836, _810834 = _810832], (2164 ^ _779448) ^ [_811053, _811055] : [_811055 = _811053, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811055) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811053))], (2170 ^ _779448) ^ [_811138, _811140] : [_811140 = _811138, -(c_Int_Osucc(_811140) = c_Int_Osucc(_811138))], (2176 ^ _779448) ^ [_811223, _811225, _811227, _811229] : [-(c_Int_Onat__aux(_811229, _811225) = c_Int_Onat__aux(_811227, _811223)), _811229 = _811227, _811225 = _811223], (2186 ^ _779448) ^ [_811372, _811374, _811376, _811378, _811380, _811382] : [-(c_Nat_Onat_Onat__rec(_811382, _811378, _811374) = c_Nat_Onat_Onat__rec(_811380, _811376, _811372)), _811382 = _811380, _811378 = _811376, _811374 = _811372], (2200 ^ _779448) ^ [_811593, _811595, _811597, _811599] : [-(c_SMT_Oz3div(_811599, _811595) = c_SMT_Oz3div(_811597, _811593)), _811599 = _811597, _811595 = _811593], (2210 ^ _779448) ^ [_811742, _811744, _811746, _811748] : [-(c_SMT_Oz3mod(_811748, _811744) = c_SMT_Oz3mod(_811746, _811742)), _811748 = _811746, _811744 = _811742], (2220 ^ _779448) ^ [_811891, _811893] : [_811893 = _811891, -(c_Int_Oring__1__class_OInts(_811893) = c_Int_Oring__1__class_OInts(_811891))], (2226 ^ _779448) ^ [_811976, _811978, _811980, _811982] : [-(c_Nat__Transfer_Otsub(_811982, _811978) = c_Nat__Transfer_Otsub(_811980, _811976)), _811982 = _811980, _811978 = _811976], (2236 ^ _779448) ^ [_812125, _812127, _812129, _812131] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_812131, _812127) = c_Code__Numeral_Odiv__mod__code__numeral(_812129, _812125)), _812131 = _812129, _812127 = _812125], (2246 ^ _779448) ^ [_812274, _812276] : [_812276 = _812274, -(c_Divides_Oadjust(_812276) = c_Divides_Oadjust(_812274))], (2252 ^ _779448) ^ [_812359, _812361, _812363, _812365] : [-(c_Divides_Odivmod__int__rel(_812365, _812361) = c_Divides_Odivmod__int__rel(_812363, _812359)), _812365 = _812363, _812361 = _812359], (2262 ^ _779448) ^ [_812508, _812510, _812512, _812514] : [-(c_Divides_OnegDivAlg(_812514, _812510) = c_Divides_OnegDivAlg(_812512, _812508)), _812514 = _812512, _812510 = _812508], (2272 ^ _779448) ^ [_812657, _812659, _812661, _812663, _812665, _812667, _812669, _812671, _812673, _812675] : [-(c_Product__Type_Oprod_Oprod__size(_812675, _812671, _812667, _812663, _812659) = c_Product__Type_Oprod_Oprod__size(_812673, _812669, _812665, _812661, _812657)), _812675 = _812673, _812671 = _812669, _812667 = _812665, _812663 = _812661, _812659 = _812657], (2294 ^ _779448) ^ [_813046, _813048, _813050, _813052] : [-(c_Divides_Odivmod__nat(_813052, _813048) = c_Divides_Odivmod__nat(_813050, _813046)), _813052 = _813050, _813048 = _813046], (2304 ^ _779448) ^ [_813195, _813197, _813199, _813201] : [-(c_Divides_Odivmod__nat__rel(_813201, _813197) = c_Divides_Odivmod__nat__rel(_813199, _813195)), _813201 = _813199, _813197 = _813195], (2314 ^ _779448) ^ [_813344, _813346, _813348, _813350, _813352, _813354, _813356, _813358, _813360, _813362] : [-(c_Product__Type_Oprod_Oprod__rec(_813362, _813358, _813354, _813350, _813346) = c_Product__Type_Oprod_Oprod__rec(_813360, _813356, _813352, _813348, _813344)), _813362 = _813360, _813358 = _813356, _813354 = _813352, _813350 = _813348, _813346 = _813344], (2336 ^ _779448) ^ [_813733, _813735, _813737, _813739] : [-(c_Orderings_Oord_Omax(_813739, _813735) = c_Orderings_Oord_Omax(_813737, _813733)), _813739 = _813737, _813735 = _813733], (2346 ^ _779448) ^ [_813882, _813884, _813886, _813888] : [-(c_Orderings_Oord_Omin(_813888, _813884) = c_Orderings_Oord_Omin(_813886, _813882)), _813888 = _813886, _813884 = _813882], (2356 ^ _779448) ^ [_814031, _814033] : [_814033 = _814031, -(c_Int_Opred(_814033) = c_Int_Opred(_814031))], (2362 ^ _779448) ^ [_814116, _814118, _814120, _814122] : [-(c_FunDef_Orp__inv__image(_814122, _814118) = c_FunDef_Orp__inv__image(_814120, _814116)), _814122 = _814120, _814118 = _814116], (2372 ^ _779448) ^ [_814265, _814267, _814269, _814271] : [-(c_Set_Othe__elem(_814271, _814267) = c_Set_Othe__elem(_814269, _814265)), _814271 = _814269, _814267 = _814265], (2382 ^ _779448) ^ [_814414, _814416, _814418, _814420, _814422, _814424, _814426, _814428] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_814428, _814424, _814420, _814416) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_814426, _814422, _814418, _814414)), _814428 = _814426, _814424 = _814422, _814420 = _814418, _814416 = _814414], (2400 ^ _779448) ^ [_814715, _814717, _814719, _814721] : [-(c_Divides_Odivmod__int(_814721, _814717) = c_Divides_Odivmod__int(_814719, _814715)), _814721 = _814719, _814717 = _814715], (2410 ^ _779448) ^ [_814864, _814866, _814868, _814870] : [-(c_Groups_Osgn__class_Osgn(_814870, _814866) = c_Groups_Osgn__class_Osgn(_814868, _814864)), _814870 = _814868, _814866 = _814864], (2420 ^ _779448) ^ [_815013, _815015, _815017, _815019] : [-(c_Divides_Opdivmod(_815019, _815015) = c_Divides_Opdivmod(_815017, _815013)), _815019 = _815017, _815015 = _815013], (2430 ^ _779448) ^ [_815162, _815164, _815166, _815168] : [-(c_Divides_OposDivAlg(_815168, _815164) = c_Divides_OposDivAlg(_815166, _815162)), _815168 = _815166, _815164 = _815162], (2440 ^ _779448) ^ [_815311, _815313, _815315, _815317] : [-(c_Nitpick_Onat__gcd(_815317, _815313) = c_Nitpick_Onat__gcd(_815315, _815311)), _815317 = _815315, _815313 = _815311], (2450 ^ _779448) ^ [_815460, _815462, _815464, _815466] : [-(c_Nitpick_Onat__lcm(_815466, _815462) = c_Nitpick_Onat__lcm(_815464, _815460)), _815466 = _815464, _815462 = _815460], (2460 ^ _779448) ^ [_815609, _815611, _815613, _815615, _815617, _815619, _815621, _815623] : [-(c_Sum__Type_OPlus(_815623, _815619, _815615, _815611) = c_Sum__Type_OPlus(_815621, _815617, _815613, _815609)), _815623 = _815621, _815619 = _815617, _815615 = _815613, _815611 = _815609], (2478 ^ _779448) ^ [_815910, _815912] : [_815912 = _815910, -(c_SetInterval_Oord__class_OatLeast(_815912) = c_SetInterval_Oord__class_OatLeast(_815910))], (2484 ^ _779448) ^ [_815995, _815997] : [_815997 = _815995, -(c_Int_OBit0(_815997) = c_Int_OBit0(_815995))], (2490 ^ _779448) ^ [_816080, _816082] : [_816082 = _816080, -(c_SetInterval_Oord__class_OgreaterThan(_816082) = c_SetInterval_Oord__class_OgreaterThan(_816080))], (2496 ^ _779448) ^ [_816165, _816167] : [_816167 = _816165, -(c_Nitpick_Ozero__frac(_816167) = c_Nitpick_Ozero__frac(_816165))], (2502 ^ _779448) ^ [_816250, _816252] : [_816252 = _816250, -(c_Nitpick_Oone__frac(_816252) = c_Nitpick_Oone__frac(_816250))], (2508 ^ _779448) ^ [_816335, _816337, _816339, _816341] : [-(c_Nitpick_Onumber__of__frac(_816341, _816337) = c_Nitpick_Onumber__of__frac(_816339, _816335)), _816341 = _816339, _816337 = _816335], (2518 ^ _779448) ^ [_816484, _816486, _816488, _816490] : [-(c_Nitpick_Onorm__frac(_816490, _816486) = c_Nitpick_Onorm__frac(_816488, _816484)), _816490 = _816488, _816486 = _816484], (2528 ^ _779448) ^ [_816633, _816635, _816637, _816639, _816641, _816643, _816645, _816647] : [-(c_Nitpick_Oprod(_816647, _816643, _816639, _816635) = c_Nitpick_Oprod(_816645, _816641, _816637, _816633)), _816647 = _816645, _816643 = _816641, _816639 = _816637, _816635 = _816633], (2546 ^ _779448) ^ [_816934, _816936, _816938, _816940, _816942, _816944, _816946, _816948] : [-(c_Product__Type_Oapsnd(_816948, _816944, _816940, _816936) = c_Product__Type_Oapsnd(_816946, _816942, _816938, _816934)), _816948 = _816946, _816944 = _816942, _816940 = _816938, _816936 = _816934], (2564 ^ _779448) ^ [_817235, _817237, _817239, _817241, _817243, _817245, _817247, _817249] : [-(c_Product__Type_Oapfst(_817249, _817245, _817241, _817237) = c_Product__Type_Oapfst(_817247, _817243, _817239, _817235)), _817249 = _817247, _817245 = _817243, _817241 = _817239, _817237 = _817235], (2582 ^ _779448) ^ [_817536, _817538] : [_817538 = _817536, -(c_Wellfounded_Omeasure(_817538) = c_Wellfounded_Omeasure(_817536))], (2588 ^ _779448) ^ [_817621, _817623, _817625, _817627] : [-(c_Wellfounded_Omin__ext(_817627, _817623) = c_Wellfounded_Omin__ext(_817625, _817621)), _817627 = _817625, _817623 = _817621], (2598 ^ _779448) ^ [_817770, _817772, _817774, _817776, _817778, _817780] : [-(c_Wellfounded_Omlex__prod(_817780, _817776, _817772) = c_Wellfounded_Omlex__prod(_817778, _817774, _817770)), _817780 = _817778, _817776 = _817774, _817772 = _817770], (2612 ^ _779448) ^ [_817991, _817993] : [_817993 = _817991, -(c_Int_Oint__ge__less__than(_817993) = c_Int_Oint__ge__less__than(_817991))], (2618 ^ _779448) ^ [_818076, _818078] : [_818078 = _818076, -(c_Int_Oint__ge__less__than2(_818078) = c_Int_Oint__ge__less__than2(_818076))], (2624 ^ _779448) ^ [_818161, _818163, _818165, _818167, _818169, _818171, _818173, _818175] : [-(c_Recdef_Osame__fst(_818175, _818171, _818167, _818163) = c_Recdef_Osame__fst(_818173, _818169, _818165, _818161)), _818175 = _818173, _818171 = _818169, _818167 = _818165, _818163 = _818161], (2642 ^ _779448) ^ [_818462, _818464, _818466, _818468, _818470, _818472] : [-(c_FunDef_Oin__rel(_818472, _818468, _818464) = c_FunDef_Oin__rel(_818470, _818466, _818462)), _818472 = _818470, _818468 = _818466, _818464 = _818462], (2656 ^ _779448) ^ [_818683, _818685, _818687, _818689] : [-(c_Predicate_OPowp(_818689, _818685) = c_Predicate_OPowp(_818687, _818683)), _818689 = _818687, _818685 = _818683], (2666 ^ _779448) ^ [_818832, _818834] : [_818834 = _818832, -(c_Set_OBall(_818834) = c_Set_OBall(_818832))], (2672 ^ _779448) ^ [_818917, _818919] : [_818919 = _818917, -(c_HOL_OAll(_818919) = c_HOL_OAll(_818917))], (2678 ^ _779448) ^ [_819002, _819004, _819006, _819008, _819010, _819012] : [-(c_Predicate_ODomainP(_819012, _819008, _819004) = c_Predicate_ODomainP(_819010, _819006, _819002)), _819012 = _819010, _819008 = _819006, _819004 = _819002], (2692 ^ _779448) ^ [_819223, _819225, _819227, _819229, _819231, _819233] : [-(c_Predicate_ORangeP(_819233, _819229, _819225) = c_Predicate_ORangeP(_819231, _819227, _819223)), _819233 = _819231, _819229 = _819227, _819225 = _819223], (2706 ^ _779448) ^ [_819444, _819446, _819448, _819450] : [-(c_Wellfounded_Omax__ext(_819450, _819446) = c_Wellfounded_Omax__ext(_819448, _819444)), _819450 = _819448, _819446 = _819444], (2716 ^ _779448) ^ [_819593, _819595, _819597, _819599, _819601, _819603, _819605, _819607] : [-(c_Random_Oiterate(_819607, _819603, _819599, _819595) = c_Random_Oiterate(_819605, _819601, _819597, _819593)), _819607 = _819605, _819603 = _819601, _819599 = _819597, _819595 = _819593], (2734 ^ _779448) ^ [_819894, _819896, _819898, _819900] : [-(c_Random_Olog(_819900, _819896) = c_Random_Olog(_819898, _819894)), _819900 = _819898, _819896 = _819894], (2744 ^ _779448) ^ [_820043, _820045, _820047, _820049, _820051, _820053] : [-(c_Random_Ominus__shift(_820053, _820049, _820045) = c_Random_Ominus__shift(_820051, _820047, _820043)), _820053 = _820051, _820049 = _820047, _820045 = _820043], (2758 ^ _779448) ^ [_820264, _820266, _820268, _820270] : [-(c_Random_Oinc__shift(_820270, _820266) = c_Random_Oinc__shift(_820268, _820264)), _820270 = _820268, _820266 = _820264], (2768 ^ _779448) ^ [_820413, _820415] : [_820415 = _820413, -(c_Relation_OField(_820415) = c_Relation_OField(_820413))], (2774 ^ _779448) ^ [_820498, _820500, _820502, _820504] : [-(c_Relation_ORange(_820504, _820500) = c_Relation_ORange(_820502, _820498)), _820504 = _820502, _820500 = _820498], (2784 ^ _779448) ^ [_820647, _820649, _820651, _820653] : [-(c_Relation_ODomain(_820653, _820649) = c_Relation_ODomain(_820651, _820647)), _820653 = _820651, _820649 = _820647], (2794 ^ _779448) ^ [_820796, _820798] : [_820798 = _820796, -(c_Nat_Ofunpow(_820798) = c_Nat_Ofunpow(_820796))], (2800 ^ _779448) ^ [_820881, _820883, _820885, _820887] : [-(c_Nitpick_Oint__lcm(_820887, _820883) = c_Nitpick_Oint__lcm(_820885, _820881)), _820887 = _820885, _820883 = _820881], (2810 ^ _779448) ^ [_821030, _821032, _821034, _821036, _821038, _821040] : [-(c_Nitpick_Otimes__frac(_821040, _821036, _821032) = c_Nitpick_Otimes__frac(_821038, _821034, _821030)), _821040 = _821038, _821036 = _821034, _821032 = _821030], (2824 ^ _779448) ^ [_821251, _821253, _821255, _821257, _821259, _821261] : [-(c_Nitpick_Oof__frac(_821261, _821257, _821253) = c_Nitpick_Oof__frac(_821259, _821255, _821251)), _821261 = _821259, _821257 = _821255, _821253 = _821251], (2838 ^ _779448) ^ [_821472, _821474] : [_821474 = _821472, -(c_Rings_Oinverse__class_Odivide(_821474) = c_Rings_Oinverse__class_Odivide(_821472))], (2844 ^ _779448) ^ [_821557, _821559] : [_821559 = _821557, -(c_Int_Oring__1__class_Oof__int(_821559) = c_Int_Oring__1__class_Oof__int(_821557))], (2850 ^ _779448) ^ [_821642, _821644, _821646, _821648] : [-(c_Nitpick_Oinverse__frac(_821648, _821644) = c_Nitpick_Oinverse__frac(_821646, _821642)), _821648 = _821646, _821644 = _821642], (2860 ^ _779448) ^ [_821791, _821793] : [_821793 = _821791, -(c_Nitpick_Ofrac(_821793) = c_Nitpick_Ofrac(_821791))], (2866 ^ _779448) ^ [_821876, _821878, _821880, _821882] : [-(c_Nitpick_OAbs__Frac(_821882, _821878) = c_Nitpick_OAbs__Frac(_821880, _821876)), _821882 = _821880, _821878 = _821876], (2876 ^ _779448) ^ [_822025, _822027, _822029, _822031, _822033, _822035] : [-(c_Nitpick_Oplus__frac(_822035, _822031, _822027) = c_Nitpick_Oplus__frac(_822033, _822029, _822025)), _822035 = _822033, _822031 = _822029, _822027 = _822025], (2890 ^ _779448) ^ [_822246, _822248, _822250, _822252] : [-(c_Nitpick_Ouminus__frac(_822252, _822248) = c_Nitpick_Ouminus__frac(_822250, _822246)), _822252 = _822250, _822248 = _822246], (2900 ^ _779448) ^ [_822395, _822397] : [_822397 = _822395, -(c_Nitpick_Odenom(_822397) = c_Nitpick_Odenom(_822395))], (2906 ^ _779448) ^ [_822480, _822482] : [_822482 = _822480, -(c_Nitpick_Onum(_822482) = c_Nitpick_Onum(_822480))], (2912 ^ _779448) ^ [_822565, _822567] : [_822567 = _822565, -(c_Nitpick_ORep__Frac(_822567) = c_Nitpick_ORep__Frac(_822565))], (2918 ^ _779448) ^ [_822650, _822652, _822654, _822656, _822658, _822660] : [-(c_Product__Type_Ointernal__split(_822660, _822656, _822652) = c_Product__Type_Ointernal__split(_822658, _822654, _822650)), _822660 = _822658, _822656 = _822654, _822652 = _822650], (2932 ^ _779448) ^ [_822871, _822873] : [_822873 = _822871, -(c_HOL_Obool_Obool__size(_822873) = c_HOL_Obool_Obool__size(_822871))], (2938 ^ _779448) ^ [_822956, _822958, _822960, _822962] : [-(c_List_Olenlex(_822962, _822958) = c_List_Olenlex(_822960, _822956)), _822962 = _822960, _822958 = _822956], (2948 ^ _779448) ^ [_823105, _823107, _823109, _823111, _823113, _823115, _823117, _823119, _823121, _823123, _823125, _823127] : [-(c_Product__Type_Omap__pair(_823127, _823123, _823119, _823115, _823111, _823107) = c_Product__Type_Omap__pair(_823125, _823121, _823117, _823113, _823109, _823105)), _823127 = _823125, _823123 = _823121, _823119 = _823117, _823115 = _823113, _823111 = _823109, _823107 = _823105], (2974 ^ _779448) ^ [_823590, _823592, _823594, _823596] : [-(c_List_Olexn(_823596, _823592) = c_List_Olexn(_823594, _823590)), _823596 = _823594, _823592 = _823590], (2984 ^ _779448) ^ [_823739, _823741, _823743, _823745] : [-(c_Wellfounded_Oacc(_823745, _823741) = c_Wellfounded_Oacc(_823743, _823739)), _823745 = _823743, _823741 = _823739], (2994 ^ _779448) ^ [_823888, _823890, _823892, _823894] : [-(c_Nitpick_Ocard_H(_823894, _823890) = c_Nitpick_Ocard_H(_823892, _823888)), _823894 = _823892, _823890 = _823888], (3004 ^ _779448) ^ [_824037, _824039, _824041, _824043, _824045, _824047] : [-(c_List_Oset__Cons(_824047, _824043, _824039) = c_List_Oset__Cons(_824045, _824041, _824037)), _824047 = _824045, _824043 = _824041, _824039 = _824037], (3018 ^ _779448) ^ [_824258, _824260, _824262, _824264] : [-(c_List_Olistset(_824264, _824260) = c_List_Olistset(_824262, _824258)), _824264 = _824262, _824260 = _824258], (3028 ^ _779448) ^ [_824407, _824409, _824411, _824413] : [-(c_List_Olistrel1(_824413, _824409) = c_List_Olistrel1(_824411, _824407)), _824413 = _824411, _824409 = _824407], (3038 ^ _779448) ^ [_824556, _824558, _824560, _824562, _824564, _824566, _824568, _824570] : [-(c_Nat_Onat_Onat__case(_824570, _824566, _824562, _824558) = c_Nat_Onat_Onat__case(_824568, _824564, _824560, _824556)), _824570 = _824568, _824566 = _824564, _824562 = _824560, _824558 = _824556], (3056 ^ _779448) ^ [_824857, _824859, _824861, _824863] : [-(c_Nat_Ocompow(_824863, _824859) = c_Nat_Ocompow(_824861, _824857)), _824863 = _824861, _824859 = _824857], (3066 ^ _779448) ^ [_825006, _825008] : [_825008 = _825006, -(c_List_Orotate1(_825008) = c_List_Orotate1(_825006))], (3072 ^ _779448) ^ [_825091, _825093, _825095, _825097] : [-(c_Finite__Set_Ofold1(_825097, _825093) = c_Finite__Set_Ofold1(_825095, _825091)), _825097 = _825095, _825093 = _825091], (3082 ^ _779448) ^ [_825240, _825242, _825244, _825246] : [-(c_Big__Operators_Olattice__class_OSup__fin(_825246, _825242) = c_Big__Operators_Olattice__class_OSup__fin(_825244, _825240)), _825246 = _825244, _825242 = _825240], (3092 ^ _779448) ^ [_825389, _825391, _825393, _825395] : [-(c_Big__Operators_Olattice__class_OInf__fin(_825395, _825391) = c_Big__Operators_Olattice__class_OInf__fin(_825393, _825389)), _825395 = _825393, _825391 = _825389], (3102 ^ _779448) ^ [_825538, _825540, _825542, _825544] : [-(c_Big__Operators_Olinorder__class_OMin(_825544, _825540) = c_Big__Operators_Olinorder__class_OMin(_825542, _825538)), _825544 = _825542, _825540 = _825538], (3112 ^ _779448) ^ [_825687, _825689, _825691, _825693] : [-(c_Big__Operators_Olinorder__class_OMax(_825693, _825689) = c_Big__Operators_Olinorder__class_OMax(_825691, _825687)), _825693 = _825691, _825689 = _825687], (3122 ^ _779448) ^ [_825836, _825838, _825840, _825842, _825844, _825846] : [-(c_Big__Operators_Olattice_OInf__fin(_825846, _825842, _825838) = c_Big__Operators_Olattice_OInf__fin(_825844, _825840, _825836)), _825846 = _825844, _825842 = _825840, _825838 = _825836], (3136 ^ _779448) ^ [_826057, _826059, _826061, _826063, _826065, _826067] : [-(c_Big__Operators_Olattice_OSup__fin(_826067, _826063, _826059) = c_Big__Operators_Olattice_OSup__fin(_826065, _826061, _826057)), _826067 = _826065, _826063 = _826061, _826059 = _826057], (3150 ^ _779448) ^ [_826278, _826280, _826282, _826284, _826286, _826288, _826290, _826292, _826294, _826296] : [-(c_Fun_Ofun__upd(_826296, _826292, _826288, _826284, _826280) = c_Fun_Ofun__upd(_826294, _826290, _826286, _826282, _826278)), _826296 = _826294, _826292 = _826290, _826288 = _826286, _826284 = _826282, _826280 = _826278], (3172 ^ _779448) ^ [_826667, _826669, _826671, _826673, _826675, _826677, _826679, _826681] : [-(c_Nitpick_Osetsum_H(_826681, _826677, _826673, _826669) = c_Nitpick_Osetsum_H(_826679, _826675, _826671, _826667)), _826681 = _826679, _826677 = _826675, _826673 = _826671, _826669 = _826667], (3190 ^ _779448) ^ [_826968, _826970, _826972, _826974, _826976, _826978] : [-(c_List_Olist_Olist__size(_826978, _826974, _826970) = c_List_Olist_Olist__size(_826976, _826972, _826968)), _826978 = _826976, _826974 = _826972, _826970 = _826968], (3204 ^ _779448) ^ [_827189, _827191, _827193, _827195] : [-(c_Random_Oselect(_827195, _827191) = c_Random_Oselect(_827193, _827189)), _827195 = _827193, _827191 = _827189], (3214 ^ _779448) ^ [_827338, _827340] : [_827340 = _827338, -(c_Random_Orange(_827340) = c_Random_Orange(_827338))], (3220 ^ _779448) ^ [_827423, _827425, _827427, _827429] : [-(c_Code__Numeral_Onat__of__aux(_827429, _827425) = c_Code__Numeral_Onat__of__aux(_827427, _827423)), _827429 = _827427, _827425 = _827423], (3230 ^ _779448) ^ [_827572, _827574] : [_827574 = _827572, -(c_Lazy__Sequence_Ohb__not__seq(_827574) = c_Lazy__Sequence_Ohb__not__seq(_827572))], (3236 ^ _779448) ^ [_827657, _827659] : [_827659 = _827657, -(c_Int_OBit1(_827659) = c_Int_OBit1(_827657))], (3242 ^ _779448) ^ [_827742, _827744, _827746, _827748] : [-(c_List_Olists(_827748, _827744) = c_List_Olists(_827746, _827742)), _827748 = _827746, _827744 = _827742], (3252 ^ _779448) ^ [_827891, _827893, _827895, _827897] : [-(c_List_Olistsp(_827897, _827893) = c_List_Olistsp(_827895, _827891)), _827897 = _827895, _827893 = _827891], (3262 ^ _779448) ^ [_828040, _828042, _828044, _828046, _828048, _828050, _828052, _828054] : [-(c_Enum_Oproduct(_828054, _828050, _828046, _828042) = c_Enum_Oproduct(_828052, _828048, _828044, _828040)), _828054 = _828052, _828050 = _828048, _828046 = _828044, _828042 = _828040], (3280 ^ _779448) ^ [_828341, _828343, _828345, _828347] : [-(c_Product__Type_OSigma(_828347, _828343) = c_Product__Type_OSigma(_828345, _828341)), _828347 = _828345, _828343 = _828341], (3290 ^ _779448) ^ [_828490, _828492] : [_828492 = _828490, -(c_Set_OPow(_828492) = c_Set_OPow(_828490))], (3296 ^ _779448) ^ [_828575, _828577, _828579, _828581] : [-(c_HOL_OLet(_828581, _828577) = c_HOL_OLet(_828579, _828575)), _828581 = _828579, _828577 = _828575], (3306 ^ _779448) ^ [_828724, _828726, _828728, _828730] : [-(c_Enum_Osublists(_828730, _828726) = c_Enum_Osublists(_828728, _828724)), _828730 = _828728, _828726 = _828724], (3316 ^ _779448) ^ [_828873, _828875, _828877, _828879] : [-(c_Enum_Oenum__the(_828879, _828875) = c_Enum_Oenum__the(_828877, _828873)), _828879 = _828877, _828875 = _828873], (3326 ^ _779448) ^ [_829022, _829024, _829026, _829028, _829030, _829032] : [-(c_Finite__Set_Ofold(_829032, _829028, _829024) = c_Finite__Set_Ofold(_829030, _829026, _829022)), _829032 = _829030, _829028 = _829026, _829024 = _829022], (3340 ^ _779448) ^ [_829243, _829245, _829247, _829249, _829251, _829253] : [-(c_Enum_On__lists(_829253, _829249, _829245) = c_Enum_On__lists(_829251, _829247, _829243)), _829253 = _829251, _829249 = _829247, _829245 = _829243], (3354 ^ _779448) ^ [_829464, _829466, _829468, _829470, _829472, _829474] : [-(c_List_Opartition(_829474, _829470, _829466) = c_List_Opartition(_829472, _829468, _829464)), _829474 = _829472, _829470 = _829468, _829466 = _829464], (3368 ^ _779448) ^ [_829685, _829687, _829689, _829691] : [-(c_List_OremoveAll(_829691, _829687) = c_List_OremoveAll(_829689, _829685)), _829691 = _829689, _829687 = _829685], (3378 ^ _779448) ^ [_829834, _829836, _829838, _829840, _829842, _829844, _829846, _829848] : [-(c_List_Olist_Olist__case(_829848, _829844, _829840, _829836) = c_List_Olist_Olist__case(_829846, _829842, _829838, _829834)), _829848 = _829846, _829844 = _829842, _829840 = _829838, _829836 = _829834], (3396 ^ _779448) ^ [_830135, _830137, _830139, _830141] : [-(c_Random_Oselect__weight(_830141, _830137) = c_Random_Oselect__weight(_830139, _830135)), _830141 = _830139, _830137 = _830135], (3406 ^ _779448) ^ [_830284, _830286, _830288, _830290] : [-(c_Random_Opick(_830290, _830286) = c_Random_Opick(_830288, _830284)), _830290 = _830288, _830286 = _830284], (3416 ^ _779448) ^ [_830433, _830435] : [_830435 = _830433, -(c_List_Otranspose__rel(_830435) = c_List_Otranspose__rel(_830433))], (3422 ^ _779448) ^ [_830518, _830520, _830522, _830524, _830526, _830528] : [-(c_List_Osublist(_830528, _830524, _830520) = c_List_Osublist(_830526, _830522, _830518)), _830528 = _830526, _830524 = _830522, _830520 = _830518], (3436 ^ _779448) ^ [_830739, _830741] : [_830741 = _830739, -(c_SetInterval_Oord__class_OlessThan(_830741) = c_SetInterval_Oord__class_OlessThan(_830739))], (3442 ^ _779448) ^ [_830824, _830826, _830828, _830830, _830832, _830834] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830834, _830830, _830826) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830832, _830828, _830824)), _830834 = _830832, _830830 = _830828, _830826 = _830824], (3456 ^ _779448) ^ [_831045, _831047, _831049, _831051, _831053, _831055] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_831055, _831051, _831047) = c_SetInterval_Oord__class_OgreaterThanLessThan(_831053, _831049, _831045)), _831055 = _831053, _831051 = _831049, _831047 = _831045], (3470 ^ _779448) ^ [_831266, _831268] : [_831268 = _831266, -(c_SetInterval_Oord__class_OatMost(_831268) = c_SetInterval_Oord__class_OatMost(_831266))], (3476 ^ _779448) ^ [_831351, _831353, _831355, _831357, _831359, _831361, _831363, _831365] : [-(c_List_Olinorder__class_Osort__key(_831365, _831361, _831357, _831353) = c_List_Olinorder__class_Osort__key(_831363, _831359, _831355, _831351)), _831365 = _831363, _831361 = _831359, _831357 = _831355, _831353 = _831351], (3494 ^ _779448) ^ [_831652, _831654, _831656, _831658, _831660, _831662, _831664, _831666, _831668, _831670] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831670, _831666, _831662, _831658, _831654) = c_List_Olinorder__class_Oinsort__insert__key(_831668, _831664, _831660, _831656, _831652)), _831670 = _831668, _831666 = _831664, _831662 = _831660, _831658 = _831656, _831654 = _831652], (3516 ^ _779448) ^ [_832041, _832043, _832045, _832047] : [-(c_List_Olinorder__class_Osorted__list__of__set(_832047, _832043) = c_List_Olinorder__class_Osorted__list__of__set(_832045, _832041)), _832047 = _832045, _832043 = _832041], (3526 ^ _779448) ^ [_832190, _832192, _832194, _832196, _832198, _832200] : [-(c_List_Oremove1(_832200, _832196, _832192) = c_List_Oremove1(_832198, _832194, _832190)), _832200 = _832198, _832196 = _832194, _832192 = _832190], (3540 ^ _779448) ^ [_832411, _832413, _832415, _832417] : [-(c_List_Orotate(_832417, _832413) = c_List_Orotate(_832415, _832411)), _832417 = _832415, _832413 = _832411], (3550 ^ _779448) ^ [_832560, _832562, _832564, _832566] : [-(c_List_Olist__update(_832566, _832562) = c_List_Olist__update(_832564, _832560)), _832566 = _832564, _832562 = _832560], (3560 ^ _779448) ^ [_832709, _832711, _832713, _832715, _832717, _832719, _832721, _832723, _832725, _832727] : [-(c_List_Ofoldr(_832727, _832723, _832719, _832715, _832711) = c_List_Ofoldr(_832725, _832721, _832717, _832713, _832709)), _832727 = _832725, _832723 = _832721, _832719 = _832717, _832715 = _832713, _832711 = _832709], (3582 ^ _779448) ^ [_833098, _833100] : [_833100 = _833098, -(c_Orderings_Oord__class_Omax(_833100) = c_Orderings_Oord__class_Omax(_833098))], (3588 ^ _779448) ^ [_833183, _833185, _833187, _833189] : [-(c_List_Otranspose(_833189, _833185) = c_List_Otranspose(_833187, _833183)), _833189 = _833187, _833185 = _833183], (3598 ^ _779448) ^ [_833332, _833334, _833336, _833338] : [-(c_List_Obutlast(_833338, _833334) = c_List_Obutlast(_833336, _833332)), _833338 = _833336, _833334 = _833332], (3608 ^ _779448) ^ [_833481, _833483] : [_833483 = _833481, -(c_List_Oreturn__list(_833483) = c_List_Oreturn__list(_833481))], (3614 ^ _779448) ^ [_833566, _833568] : [_833568 = _833566, -(c_List_Oembed__list(_833568) = c_List_Oembed__list(_833566))], (3620 ^ _779448) ^ [_833651, _833653] : [_833653 = _833651, -(c_List_Omonoid__add__class_Olistsum(_833653) = c_List_Omonoid__add__class_Olistsum(_833651))], (3626 ^ _779448) ^ [_833736, _833738, _833740, _833742] : [-(c_List_Oremdups(_833742, _833738) = c_List_Oremdups(_833740, _833736)), _833742 = _833740, _833738 = _833736], (3636 ^ _779448) ^ [_833885, _833887, _833889, _833891, _833893, _833895] : [-(c_List_Oinsert(_833895, _833891, _833887) = c_List_Oinsert(_833893, _833889, _833885)), _833895 = _833893, _833891 = _833889, _833887 = _833885], (3650 ^ _779448) ^ [_834106, _834108, _834110, _834112, _834114, _834116, _834118, _834120] : [-(c_List_Omaps(_834120, _834116, _834112, _834108) = c_List_Omaps(_834118, _834114, _834110, _834106)), _834120 = _834118, _834116 = _834114, _834112 = _834110, _834108 = _834106], (3668 ^ _779448) ^ [_834407, _834409, _834411, _834413] : [-(c_List_Olex(_834413, _834409) = c_List_Olex(_834411, _834407)), _834413 = _834411, _834409 = _834407], (3678 ^ _779448) ^ [_834556, _834558, _834560, _834562] : [-(c_List_Omeasures(_834562, _834558) = c_List_Omeasures(_834560, _834556)), _834562 = _834560, _834558 = _834556], (3688 ^ _779448) ^ [_834705, _834707, _834709, _834711, _834713, _834715, _834717, _834719] : [-(c_List_Ofoldl(_834719, _834715, _834711, _834707) = c_List_Ofoldl(_834717, _834713, _834709, _834705)), _834719 = _834717, _834715 = _834713, _834711 = _834709, _834707 = _834705], (3706 ^ _779448) ^ [_835006, _835008] : [_835008 = _835006, -(c_Enum_Oenum__class_Oenum__ex(_835008) = c_Enum_Oenum__class_Oenum__ex(_835006))], (3712 ^ _779448) ^ [_835091, _835093, _835095, _835097, _835099, _835101, _835103, _835105] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_835105, _835101, _835097, _835093) = c_New__Random__Sequence_Opos__not__random__dseq(_835103, _835099, _835095, _835091)), _835105 = _835103, _835101 = _835099, _835097 = _835095, _835093 = _835091], (3730 ^ _779448) ^ [_835392, _835394] : [_835394 = _835392, -(c_New__DSequence_Opos__not__seq(_835394) = c_New__DSequence_Opos__not__seq(_835392))], (3736 ^ _779448) ^ [_835477, _835479, _835481, _835483, _835485, _835487] : [-(c_List_OdropWhile(_835487, _835483, _835479) = c_List_OdropWhile(_835485, _835481, _835477)), _835487 = _835485, _835483 = _835481, _835479 = _835477], (3750 ^ _779448) ^ [_835698, _835700] : [_835700 = _835698, -(c_List_Odistinct(_835700) = c_List_Odistinct(_835698))], (3756 ^ _779448) ^ [_835783, _835785, _835787, _835789, _835791, _835793] : [-(c_List_OtakeWhile(_835793, _835789, _835785) = c_List_OtakeWhile(_835791, _835787, _835783)), _835793 = _835791, _835789 = _835787, _835785 = _835783], (3770 ^ _779448) ^ [_836004, _836006, _836008, _836010, _836012, _836014] : [-(c_List_Olinorder__class_Oinsort__key(_836014, _836010, _836006) = c_List_Olinorder__class_Oinsort__key(_836012, _836008, _836004)), _836014 = _836012, _836010 = _836008, _836006 = _836004], (3784 ^ _779448) ^ [_836225, _836227] : [_836227 = _836225, -(c_Enum_Oenum__class_Oenum__all(_836227) = c_Enum_Oenum__class_Oenum__all(_836225))], (3790 ^ _779448) ^ [_836310, _836312] : [_836312 = _836310, -(c_Nat_Osemiring__1__class_Oof__nat(_836312) = c_Nat_Osemiring__1__class_Oof__nat(_836310))], (3796 ^ _779448) ^ [_836395, _836397] : [_836397 = _836395, -(c_Lazy__Sequence_Ohit__bound(_836397) = c_Lazy__Sequence_Ohit__bound(_836395))], (3802 ^ _779448) ^ [_836480, _836482, _836484, _836486, _836488, _836490, _836492, _836494, _836496, _836498, _836500, _836502, _836504, _836506] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836506, _836502, _836498, _836494, _836490, _836486, _836482) = c_New__Random__Sequence_Oneg__decr__bind(_836504, _836500, _836496, _836492, _836488, _836484, _836480)), _836506 = _836504, _836502 = _836500, _836498 = _836496, _836494 = _836492, _836490 = _836488, _836486 = _836484, _836482 = _836480], (3832 ^ _779448) ^ [_837069, _837071, _837073, _837075, _837077, _837079, _837081, _837083] : [-(c_New__DSequence_Oneg__decr__bind(_837083, _837079, _837075, _837071) = c_New__DSequence_Oneg__decr__bind(_837081, _837077, _837073, _837069)), _837083 = _837081, _837079 = _837077, _837075 = _837073, _837071 = _837069], (3850 ^ _779448) ^ [_837370, _837372, _837374, _837376, _837378, _837380, _837382, _837384, _837386, _837388, _837390, _837392, _837394, _837396] : [-(c_New__Random__Sequence_Opos__decr__bind(_837396, _837392, _837388, _837384, _837380, _837376, _837372) = c_New__Random__Sequence_Opos__decr__bind(_837394, _837390, _837386, _837382, _837378, _837374, _837370)), _837396 = _837394, _837392 = _837390, _837388 = _837386, _837384 = _837382, _837380 = _837378, _837376 = _837374, _837372 = _837370], (3880 ^ _779448) ^ [_837959, _837961, _837963, _837965, _837967, _837969, _837971, _837973] : [-(c_New__DSequence_Opos__decr__bind(_837973, _837969, _837965, _837961) = c_New__DSequence_Opos__decr__bind(_837971, _837967, _837963, _837959)), _837973 = _837971, _837969 = _837967, _837965 = _837963, _837961 = _837959], (3898 ^ _779448) ^ [_838260, _838262, _838264, _838266, _838268, _838270, _838272, _838274] : [-(c_Lazy__Sequence_Ohb__bind(_838274, _838270, _838266, _838262) = c_Lazy__Sequence_Ohb__bind(_838272, _838268, _838264, _838260)), _838274 = _838272, _838270 = _838268, _838266 = _838264, _838262 = _838260], (3916 ^ _779448) ^ [_838561, _838563, _838565, _838567, _838569, _838571, _838573, _838575] : [-(c_New__Random__Sequence_Opos__empty(_838575, _838571, _838567, _838563) = c_New__Random__Sequence_Opos__empty(_838573, _838569, _838565, _838561)), _838575 = _838573, _838571 = _838569, _838567 = _838565, _838563 = _838561], (3934 ^ _779448) ^ [_838862, _838864] : [_838864 = _838862, -(c_New__DSequence_Opos__empty(_838864) = c_New__DSequence_Opos__empty(_838862))], (3940 ^ _779448) ^ [_838947, _838949, _838951, _838953, _838955, _838957, _838959, _838961] : [-(c_New__DSequence_Oneg__bind(_838961, _838957, _838953, _838949) = c_New__DSequence_Oneg__bind(_838959, _838955, _838951, _838947)), _838961 = _838959, _838957 = _838955, _838953 = _838951, _838949 = _838947], (3958 ^ _779448) ^ [_839248, _839250, _839252, _839254, _839256, _839258, _839260, _839262] : [-(c_New__Random__Sequence_Oneg__map(_839262, _839258, _839254, _839250) = c_New__Random__Sequence_Oneg__map(_839260, _839256, _839252, _839248)), _839262 = _839260, _839258 = _839256, _839254 = _839252, _839250 = _839248], (3976 ^ _779448) ^ [_839549, _839551, _839553, _839555, _839557, _839559, _839561, _839563] : [-(c_New__Random__Sequence_Oneg__bind(_839563, _839559, _839555, _839551) = c_New__Random__Sequence_Oneg__bind(_839561, _839557, _839553, _839549)), _839563 = _839561, _839559 = _839557, _839555 = _839553, _839551 = _839549], (3994 ^ _779448) ^ [_839850, _839852] : [_839852 = _839850, -(c_New__Random__Sequence_Oneg__single(_839852) = c_New__Random__Sequence_Oneg__single(_839850))], (4000 ^ _779448) ^ [_839935, _839937, _839939, _839941, _839943, _839945, _839947, _839949] : [-(c_New__DSequence_Opos__bind(_839949, _839945, _839941, _839937) = c_New__DSequence_Opos__bind(_839947, _839943, _839939, _839935)), _839949 = _839947, _839945 = _839943, _839941 = _839939, _839937 = _839935], (4018 ^ _779448) ^ [_840236, _840238, _840240, _840242] : [-(c_New__DSequence_Oneg__single(_840242, _840238) = c_New__DSequence_Oneg__single(_840240, _840236)), _840242 = _840240, _840238 = _840236], (4028 ^ _779448) ^ [_840385, _840387, _840389, _840391] : [-(c_Lazy__Sequence_Ohb__single(_840391, _840387) = c_Lazy__Sequence_Ohb__single(_840389, _840385)), _840391 = _840389, _840387 = _840385], (4038 ^ _779448) ^ [_840534, _840536, _840538, _840540, _840542, _840544, _840546, _840548] : [-(c_New__Random__Sequence_Opos__map(_840548, _840544, _840540, _840536) = c_New__Random__Sequence_Opos__map(_840546, _840542, _840538, _840534)), _840548 = _840546, _840544 = _840542, _840540 = _840538, _840536 = _840534], (4056 ^ _779448) ^ [_840835, _840837, _840839, _840841, _840843, _840845, _840847, _840849] : [-(c_New__Random__Sequence_Opos__bind(_840849, _840845, _840841, _840837) = c_New__Random__Sequence_Opos__bind(_840847, _840843, _840839, _840835)), _840849 = _840847, _840845 = _840843, _840841 = _840839, _840837 = _840835], (4074 ^ _779448) ^ [_841136, _841138] : [_841138 = _841136, -(c_New__Random__Sequence_Opos__single(_841138) = c_New__Random__Sequence_Opos__single(_841136))], (4080 ^ _779448) ^ [_841221, _841223, _841225, _841227, _841229, _841231] : [-(c_List_Osplice(_841231, _841227, _841223) = c_List_Osplice(_841229, _841225, _841221)), _841231 = _841229, _841227 = _841225, _841223 = _841221], (4094 ^ _779448) ^ [_841442, _841444, _841446, _841448] : [-(c_New__DSequence_Opos__single(_841448, _841444) = c_New__DSequence_Opos__single(_841446, _841442)), _841448 = _841446, _841444 = _841442], (4104 ^ _779448) ^ [_841591, _841593, _841595, _841597, _841599, _841601] : [-(c_Predicate_Oconversep(_841601, _841597, _841593) = c_Predicate_Oconversep(_841599, _841595, _841591)), _841601 = _841599, _841597 = _841595, _841593 = _841591], (4118 ^ _779448) ^ [_841812, _841814] : [_841814 = _841812, -(c_List_Otl(_841814) = c_List_Otl(_841812))], (4124 ^ _779448) ^ [_841897, _841899] : [_841899 = _841897, -(c_List_Orev(_841899) = c_List_Orev(_841897))], (4130 ^ _779448) ^ [_841982, _841984] : [_841984 = _841982, -(c_List_Odrop(_841984) = c_List_Odrop(_841982))], (4136 ^ _779448) ^ [_842067, _842069] : [_842069 = _842067, -(c_List_Ohd(_842069) = c_List_Ohd(_842067))], (4142 ^ _779448) ^ [_842152, _842154, _842156, _842158] : [-(c_List_Olast(_842158, _842154) = c_List_Olast(_842156, _842152)), _842158 = _842156, _842154 = _842152], (4152 ^ _779448) ^ [_842301, _842303] : [_842303 = _842301, -(c_List_Otake(_842303) = c_List_Otake(_842301))], (4158 ^ _779448) ^ [_842386, _842388, _842390, _842392] : [-(c_List_Ozip(_842392, _842388) = c_List_Ozip(_842390, _842386)), _842392 = _842390, _842388 = _842386], (4168 ^ _779448) ^ [_842535, _842537] : [_842537 = _842535, -(c_Orderings_Oord__class_Omin(_842537) = c_Orderings_Oord__class_Omin(_842535))], (4174 ^ _779448) ^ [_842620, _842622] : [_842622 = _842620, -(c_List_Onth(_842622) = c_List_Onth(_842620))], (4180 ^ _779448) ^ [_842705, _842707, _842709, _842711] : [-(c_List_Ofilter(_842711, _842707) = c_List_Ofilter(_842709, _842705)), _842711 = _842709, _842707 = _842705], (4190 ^ _779448) ^ [_842854, _842856, _842858, _842860] : [-(c_List_Oconcat(_842860, _842856) = c_List_Oconcat(_842858, _842854)), _842860 = _842858, _842856 = _842854], (4200 ^ _779448) ^ [_843003, _843005] : [_843005 = _843003, -(c_List_Oappend(_843005) = c_List_Oappend(_843003))], (4206 ^ _779448) ^ [_843088, _843090, _843092, _843094] : [-(c_List_Omap(_843094, _843090) = c_List_Omap(_843092, _843088)), _843094 = _843092, _843090 = _843088], (4216 ^ _779448) ^ [_843237, _843239, _843241, _843243, _843245, _843247] : [-(c_List_Oreplicate(_843247, _843243, _843239) = c_List_Oreplicate(_843245, _843241, _843237)), _843247 = _843245, _843243 = _843241, _843239 = _843237], (4230 ^ _779448) ^ [_843458, _843460] : [_843460 = _843458, -(c_If(_843460) = c_If(_843458))], (4236 ^ _779448) ^ [_843543, _843545, _843547, _843549, _843551, _843553, _843555, _843557, _843559, _843561] : [-(c_Predicate_Opred__comp(_843561, _843557, _843553, _843549, _843545) = c_Predicate_Opred__comp(_843559, _843555, _843551, _843547, _843543)), _843561 = _843559, _843557 = _843555, _843553 = _843551, _843549 = _843547, _843545 = _843543], (4258 ^ _779448) ^ [_843932, _843934, _843936, _843938, _843940, _843942, _843944, _843946] : [-(c_Lazy__Sequence_Oproduct(_843946, _843942, _843938, _843934) = c_Lazy__Sequence_Oproduct(_843944, _843940, _843936, _843932)), _843946 = _843944, _843942 = _843940, _843938 = _843936, _843934 = _843932], (4276 ^ _779448) ^ [_844233, _844235, _844237, _844239, _844241, _844243, _844245, _844247, _844249, _844251, _844253, _844255] : [-(c_New__Random__Sequence_Opos__union(_844255, _844251, _844247, _844243, _844239, _844235) = c_New__Random__Sequence_Opos__union(_844253, _844249, _844245, _844241, _844237, _844233)), _844255 = _844253, _844251 = _844249, _844247 = _844245, _844243 = _844241, _844239 = _844237, _844235 = _844233], (4302 ^ _779448) ^ [_844718, _844720, _844722, _844724, _844726, _844728] : [-(c_New__DSequence_Opos__union(_844728, _844724, _844720) = c_New__DSequence_Opos__union(_844726, _844722, _844718)), _844728 = _844726, _844724 = _844722, _844720 = _844718], (4316 ^ _779448) ^ [_844939, _844941, _844943, _844945] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844945, _844941) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844943, _844939)), _844945 = _844943, _844941 = _844939], (4326 ^ _779448) ^ [_845088, _845090] : [_845090 = _845088, -(c_Lazy__Sequence_Oempty(_845090) = c_Lazy__Sequence_Oempty(_845088))], (4332 ^ _779448) ^ [_845173, _845175] : [_845175 = _845173, -(c_Lazy__Sequence_Osingle(_845175) = c_Lazy__Sequence_Osingle(_845173))], (4338 ^ _779448) ^ [_845258, _845260, _845262, _845264] : [-(c_Lazy__Sequence_Osmall__lazy_H(_845264, _845260) = c_Lazy__Sequence_Osmall__lazy_H(_845262, _845258)), _845264 = _845262, _845260 = _845258], (4348 ^ _779448) ^ [_845407, _845409, _845411, _845413] : [-(c_Wellfounded_Oaccp(_845413, _845409) = c_Wellfounded_Oaccp(_845411, _845407)), _845413 = _845411, _845409 = _845407], (4358 ^ _779448) ^ [_845556, _845558, _845560, _845562, _845564, _845566, _845568, _845570, _845572, _845574] : [-(c_Option_Ooption_Ooption__case(_845574, _845570, _845566, _845562, _845558) = c_Option_Ooption_Ooption__case(_845572, _845568, _845564, _845560, _845556)), _845574 = _845572, _845570 = _845568, _845566 = _845564, _845562 = _845560, _845558 = _845556], (4380 ^ _779448) ^ [_845945, _845947] : [_845947 = _845945, -(c_Lazy__Sequence_Oyieldn(_845947) = c_Lazy__Sequence_Oyieldn(_845945))], (4386 ^ _779448) ^ [_846030, _846032, _846034, _846036, _846038, _846040] : [-(c_Lazy__Sequence_Oanamorph(_846040, _846036, _846032) = c_Lazy__Sequence_Oanamorph(_846038, _846034, _846030)), _846040 = _846038, _846036 = _846034, _846032 = _846030], (4400 ^ _779448) ^ [_846251, _846253] : [_846253 = _846251, -(c_Lazy__Sequence_Oyield(_846253) = c_Lazy__Sequence_Oyield(_846251))], (4406 ^ _779448) ^ [_846336, _846338] : [_846338 = _846336, -(c_List_Olist_OCons(_846338) = c_List_Olist_OCons(_846336))], (4412 ^ _779448) ^ [_846421, _846423] : [_846423 = _846421, -(c_List_Olist_ONil(_846423) = c_List_Olist_ONil(_846421))], (4418 ^ _779448) ^ [_846506, _846508] : [_846508 = _846506, -(c_List_Omember(_846508) = c_List_Omember(_846506))], (4424 ^ _779448) ^ [_846591, _846593, _846595, _846597] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846597, _846593) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846595, _846591)), _846597 = _846595, _846593 = _846591], (4434 ^ _779448) ^ [_846740, _846742, _846744, _846746] : [-(c_HOL_OThe(_846746, _846742) = c_HOL_OThe(_846744, _846740)), _846746 = _846744, _846742 = _846740], (4444 ^ _779448) ^ [_846889, _846891, _846893, _846895, _846897, _846899] : [-(c_FunDef_OTHE__default(_846899, _846895, _846891) = c_FunDef_OTHE__default(_846897, _846893, _846889)), _846899 = _846897, _846895 = _846893, _846891 = _846889], (4458 ^ _779448) ^ [_847110, _847112, _847114, _847116] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847116, _847112) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847114, _847110)), _847116 = _847114, _847112 = _847110], (4468 ^ _779448) ^ [_847259, _847261] : [_847261 = _847259, -(c_Nat_Osize__class_Osize(_847261) = c_Nat_Osize__class_Osize(_847259))], (4474 ^ _779448) ^ [_847344, _847346, _847348, _847350, _847352, _847354, _847356, _847358, _847360, _847362] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847362, _847358, _847354, _847350, _847346) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847360, _847356, _847352, _847348, _847344)), _847362 = _847360, _847358 = _847356, _847354 = _847352, _847350 = _847348, _847346 = _847344], (4496 ^ _779448) ^ [_847733, _847735, _847737, _847739] : [-(c_List_Oupto(_847739, _847735) = c_List_Oupto(_847737, _847733)), _847739 = _847737, _847735 = _847733], (4506 ^ _779448) ^ [_847882, _847884] : [_847884 = _847882, -(c_Code__Numeral_OSuc__code__numeral(_847884) = c_Code__Numeral_OSuc__code__numeral(_847882))], (4512 ^ _779448) ^ [_847967, _847969, _847971, _847973, _847975, _847977, _847979, _847981] : [-(c_Product__Type_Oscomp(_847981, _847977, _847973, _847969) = c_Product__Type_Oscomp(_847979, _847975, _847971, _847967)), _847981 = _847979, _847977 = _847975, _847973 = _847971, _847969 = _847967], (4530 ^ _779448) ^ [_848268, _848270, _848272, _848274, _848276, _848278, _848280, _848282] : [-(c_Random__Sequence_ORandom(_848282, _848278, _848274, _848270) = c_Random__Sequence_ORandom(_848280, _848276, _848272, _848268)), _848282 = _848280, _848278 = _848276, _848274 = _848272, _848270 = _848268], (4548 ^ _779448) ^ [_848569, _848571] : [_848571 = _848569, -(c_DSequence_Ounion(_848571) = c_DSequence_Ounion(_848569))], (4554 ^ _779448) ^ [_848654, _848656, _848658, _848660, _848662, _848664, _848666, _848668] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848668, _848664, _848660, _848656) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848666, _848662, _848658, _848654)), _848668 = _848666, _848664 = _848662, _848660 = _848658, _848656 = _848654], (4572 ^ _779448) ^ [_848955, _848957, _848959, _848961, _848963, _848965] : [-(c_Random__Sequence_Oempty(_848965, _848961, _848957) = c_Random__Sequence_Oempty(_848963, _848959, _848955)), _848965 = _848963, _848961 = _848959, _848957 = _848955], (4586 ^ _779448) ^ [_849176, _849178] : [_849178 = _849176, -(c_DSequence_Oempty(_849178) = c_DSequence_Oempty(_849176))], (4592 ^ _779448) ^ [_849261, _849263] : [_849263 = _849261, -(c_DSequence_Osingle(_849263) = c_DSequence_Osingle(_849261))], (4598 ^ _779448) ^ [_849346, _849348, _849350, _849352, _849354, _849356, _849358, _849360] : [-(c_Random__Sequence_Omap(_849360, _849356, _849352, _849348) = c_Random__Sequence_Omap(_849358, _849354, _849350, _849346)), _849360 = _849358, _849356 = _849354, _849352 = _849350, _849348 = _849346], (4616 ^ _779448) ^ [_849647, _849649, _849651, _849653, _849655, _849657, _849659, _849661] : [-(c_Random__Sequence_Obind(_849661, _849657, _849653, _849649) = c_Random__Sequence_Obind(_849659, _849655, _849651, _849647)), _849661 = _849659, _849657 = _849655, _849653 = _849651, _849649 = _849647], (4634 ^ _779448) ^ [_849948, _849950] : [_849950 = _849948, -(c_Random__Sequence_Osingle(_849950) = c_Random__Sequence_Osingle(_849948))], (4640 ^ _779448) ^ [_850033, _850035, _850037, _850039] : [-(c_Product__Type_Osnd(_850039, _850035) = c_Product__Type_Osnd(_850037, _850033)), _850039 = _850037, _850035 = _850033], (4650 ^ _779448) ^ [_850182, _850184, _850186, _850188] : [-(c_Product__Type_Ofst(_850188, _850184) = c_Product__Type_Ofst(_850186, _850182)), _850188 = _850186, _850184 = _850182], (4660 ^ _779448) ^ [_850331, _850333, _850335, _850337, _850339, _850341] : [-(c_Relation_OImage(_850341, _850337, _850333) = c_Relation_OImage(_850339, _850335, _850331)), _850341 = _850339, _850337 = _850335, _850333 = _850331], (4674 ^ _779448) ^ [_850552, _850554, _850556, _850558, _850560, _850562, _850564, _850566] : [-(c_Wellfounded_Olex__prod(_850566, _850562, _850558, _850554) = c_Wellfounded_Olex__prod(_850564, _850560, _850556, _850552)), _850566 = _850564, _850562 = _850560, _850558 = _850556, _850554 = _850552], (4692 ^ _779448) ^ [_850853, _850855] : [_850855 = _850853, -(c_Set_OBex(_850855) = c_Set_OBex(_850853))], (4698 ^ _779448) ^ [_850938, _850940, _850942, _850944] : [-(c_List_Olexord(_850944, _850940) = c_List_Olexord(_850942, _850938)), _850944 = _850942, _850940 = _850938], (4708 ^ _779448) ^ [_851087, _851089] : [_851089 = _851087, -(c_Wellfounded_Ofinite__psubset(_851089) = c_Wellfounded_Ofinite__psubset(_851087))], (4714 ^ _779448) ^ [_851172, _851174] : [_851174 = _851172, -(c_List_Oset(_851174) = c_List_Oset(_851172))], (4720 ^ _779448) ^ [_851257, _851259, _851261, _851263] : [-(c_Complete__Lattice_OSup__class_OSup(_851263, _851259) = c_Complete__Lattice_OSup__class_OSup(_851261, _851257)), _851263 = _851261, _851259 = _851257], (4730 ^ _779448) ^ [_851406, _851408, _851410, _851412] : [-(c_Complete__Lattice_OInf__class_OInf(_851412, _851408) = c_Complete__Lattice_OInf__class_OInf(_851410, _851406)), _851412 = _851410, _851408 = _851406], (4740 ^ _779448) ^ [_851555, _851557, _851559, _851561, _851563, _851565, _851567, _851569, _851571, _851573, _851575, _851577] : [-(c_Partial__Function_Ofun__lub(_851577, _851573, _851569, _851565, _851561, _851557) = c_Partial__Function_Ofun__lub(_851575, _851571, _851567, _851563, _851559, _851555)), _851577 = _851575, _851573 = _851571, _851569 = _851567, _851565 = _851563, _851561 = _851559, _851557 = _851555], (4766 ^ _779448) ^ [_852040, _852042, _852044, _852046, _852048, _852050] : [-(c_Relation_Orel__comp(_852050, _852046, _852042) = c_Relation_Orel__comp(_852048, _852044, _852040)), _852050 = _852048, _852046 = _852044, _852042 = _852040], (4780 ^ _779448) ^ [_852261, _852263, _852265, _852267] : [-(c_Relation_Oinv__image(_852267, _852263) = c_Relation_Oinv__image(_852265, _852261)), _852267 = _852265, _852263 = _852261], (4790 ^ _779448) ^ [_852410, _852412, _852414, _852416] : [-(c_List_Olistrel(_852416, _852412) = c_List_Olistrel(_852414, _852410)), _852416 = _852414, _852412 = _852410], (4800 ^ _779448) ^ [_852559, _852561] : [_852561 = _852559, -(c_Relation_OId(_852561) = c_Relation_OId(_852559))], (4806 ^ _779448) ^ [_852644, _852646, _852648, _852650] : [-(c_Relation_OId__on(_852650, _852646) = c_Relation_OId__on(_852648, _852644)), _852650 = _852648, _852646 = _852644], (4816 ^ _779448) ^ [_852793, _852795, _852797, _852799] : [-(c_Relation_Oconverse(_852799, _852795) = c_Relation_Oconverse(_852797, _852793)), _852799 = _852797, _852795 = _852793], (4826 ^ _779448) ^ [_852942, _852944] : [_852944 = _852942, -(c_HOL_OEx(_852944) = c_HOL_OEx(_852942))], (4832 ^ _779448) ^ [_853027, _853029, _853031, _853033] : [-(c_Hilbert__Choice_OEps(_853033, _853029) = c_Hilbert__Choice_OEps(_853031, _853027)), _853033 = _853031, _853029 = _853027], (4842 ^ _779448) ^ [_853176, _853178, _853180, _853182, _853184, _853186] : [-(c_Finite__Set_Ofold__image(_853186, _853182, _853178) = c_Finite__Set_Ofold__image(_853184, _853180, _853176)), _853186 = _853184, _853182 = _853180, _853178 = _853176], (4856 ^ _779448) ^ [_853397, _853399, _853401, _853403] : [-(c_Quickcheck_Obeyond(_853403, _853399) = c_Quickcheck_Obeyond(_853401, _853397)), _853403 = _853401, _853399 = _853397], (4866 ^ _779448) ^ [_853546, _853548, _853550, _853552, _853554, _853556, _853558, _853560, _853562, _853564] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853564, _853560, _853556, _853552, _853548) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853562, _853558, _853554, _853550, _853546)), _853564 = _853562, _853560 = _853558, _853556 = _853554, _853552 = _853550, _853548 = _853546], (4888 ^ _779448) ^ [_853935, _853937] : [_853937 = _853935, -(c_Set_OCollect(_853937) = c_Set_OCollect(_853935))], (4894 ^ _779448) ^ [_854020, _854022] : [_854022 = _854020, -(c_Lattices_Osemilattice__inf__class_Oinf(_854022) = c_Lattices_Osemilattice__inf__class_Oinf(_854020))], (4900 ^ _779448) ^ [_854105, _854107] : [_854107 = _854105, -(c_Lattices_Osemilattice__sup__class_Osup(_854107) = c_Lattices_Osemilattice__sup__class_Osup(_854105))], (4906 ^ _779448) ^ [_854190, _854192] : [_854192 = _854190, -(c_Fun_Oid(_854192) = c_Fun_Oid(_854190))], (4912 ^ _779448) ^ [_854275, _854277, _854279, _854281, _854283, _854285, _854287, _854289] : [-(c_Fun_Othe__inv__into(_854289, _854285, _854281, _854277) = c_Fun_Othe__inv__into(_854287, _854283, _854279, _854275)), _854289 = _854287, _854285 = _854283, _854281 = _854279, _854277 = _854275], (4930 ^ _779448) ^ [_854576, _854578, _854580, _854582, _854584, _854586] : [-(c_Product__Type_Oprod_Oprod__case(_854586, _854582, _854578) = c_Product__Type_Oprod_Oprod__case(_854584, _854580, _854576)), _854586 = _854584, _854582 = _854580, _854578 = _854576], (4944 ^ _779448) ^ [_854797, _854799, _854801, _854803, _854805, _854807, _854809, _854811] : [-(c_Product__Type_Ocurry(_854811, _854807, _854803, _854799) = c_Product__Type_Ocurry(_854809, _854805, _854801, _854797)), _854811 = _854809, _854807 = _854805, _854803 = _854801, _854799 = _854797], (4962 ^ _779448) ^ [_855098, _855100, _855102, _855104, _855106, _855108] : [-(c_Set_Ovimage(_855108, _855104, _855100) = c_Set_Ovimage(_855106, _855102, _855098)), _855108 = _855106, _855104 = _855102, _855100 = _855098], (4976 ^ _779448) ^ [_855319, _855321, _855323, _855325, _855327, _855329, _855331, _855333] : [-(c_Hilbert__Choice_Oinv__into(_855333, _855329, _855325, _855321) = c_Hilbert__Choice_Oinv__into(_855331, _855327, _855323, _855319)), _855333 = _855331, _855329 = _855327, _855325 = _855323, _855321 = _855319], (4994 ^ _779448) ^ [_855620, _855622] : [_855622 = _855620, -(c_Orderings_Otop__class_Otop(_855622) = c_Orderings_Otop__class_Otop(_855620))], (5000 ^ _779448) ^ [_855705, _855707, _855709, _855711, _855713, _855715] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855715, _855711, _855707) = c_SetInterval_Oord__class_OatLeastAtMost(_855713, _855709, _855705)), _855715 = _855713, _855711 = _855709, _855707 = _855705], (5014 ^ _779448) ^ [_855926, _855928, _855930, _855932] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855932, _855928) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855930, _855926)), _855932 = _855930, _855928 = _855926], (5024 ^ _779448) ^ [_856075, _856077, _856079, _856081] : [-(c_Quotient_ORespects(_856081, _856077) = c_Quotient_ORespects(_856079, _856075)), _856081 = _856079, _856077 = _856075], (5034 ^ _779448) ^ [_856224, _856226, _856228, _856230, _856232, _856234, _856236, _856238] : [-(c_Quotient_OBabs(_856238, _856234, _856230, _856226) = c_Quotient_OBabs(_856236, _856232, _856228, _856224)), _856238 = _856236, _856234 = _856232, _856230 = _856228, _856226 = _856224], (5052 ^ _779448) ^ [_856525, _856527, _856529, _856531] : [-(c_Transitive__Closure_Otrancl(_856531, _856527) = c_Transitive__Closure_Otrancl(_856529, _856525)), _856531 = _856529, _856527 = _856525], (5062 ^ _779448) ^ [_856674, _856676, _856678, _856680] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856680, _856676) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856678, _856674)), _856680 = _856678, _856676 = _856674], (5072 ^ _779448) ^ [_856823, _856825, _856827, _856829] : [-(c_Transitive__Closure_Ortrancl(_856829, _856825) = c_Transitive__Closure_Ortrancl(_856827, _856823)), _856829 = _856827, _856825 = _856823], (5082 ^ _779448) ^ [_856972, _856974, _856976, _856978] : [-(c_Product__Type_OPair(_856978, _856974) = c_Product__Type_OPair(_856976, _856972)), _856978 = _856976, _856974 = _856972], (5092 ^ _779448) ^ [_857121, _857123, _857125, _857127, _857129, _857131] : [-(c_Lazy__Sequence_Oappend(_857131, _857127, _857123) = c_Lazy__Sequence_Oappend(_857129, _857125, _857121)), _857131 = _857129, _857127 = _857125, _857123 = _857121], (5106 ^ _779448) ^ [_857342, _857344, _857346, _857348] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_857348, _857344) = c_SetInterval_Oord__class_OatLeastLessThan(_857346, _857342)), _857348 = _857346, _857344 = _857342], (5116 ^ _779448) ^ [_857491, _857493, _857495, _857497] : [-(c_List_Oupt(_857497, _857493) = c_List_Oupt(_857495, _857491)), _857497 = _857495, _857493 = _857491], (5126 ^ _779448) ^ [_857640, _857642, _857644, _857646, _857648, _857650, _857652, _857654] : [-(c_Fun_Ocomp(_857654, _857650, _857646, _857642) = c_Fun_Ocomp(_857652, _857648, _857644, _857640)), _857654 = _857652, _857650 = _857648, _857646 = _857644, _857642 = _857640], (5144 ^ _779448) ^ [_857941, _857943, _857945, _857947, _857949, _857951] : [-(c_Lazy__Sequence_Obind(_857951, _857947, _857943) = c_Lazy__Sequence_Obind(_857949, _857945, _857941)), _857951 = _857949, _857947 = _857945, _857943 = _857941], (5158 ^ _779448) ^ [_858162, _858164, _858166, _858168] : [-(c_Lazy__Sequence_Oflat(_858168, _858164) = c_Lazy__Sequence_Oflat(_858166, _858162)), _858168 = _858166, _858164 = _858162], (5168 ^ _779448) ^ [_858311, _858313, _858315, _858317, _858319, _858321] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_858321, _858317, _858313) = c_Lazy__Sequence_Olazy__sequence_OInsert(_858319, _858315, _858311)), _858321 = _858319, _858317 = _858315, _858313 = _858311], (5182 ^ _779448) ^ [_858532, _858534] : [_858534 = _858532, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858534) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858532))], (5188 ^ _779448) ^ [_858617, _858619, _858621, _858623, _858625, _858627, _858629, _858631, _858633, _858635] : [-(c_New__DSequence_Opos__map(_858635, _858631, _858627, _858623, _858619) = c_New__DSequence_Opos__map(_858633, _858629, _858625, _858621, _858617)), _858635 = _858633, _858631 = _858629, _858627 = _858625, _858623 = _858621, _858619 = _858617], (5210 ^ _779448) ^ [_859006, _859008, _859010, _859012, _859014, _859016, _859018, _859020] : [-(c_Lazy__Sequence_Omap(_859020, _859016, _859012, _859008) = c_Lazy__Sequence_Omap(_859018, _859014, _859010, _859006)), _859020 = _859018, _859016 = _859014, _859012 = _859010, _859008 = _859006], (5228 ^ _779448) ^ [_859307, _859309] : [_859309 = _859307, -(c_Int_Onumber__class_Onumber__of(_859309) = c_Int_Onumber__class_Onumber__of(_859307))], (5234 ^ _779448) ^ [_859392, _859394, _859396, _859398, _859400, _859402] : [-(c_SetInterval_Oord_OatLeast(_859402, _859398, _859394) = c_SetInterval_Oord_OatLeast(_859400, _859396, _859392)), _859402 = _859400, _859398 = _859396, _859394 = _859392], (5248 ^ _779448) ^ [_859613, _859615, _859617, _859619, _859621, _859623] : [-(c_SetInterval_Oord_OatMost(_859623, _859619, _859615) = c_SetInterval_Oord_OatMost(_859621, _859617, _859613)), _859623 = _859621, _859619 = _859617, _859615 = _859613], (5262 ^ _779448) ^ [_859834, _859836, _859838, _859840, _859842, _859844] : [-(c_SetInterval_Oord_OlessThan(_859844, _859840, _859836) = c_SetInterval_Oord_OlessThan(_859842, _859838, _859834)), _859844 = _859842, _859840 = _859838, _859836 = _859834], (5276 ^ _779448) ^ [_860055, _860057, _860059, _860061, _860063, _860065] : [-(c_SetInterval_Oord_OgreaterThan(_860065, _860061, _860057) = c_SetInterval_Oord_OgreaterThan(_860063, _860059, _860055)), _860065 = _860063, _860061 = _860059, _860057 = _860055], (5290 ^ _779448) ^ [_860276, _860278] : [_860278 = _860276, -(c_Groups_Oabs__class_Oabs(_860278) = c_Groups_Oabs__class_Oabs(_860276))], (5296 ^ _779448) ^ [_860361, _860363, _860365, _860367, _860369, _860371] : [-(c_Divides_Odiv__class_Omod(_860371, _860367, _860363) = c_Divides_Odiv__class_Omod(_860369, _860365, _860361)), _860371 = _860369, _860367 = _860365, _860363 = _860361], (5310 ^ _779448) ^ [_860582, _860584] : [_860584 = _860582, -(c_Groups_Ouminus__class_Ouminus(_860584) = c_Groups_Ouminus__class_Ouminus(_860582))], (5316 ^ _779448) ^ [_860667, _860669, _860671, _860673, _860675, _860677, _860679, _860681] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_860681, _860677, _860673, _860669) = c_SetInterval_Oord_OgreaterThanLessThan(_860679, _860675, _860671, _860667)), _860681 = _860679, _860677 = _860675, _860673 = _860671, _860669 = _860667], (5334 ^ _779448) ^ [_860968, _860970, _860972, _860974, _860976, _860978, _860980, _860982, _860984, _860986] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_860986, _860982, _860978, _860974, _860970) = c_SetInterval_Oord_OgreaterThanAtMost(_860984, _860980, _860976, _860972, _860968)), _860986 = _860984, _860982 = _860980, _860978 = _860976, _860974 = _860972, _860970 = _860968], (5356 ^ _779448) ^ [_861357, _861359, _861361, _861363, _861365, _861367, _861369, _861371, _861373, _861375] : [-(c_SetInterval_Oord_OatLeastLessThan(_861375, _861371, _861367, _861363, _861359) = c_SetInterval_Oord_OatLeastLessThan(_861373, _861369, _861365, _861361, _861357)), _861375 = _861373, _861371 = _861369, _861367 = _861365, _861363 = _861361, _861359 = _861357], (5378 ^ _779448) ^ [_861746, _861748, _861750, _861752, _861754, _861756, _861758, _861760] : [-(c_SetInterval_Oord_OatLeastAtMost(_861760, _861756, _861752, _861748) = c_SetInterval_Oord_OatLeastAtMost(_861758, _861754, _861750, _861746)), _861760 = _861758, _861756 = _861754, _861752 = _861750, _861748 = _861746], (5396 ^ _779448) ^ [_862047, _862049] : [_862049 = _862047, -(c_Divides_Odiv__class_Odiv(_862049) = c_Divides_Odiv__class_Odiv(_862047))], (5402 ^ _779448) ^ [_862132, _862134] : [_862134 = _862132, -(c_Groups_Oplus__class_Oplus(_862134) = c_Groups_Oplus__class_Oplus(_862132))], (5408 ^ _779448) ^ [_862217, _862219, _862221, _862223] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862223, _862219) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862221, _862217)), _862223 = _862221, _862219 = _862217], (5418 ^ _779448) ^ [_862366, _862368] : [_862368 = _862366, -(c_Power_Opower__class_Opower(_862368) = c_Power_Opower__class_Opower(_862366))], (5424 ^ _779448) ^ [_862451, _862453] : [_862453 = _862451, -(c_Groups_Otimes__class_Otimes(_862453) = c_Groups_Otimes__class_Otimes(_862451))], (5430 ^ _779448) ^ [_862536, _862538] : [_862538 = _862536, -(c_Groups_Oone__class_Oone(_862538) = c_Groups_Oone__class_Oone(_862536))], (5436 ^ _779448) ^ [_862621, _862623] : [_862623 = _862621, -(c_Equiv__Relations_Oquotient(_862623) = c_Equiv__Relations_Oquotient(_862621))], (5442 ^ _779448) ^ [_862706, _862708] : [_862708 = _862706, -(c_Orderings_Oord__class_Oless(_862708) = c_Orderings_Oord__class_Oless(_862706))], (5448 ^ _779448) ^ [_862791, _862793] : [_862793 = _862791, -(c_Groups_Ozero__class_Ozero(_862793) = c_Groups_Ozero__class_Ozero(_862791))], (5454 ^ _779448) ^ [_862876, _862878] : [_862878 = _862876, -(c_Rings_Odvd__class_Odvd(_862878) = c_Rings_Odvd__class_Odvd(_862876))], (5460 ^ _779448) ^ [_862961, _862963] : [_862963 = _862961, -(tc_List_Olist(_862963) = tc_List_Olist(_862961))], (5466 ^ _779448) ^ [_863046, _863048, _863050, _863052] : [-(tc_sum(_863052, _863048) = tc_sum(_863050, _863046)), _863052 = _863050, _863048 = _863046], (5476 ^ _779448) ^ [_863195, _863197] : [_863197 = _863195, -(tc_Option_Ooption(_863197) = tc_Option_Ooption(_863195))], (5482 ^ _779448) ^ [_863280, _863282, _863284, _863286] : [-(tc_Nitpick_Opair__box(_863286, _863282) = tc_Nitpick_Opair__box(_863284, _863280)), _863286 = _863284, _863282 = _863280], (5492 ^ _779448) ^ [_863429, _863431, _863433, _863435] : [-(tc_prod(_863435, _863431) = tc_prod(_863433, _863429)), _863435 = _863433, _863431 = _863429], (5502 ^ _779448) ^ [_863578, _863580] : [_863580 = _863578, -(tc_Lazy__Sequence_Olazy__sequence(_863580) = tc_Lazy__Sequence_Olazy__sequence(_863578))], (5508 ^ _779448) ^ [_863663, _863665] : [_863665 = _863663, -(c_COMBI(_863665) = c_COMBI(_863663))], (5514 ^ _779448) ^ [_863748, _863750, _863752, _863754] : [-(c_COMBK(_863754, _863750) = c_COMBK(_863752, _863748)), _863754 = _863752, _863750 = _863748], (5524 ^ _779448) ^ [_863897, _863899, _863901, _863903, _863905, _863907] : [-(c_COMBB(_863907, _863903, _863899) = c_COMBB(_863905, _863901, _863897)), _863907 = _863905, _863903 = _863901, _863899 = _863897], (5538 ^ _779448) ^ [_864118, _864120, _864122, _864124, _864126, _864128] : [-(c_COMBC(_864128, _864124, _864120) = c_COMBC(_864126, _864122, _864118)), _864128 = _864126, _864124 = _864122, _864120 = _864118], (5552 ^ _779448) ^ [_864339, _864341, _864343, _864345, _864347, _864349] : [-(c_COMBS(_864349, _864345, _864341) = c_COMBS(_864347, _864343, _864339)), _864349 = _864347, _864345 = _864343, _864341 = _864339], (5566 ^ _779448) ^ [_864560, _864562] : [_864562 = _864560, -(c_Finite__Set_Ofinite(_864562) = c_Finite__Set_Ofinite(_864560))], (5572 ^ _779448) ^ [_864645, _864647] : [_864647 = _864645, -(v_mgt(_864647) = v_mgt(_864645))], (5578 ^ _779448) ^ [_864730, _864732] : [_864732 = _864730, -(c_Groups_Ominus__class_Ominus(_864732) = c_Groups_Ominus__class_Ominus(_864730))], (5584 ^ _779448) ^ [_864815, _864817] : [_864817 = _864815, -(c_Finite__Set_Ocard(_864817) = c_Finite__Set_Ocard(_864815))], (5590 ^ _779448) ^ [_864900, _864902, _864904, _864906, _864908, _864910] : [-(c_Set_Oimage(_864910, _864906, _864902) = c_Set_Oimage(_864908, _864904, _864900)), _864910 = _864908, _864906 = _864904, _864902 = _864900], (5604 ^ _779448) ^ [_865121, _865123] : [_865123 = _865121, -(c_member(_865123) = c_member(_865121))], (5610 ^ _779448) ^ [_865206, _865208] : [_865208 = _865206, -(c_Orderings_Oord__class_Oless__eq(_865208) = c_Orderings_Oord__class_Oless__eq(_865206))], (5616 ^ _779448) ^ [_865291, _865293] : [_865293 = _865291, -(c_Set_Oinsert(_865293) = c_Set_Oinsert(_865291))], (5622 ^ _779448) ^ [_865376, _865378, _865380, _865382] : [-(hAPP(_865382, _865378) = hAPP(_865380, _865376)), _865382 = _865380, _865378 = _865376], (5632 ^ _779448) ^ [_865525, _865527] : [_865527 = _865525, -(c_Orderings_Obot__class_Obot(_865527) = c_Orderings_Obot__class_Obot(_865525))], (5638 ^ _779448) ^ [_865606, _865608, _865610, _865612] : [-(tc_fun(_865612, _865608) = tc_fun(_865610, _865606)), _865612 = _865610, _865608 = _865606], (5648 ^ _779448) ^ [_868521, _868523] : [hAPP(_868521, 5649 ^ [_868521, _868523]) = hAPP(_868523, 5649 ^ [_868521, _868523]), -(_868521 = _868523)], (5655 ^ _779448) ^ [_868647, _868649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _868647), _868649)), -(v_P(_868649, _868647))], (5661 ^ _779448) ^ [_868734, _868736] : [v_wt(_868734), 5667 ^ _779448 : [(5668 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 5666 ^ [_868734, _868736]), v_U)))], (5670 ^ _779448) ^ [] : [v_P(_868736, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, 5666 ^ [_868734, _868736])), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))]], -(v_P(_868736, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_868734)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (5674 ^ _779448) ^ [_868977, _868979, _868981, _868983] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868977), _868979)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868981), hAPP(c_Set_Oimage(_868977, _868981, _868983), _868979))))], (5680 ^ _779448) ^ [_869088, _869090, _869092] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869088), _869090)), 5683 ^ _779448 : [(5684 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869088), _869092), _869090)), -(hAPP(c_Finite__Set_Ocard(_869088), hAPP(hAPP(c_Set_Oinsert(_869088), _869092), _869090)) = hAPP(c_Finite__Set_Ocard(_869088), _869090))], (5690 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_869088), _869092), _869090))), -(hAPP(c_Finite__Set_Ocard(_869088), hAPP(hAPP(c_Set_Oinsert(_869088), _869092), _869090)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_869088), _869090)))]]], (5696 ^ _779448) ^ [_869382, _869384, _869386] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869382), _869384)), -(hBOOL(hAPP(hAPP(c_member(_869382), _869386), _869384))), -(hAPP(c_Finite__Set_Ocard(_869382), hAPP(hAPP(c_Set_Oinsert(_869382), _869386), _869384)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_869382), _869384)))], (5706 ^ _779448) ^ [_869540, _869542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869540, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_869540, tc_HOL_Obool))), _869542)))], (5708 ^ _779448) ^ [_869580, _869582, _869584] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869580), _869582)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_869580), hAPP(hAPP(c_Set_Oinsert(_869580), _869584), _869582))))], (5714 ^ _779448) ^ [_869691] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_869691), c_Orderings_Obot__class_Obot(tc_fun(_869691, tc_HOL_Obool)))))], (5716 ^ _779448) ^ [_869723, _869725, _869727, _869729, _869731, _869733] : [_869723 = hAPP(_869725, _869727), hBOOL(hAPP(hAPP(c_member(_869729), _869727), _869731)), -(hBOOL(hAPP(hAPP(c_member(_869733), _869723), hAPP(c_Set_Oimage(_869729, _869733, _869725), _869731))))], (5726 ^ _779448) ^ [_869916, _869918, _869920, _869922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869916, tc_HOL_Obool)), _869918), _869920)), hBOOL(hAPP(hAPP(c_member(_869916), _869922), _869918)), -(hBOOL(hAPP(hAPP(c_member(_869916), _869922), _869920)))], (5736 ^ _779448) ^ [_870101, _870103, _870105, _870107] : [hBOOL(hAPP(hAPP(c_member(_870101), _870103), hAPP(hAPP(c_Set_Oinsert(_870101), _870105), _870107))), -(_870103 = _870105), -(hBOOL(hAPP(hAPP(c_member(_870101), _870103), _870107)))], (5746 ^ _779448) ^ [_870241, _870243, _870245, _870247] : [5747 ^ _779448 : [(5748 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870241), _870243), _870245))], (5750 ^ _779448) ^ [] : [_870243 = _870247]], -(hBOOL(hAPP(hAPP(c_member(_870241), _870243), hAPP(hAPP(c_Set_Oinsert(_870241), _870247), _870245))))], (5754 ^ _779448) ^ [_870418, _870420] : [hBOOL(hAPP(hAPP(c_member(_870418), _870420), c_Orderings_Obot__class_Obot(tc_fun(_870418, tc_HOL_Obool))))], (5756 ^ _779448) ^ [_870455, _870457, _870459, _870461] : [_870455 = _870457, 5761 ^ _779448 : [(5762 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_870459), _870461), _870455)))], (5764 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_870459), _870461), _870457)))]], 5765 ^ _779448 : [(5766 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870459), _870461), _870455))], (5768 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870459), _870461), _870457))]]], (5770 ^ _779448) ^ [_870718, _870720, _870722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870718, tc_HOL_Obool)), _870720), _870722)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870718, tc_HOL_Obool)), _870722), _870720)), -(_870720 = _870722)], (5780 ^ _779448) ^ [_870891, _870893, _870895, _870897] : [_870891 = _870893, hBOOL(hAPP(hAPP(c_member(_870895), _870893), _870897)), -(hBOOL(hAPP(hAPP(c_member(_870895), _870891), _870897)))], (5790 ^ _779448) ^ [_871056, _871058, _871060, _871062] : [_871056 = _871058, 5793 ^ _779448 : [(5794 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871060), _871056), _871062)), -(hBOOL(hAPP(hAPP(c_member(_871060), _871058), _871062)))], (5800 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871060), _871058), _871062)), -(hBOOL(hAPP(hAPP(c_member(_871060), _871056), _871062)))]]], (5806 ^ _779448) ^ [_871317, _871319, _871321, _871323] : [_871317 = _871319, 5809 ^ _779448 : [(5810 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871321), _871323), _871317)), -(hBOOL(hAPP(hAPP(c_member(_871321), _871323), _871319)))], (5816 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871321), _871323), _871319)), -(hBOOL(hAPP(hAPP(c_member(_871321), _871323), _871317)))]]], (5822 ^ _779448) ^ [_871596, _871598, _871600] : [hBOOL(hAPP(hAPP(c_member(_871596), _871598), _871600)), -(hBOOL(hAPP(_871600, _871598)))], (5828 ^ _779448) ^ [_871689, _871691, _871693] : [hBOOL(hAPP(_871693, _871691)), -(hBOOL(hAPP(hAPP(c_member(_871689), _871691), _871693)))], (5834 ^ _779448) ^ [_871788, _871790] : [class_Finite__Set_Ofinite(_871788), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871788), _871790)))], (5840 ^ _779448) ^ [_871871, _871873] : [class_Finite__Set_Ofinite(_871871), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871871), _871873)))], (5856 ^ _779448) ^ [_872089, _872091, _872093, _872095] : [5857 ^ _779448 : [(5858 ^ _779448) ^ [] : [_872091 = _872095], (5860 ^ _779448) ^ [] : [hBOOL(hAPP(_872093, _872095))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872089), _872091), _872093), _872095)))], (5846 ^ _779448) ^ [_871975, _871977, _871979, _871981] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871975), _871977), _871979), _871981)), -(_871977 = _871981), -(hBOOL(hAPP(_871979, _871981)))], (5864 ^ _779448) ^ [_872234, _872236, _872238, _872240] : [-(hAPP(hAPP(c_Set_Oinsert(_872234), _872236), hAPP(hAPP(c_Set_Oinsert(_872234), _872238), _872240)) = hAPP(hAPP(c_Set_Oinsert(_872234), _872238), hAPP(hAPP(c_Set_Oinsert(_872234), _872236), _872240)))], (5866 ^ _779448) ^ [_872295, _872297, _872299] : [-(hAPP(hAPP(c_Set_Oinsert(_872295), _872297), hAPP(hAPP(c_Set_Oinsert(_872295), _872297), _872299)) = hAPP(hAPP(c_Set_Oinsert(_872295), _872297), _872299))], (5868 ^ _779448) ^ [_872346, _872348, _872350] : [_872346 = _872348, 5871 ^ _779448 : [(5872 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872350, tc_HOL_Obool)), _872346), _872348)))], (5874 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872350, tc_HOL_Obool)), _872348), _872346)))]]], (5876 ^ _779448) ^ [_872495, _872497, _872499, _872501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872495, tc_HOL_Obool)), _872497), _872499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872495, tc_HOL_Obool)), _872499), _872501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872495, tc_HOL_Obool)), _872497), _872501)))], (5886 ^ _779448) ^ [_872692, _872694, _872696] : [_872692 = _872694, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872696, tc_HOL_Obool)), _872694), _872692)))], (5892 ^ _779448) ^ [_872791, _872793, _872795] : [_872791 = _872793, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872795, tc_HOL_Obool)), _872791), _872793)))], (5898 ^ _779448) ^ [_872908, _872910, _872912] : [_872908 = _872910, 5901 ^ _779448 : [(5902 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872912, tc_HOL_Obool)), _872908), _872910)))], (5904 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872912, tc_HOL_Obool)), _872910), _872908)))]]], (5906 ^ _779448) ^ [_873049, _873051, _873053] : [-(_873049 = _873051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873053, tc_HOL_Obool)), _873049), _873051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873053, tc_HOL_Obool)), _873051), _873049))], (5916 ^ _779448) ^ [_873224, _873226] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873224, tc_HOL_Obool)), _873226), _873226)))], (5918 ^ _779448) ^ [_873259, _873261, _873263, _873265, _873267, _873269] : [-(hAPP(c_Set_Oimage(_873259, _873261, _873263), hAPP(c_Set_Oimage(_873265, _873259, _873267), _873269)) = hAPP(c_Set_Oimage(_873265, _873261, hAPP(hAPP(c_COMBB(_873259, _873261, _873265), _873263), _873267)), _873269))], (5920 ^ _779448) ^ [_873323, _873325, _873327] : [_873323 = c_Orderings_Obot__class_Obot(tc_fun(_873325, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_873325), _873327), _873323))], (5926 ^ _779448) ^ [_873439, _873441] : [hBOOL(hAPP(hAPP(c_member(_873439), _873441), c_Orderings_Obot__class_Obot(tc_fun(_873439, tc_HOL_Obool))))], (5928 ^ _779448) ^ [_873491, _873493] : [5929 ^ _779448 : [(5930 ^ _779448) ^ [_873544] : [hBOOL(hAPP(hAPP(c_member(_873491), _873544), _873493))]], _873493 = c_Orderings_Obot__class_Obot(tc_fun(_873491, tc_HOL_Obool))], (5934 ^ _779448) ^ [_873600, _873602] : [-(_873602 = c_Orderings_Obot__class_Obot(tc_fun(_873600, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_873600), 5937 ^ [_873600, _873602]), _873602)))], (5941 ^ _779448) ^ [_873666, _873668] : [-(hBOOL(hAPP(hAPP(c_member(_873666), 5942 ^ [_873666, _873668]), _873668))), -(_873668 = c_Orderings_Obot__class_Obot(tc_fun(_873666, tc_HOL_Obool)))], (5948 ^ _779448) ^ [_873717, _873719] : [_873719 = c_Orderings_Obot__class_Obot(tc_fun(_873717, tc_HOL_Obool)), 5951 ^ _779448 : [(5952 ^ _779448) ^ [_873797] : [hBOOL(hAPP(hAPP(c_member(_873717), _873797), _873719))]]], (5954 ^ _779448) ^ [_873833, _873835, _873837] : [hBOOL(hAPP(hAPP(c_member(_873833), _873835), _873837)), -(hAPP(hAPP(c_Set_Oinsert(_873833), _873835), _873837) = _873837)], (5960 ^ _779448) ^ [_873942, _873944, _873946, _873948] : [hBOOL(hAPP(hAPP(c_member(_873942), _873944), _873946)), -(hBOOL(hAPP(hAPP(c_member(_873942), _873944), hAPP(hAPP(c_Set_Oinsert(_873942), _873948), _873946))))], (5966 ^ _779448) ^ [_874066, _874068, _874070, _874072] : [-(hBOOL(hAPP(hAPP(c_member(_874066), _874068), _874070))), -(hBOOL(hAPP(hAPP(c_member(_874066), _874068), _874072))), 5973 ^ _779448 : [(5974 ^ _779448) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_874066), _874068), _874070) = hAPP(hAPP(c_Set_Oinsert(_874066), _874068), _874072), -(_874070 = _874072)], (5980 ^ _779448) ^ [] : [_874070 = _874072, -(hAPP(hAPP(c_Set_Oinsert(_874066), _874068), _874070) = hAPP(hAPP(c_Set_Oinsert(_874066), _874068), _874072))]]], (5996 ^ _779448) ^ [_874566, _874568, _874570, _874572] : [5997 ^ _779448 : [(5998 ^ _779448) ^ [] : [_874568 = _874570], (6000 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874566), _874568), _874572))]], -(hBOOL(hAPP(hAPP(c_member(_874566), _874568), hAPP(hAPP(c_Set_Oinsert(_874566), _874570), _874572))))], (5986 ^ _779448) ^ [_874432, _874434, _874436, _874438] : [hBOOL(hAPP(hAPP(c_member(_874432), _874434), hAPP(hAPP(c_Set_Oinsert(_874432), _874436), _874438))), -(_874434 = _874436), -(hBOOL(hAPP(hAPP(c_member(_874432), _874434), _874438)))], (6004 ^ _779448) ^ [_874731, _874733, _874735] : [-(hBOOL(hAPP(hAPP(c_member(_874731), _874733), hAPP(hAPP(c_Set_Oinsert(_874731), _874733), _874735))))], (6006 ^ _779448) ^ [_874773, _874775, _874777, _874779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874773, tc_HOL_Obool)), _874775), _874777)), hBOOL(hAPP(hAPP(c_member(_874773), _874779), _874775)), -(hBOOL(hAPP(hAPP(c_member(_874773), _874779), _874777)))], (6016 ^ _779448) ^ [_874958, _874960, _874962, _874964] : [hBOOL(hAPP(hAPP(c_member(_874958), _874960), _874962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874958, tc_HOL_Obool)), _874962), _874964)), -(hBOOL(hAPP(hAPP(c_member(_874958), _874960), _874964)))], (6026 ^ _779448) ^ [_875143, _875145, _875147, _875149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875143, tc_HOL_Obool)), _875145), _875147)), hBOOL(hAPP(hAPP(c_member(_875143), _875149), _875145)), -(hBOOL(hAPP(hAPP(c_member(_875143), _875149), _875147)))], (6036 ^ _779448) ^ [_875328, _875330, _875332, _875334, _875336, _875338] : [hBOOL(hAPP(hAPP(c_member(_875328), _875330), _875332)), _875334 = hAPP(_875336, _875330), -(hBOOL(hAPP(hAPP(c_member(_875338), _875334), hAPP(c_Set_Oimage(_875328, _875338, _875336), _875332))))], (6046 ^ _779448) ^ [_875521, _875523, _875525, _875527, _875529] : [hBOOL(hAPP(hAPP(c_member(_875521), _875523), _875525)), -(hBOOL(hAPP(hAPP(c_member(_875527), hAPP(_875529, _875523)), hAPP(c_Set_Oimage(_875521, _875527, _875529), _875525))))], (6052 ^ _779448) ^ [_875676, _875678, _875680, _875682, _875684] : [hBOOL(hAPP(hAPP(c_member(_875676), _875678), hAPP(c_Set_Oimage(_875680, _875676, _875682), _875684))), 6056 ^ _779448 : [(6057 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_875680), 6055 ^ [_875676, _875678, _875680, _875682, _875684]), _875684)))], (6059 ^ _779448) ^ [] : [-(_875678 = hAPP(_875682, 6055 ^ [_875676, _875678, _875680, _875682, _875684]))]]], (6061 ^ _779448) ^ [_875860, _875862, _875864, _875866, _875868] : [-(hBOOL(hAPP(hAPP(c_member(_875860), _875862), hAPP(c_Set_Oimage(_875864, _875860, _875866), _875868)))), 6062 ^ _779448 : [(6063 ^ _779448) ^ [_875930] : [hBOOL(hAPP(hAPP(c_member(_875864), _875930), _875868)), _875862 = hAPP(_875866, _875930)]]], (6071 ^ _779448) ^ [_876078] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_876078), c_Orderings_Obot__class_Obot(tc_fun(_876078, tc_HOL_Obool)))))], (6073 ^ _779448) ^ [_876110, _876112, _876114] : [hAPP(hAPP(c_Set_Oinsert(_876110), _876112), c_Orderings_Obot__class_Obot(tc_fun(_876110, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_876110), _876114), c_Orderings_Obot__class_Obot(tc_fun(_876110, tc_HOL_Obool))), -(_876112 = _876114)], (6079 ^ _779448) ^ [_876265, _876267, _876269, _876271, _876273] : [hAPP(hAPP(c_Set_Oinsert(_876265), _876267), hAPP(hAPP(c_Set_Oinsert(_876265), _876269), c_Orderings_Obot__class_Obot(tc_fun(_876265, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_876265), _876271), hAPP(hAPP(c_Set_Oinsert(_876265), _876273), c_Orderings_Obot__class_Obot(tc_fun(_876265, tc_HOL_Obool)))), 6084 ^ _779448 : [(6085 ^ _779448) ^ [] : [-(_876267 = _876271)], (6087 ^ _779448) ^ [] : [-(_876269 = _876273)]], 6088 ^ _779448 : [(6089 ^ _779448) ^ [] : [-(_876267 = _876273)], (6091 ^ _779448) ^ [] : [-(_876269 = _876271)]]], (6093 ^ _779448) ^ [_876527, _876529, _876531, _876533, _876535] : [-(hAPP(hAPP(c_Set_Oinsert(_876527), _876529), hAPP(hAPP(c_Set_Oinsert(_876527), _876531), c_Orderings_Obot__class_Obot(tc_fun(_876527, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_876527), _876533), hAPP(hAPP(c_Set_Oinsert(_876527), _876535), c_Orderings_Obot__class_Obot(tc_fun(_876527, tc_HOL_Obool))))), 6094 ^ _779448 : [(6095 ^ _779448) ^ [] : [_876529 = _876533, _876531 = _876535], (6101 ^ _779448) ^ [] : [_876529 = _876535, _876531 = _876533]]], (6109 ^ _779448) ^ [_876858, _876860, _876862] : [hAPP(hAPP(c_Set_Oinsert(_876858), _876860), _876862) = c_Orderings_Obot__class_Obot(tc_fun(_876858, tc_HOL_Obool))], (6111 ^ _779448) ^ [_876913, _876915, _876917] : [c_Orderings_Obot__class_Obot(tc_fun(_876913, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_876913), _876915), _876917)], (6113 ^ _779448) ^ [_876971, _876973, _876975] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876971), hAPP(hAPP(c_Set_Oinsert(_876971), _876973), _876975))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876971), _876975)))], (6119 ^ _779448) ^ [_877078, _877080, _877082] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_877078), _877082)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_877078), hAPP(hAPP(c_Set_Oinsert(_877078), _877080), _877082))))], (6125 ^ _779448) ^ [_877206, _877208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877206, tc_HOL_Obool)), _877208), c_Orderings_Obot__class_Obot(tc_fun(_877206, tc_HOL_Obool)))), -(_877208 = c_Orderings_Obot__class_Obot(tc_fun(_877206, tc_HOL_Obool)))], (6131 ^ _779448) ^ [_877319, _877321] : [_877321 = c_Orderings_Obot__class_Obot(tc_fun(_877319, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877319, tc_HOL_Obool)), _877321), c_Orderings_Obot__class_Obot(tc_fun(_877319, tc_HOL_Obool)))))], (6137 ^ _779448) ^ [_877459, _877461, _877463, _877465] : [hAPP(c_Set_Oimage(_877459, _877461, _877463), _877465) = c_Orderings_Obot__class_Obot(tc_fun(_877461, tc_HOL_Obool)), -(_877465 = c_Orderings_Obot__class_Obot(tc_fun(_877459, tc_HOL_Obool)))], (6143 ^ _779448) ^ [_877570, _877572, _877574, _877576] : [_877576 = c_Orderings_Obot__class_Obot(tc_fun(_877570, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_877570, _877572, _877574), _877576) = c_Orderings_Obot__class_Obot(tc_fun(_877572, tc_HOL_Obool)))], (6149 ^ _779448) ^ [_877687, _877689, _877691] : [-(hAPP(c_Set_Oimage(_877687, _877689, _877691), c_Orderings_Obot__class_Obot(tc_fun(_877687, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_877689, tc_HOL_Obool)))], (6151 ^ _779448) ^ [_877752, _877754, _877756, _877758] : [c_Orderings_Obot__class_Obot(tc_fun(_877752, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_877754, _877752, _877756), _877758), -(_877758 = c_Orderings_Obot__class_Obot(tc_fun(_877754, tc_HOL_Obool)))], (6157 ^ _779448) ^ [_877863, _877865, _877867, _877869] : [_877869 = c_Orderings_Obot__class_Obot(tc_fun(_877865, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_877863, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_877865, _877863, _877867), _877869))], (6163 ^ _779448) ^ [_877980, _877982, _877984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877980, tc_HOL_Obool)), _877982), _877984)), hBOOL(hAPP(c_Finite__Set_Ofinite(_877980), _877984)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_877980), _877982)))], (6173 ^ _779448) ^ [_878149, _878151, _878153] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_878149), _878151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878149, tc_HOL_Obool)), _878153), _878151)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878149), _878153)))], (6183 ^ _779448) ^ [_878318, _878320, _878322, _878324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878318, tc_HOL_Obool)), _878320), _878322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878318, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_878318), _878324), _878320)), hAPP(hAPP(c_Set_Oinsert(_878318), _878324), _878322))))], (6189 ^ _779448) ^ [_878471, _878473, _878475, _878477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878471, tc_HOL_Obool)), _878473), _878475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878471, tc_HOL_Obool)), _878473), hAPP(hAPP(c_Set_Oinsert(_878471), _878477), _878475))))], (6195 ^ _779448) ^ [_878608, _878610, _878612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878608, tc_HOL_Obool)), _878610), hAPP(hAPP(c_Set_Oinsert(_878608), _878612), _878610))))], (6197 ^ _779448) ^ [_878653, _878655, _878657, _878659, _878661] : [-(hAPP(c_Set_Oimage(_878653, _878655, _878657), hAPP(hAPP(c_Set_Oinsert(_878653), _878659), _878661)) = hAPP(hAPP(c_Set_Oinsert(_878655), hAPP(_878657, _878659)), hAPP(c_Set_Oimage(_878653, _878655, _878657), _878661)))], (6199 ^ _779448) ^ [_878717, _878719, _878721, _878723, _878725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878717, tc_HOL_Obool)), _878719), _878721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878723, tc_HOL_Obool)), hAPP(c_Set_Oimage(_878717, _878723, _878725), _878719)), hAPP(c_Set_Oimage(_878717, _878723, _878725), _878721))))], (6205 ^ _779448) ^ [_878892, _878894, _878896, _878898, _878900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878892, tc_HOL_Obool)), _878894), hAPP(c_Set_Oimage(_878896, _878892, _878898), _878900))), 6209 ^ _779448 : [(6210 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878896, tc_HOL_Obool)), 6208 ^ [_878892, _878894, _878896, _878898, _878900]), _878900)))], (6212 ^ _779448) ^ [] : [-(_878894 = hAPP(c_Set_Oimage(_878896, _878892, _878898), 6208 ^ [_878892, _878894, _878896, _878898, _878900]))]]], (6214 ^ _779448) ^ [_879096, _879098, _879100, _879102, _879104] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879096, tc_HOL_Obool)), _879098), hAPP(c_Set_Oimage(_879100, _879096, _879102), _879104)))), 6215 ^ _779448 : [(6216 ^ _779448) ^ [_879176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879100, tc_HOL_Obool)), _879176), _879104)), _879098 = hAPP(c_Set_Oimage(_879100, _879096, _879102), _879176)]]], (6224 ^ _779448) ^ [_879341, _879343, _879345] : [hBOOL(hAPP(hAPP(c_member(_879341), _879343), hAPP(hAPP(c_Set_Oinsert(_879341), _879345), c_Orderings_Obot__class_Obot(tc_fun(_879341, tc_HOL_Obool))))), -(_879343 = _879345)], (6230 ^ _779448) ^ [_879478, _879480, _879482] : [hBOOL(hAPP(hAPP(c_member(_879478), _879480), hAPP(hAPP(c_Set_Oinsert(_879478), _879482), c_Orderings_Obot__class_Obot(tc_fun(_879478, tc_HOL_Obool))))), -(_879480 = _879482)], (6236 ^ _779448) ^ [_879593, _879595, _879597] : [_879595 = _879597, -(hBOOL(hAPP(hAPP(c_member(_879593), _879595), hAPP(hAPP(c_Set_Oinsert(_879593), _879597), c_Orderings_Obot__class_Obot(tc_fun(_879593, tc_HOL_Obool))))))], (6242 ^ _779448) ^ [_879713, _879715, _879717, _879719] : [-(hBOOL(hAPP(hAPP(c_member(_879713), _879715), _879717))), 6245 ^ _779448 : [(6246 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879713, tc_HOL_Obool)), _879717), hAPP(hAPP(c_Set_Oinsert(_879713), _879715), _879719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879713, tc_HOL_Obool)), _879717), _879719)))], (6252 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879713, tc_HOL_Obool)), _879717), _879719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879713, tc_HOL_Obool)), _879717), hAPP(hAPP(c_Set_Oinsert(_879713), _879715), _879719))))]]], (6258 ^ _779448) ^ [_880042, _880044, _880046, _880048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880042, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_880042), _880044), _880046)), _880048)), 6261 ^ _779448 : [(6262 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_880042), _880044), _880048)))], (6264 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880042, tc_HOL_Obool)), _880046), _880048)))]]], (6266 ^ _779448) ^ [_880215, _880217, _880219, _880221] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880215, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_880215), _880217), _880219)), _880221))), hBOOL(hAPP(hAPP(c_member(_880215), _880217), _880221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880215, tc_HOL_Obool)), _880219), _880221))], (6276 ^ _779448) ^ [_880424, _880426, _880428, _880430, _880432] : [hBOOL(hAPP(hAPP(c_member(_880424), _880426), _880428)), -(hAPP(hAPP(c_Set_Oinsert(_880430), hAPP(_880432, _880426)), hAPP(c_Set_Oimage(_880424, _880430, _880432), _880428)) = hAPP(c_Set_Oimage(_880424, _880430, _880432), _880428))], (6282 ^ _779448) ^ [_880571, _880573, _880575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880571, tc_HOL_Obool)), _880573), hAPP(hAPP(c_Set_Oinsert(_880571), _880575), c_Orderings_Obot__class_Obot(tc_fun(_880571, tc_HOL_Obool))))), -(_880573 = c_Orderings_Obot__class_Obot(tc_fun(_880571, tc_HOL_Obool))), -(_880573 = hAPP(hAPP(c_Set_Oinsert(_880571), _880575), c_Orderings_Obot__class_Obot(tc_fun(_880571, tc_HOL_Obool))))], (6292 ^ _779448) ^ [_880745, _880747, _880749, _880751, _880753] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_880745), _880747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880749, tc_HOL_Obool)), _880751), hAPP(c_Set_Oimage(_880745, _880749, _880753), _880747))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_880749), _880751)))], (6302 ^ _779448) ^ [_880951, _880953, _880955, _880957] : [_880951 = c_Orderings_Obot__class_Obot(tc_fun(_880953, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_880953, _880955, hAPP(c_COMBK(_880955, _880953), _880957)), _880951) = c_Orderings_Obot__class_Obot(tc_fun(_880955, tc_HOL_Obool)))], (6308 ^ _779448) ^ [_881072, _881074, _881076, _881078] : [-(_881072 = c_Orderings_Obot__class_Obot(tc_fun(_881074, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_881074, _881076, hAPP(c_COMBK(_881076, _881074), _881078)), _881072) = hAPP(hAPP(c_Set_Oinsert(_881076), _881078), c_Orderings_Obot__class_Obot(tc_fun(_881076, tc_HOL_Obool))))], (6314 ^ _779448) ^ [_881145, _881147, _881149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881145), _881147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_881145), _881147)), hAPP(c_Finite__Set_Ocard(_881145), hAPP(hAPP(c_Set_Oinsert(_881145), _881149), _881147)))))], (6320 ^ _779448) ^ [_881278, _881280, _881282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881278), _881280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881278, tc_HOL_Obool)), _881282), _881280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_881278), _881280)), hAPP(c_Finite__Set_Ocard(_881278), _881282))), -(_881282 = _881280)], (6334 ^ _779448) ^ [_881523, _881525, _881527] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881523), _881525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881523, tc_HOL_Obool)), _881527), _881525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_881523), _881527)), hAPP(c_Finite__Set_Ocard(_881523), _881525))))], (6344 ^ _779448) ^ [_881714, _881716, _881718, _881720] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881714), _881716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_881718), hAPP(c_Set_Oimage(_881714, _881718, _881720), _881716))), hAPP(c_Finite__Set_Ocard(_881714), _881716))))], (6350 ^ _779448) ^ [_881847, _881849, _881851, _881853, _881855] : [hBOOL(hAPP(hAPP(c_member(_881847), _881849), _881851)), -(hAPP(c_Set_Oimage(_881847, _881853, hAPP(c_COMBK(_881853, _881847), _881855)), _881851) = hAPP(hAPP(c_Set_Oinsert(_881853), _881855), c_Orderings_Obot__class_Obot(tc_fun(_881853, tc_HOL_Obool))))], (6356 ^ _779448) ^ [_881996, _881998] : [v_P(hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _881996)), _881998), hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_881996)))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), -(v_P(_881998, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _881996)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (6362 ^ _779448) ^ [_882135, _882137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _882135), _882137)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _882137)), _882135) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _882137), _882135)))], (6368 ^ _779448) ^ [_882258] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _882258), v_U)), -(v_wt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_882258))))], (6374 ^ _779448) ^ [_882351, _882353] : [-(c_Set_Othe__elem(_882351, hAPP(hAPP(c_Set_Oinsert(_882351), _882353), c_Orderings_Obot__class_Obot(tc_fun(_882351, tc_HOL_Obool)))) = _882353)], (6376 ^ _779448) ^ [_882392, _882394] : [class_Orderings_Opreorder(_882392), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882392), _882394), _882394)))], (6382 ^ _779448) ^ [_882481, _882483, _882485] : [class_Orderings_Obot(_882481), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_882483, _882481)), _882485) = c_Orderings_Obot__class_Obot(_882481))], (6388 ^ _779448) ^ [_882596, _882598, _882600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882596, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_882596, tc_fun(_882596, tc_HOL_Obool), tc_HOL_Obool), c_member(_882596)), _882598)), hAPP(hAPP(c_COMBC(_882596, tc_fun(_882596, tc_HOL_Obool), tc_HOL_Obool), c_member(_882596)), _882600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882596, tc_HOL_Obool)), _882598), _882600)))], (6394 ^ _779448) ^ [_882771, _882773, _882775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882771, tc_HOL_Obool)), _882773), _882775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882771, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_882771, tc_fun(_882771, tc_HOL_Obool), tc_HOL_Obool), c_member(_882771)), _882773)), hAPP(hAPP(c_COMBC(_882771, tc_fun(_882771, tc_HOL_Obool), tc_HOL_Obool), c_member(_882771)), _882775))))], (6400 ^ _779448) ^ [_882967, _882969] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_882967, tc_HOL_Obool)), _882969)), -(hBOOL(hAPP(hAPP(c_member(_882967), _882969), c_Orderings_Obot__class_Obot(tc_fun(_882967, tc_HOL_Obool)))))], (6406 ^ _779448) ^ [_883078, _883080] : [hBOOL(hAPP(hAPP(c_member(_883078), _883080), c_Orderings_Obot__class_Obot(tc_fun(_883078, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_883078, tc_HOL_Obool)), _883080)))], (6412 ^ _779448) ^ [_883195, _883197, _883199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883195), _883197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883195), _883199)), 6419 ^ _779448 : [(6420 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883197), _883195)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883199), _883195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883197), _883199)))], (6426 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883197), _883199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883197), _883195)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883199), _883195))))]]], (6432 ^ _779448) ^ [_883548, _883550, _883552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883548), _883550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883548), _883552)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883550), _883548)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883552), _883548)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883550), _883552))], (6442 ^ _779448) ^ [_883749, _883751, _883753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883749), _883751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _883749), _883753)), 6449 ^ _779448 : [(6450 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883751), _883749) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883753), _883749), -(_883751 = _883753)], (6456 ^ _779448) ^ [] : [_883751 = _883753, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883751), _883749) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _883753), _883749))]]], (6462 ^ _779448) ^ [_884072, _884074, _884076] : [class_Orderings_Olinorder(_884072), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884072), _884074), _884076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884072), _884076), _884074)))], (6472 ^ _779448) ^ [_884190, _884192, _884194] : [class_Orderings_Oorder(_884190), 6475 ^ _779448 : [(6476 ^ _779448) ^ [] : [_884192 = _884194, 6479 ^ _779448 : [(6480 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884190), _884192), _884194)))], (6482 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884190), _884194), _884192)))]]], (6484 ^ _779448) ^ [] : [-(_884192 = _884194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884190), _884192), _884194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884190), _884194), _884192))]]], (6494 ^ _779448) ^ [_884517, _884519, _884521] : [class_Orderings_Opreorder(_884517), _884519 = _884521, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884517), _884519), _884521)))], (6504 ^ _779448) ^ [_884662, _884664, _884666] : [class_Orderings_Oorder(_884662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884662), _884664), _884666)), 6511 ^ _779448 : [(6512 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884662), _884666), _884664)), -(_884666 = _884664)], (6518 ^ _779448) ^ [] : [_884666 = _884664, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884662), _884666), _884664)))]]], (6524 ^ _779448) ^ [_884962, _884964, _884966, _884968] : [class_Orderings_Oord(_884962), _884964 = _884966, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884962), _884966), _884968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884962), _884964), _884968)))], (6538 ^ _779448) ^ [_885181, _885183, _885185, _885187] : [class_Orderings_Oorder(_885181), _885183 = _885185, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885181), _885187), _885185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885181), _885187), _885183)))], (6552 ^ _779448) ^ [_885400, _885402, _885404, _885406] : [class_Orderings_Oord(_885400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885400), _885402), _885404)), _885404 = _885406, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885400), _885402), _885406)))], (6566 ^ _779448) ^ [_885619, _885621, _885623, _885625] : [class_Orderings_Oorder(_885619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885619), _885621), _885623)), _885621 = _885625, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885619), _885625), _885623)))], (6580 ^ _779448) ^ [_885838, _885840, _885842] : [class_Orderings_Oorder(_885838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885838), _885840), _885842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885838), _885842), _885840)), -(_885840 = _885842)], (6594 ^ _779448) ^ [_886051, _886053, _886055, _886057] : [class_Orderings_Opreorder(_886051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886051), _886053), _886055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886051), _886055), _886057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886051), _886053), _886057)))], (6608 ^ _779448) ^ [_886284, _886286, _886288] : [class_Orderings_Oorder(_886284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886284), _886286), _886288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886284), _886288), _886286)), -(_886288 = _886286)], (6622 ^ _779448) ^ [_886497, _886499, _886501, _886503] : [class_Orderings_Oorder(_886497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886497), _886499), _886501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886497), _886503), _886499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886497), _886503), _886501)))], (6636 ^ _779448) ^ [_886730, _886732, _886734] : [class_Orderings_Olinorder(_886730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886730), _886732), _886734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886730), _886734), _886732)))], (6646 ^ _779448) ^ [_886868, _886870, _886872] : [hBOOL(hAPP(hAPP(c_member(_886868), _886870), hAPP(c_fequal, _886872))), -(_886870 = _886872)], (6652 ^ _779448) ^ [_886963, _886965, _886967] : [_886965 = _886967, -(hBOOL(hAPP(hAPP(c_member(_886963), _886965), hAPP(c_fequal, _886967))))], (6658 ^ _779448) ^ [_887073] : [_887073 = hAPP(c_Nat_OSuc, _887073)], (6660 ^ _779448) ^ [_887108] : [hAPP(c_Nat_OSuc, _887108) = _887108], (6662 ^ _779448) ^ [_887149, _887151] : [hAPP(c_Nat_OSuc, _887149) = hAPP(c_Nat_OSuc, _887151), -(_887149 = _887151)], (6668 ^ _779448) ^ [_887234, _887236] : [_887234 = _887236, -(hAPP(c_Nat_OSuc, _887234) = hAPP(c_Nat_OSuc, _887236))], (6674 ^ _779448) ^ [_887325, _887327] : [hAPP(c_Nat_OSuc, _887325) = hAPP(c_Nat_OSuc, _887327), -(_887325 = _887327)], (6680 ^ _779448) ^ [_887414, _887416, _887418, _887420] : [hBOOL(hAPP(_887414, _887416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887418, tc_HOL_Obool)), _887414), _887420)), -(hBOOL(hAPP(_887420, _887416)))], (6690 ^ _779448) ^ [_887579, _887581, _887583, _887585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887579, tc_HOL_Obool)), _887581), _887583)), hBOOL(hAPP(_887581, _887585)), -(hBOOL(hAPP(_887583, _887585)))], (6700 ^ _779448) ^ [_887744] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887744), _887744)))], (6702 ^ _779448) ^ [_887768, _887770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887768), _887770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887770), _887768)))], (6708 ^ _779448) ^ [_887814, _887816] : [_887814 = _887816, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887814), _887816)))], (6714 ^ _779448) ^ [_887901, _887903, _887905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887901), _887903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887903), _887905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887901), _887905)))], (6724 ^ _779448) ^ [_888064, _888066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _888064), _888066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _888066), _888064)), -(_888064 = _888066)], (6734 ^ _779448) ^ [_888213, _888215, _888217] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _888213), _888215)), _888217) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _888213), _888217)), _888215))], (6736 ^ _779448) ^ [_888282, _888284, _888286] : [hAPP(hAPP(c_COMBC(_888282, tc_fun(_888282, tc_HOL_Obool), tc_HOL_Obool), c_member(_888282)), _888284) = hAPP(hAPP(c_COMBC(_888282, tc_fun(_888282, tc_HOL_Obool), tc_HOL_Obool), c_member(_888282)), _888286), -(_888284 = _888286)], (6742 ^ _779448) ^ [_888417, _888419, _888421] : [_888419 = _888421, -(hAPP(hAPP(c_COMBC(_888417, tc_fun(_888417, tc_HOL_Obool), tc_HOL_Obool), c_member(_888417)), _888419) = hAPP(hAPP(c_COMBC(_888417, tc_fun(_888417, tc_HOL_Obool), tc_HOL_Obool), c_member(_888417)), _888421))], (6748 ^ _779448) ^ [_888558, _888560] : [class_Orderings_Obot(_888558), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888558), c_Orderings_Obot__class_Obot(_888558)), _888560)))], (6754 ^ _779448) ^ [_888651, _888653, _888655, _888657] : [class_Orderings_Oord(_888651), 6757 ^ _779448 : [(6758 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888653, _888651)), _888655), _888657)), 6761 ^ _779448 : [(6762 ^ _779448) ^ [_888808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888651), hAPP(_888655, _888808)), hAPP(_888657, _888808))))]]], (6764 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888651), hAPP(_888655, 6765 ^ [_888651, _888653, _888655, _888657])), hAPP(_888657, 6765 ^ [_888651, _888653, _888655, _888657]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888653, _888651)), _888655), _888657)))]]], (6771 ^ _779448) ^ [_888997, _888999, _889001, _889003, _889005] : [class_Orderings_Oord(_888997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888999, _888997)), _889001), _889003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888997), hAPP(_889001, _889005)), hAPP(_889003, _889005))))], (6781 ^ _779448) ^ [_889182, _889184, _889186, _889188, _889190] : [class_Orderings_Oord(_889182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889184, _889182)), _889186), _889188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889182), hAPP(_889186, _889190)), hAPP(_889188, _889190))))], (6791 ^ _779448) ^ [_889367, _889369, _889371] : [class_Orderings_Obot(_889367), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_889369, _889367)), _889371) = c_Orderings_Obot__class_Obot(_889367))], (6797 ^ _779448) ^ [_889473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889473)), _889473))], (6799 ^ _779448) ^ [_889513, _889515] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889513), _889515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889515)), _889513)))], (6805 ^ _779448) ^ [_889558, _889560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889560)), _889558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889558), _889560))], (6821 ^ _779448) ^ [_889797, _889799] : [6822 ^ _779448 : [(6823 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889797), _889799))], (6825 ^ _779448) ^ [] : [_889797 = hAPP(c_Nat_OSuc, _889799)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889797), hAPP(c_Nat_OSuc, _889799))))], (6811 ^ _779448) ^ [_889679, _889681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889679), hAPP(c_Nat_OSuc, _889681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889679), _889681))), -(_889679 = hAPP(c_Nat_OSuc, _889681))], (6829 ^ _779448) ^ [_889961, _889963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _889961)), hAPP(c_Nat_OSuc, _889963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _889961), _889963)))], (6835 ^ _779448) ^ [_890066, _890068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890066), _890068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890066)), hAPP(c_Nat_OSuc, _890068))))], (6841 ^ _779448) ^ [_890177, _890179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890177), _890179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890177), hAPP(c_Nat_OSuc, _890179))))], (6847 ^ _779448) ^ [_890280, _890282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890280), hAPP(c_Nat_OSuc, _890282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890280), _890282))), -(_890280 = hAPP(c_Nat_OSuc, _890282))], (6857 ^ _779448) ^ [_890404, _890406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890404)), _890406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890404), _890406)))], (6863 ^ _779448) ^ [_890507, _890509] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890507)), hAPP(c_Nat_OSuc, _890509)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890507), _890509))], (6865 ^ _779448) ^ [_890550, _890552, _890554] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _890550)), _890552)), hAPP(c_Nat_OSuc, _890554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890550), _890552)), _890554))], (6867 ^ _779448) ^ [_890607, _890609] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890607), _890609)), _890607)))], (6869 ^ _779448) ^ [_890643, _890645, _890647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890643), _890645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890647), _890645)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890647), _890643))))], (6875 ^ _779448) ^ [_890766, _890768, _890770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890766), _890768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890766), _890770)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890768), _890770))))], (6881 ^ _779448) ^ [_890889, _890891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _890889), _890891)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _890891), _890889)) = _890889)], (6887 ^ _779448) ^ [_891000, _891002, _891004, _891006, _891008] : [c_Finite__Set_Ofolding__one(_891000, _891002, _891004), hBOOL(hAPP(c_Finite__Set_Ofinite(_891000), _891006)), -(hBOOL(hAPP(hAPP(c_member(_891000), _891008), _891006))), -(_891006 = c_Orderings_Obot__class_Obot(tc_fun(_891000, tc_HOL_Obool))), -(hAPP(_891004, hAPP(hAPP(c_Set_Oinsert(_891000), _891008), _891006)) = hAPP(hAPP(_891002, _891008), hAPP(_891004, _891006)))], (6905 ^ _779448) ^ [_891245, _891247, _891249, _891251, _891253] : [class_Groups_Oordered__ab__group__add(_891245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_891245), _891247), _891249) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_891245), _891251), _891253), 6912 ^ _779448 : [(6913 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891245), _891247), _891249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891245), _891251), _891253)))], (6919 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891245), _891251), _891253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_891245), _891247), _891249)))]]], (6925 ^ _779448) ^ [_891600, _891602, _891604, _891606, _891608] : [c_Finite__Set_Ofolding__one__idem(_891600, _891602, _891604), hBOOL(hAPP(c_Finite__Set_Ofinite(_891600), _891606)), -(_891608 = c_Orderings_Obot__class_Obot(tc_fun(_891600, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891600, tc_HOL_Obool)), _891608), _891606)), -(hAPP(hAPP(_891602, hAPP(_891604, _891608)), hAPP(_891604, _891606)) = hAPP(_891604, _891606))], (6943 ^ _779448) ^ [_891930, _891932, _891934, _891936] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891930), _891932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891930, tc_HOL_Obool)), _891932), _891934)), hBOOL(hAPP(_891936, c_Orderings_Obot__class_Obot(tc_fun(_891930, tc_HOL_Obool)))), 6958 ^ _779448 : [(6959 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891930), 6957 ^ [_891930, _891932, _891934, _891936])))], (6961 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_891930), 6956 ^ [_891930, _891932, _891934, _891936]), _891934)))], (6963 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_891930), 6956 ^ [_891930, _891932, _891934, _891936]), 6957 ^ [_891930, _891932, _891934, _891936]))], (6965 ^ _779448) ^ [] : [-(hBOOL(hAPP(_891936, 6957 ^ [_891930, _891932, _891934, _891936])))], (6967 ^ _779448) ^ [] : [hBOOL(hAPP(_891936, hAPP(hAPP(c_Set_Oinsert(_891930), 6956 ^ [_891930, _891932, _891934, _891936]), 6957 ^ [_891930, _891932, _891934, _891936])))]], -(hBOOL(hAPP(_891936, _891932)))], (6971 ^ _779448) ^ [_892595, _892597, _892599, _892601, _892603] : [c_Finite__Set_Ofolding__one__idem(_892595, _892597, _892599), hBOOL(hAPP(c_Finite__Set_Ofinite(_892595), _892601)), -(_892601 = c_Orderings_Obot__class_Obot(tc_fun(_892595, tc_HOL_Obool))), -(hAPP(_892599, hAPP(hAPP(c_Set_Oinsert(_892595), _892603), _892601)) = hAPP(hAPP(_892597, _892603), hAPP(_892599, _892601)))], (6985 ^ _779448) ^ [_892811, _892813, _892815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892811), _892813)), hBOOL(hAPP(hAPP(c_member(_892811), _892815), _892813)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_892811), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892811, tc_HOL_Obool)), _892813), hAPP(hAPP(c_Set_Oinsert(_892811), _892815), c_Orderings_Obot__class_Obot(tc_fun(_892811, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_892811), _892813))], (6995 ^ _779448) ^ [_893040, _893042] : [-(c_Set_Othe__elem(_893040, _893042) = c_HOL_OThe(_893040, hAPP(hAPP(c_COMBB(tc_fun(_893040, tc_HOL_Obool), tc_HOL_Obool, _893040), hAPP(c_fequal, _893042)), hAPP(hAPP(c_COMBC(_893040, tc_fun(_893040, tc_HOL_Obool), tc_fun(_893040, tc_HOL_Obool)), c_Set_Oinsert(_893040)), c_Orderings_Obot__class_Obot(tc_fun(_893040, tc_HOL_Obool))))))], (6997 ^ _779448) ^ [_893110, _893112, _893114, _893116, _893118, _893120, _893122, _893124] : [c_Finite__Set_Ofolding__image__simple(_893110, _893112, _893114, _893116, _893118, _893120), hBOOL(hAPP(c_Finite__Set_Ofinite(_893112), _893122)), -(hBOOL(hAPP(hAPP(c_member(_893112), _893124), _893122))), -(hAPP(_893120, hAPP(hAPP(c_Set_Oinsert(_893112), _893124), _893122)) = hAPP(hAPP(_893114, hAPP(_893118, _893124)), hAPP(_893120, _893122)))], (7011 ^ _779448) ^ [_893369, _893371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _893369)), _893371)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _893369), _893371)))], (7017 ^ _779448) ^ [_893472, _893474] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _893472), _893474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _893472)), _893474)))], (7023 ^ _779448) ^ [_893581, _893583, _893585, _893587, _893589, _893591, _893593, _893595] : [c_Finite__Set_Ofolding__image__simple__idem(_893581, _893583, _893585, _893587, _893589, _893591), hBOOL(hAPP(c_Finite__Set_Ofinite(_893583), _893593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893583, tc_HOL_Obool)), _893595), _893593)), -(hAPP(hAPP(_893585, hAPP(_893591, _893595)), hAPP(_893591, _893593)) = hAPP(_893591, _893593))], (7037 ^ _779448) ^ [_893864, _893866, _893868, _893870, _893872, _893874, _893876, _893878] : [c_Finite__Set_Ofolding__image__simple__idem(_893864, _893866, _893868, _893870, _893872, _893874), hBOOL(hAPP(c_Finite__Set_Ofinite(_893866), _893876)), -(hAPP(_893874, hAPP(hAPP(c_Set_Oinsert(_893866), _893878), _893876)) = hAPP(hAPP(_893868, hAPP(_893872, _893878)), hAPP(_893874, _893876)))], (7047 ^ _779448) ^ [_894079, _894081, _894083, _894085] : [hBOOL(hAPP(hAPP(c_member(_894079), _894081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894079, tc_HOL_Obool)), _894083), _894085))), 7050 ^ _779448 : [(7051 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894079), _894081), _894083)))], (7053 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894079), _894081), _894085))]]], (7055 ^ _779448) ^ [_894258, _894260, _894262, _894264] : [hBOOL(hAPP(hAPP(c_member(_894258), _894260), _894262)), -(hBOOL(hAPP(hAPP(c_member(_894258), _894260), _894264))), -(hBOOL(hAPP(hAPP(c_member(_894258), _894260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894258, tc_HOL_Obool)), _894262), _894264))))], (7065 ^ _779448) ^ [_894418, _894420, _894422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894418), _894420)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_894418), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894418, tc_HOL_Obool)), _894420), _894422))))], (7071 ^ _779448) ^ [_894535, _894537, _894539] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894535, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894535, tc_HOL_Obool)), _894537), _894539)), _894539) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894535, tc_HOL_Obool)), _894537), _894539))], (7073 ^ _779448) ^ [_894595, _894597, _894599, _894601] : [c_Finite__Set_Ofolding__one__idem(_894595, _894597, _894599), -(hAPP(hAPP(_894597, _894601), _894601) = _894601)], (7079 ^ _779448) ^ [_894690, _894692, _894694, _894696, _894698, _894700, _894702] : [c_Finite__Set_Ofolding__image__simple__idem(_894690, _894692, _894694, _894696, _894698, _894700), -(hAPP(hAPP(_894694, _894702), _894702) = _894702)], (7085 ^ _779448) ^ [_894797, _894799, _894801, _894803] : [hBOOL(hAPP(hAPP(c_member(_894797), _894799), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894797, tc_HOL_Obool)), _894801), _894803))), hBOOL(hAPP(hAPP(c_member(_894797), _894799), _894803))], (7091 ^ _779448) ^ [_894929, _894931, _894933, _894935] : [hBOOL(hAPP(hAPP(c_member(_894929), _894931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894929, tc_HOL_Obool)), _894933), _894935))), -(hBOOL(hAPP(hAPP(c_member(_894929), _894931), _894933)))], (7097 ^ _779448) ^ [_895081, _895083, _895085, _895087] : [hBOOL(hAPP(hAPP(c_member(_895081), _895083), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895081, tc_HOL_Obool)), _895085), _895087))), 7100 ^ _779448 : [(7101 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895081), _895083), _895085)))], (7103 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895081), _895083), _895087))]]], (7105 ^ _779448) ^ [_895256, _895258, _895260, _895262] : [-(hBOOL(hAPP(hAPP(c_member(_895256), _895258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895256, tc_HOL_Obool)), _895260), _895262)))), hBOOL(hAPP(hAPP(c_member(_895256), _895258), _895260)), -(hBOOL(hAPP(hAPP(c_member(_895256), _895258), _895262)))], (7115 ^ _779448) ^ [_895462, _895464] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895462, tc_HOL_Obool)), _895464), _895464) = c_Orderings_Obot__class_Obot(tc_fun(_895462, tc_HOL_Obool)))], (7117 ^ _779448) ^ [_895503, _895505] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895503, tc_HOL_Obool)), _895505), c_Orderings_Obot__class_Obot(tc_fun(_895503, tc_HOL_Obool))) = _895505)], (7119 ^ _779448) ^ [_895544, _895546] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895544, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_895544, tc_HOL_Obool))), _895546) = c_Orderings_Obot__class_Obot(tc_fun(_895544, tc_HOL_Obool)))], (7121 ^ _779448) ^ [_895590, _895592, _895594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895590), _895592)), 7124 ^ _779448 : [(7125 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895590, tc_HOL_Obool)), _895594), _895592))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_895590), _895594)))], (7131 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895590), _895594)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_895590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895590, tc_HOL_Obool)), _895594), _895592))))]]], (7137 ^ _779448) ^ [_895868, _895870, _895872, _895874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895868, tc_HOL_Obool)), _895870), _895872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895868, tc_HOL_Obool)), _895872), _895874)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895868, tc_HOL_Obool)), _895872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895868, tc_HOL_Obool)), _895874), _895870)) = _895870)], (7147 ^ _779448) ^ [_896089, _896091, _896093, _896095, _896097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896089, tc_HOL_Obool)), _896091), _896093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896089, tc_HOL_Obool)), _896095), _896097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896089, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896089, tc_HOL_Obool)), _896091), _896097)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896089, tc_HOL_Obool)), _896093), _896095))))], (7157 ^ _779448) ^ [_896334, _896336, _896338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896334, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896334, tc_HOL_Obool)), _896336), _896338)), _896336)))], (7159 ^ _779448) ^ [_896382, _896384, _896386, _896388, _896390, _896392, _896394, _896396] : [c_Finite__Set_Ofolding__image__simple(_896382, _896384, _896386, _896388, _896390, _896392), hBOOL(hAPP(c_Finite__Set_Ofinite(_896384), _896394)), -(hAPP(_896392, hAPP(hAPP(c_Set_Oinsert(_896384), _896396), _896394)) = hAPP(hAPP(_896386, hAPP(_896390, _896396)), hAPP(_896392, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896384, tc_HOL_Obool)), _896394), hAPP(hAPP(c_Set_Oinsert(_896384), _896396), c_Orderings_Obot__class_Obot(tc_fun(_896384, tc_HOL_Obool)))))))], (7169 ^ _779448) ^ [_896645, _896647, _896649, _896651, _896653] : [c_Finite__Set_Ofolding__one(_896645, _896647, _896649), hBOOL(hAPP(c_Finite__Set_Ofinite(_896645), _896651)), 7176 ^ _779448 : [(7177 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896645, tc_HOL_Obool)), _896651), hAPP(hAPP(c_Set_Oinsert(_896645), _896653), c_Orderings_Obot__class_Obot(tc_fun(_896645, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_896645, tc_HOL_Obool)), -(hAPP(_896649, hAPP(hAPP(c_Set_Oinsert(_896645), _896653), _896651)) = _896653)], (7183 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896645, tc_HOL_Obool)), _896651), hAPP(hAPP(c_Set_Oinsert(_896645), _896653), c_Orderings_Obot__class_Obot(tc_fun(_896645, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_896645, tc_HOL_Obool))), -(hAPP(_896649, hAPP(hAPP(c_Set_Oinsert(_896645), _896653), _896651)) = hAPP(hAPP(_896647, _896653), hAPP(_896649, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896645, tc_HOL_Obool)), _896651), hAPP(hAPP(c_Set_Oinsert(_896645), _896653), c_Orderings_Obot__class_Obot(tc_fun(_896645, tc_HOL_Obool)))))))]]], (7189 ^ _779448) ^ [_897127, _897129, _897131, _897133] : [hBOOL(hAPP(hAPP(c_member(_897127), _897129), _897131)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897127, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897127), _897129), _897133)), _897131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897127, tc_HOL_Obool)), _897133), _897131))], (7195 ^ _779448) ^ [_897297, _897299, _897301, _897303] : [hBOOL(hAPP(hAPP(c_member(_897297), _897299), _897301)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897297, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897297), _897299), _897303)), _897301) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897297, tc_HOL_Obool)), _897303), _897301))], (7201 ^ _779448) ^ [_897446, _897448, _897450, _897452] : [-(hBOOL(hAPP(hAPP(c_member(_897446), _897448), _897450))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897446, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_897446), _897448), _897452)), _897450) = hAPP(hAPP(c_Set_Oinsert(_897446), _897448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897446, tc_HOL_Obool)), _897452), _897450)))], (7207 ^ _779448) ^ [_897533, _897535, _897537] : [-(hAPP(hAPP(c_Set_Oinsert(_897533), _897535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897533, tc_HOL_Obool)), _897537), hAPP(hAPP(c_Set_Oinsert(_897533), _897535), c_Orderings_Obot__class_Obot(tc_fun(_897533, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_897533), _897535), _897537))], (7209 ^ _779448) ^ [_897600, _897602, _897604, _897606] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897600, tc_HOL_Obool)), _897602), hAPP(hAPP(c_Set_Oinsert(_897600), _897604), _897606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897600, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897600, tc_HOL_Obool)), _897602), hAPP(hAPP(c_Set_Oinsert(_897600), _897604), c_Orderings_Obot__class_Obot(tc_fun(_897600, tc_HOL_Obool))))), _897606))], (7211 ^ _779448) ^ [_897683, _897685, _897687, _897689] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897683, tc_HOL_Obool)), _897685), hAPP(hAPP(c_Set_Oinsert(_897683), _897687), _897689)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897683, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897683, tc_HOL_Obool)), _897685), _897689)), hAPP(hAPP(c_Set_Oinsert(_897683), _897687), c_Orderings_Obot__class_Obot(tc_fun(_897683, tc_HOL_Obool)))))], (7213 ^ _779448) ^ [_897787, _897789, _897791, _897793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897787, tc_HOL_Obool)), _897789), hAPP(hAPP(c_Set_Oinsert(_897787), _897791), _897793)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_897787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897787, tc_HOL_Obool)), _897789), _897793))))], (7219 ^ _779448) ^ [_897940, _897942, _897944, _897946] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_897940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897940, tc_HOL_Obool)), _897942), _897946))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_897940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897940, tc_HOL_Obool)), _897942), hAPP(hAPP(c_Set_Oinsert(_897940), _897944), _897946)))))], (7225 ^ _779448) ^ [_898099, _898101, _898103, _898105, _898107] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898099, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898099, tc_HOL_Obool)), hAPP(c_Set_Oimage(_898101, _898099, _898103), _898105)), hAPP(c_Set_Oimage(_898101, _898099, _898103), _898107))), hAPP(c_Set_Oimage(_898101, _898099, _898103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898101, tc_HOL_Obool)), _898105), _898107)))))], (7227 ^ _779448) ^ [_898183, _898185, _898187, _898189, _898191, _898193] : [c_Finite__Set_Ofolding__image__simple(_898183, _898185, _898187, _898189, _898191, _898193), -(hAPP(_898193, c_Orderings_Obot__class_Obot(tc_fun(_898185, tc_HOL_Obool))) = _898189)], (7233 ^ _779448) ^ [_898292, _898294, _898296, _898298, _898300, _898302, _898304, _898306] : [c_Finite__Set_Ofolding__image__simple(_898292, _898294, _898296, _898298, _898300, _898302), hBOOL(hAPP(c_Finite__Set_Ofinite(_898294), _898304)), hBOOL(hAPP(hAPP(c_member(_898294), _898306), _898304)), -(hAPP(_898302, _898304) = hAPP(hAPP(_898296, hAPP(_898300, _898306)), hAPP(_898302, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898294, tc_HOL_Obool)), _898304), hAPP(hAPP(c_Set_Oinsert(_898294), _898306), c_Orderings_Obot__class_Obot(tc_fun(_898294, tc_HOL_Obool)))))))], (7247 ^ _779448) ^ [_898617, _898619, _898621, _898623, _898625] : [c_Finite__Set_Ofolding__one(_898617, _898619, _898621), hBOOL(hAPP(c_Finite__Set_Ofinite(_898617), _898623)), hBOOL(hAPP(hAPP(c_member(_898617), _898625), _898623)), 7258 ^ _779448 : [(7259 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898617, tc_HOL_Obool)), _898623), hAPP(hAPP(c_Set_Oinsert(_898617), _898625), c_Orderings_Obot__class_Obot(tc_fun(_898617, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_898617, tc_HOL_Obool)), -(hAPP(_898621, _898623) = _898625)], (7265 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898617, tc_HOL_Obool)), _898623), hAPP(hAPP(c_Set_Oinsert(_898617), _898625), c_Orderings_Obot__class_Obot(tc_fun(_898617, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_898617, tc_HOL_Obool))), -(hAPP(_898621, _898623) = hAPP(hAPP(_898619, _898625), hAPP(_898621, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898617, tc_HOL_Obool)), _898623), hAPP(hAPP(c_Set_Oinsert(_898617), _898625), c_Orderings_Obot__class_Obot(tc_fun(_898617, tc_HOL_Obool)))))))]]], (7271 ^ _779448) ^ [_899139, _899141, _899143, _899145] : [-(c_Nat_Onat_Onat__case(_899139, _899141, _899143, hAPP(c_Nat_OSuc, _899145)) = hAPP(_899143, _899145))], (7273 ^ _779448) ^ [_899179, _899181, _899183] : [hBOOL(hAPP(hAPP(c_member(_899179), _899181), _899183)), -(hAPP(hAPP(c_Set_Oinsert(_899179), _899181), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899179, tc_HOL_Obool)), _899183), hAPP(hAPP(c_Set_Oinsert(_899179), _899181), c_Orderings_Obot__class_Obot(tc_fun(_899179, tc_HOL_Obool))))) = _899183)], (7279 ^ _779448) ^ [_899332, _899334, _899336] : [-(hBOOL(hAPP(hAPP(c_member(_899332), _899334), _899336))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899332, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_899332), _899334), _899336)), hAPP(hAPP(c_Set_Oinsert(_899332), _899334), c_Orderings_Obot__class_Obot(tc_fun(_899332, tc_HOL_Obool)))) = _899336)], (7285 ^ _779448) ^ [_899409, _899411, _899413, _899415, _899417] : [class_Groups_Oab__group__add(_899409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_899409), _899411), _899413) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_899409), _899415), _899417), 7292 ^ _779448 : [(7293 ^ _779448) ^ [] : [_899411 = _899413, -(_899415 = _899417)], (7299 ^ _779448) ^ [] : [_899415 = _899417, -(_899411 = _899413)]]], (7305 ^ _779448) ^ [_899722, _899724, _899726, _899728] : [c_Finite__Set_Ofolding__one(_899722, _899724, _899726), -(hAPP(_899726, hAPP(hAPP(c_Set_Oinsert(_899722), _899728), c_Orderings_Obot__class_Obot(tc_fun(_899722, tc_HOL_Obool)))) = _899728)], (7311 ^ _779448) ^ [_899837, _899839, _899841, _899843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899837, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899837, tc_HOL_Obool)), _899839), hAPP(hAPP(c_Set_Oinsert(_899837), _899841), c_Orderings_Obot__class_Obot(tc_fun(_899837, tc_HOL_Obool))))), _899843)), hBOOL(hAPP(hAPP(c_member(_899837), _899841), _899839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899837, tc_HOL_Obool)), _899839), hAPP(hAPP(c_Set_Oinsert(_899837), _899841), _899843))))], (7337 ^ _779448) ^ [_900445, _900447, _900449, _900451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900445, tc_HOL_Obool)), _900447), hAPP(hAPP(c_Set_Oinsert(_900445), _900449), _900451)))), 7340 ^ _779448 : [(7341 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900445), _900449), _900447)))], (7343 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900445, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900445, tc_HOL_Obool)), _900447), hAPP(hAPP(c_Set_Oinsert(_900445), _900449), c_Orderings_Obot__class_Obot(tc_fun(_900445, tc_HOL_Obool))))), _900451))]], 7344 ^ _779448 : [(7345 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900445), _900449), _900447))], (7347 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900445, tc_HOL_Obool)), _900447), _900451))]]], (7321 ^ _779448) ^ [_900113, _900115, _900117, _900119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900113, tc_HOL_Obool)), _900115), hAPP(hAPP(c_Set_Oinsert(_900113), _900117), _900119))), 7324 ^ _779448 : [(7325 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_900113), _900117), _900115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900113, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900113, tc_HOL_Obool)), _900115), hAPP(hAPP(c_Set_Oinsert(_900113), _900117), c_Orderings_Obot__class_Obot(tc_fun(_900113, tc_HOL_Obool))))), _900119)))], (7331 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_900113), _900117), _900115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900113, tc_HOL_Obool)), _900115), _900119)))]]], (7351 ^ _779448) ^ [_900809, _900811, _900813] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900809), _900811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900809, tc_HOL_Obool)), _900811), _900813)), -(hAPP(c_Finite__Set_Ocard(_900809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900809, tc_HOL_Obool)), _900813), _900811)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_900809), _900813)), hAPP(c_Finite__Set_Ocard(_900809), _900811)))], (7361 ^ _779448) ^ [_901034, _901036, _901038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901034), _901036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_901034), _901038)), hAPP(c_Finite__Set_Ocard(_901034), _901036))), hAPP(c_Finite__Set_Ocard(_901034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901034, tc_HOL_Obool)), _901038), _901036)))))], (7367 ^ _779448) ^ [_901195, _901197, _901199, _901201, _901203] : [c_Finite__Set_Ofolding__one__idem(_901195, _901197, _901199), hBOOL(hAPP(c_Finite__Set_Ofinite(_901195), _901201)), hBOOL(hAPP(hAPP(c_member(_901195), _901203), _901201)), -(hAPP(hAPP(_901197, _901203), hAPP(_901199, _901201)) = hAPP(_901199, _901201))], (7381 ^ _779448) ^ [_901442, _901444, _901446, _901448, _901450, _901452, _901454, _901456] : [c_Finite__Set_Ofolding__image__simple__idem(_901442, _901444, _901446, _901448, _901450, _901452), hBOOL(hAPP(c_Finite__Set_Ofinite(_901444), _901454)), hBOOL(hAPP(hAPP(c_member(_901444), _901456), _901454)), -(hAPP(hAPP(_901446, hAPP(_901450, _901456)), hAPP(_901452, _901454)) = hAPP(_901452, _901454))], (7395 ^ _779448) ^ [_901719, _901721, _901723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901719), _901721)), -(hAPP(c_Finite__Set_Ocard(_901719), hAPP(hAPP(c_Set_Oinsert(_901719), _901723), _901721)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_901719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901719, tc_HOL_Obool)), _901721), hAPP(hAPP(c_Set_Oinsert(_901719), _901723), c_Orderings_Obot__class_Obot(tc_fun(_901719, tc_HOL_Obool)))))))], (7401 ^ _779448) ^ [_901896, _901898, _901900] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901896), _901898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_901896), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901896, tc_HOL_Obool)), _901898), hAPP(hAPP(c_Set_Oinsert(_901896), _901900), c_Orderings_Obot__class_Obot(tc_fun(_901896, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_901896), _901898))))], (7407 ^ _779448) ^ [_902061, _902063, _902065, _902067, _902069] : [class_Groups_Ominus(_902061), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902063, _902061)), _902065), _902067), _902069) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_902061), hAPP(_902065, _902069)), hAPP(_902067, _902069)))], (7413 ^ _779448) ^ [_902210, _902212, _902214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902210, tc_HOL_Obool)), _902212), hAPP(hAPP(c_Set_Oinsert(_902210), _902214), c_Orderings_Obot__class_Obot(tc_fun(_902210, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_902210, _902214, _902212) = _902214)], (7419 ^ _779448) ^ [_902337, _902339, _902341] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902337, tc_HOL_Obool)), _902339), hAPP(hAPP(c_Set_Oinsert(_902337), _902341), c_Orderings_Obot__class_Obot(tc_fun(_902337, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_902337, _902341, _902339) = c_HOL_OThe(_902337, hAPP(hAPP(c_COMBC(_902337, tc_fun(_902337, tc_HOL_Obool), tc_HOL_Obool), c_member(_902337)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902337, tc_HOL_Obool)), _902339), hAPP(hAPP(c_Set_Oinsert(_902337), _902341), c_Orderings_Obot__class_Obot(tc_fun(_902337, tc_HOL_Obool)))))))], (7425 ^ _779448) ^ [_902446, _902448, _902450] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902446), _902448)), hBOOL(hAPP(hAPP(c_member(_902446), _902450), _902448)), -(hAPP(c_Finite__Set_Ocard(_902446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902446, tc_HOL_Obool)), _902448), hAPP(hAPP(c_Set_Oinsert(_902446), _902450), c_Orderings_Obot__class_Obot(tc_fun(_902446, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_902446), _902448)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7435 ^ _779448) ^ [_902681, _902683, _902685] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902681), _902683)), 7438 ^ _779448 : [(7439 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902681), _902685), _902683)), -(hAPP(c_Finite__Set_Ocard(_902681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902681, tc_HOL_Obool)), _902683), hAPP(hAPP(c_Set_Oinsert(_902681), _902685), c_Orderings_Obot__class_Obot(tc_fun(_902681, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_902681), _902683)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7445 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902681), _902685), _902683))), -(hAPP(c_Finite__Set_Ocard(_902681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902681, tc_HOL_Obool)), _902683), hAPP(hAPP(c_Set_Oinsert(_902681), _902685), c_Orderings_Obot__class_Obot(tc_fun(_902681, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_902681), _902683))]]], (7451 ^ _779448) ^ [_903045, _903047, _903049, _903051, _903053] : [class_Groups_Ominus(_903045), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903047, _903045)), _903049), _903051), _903053) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903045), hAPP(_903049, _903053)), hAPP(_903051, _903053)))], (7457 ^ _779448) ^ [_903182, _903184, _903186, _903188] : [c_Finite__Set_Ofolding__one(_903182, _903184, _903186), hBOOL(hAPP(c_Finite__Set_Ofinite(_903182), _903188)), -(_903188 = c_Orderings_Obot__class_Obot(tc_fun(_903182, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_903182), hAPP(hAPP(_903184, 7470 ^ [_903182, _903184, _903186, _903188]), 7471 ^ [_903182, _903184, _903186, _903188])), hAPP(hAPP(c_Set_Oinsert(_903182), 7470 ^ [_903182, _903184, _903186, _903188]), hAPP(hAPP(c_Set_Oinsert(_903182), 7471 ^ [_903182, _903184, _903186, _903188]), c_Orderings_Obot__class_Obot(tc_fun(_903182, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_903182), hAPP(_903186, _903188)), _903188)))], (7477 ^ _779448) ^ [_903668, _903670, _903672, _903674] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903668), _903670)), hBOOL(hAPP(hAPP(c_member(_903668), _903672), _903670)), -(hBOOL(hAPP(hAPP(c_member(_903668), _903672), _903674))), -(hAPP(c_Finite__Set_Ocard(_903668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903668, tc_HOL_Obool)), _903670), hAPP(hAPP(c_Set_Oinsert(_903668), _903672), _903674))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_903668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903668, tc_HOL_Obool)), _903670), _903674))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7491 ^ _779448) ^ [_903948, _903950, _903952, _903954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903948), _903950)), hBOOL(hAPP(hAPP(c_member(_903948), _903952), _903950)), hBOOL(hAPP(hAPP(c_member(_903948), _903954), _903950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_903948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903948, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903948, tc_HOL_Obool)), _903950), hAPP(hAPP(c_Set_Oinsert(_903948), _903952), c_Orderings_Obot__class_Obot(tc_fun(_903948, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_903948), _903954), c_Orderings_Obot__class_Obot(tc_fun(_903948, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_903948), _903950))))], (7505 ^ _779448) ^ [_904303, _904305, _904307] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904303), _904305)), hBOOL(hAPP(hAPP(c_member(_904303), _904307), _904305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_904303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904303, tc_HOL_Obool)), _904305), hAPP(hAPP(c_Set_Oinsert(_904303), _904307), c_Orderings_Obot__class_Obot(tc_fun(_904303, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_904303), _904305))))], (7515 ^ _779448) ^ [_904536, _904538, _904540] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904536), _904538)), hBOOL(hAPP(_904540, _904538)), 7526 ^ _779448 : [(7527 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_904536), 7525 ^ [_904536, _904538, _904540])))], (7529 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_904536), 7524 ^ [_904536, _904538, _904540]), 7525 ^ [_904536, _904538, _904540])))], (7531 ^ _779448) ^ [] : [-(hBOOL(hAPP(_904540, 7525 ^ [_904536, _904538, _904540])))], (7533 ^ _779448) ^ [] : [hBOOL(hAPP(_904540, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904536, tc_HOL_Obool)), 7525 ^ [_904536, _904538, _904540]), hAPP(hAPP(c_Set_Oinsert(_904536), 7524 ^ [_904536, _904538, _904540]), c_Orderings_Obot__class_Obot(tc_fun(_904536, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_904540, c_Orderings_Obot__class_Obot(tc_fun(_904536, tc_HOL_Obool)))))], (7537 ^ _779448) ^ [_905061, _905063, _905065, _905067, _905069] : [c_Finite__Set_Ofolding__one__idem(_905061, _905063, _905065), hAPP(_905067, hAPP(hAPP(_905063, 7542 ^ [_905061, _905063, _905065, _905067, _905069]), 7543 ^ [_905061, _905063, _905065, _905067, _905069])) = hAPP(hAPP(_905063, hAPP(_905067, 7542 ^ [_905061, _905063, _905065, _905067, _905069])), hAPP(_905067, 7543 ^ [_905061, _905063, _905065, _905067, _905069])), hBOOL(hAPP(c_Finite__Set_Ofinite(_905061), _905069)), -(_905069 = c_Orderings_Obot__class_Obot(tc_fun(_905061, tc_HOL_Obool))), -(hAPP(_905067, hAPP(_905065, _905069)) = hAPP(_905065, hAPP(c_Set_Oimage(_905061, _905061, _905067), _905069)))], (7557 ^ _779448) ^ [_905496] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905496), hAPP(c_Nat_OSuc, _905496))))], (7559 ^ _779448) ^ [_905527, _905529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905527), _905529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _905527)), hAPP(c_Nat_OSuc, _905529))))], (7565 ^ _779448) ^ [_905636, _905638] : [class_Groups_Oone(_905636), 7568 ^ _779448 : [(7569 ^ _779448) ^ [] : [c_Groups_Oone__class_Oone(_905636) = _905638, -(_905638 = c_Groups_Oone__class_Oone(_905636))], (7575 ^ _779448) ^ [] : [_905638 = c_Groups_Oone__class_Oone(_905636), -(c_Groups_Oone__class_Oone(_905636) = _905638)]]], (7581 ^ _779448) ^ [_905862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905862), _905862))], (7583 ^ _779448) ^ [_905890, _905892] : [class_Orderings_Opreorder(_905890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905890), _905892), _905892))], (7599 ^ _779448) ^ [_906038, _906040] : [7600 ^ _779448 : [(7601 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906038), _906040))], (7603 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _906040), _906038))]], _906038 = _906040], (7589 ^ _779448) ^ [_905989, _905991] : [-(_905989 = _905991), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905989), _905991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _905991), _905989)))], (7607 ^ _779448) ^ [_906176, _906178, _906180] : [class_Orderings_Olinorder(_906176), 7610 ^ _779448 : [(7621 ^ _779448) ^ [] : [7622 ^ _779448 : [(7623 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906176), _906178), _906180))], (7625 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906176), _906180), _906178))]], _906178 = _906180], (7611 ^ _779448) ^ [] : [-(_906178 = _906180), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906176), _906178), _906180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906176), _906180), _906178)))]]], (7629 ^ _779448) ^ [_906430, _906432, _906434] : [class_Orderings_Olinorder(_906430), 7632 ^ _779448 : [(7643 ^ _779448) ^ [] : [7644 ^ _779448 : [(7645 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906430), _906434), _906432))], (7647 ^ _779448) ^ [] : [_906432 = _906434]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906430), _906432), _906434))], (7633 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906430), _906432), _906434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906430), _906434), _906432))), -(_906432 = _906434)]]], (7651 ^ _779448) ^ [_906684, _906686, _906688] : [class_Orderings_Olinorder(_906684), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906684), _906686), _906688))), -(_906686 = _906688), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906684), _906688), _906686)))], (7665 ^ _779448) ^ [_906815, _906817, _906819] : [class_Orderings_Olinorder(_906815), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906815), _906817), _906819))), 7672 ^ _779448 : [(7673 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906815), _906819), _906817))), -(_906819 = _906817)], (7679 ^ _779448) ^ [] : [_906819 = _906817, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906815), _906819), _906817))]]], (7685 ^ _779448) ^ [_907074, _907076, _907078] : [class_Orderings_Olinorder(_907074), -(_907076 = _907078), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907074), _907076), _907078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907074), _907078), _907076)))], (7699 ^ _779448) ^ [_907205, _907207] : [-(_907205 = _907207), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907205), _907207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907207), _907205)))], (7709 ^ _779448) ^ [_907267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907267), _907267))], (7711 ^ _779448) ^ [_907295, _907297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907295), _907297)), _907297 = _907295], (7717 ^ _779448) ^ [_907383, _907385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _907383), _907385)), _907383 = _907385], (7723 ^ _779448) ^ [_907471, _907473, _907475] : [class_Orderings_Oorder(_907471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907471), _907473), _907475)), _907473 = _907475], (7733 ^ _779448) ^ [_907617, _907619, _907621] : [class_Orderings_Opreorder(_907617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907617), _907619), _907621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907617), _907621), _907619))], (7743 ^ _779448) ^ [_907777, _907779, _907781] : [class_Orderings_Opreorder(_907777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907777), _907779), _907781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907777), _907781), _907779))], (7753 ^ _779448) ^ [_907937, _907939, _907941] : [class_Orderings_Oorder(_907937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907937), _907939), _907941)), _907939 = _907941], (7763 ^ _779448) ^ [_908083, _908085, _908087] : [class_Orderings_Oorder(_908083), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908083), _908085), _908087)), _908087 = _908085], (7773 ^ _779448) ^ [_908229, _908231, _908233] : [class_Orderings_Opreorder(_908229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908229), _908231), _908233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908229), _908233), _908231))], (7783 ^ _779448) ^ [_908389, _908391, _908393] : [class_Orderings_Oorder(_908389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908389), _908391), _908393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908389), _908393), _908391))], (7793 ^ _779448) ^ [_908549, _908551, _908553, _908555] : [class_Orderings_Oord(_908549), _908551 = _908553, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908549), _908553), _908555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908549), _908551), _908555)))], (7807 ^ _779448) ^ [_908768, _908770, _908772, _908774] : [class_Orderings_Oorder(_908768), _908770 = _908772, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908768), _908774), _908772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908768), _908774), _908770)))], (7821 ^ _779448) ^ [_908987, _908989, _908991, _908993] : [class_Orderings_Oord(_908987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908987), _908989), _908991)), _908991 = _908993, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908987), _908989), _908993)))], (7835 ^ _779448) ^ [_909206, _909208, _909210, _909212] : [class_Orderings_Oorder(_909206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909206), _909208), _909210)), _909208 = _909212, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909206), _909212), _909210)))], (7849 ^ _779448) ^ [_909425, _909427, _909429, _909431] : [class_Orderings_Opreorder(_909425), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909425), _909427), _909429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909425), _909429), _909431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909425), _909427), _909431)))], (7863 ^ _779448) ^ [_909658, _909660, _909662, _909664] : [class_Orderings_Oorder(_909658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909658), _909660), _909662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909658), _909664), _909660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909658), _909664), _909662)))], (7877 ^ _779448) ^ [_909891, _909893, _909895] : [class_Orderings_Opreorder(_909891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909891), _909893), _909895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_909891), _909895), _909893))], (7887 ^ _779448) ^ [_910051, _910053, _910055] : [class_Orderings_Olinorder(_910051), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910051), _910053), _910055))), -(_910053 = _910055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910051), _910055), _910053)))], (7901 ^ _779448) ^ [_910186, _910188, _910190] : [7902 ^ _779448 : [(7903 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910186), _910188)))], (7905 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_910190, _910188), _910186))]], 7908 ^ _779448 : [(7909 ^ _779448) ^ [] : [-(_910186 = _910188)], (7911 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_910190, _910188), _910186))]], 7914 ^ _779448 : [(7915 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _910188), _910186)))], (7917 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_910190, _910188), _910186))]], -(hBOOL(hAPP(hAPP(_910190, _910188), _910186)))], (7921 ^ _779448) ^ [_910532, _910534, _910536] : [class_Orderings_Olinorder(_910532), 7924 ^ _779448 : [(7925 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910532), _910534), _910536))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910532), _910536), _910534)))], (7931 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910532), _910536), _910534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910532), _910534), _910536))]]], (7937 ^ _779448) ^ [_910741, _910743, _910745] : [class_Orderings_Olinorder(_910741), 7940 ^ _779448 : [(7941 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910741), _910743), _910745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910741), _910745), _910743)))], (7947 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910741), _910745), _910743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910741), _910743), _910745))]]], (7953 ^ _779448) ^ [_910950, _910952, _910954] : [class_Orderings_Olinorder(_910950), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910950), _910952), _910954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_910950), _910954), _910952)))], (7963 ^ _779448) ^ [_911068, _911070, _911072] : [class_Orderings_Oorder(_911068), 7966 ^ _779448 : [(7967 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911068), _911070), _911072)), 7970 ^ _779448 : [(7971 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911068), _911070), _911072)))], (7973 ^ _779448) ^ [] : [_911070 = _911072]]], (7975 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911068), _911070), _911072))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911068), _911070), _911072)), -(_911070 = _911072)]]], (7985 ^ _779448) ^ [_911404, _911406, _911408] : [class_Orderings_Opreorder(_911404), 7988 ^ _779448 : [(7989 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911404), _911406), _911408)), 7992 ^ _779448 : [(7993 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911404), _911406), _911408)))], (7995 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911404), _911408), _911406))]]], (7997 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911404), _911406), _911408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911404), _911406), _911408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911404), _911408), _911406)))]]], (8007 ^ _779448) ^ [_911761, _911763, _911765] : [class_Orderings_Oorder(_911761), 8010 ^ _779448 : [(8021 ^ _779448) ^ [] : [8022 ^ _779448 : [(8023 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911761), _911763), _911765))], (8025 ^ _779448) ^ [] : [_911763 = _911765]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911761), _911763), _911765)))], (8011 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911761), _911763), _911765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_911761), _911763), _911765))), -(_911763 = _911765)]]], (8029 ^ _779448) ^ [_912059, _912061, _912063] : [class_Orderings_Olinorder(_912059), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912059), _912061), _912063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912059), _912063), _912061)))], (8039 ^ _779448) ^ [_912179, _912181, _912183] : [class_Orderings_Olinorder(_912179), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912179), _912181), _912183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912179), _912183), _912181)))], (8049 ^ _779448) ^ [_912299, _912301, _912303] : [class_Orderings_Olinorder(_912299), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912299), _912301), _912303))), 8056 ^ _779448 : [(8057 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912299), _912301), _912303)), -(_912301 = _912303)], (8063 ^ _779448) ^ [] : [_912301 = _912303, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912299), _912301), _912303)))]]], (8069 ^ _779448) ^ [_912602, _912604, _912606] : [class_Orderings_Oorder(_912602), -(_912604 = _912606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912602), _912604), _912606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912602), _912604), _912606)))], (8083 ^ _779448) ^ [_912818, _912820, _912822] : [class_Orderings_Oorder(_912818), -(_912820 = _912822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912818), _912822), _912820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_912818), _912822), _912820)))], (8097 ^ _779448) ^ [_913034, _913036, _913038] : [class_Orderings_Olinorder(_913034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913034), _913036), _913038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913034), _913038), _913036))], (8107 ^ _779448) ^ [_913194, _913196, _913198] : [class_Orderings_Opreorder(_913194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913194), _913196), _913198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913194), _913196), _913198)))], (8117 ^ _779448) ^ [_913353, _913355, _913357] : [class_Orderings_Olinorder(_913353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913353), _913355), _913357)), 8124 ^ _779448 : [(8125 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913353), _913355), _913357))), -(_913355 = _913357)], (8131 ^ _779448) ^ [] : [_913355 = _913357, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913353), _913355), _913357))]]], (8137 ^ _779448) ^ [_913609, _913611, _913613] : [class_Orderings_Oorder(_913609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913609), _913611), _913613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913609), _913611), _913613))), -(_913611 = _913613)], (8151 ^ _779448) ^ [_913781, _913783, _913785] : [class_Orderings_Oorder(_913781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913781), _913783), _913785)), -(_913783 = _913785), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913781), _913783), _913785)))], (8165 ^ _779448) ^ [_913955, _913957, _913959] : [class_Orderings_Oorder(_913955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_913955), _913957), _913959)), -(_913959 = _913957), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_913955), _913957), _913959)))], (8179 ^ _779448) ^ [_914129, _914131, _914133, _914135] : [class_Orderings_Opreorder(_914129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914129), _914131), _914133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914129), _914133), _914135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914129), _914131), _914135)))], (8193 ^ _779448) ^ [_914362, _914364, _914366, _914368] : [class_Orderings_Oorder(_914362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914362), _914364), _914366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914362), _914368), _914364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914362), _914368), _914366)))], (8207 ^ _779448) ^ [_914595, _914597, _914599, _914601] : [class_Orderings_Opreorder(_914595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914595), _914597), _914599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914595), _914599), _914601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914595), _914597), _914601)))], (8221 ^ _779448) ^ [_914828, _914830, _914832, _914834] : [class_Orderings_Oorder(_914828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_914828), _914830), _914832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914828), _914834), _914830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_914828), _914834), _914832)))], (8235 ^ _779448) ^ [_915061, _915063, _915065, _915067, _915069] : [class_Groups_Oordered__ab__group__add(_915061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915061), _915063), _915065) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_915061), _915067), _915069), 8242 ^ _779448 : [(8243 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915061), _915063), _915065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915061), _915067), _915069)))], (8249 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915061), _915067), _915069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_915061), _915063), _915065)))]]], (8255 ^ _779448) ^ [_915425, _915427] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915425), _915427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915427), hAPP(c_Nat_OSuc, _915425))))], (8261 ^ _779448) ^ [_915470, _915472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915472), hAPP(c_Nat_OSuc, _915470))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915470), _915472))], (8277 ^ _779448) ^ [_915703, _915705] : [8278 ^ _779448 : [(8279 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915703), _915705))], (8281 ^ _779448) ^ [] : [_915703 = _915705]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915703), hAPP(c_Nat_OSuc, _915705))))], (8267 ^ _779448) ^ [_915591, _915593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915591), hAPP(c_Nat_OSuc, _915593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915591), _915593))), -(_915591 = _915593)], (8285 ^ _779448) ^ [_915861, _915863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _915861)), hAPP(c_Nat_OSuc, _915863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915861), _915863)))], (8291 ^ _779448) ^ [_915966, _915968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _915966), _915968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _915966)), hAPP(c_Nat_OSuc, _915968))))], (8297 ^ _779448) ^ [_916076, _916078] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916076), _916078))), 8300 ^ _779448 : [(8301 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916076), hAPP(c_Nat_OSuc, _916078))), -(_916076 = _916078)], (8307 ^ _779448) ^ [] : [_916076 = _916078, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916076), hAPP(c_Nat_OSuc, _916078))))]]], (8313 ^ _779448) ^ [_916309, _916311] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916309), _916311))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916309), hAPP(c_Nat_OSuc, _916311))), -(_916311 = _916309)], (8323 ^ _779448) ^ [_916457, _916459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916457), _916459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916457), hAPP(c_Nat_OSuc, _916459))))], (8329 ^ _779448) ^ [_916560, _916562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916560), _916562)), -(hAPP(c_Nat_OSuc, _916560) = _916562), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _916560)), _916562)))], (8339 ^ _779448) ^ [_916684, _916686, _916688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916684), _916686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916686), _916688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _916684)), _916688)))], (8349 ^ _779448) ^ [_916853, _916855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916853), hAPP(c_Nat_OSuc, _916855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916853), _916855))), -(_916853 = _916855)], (8359 ^ _779448) ^ [_916971, _916973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _916971)), _916973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _916971), _916973)))], (8365 ^ _779448) ^ [_917074, _917076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _917074)), hAPP(c_Nat_OSuc, _917076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917074), _917076)))], (8371 ^ _779448) ^ [_917198, _917200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917198), _917200)), 8374 ^ _779448 : [(8375 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917198), _917200)))], (8377 ^ _779448) ^ [] : [_917198 = _917200]]], (8379 ^ _779448) ^ [_917325, _917327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917325), _917327))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917325), _917327)), -(_917325 = _917327)], (8399 ^ _779448) ^ [_917600, _917602] : [8400 ^ _779448 : [(8401 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917600), _917602))], (8403 ^ _779448) ^ [] : [_917600 = _917602]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917600), _917602)))], (8389 ^ _779448) ^ [_917494, _917496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917494), _917496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917494), _917496))), -(_917494 = _917496)], (8407 ^ _779448) ^ [_917737, _917739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917737), _917739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917737), _917739)))], (8413 ^ _779448) ^ [_917834, _917836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917834), _917836)), -(_917834 = _917836), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917834), _917836)))], (8423 ^ _779448) ^ [_917946, _917948] : [8424 ^ _779448 : [(8425 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _917946), _917948))], (8427 ^ _779448) ^ [] : [_917946 = _917948]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _917946), _917948)))], (8431 ^ _779448) ^ [_918081, _918083, _918085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918081), _918083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _918081), _918085)), _918083)))], (8437 ^ _779448) ^ [_918192, _918194, _918196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918192), _918194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918192), _918196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _918196), _918194)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _918196), _918192))))], (8447 ^ _779448) ^ [_918394, _918396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918394), _918396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _918394)), _918396)))], (8453 ^ _779448) ^ [_918493, _918495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _918493)), _918495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918493), _918495)))], (8459 ^ _779448) ^ [_918613, _918615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918613), hAPP(c_Nat_OSuc, _918615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918613), _918615)))], (8465 ^ _779448) ^ [_918712, _918714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _918712), _918714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918712), hAPP(c_Nat_OSuc, _918714))))], (8471 ^ _779448) ^ [_918832, _918834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _918832)), _918834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918832), _918834)))], (8477 ^ _779448) ^ [_918931, _918933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _918931), _918933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _918931)), _918933)))], (8483 ^ _779448) ^ [_919036, _919038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919036), _919038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919036), hAPP(c_Nat_OSuc, _919038))))], (8489 ^ _779448) ^ [_919139, _919141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919139), _919141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _919139)), _919141)))], (8495 ^ _779448) ^ [_919242, _919244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919242), _919244)), 8498 ^ _779448 : [(8499 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919244), hAPP(c_Nat_OSuc, _919242))), -(_919244 = _919242)], (8505 ^ _779448) ^ [] : [_919244 = _919242, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919244), hAPP(c_Nat_OSuc, _919242))))]]], (8511 ^ _779448) ^ [_919483, _919485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _919483)), _919485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919483), _919485)))], (8517 ^ _779448) ^ [_919586, _919588] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919586), _919588)), hAPP(c_Nat_OSuc, _919586))))], (8519 ^ _779448) ^ [_919625, _919627] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919625), hAPP(c_Nat_OSuc, _919627)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919625), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _919627))], (8521 ^ _779448) ^ [_919671] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _919671)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _919671)], (8523 ^ _779448) ^ [_919703, _919705, _919707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919703), _919705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919707), _919703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919703), _919707)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919705), _919707))))], (8533 ^ _779448) ^ [_919890, _919892, _919894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919890), _919892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919890), _919894)), 8540 ^ _779448 : [(8541 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919892), _919890)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919894), _919890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919892), _919894)))], (8547 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _919892), _919894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919892), _919890)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _919894), _919890))))]]], (8553 ^ _779448) ^ [_920243] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920243) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _920243)))], (8555 ^ _779448) ^ [_920275, _920277, _920279] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_920275), _920277)), hBOOL(hAPP(hAPP(c_member(_920275), _920279), _920277)), -(hAPP(c_Finite__Set_Ocard(_920275), _920277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_920275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920275, tc_HOL_Obool)), _920277), hAPP(hAPP(c_Set_Oinsert(_920275), _920279), c_Orderings_Obot__class_Obot(tc_fun(_920275, tc_HOL_Obool)))))))], (8565 ^ _779448) ^ [_920504, _920506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _920504), _920506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920504), _920506)))], (8571 ^ _779448) ^ [_920601, _920603, _920605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_920601), _920603)), -(hAPP(c_Finite__Set_Ocard(_920601), hAPP(hAPP(c_Set_Oinsert(_920601), _920605), _920603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_920601), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920601, tc_HOL_Obool)), _920603), hAPP(hAPP(c_Set_Oinsert(_920601), _920605), c_Orderings_Obot__class_Obot(tc_fun(_920601, tc_HOL_Obool)))))))], (8577 ^ _779448) ^ [_920778] : [-(c_Finite__Set_Ofun__left__comm__idem(_920778, tc_fun(_920778, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_920778, tc_HOL_Obool), tc_fun(tc_fun(_920778, tc_HOL_Obool), tc_fun(_920778, tc_HOL_Obool)), _920778), hAPP(c_COMBC(tc_fun(_920778, tc_HOL_Obool), tc_fun(_920778, tc_HOL_Obool), tc_fun(_920778, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_920778, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_920778, tc_fun(_920778, tc_HOL_Obool), tc_fun(_920778, tc_HOL_Obool)), c_Set_Oinsert(_920778)), c_Orderings_Obot__class_Obot(tc_fun(_920778, tc_HOL_Obool))))))], (8579 ^ _779448) ^ [_920871, _920873] : [-(c_HOL_OThe(_920871, hAPP(hAPP(c_COMBC(_920871, _920871, tc_HOL_Obool), c_fequal), _920873)) = _920873)], (8581 ^ _779448) ^ [_920909, _920911] : [-(c_HOL_OThe(_920909, hAPP(c_fequal, _920911)) = _920911)], (8583 ^ _779448) ^ [_920940, _920942, _920944] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_920940), _920942)), -(hBOOL(hAPP(hAPP(c_member(_920940), _920944), _920942))), -(hAPP(c_Finite__Set_Ocard(_920940), hAPP(hAPP(c_Set_Oinsert(_920940), _920944), _920942)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_920940), _920942)))], (8619 ^ _779448) ^ [_921646, _921648, _921650, _921652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921646, tc_HOL_Obool)), _921648), hAPP(hAPP(c_Set_Oinsert(_921646), _921650), _921652)))), 8622 ^ _779448 : [(8623 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921646), _921650), _921652)))], (8625 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921646, tc_HOL_Obool)), _921648), _921652))]], 8626 ^ _779448 : [(8627 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921646), _921650), _921652))], (8629 ^ _779448) ^ [] : [8630 ^ _779448 : [(8631 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921646), _921650), _921648)))], (8633 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921646, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921646, tc_HOL_Obool)), _921648), hAPP(hAPP(c_Set_Oinsert(_921646), _921650), c_Orderings_Obot__class_Obot(tc_fun(_921646, tc_HOL_Obool))))), _921652))]], 8634 ^ _779448 : [(8635 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921646), _921650), _921648))], (8637 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921646, tc_HOL_Obool)), _921648), _921652))]]]]], (8593 ^ _779448) ^ [_921119, _921121, _921123, _921125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921119, tc_HOL_Obool)), _921121), hAPP(hAPP(c_Set_Oinsert(_921119), _921123), _921125))), 8596 ^ _779448 : [(8597 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921119), _921123), _921125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921119, tc_HOL_Obool)), _921121), _921125)))], (8603 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921119), _921123), _921125))), 8606 ^ _779448 : [(8607 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921119), _921123), _921121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921119, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921119, tc_HOL_Obool)), _921121), hAPP(hAPP(c_Set_Oinsert(_921119), _921123), c_Orderings_Obot__class_Obot(tc_fun(_921119, tc_HOL_Obool))))), _921125)))], (8613 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921119), _921123), _921121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921119, tc_HOL_Obool)), _921121), _921125)))]]]]], (8641 ^ _779448) ^ [_922185, _922187, _922189] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922185), _922187)), hBOOL(hAPP(_922189, c_Orderings_Obot__class_Obot(tc_fun(_922185, tc_HOL_Obool)))), 8652 ^ _779448 : [(8653 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_922185), 8651 ^ [_922185, _922187, _922189])))], (8655 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922185), 8650 ^ [_922185, _922187, _922189]), 8651 ^ [_922185, _922187, _922189]))], (8657 ^ _779448) ^ [] : [-(hBOOL(hAPP(_922189, 8651 ^ [_922185, _922187, _922189])))], (8659 ^ _779448) ^ [] : [hBOOL(hAPP(_922189, hAPP(hAPP(c_Set_Oinsert(_922185), 8650 ^ [_922185, _922187, _922189]), 8651 ^ [_922185, _922187, _922189])))]], -(hBOOL(hAPP(_922189, _922187)))], (8663 ^ _779448) ^ [_922672, _922674, _922676, _922678, _922680, _922682, _922684] : [hBOOL(hAPP(hAPP(c_member(_922672), _922674), _922676)), c_Nitpick_Ofold__graph_H(_922672, _922678, _922680, _922682, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922672, tc_HOL_Obool)), _922676), hAPP(hAPP(c_Set_Oinsert(_922672), _922674), c_Orderings_Obot__class_Obot(tc_fun(_922672, tc_HOL_Obool)))), _922684), -(c_Nitpick_Ofold__graph_H(_922672, _922678, _922680, _922682, _922676, hAPP(hAPP(_922680, _922674), _922684)))], (8673 ^ _779448) ^ [_922911, _922913, _922915, _922917, _922919, _922921, _922923] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922911, _922913, _922915, _922917, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922911, tc_HOL_Obool)), _922919), hAPP(hAPP(c_Set_Oinsert(_922911), _922921), c_Orderings_Obot__class_Obot(tc_fun(_922911, tc_HOL_Obool))))), _922923)), hBOOL(hAPP(hAPP(c_member(_922911), _922921), _922919)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922911, _922913, _922915, _922917, _922919), hAPP(hAPP(_922915, _922921), _922923))))], (8683 ^ _779448) ^ [_923166, _923168, _923170, _923172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923166, tc_HOL_Obool)), _923168), _923170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923166, tc_HOL_Obool)), _923170), _923172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_923166, tc_HOL_Obool)), _923168), _923172)))], (8693 ^ _779448) ^ [_923363, _923365, _923367, _923369, _923371] : [c_Finite__Set_Ofun__left__comm__idem(_923363, _923365, _923367), -(hAPP(hAPP(_923367, _923369), hAPP(hAPP(_923367, _923369), _923371)) = hAPP(hAPP(_923367, _923369), _923371))], (8699 ^ _779448) ^ [_923502, _923504, _923506] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923502), _923504) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923506), _923504), -(_923502 = _923506)], (8705 ^ _779448) ^ [_923601, _923603, _923605] : [_923601 = _923605, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923601), _923603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923605), _923603))], (8711 ^ _779448) ^ [_923724, _923726, _923728] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923724), _923726) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923724), _923728), -(_923726 = _923728)], (8717 ^ _779448) ^ [_923823, _923825, _923827] : [_923825 = _923827, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923823), _923825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923823), _923827))], (8723 ^ _779448) ^ [_923928, _923930, _923932] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923928), _923930)), _923932) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923930), _923932)))], (8725 ^ _779448) ^ [_923979, _923981, _923983] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923981), _923983)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923979), _923983)))], (8727 ^ _779448) ^ [_924030, _924032] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _924030), _924032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _924032), _924030))], (8729 ^ _779448) ^ [_924067, _924069, _924071, _924073] : [class_Groups_Ocancel__semigroup__add(_924067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924067), _924069), _924071) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924067), _924073), _924071), -(_924069 = _924073)], (8739 ^ _779448) ^ [_924234, _924236, _924238, _924240] : [class_Groups_Ocancel__ab__semigroup__add(_924234), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924234), _924236), _924238) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924234), _924236), _924240), -(_924238 = _924240)], (8749 ^ _779448) ^ [_924401, _924403, _924405, _924407] : [class_Groups_Ocancel__semigroup__add(_924401), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924401), _924403), _924405) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924401), _924403), _924407), -(_924405 = _924407)], (8759 ^ _779448) ^ [_924568, _924570, _924572, _924574] : [class_Groups_Ocancel__semigroup__add(_924568), 8762 ^ _779448 : [(8763 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924568), _924570), _924572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924568), _924574), _924572), -(_924570 = _924574)], (8769 ^ _779448) ^ [] : [_924570 = _924574, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924568), _924570), _924572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924568), _924574), _924572))]]], (8775 ^ _779448) ^ [_924833, _924835, _924837, _924839] : [class_Groups_Ocancel__semigroup__add(_924833), 8778 ^ _779448 : [(8779 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924833), _924835), _924837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924833), _924835), _924839), -(_924837 = _924839)], (8785 ^ _779448) ^ [] : [_924837 = _924839, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924833), _924835), _924837) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924833), _924835), _924839))]]], (8791 ^ _779448) ^ [_925098, _925100, _925102, _925104] : [class_Groups_Oab__semigroup__add(_925098), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925098), _925100), _925102)), _925104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925098), _925100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925098), _925102), _925104)))], (8797 ^ _779448) ^ [_925241, _925243, _925245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _925241), _925243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _925241), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _925243), _925245))))], (8803 ^ _779448) ^ [_925352, _925354, _925356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _925352), _925354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _925352), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _925356), _925354))))], (8809 ^ _779448) ^ [_925463, _925465, _925467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _925463), _925465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _925463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _925467), _925465))))], (8815 ^ _779448) ^ [_925574, _925576, _925578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _925574), _925576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _925574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _925576), _925578))))], (8821 ^ _779448) ^ [_925685, _925687, _925689, _925691, _925693] : [c_Finite__Set_Ofun__left__comm__idem(_925685, _925687, _925689), -(c_Finite__Set_Ofun__left__comm__idem(_925691, _925687, hAPP(hAPP(c_COMBB(_925685, tc_fun(_925687, _925687), _925691), _925689), _925693)))], (8827 ^ _779448) ^ [_925798, _925800, _925802, _925804] : [-(c_Nitpick_Ofold__graph_H(_925798, _925800, _925802, _925804, c_Orderings_Obot__class_Obot(tc_fun(_925798, tc_HOL_Obool)), _925804))], (8829 ^ _779448) ^ [_925836, _925838, _925840, _925842] : [-(c_Nitpick_Ofold__graph_H(_925836, _925838, _925840, _925842, c_Orderings_Obot__class_Obot(tc_fun(_925836, tc_HOL_Obool)), _925842))], (8831 ^ _779448) ^ [_925874, _925876, _925878, _925880] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925874), _925876), _925878)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925874), _925876), _925880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925874), _925878), _925880)))], (8841 ^ _779448) ^ [_926069, _926071, _926073, _926075] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_926069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926069), _926071), _926073)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926069), _926075), _926073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926069), _926071), _926075)))], (8851 ^ _779448) ^ [_926264, _926266, _926268, _926270, _926272] : [class_Groups_Oordered__ab__semigroup__add(_926264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926264), _926266), _926268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926264), _926270), _926272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926264), _926266), _926270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926264), _926268), _926272))))], (8865 ^ _779448) ^ [_926535, _926537, _926539, _926541] : [class_Groups_Oordered__ab__semigroup__add(_926535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926535), _926537), _926539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926535), _926541), _926537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926535), _926541), _926539))))], (8875 ^ _779448) ^ [_926730, _926732, _926734, _926736] : [class_Groups_Oordered__ab__semigroup__add(_926730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926730), _926732), _926734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926730), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926730), _926732), _926736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926730), _926734), _926736))))], (8885 ^ _779448) ^ [_926925, _926927, _926929, _926931] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_926925), 8888 ^ _779448 : [(8889 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926925), _926927), _926929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926925), _926927), _926931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926925), _926929), _926931)))], (8895 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926925), _926929), _926931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926925), _926927), _926929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926925), _926927), _926931))))]]], (8901 ^ _779448) ^ [_927232, _927234, _927236, _927238] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927232), 8904 ^ _779448 : [(8905 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927232), _927234), _927236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927232), _927238), _927236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927232), _927234), _927238)))], (8911 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927232), _927234), _927238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927232), _927234), _927236)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927232), _927238), _927236))))]]], (8917 ^ _779448) ^ [_927539, _927541, _927543, _927545] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927539), _927541), _927543)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927539), _927541), _927545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927539), _927543), _927545)))], (8927 ^ _779448) ^ [_927734, _927736, _927738, _927740] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927734), _927736), _927738)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927734), _927740), _927738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927734), _927736), _927740)))], (8937 ^ _779448) ^ [_927929, _927931, _927933, _927935, _927937] : [class_Groups_Oordered__cancel__ab__semigroup__add(_927929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927929), _927931), _927933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927929), _927935), _927937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927929), _927931), _927935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927929), _927933), _927937))))], (8951 ^ _779448) ^ [_928200, _928202, _928204, _928206] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928200), _928202), _928204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928200), _928206), _928202)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928200), _928206), _928204))))], (8961 ^ _779448) ^ [_928395, _928397, _928399, _928401] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928395), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928395), _928397), _928399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928395), _928397), _928401)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928395), _928399), _928401))))], (8971 ^ _779448) ^ [_928590, _928592, _928594, _928596] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_928590), 8974 ^ _779448 : [(8975 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928590), _928592), _928594)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928590), _928592), _928596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928590), _928594), _928596)))], (8981 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928590), _928594), _928596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928590), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928590), _928592), _928594)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928590), _928592), _928596))))]]], (8987 ^ _779448) ^ [_928897, _928899, _928901, _928903] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_928897), 8990 ^ _779448 : [(8991 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928897), _928899), _928901)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928897), _928903), _928901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928897), _928899), _928903)))], (8997 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928897), _928899), _928903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928897), _928899), _928901)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928897), _928903), _928901))))]]], (9003 ^ _779448) ^ [_929204, _929206, _929208, _929210] : [class_Orderings_Oord(_929204), 9006 ^ _779448 : [(9007 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929206, _929204)), _929208), _929210)), 9010 ^ _779448 : [(9011 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929206, _929204)), _929208), _929210)))], (9013 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929206, _929204)), _929210), _929208))]]], (9015 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929206, _929204)), _929208), _929210))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929206, _929204)), _929208), _929210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929206, _929204)), _929210), _929208)))]]], (9025 ^ _779448) ^ [_929596, _929598, _929600] : [class_Groups_Ogroup__add(_929596), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929596), _929598), _929600)), _929600) = _929598)], (9031 ^ _779448) ^ [_929705, _929707, _929709] : [class_Groups_Ogroup__add(_929705), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929705), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929705), _929707), _929709)), _929709) = _929707)], (9037 ^ _779448) ^ [_929814, _929816, _929818, _929820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929814, tc_HOL_Obool)), _929816), _929818)), hBOOL(hAPP(hAPP(c_member(_929814), _929820), _929816)), -(hBOOL(hAPP(hAPP(c_member(_929814), _929820), _929818)))], (9047 ^ _779448) ^ [_930011, _930013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_930011, tc_HOL_Obool)), _930013), c_Orderings_Obot__class_Obot(tc_fun(_930011, tc_HOL_Obool))))], (9049 ^ _779448) ^ [_930051, _930053] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930051)), _930053) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930051), hAPP(c_Nat_OSuc, _930053)))], (9051 ^ _779448) ^ [_930094, _930096] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _930094)), _930096) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930094), _930096)))], (9053 ^ _779448) ^ [_930137, _930139] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930137), hAPP(c_Nat_OSuc, _930139)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930137), _930139)))], (9055 ^ _779448) ^ [_930180, _930182, _930184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930180), _930182)), _930184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930180), _930184)))], (9061 ^ _779448) ^ [_930291, _930293, _930295, _930297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930291), _930293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930295), _930293) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930291), _930297), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930295), _930297)))], (9071 ^ _779448) ^ [_930472, _930474, _930476, _930478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930472), _930474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930476), _930478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930472), _930476)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930474), _930478))))], (9081 ^ _779448) ^ [_930663, _930665, _930667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930663), _930665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930663), _930667)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930665), _930667))))], (9087 ^ _779448) ^ [_930786, _930788, _930790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930786), _930788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930790), _930788))))], (9093 ^ _779448) ^ [_930897, _930899, _930901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930897), _930899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _930897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _930899), _930901))))], (9099 ^ _779448) ^ [_931026, _931028, _931030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931026), _931028)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931026), _931030))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931028), _931030)))], (9105 ^ _779448) ^ [_931145, _931147, _931149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931147), _931149)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931145), _931147)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931145), _931149))))], (9111 ^ _779448) ^ [_931282, _931284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931282), _931284)), _931284))], (9113 ^ _779448) ^ [_931330, _931332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _931330), _931332)), _931330))], (9115 ^ _779448) ^ [_931366, _931368, _931370, _931372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931366, tc_HOL_Obool)), _931368), _931370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931366, tc_HOL_Obool)), _931370), _931372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931366, tc_HOL_Obool)), _931368), _931372)))], (9125 ^ _779448) ^ [_931563, _931565, _931567, _931569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931563, tc_HOL_Obool)), _931565), _931567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931563, tc_HOL_Obool)), _931567), _931569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931563, tc_HOL_Obool)), _931565), _931569)))], (9135 ^ _779448) ^ [_931760, _931762, _931764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931760, tc_HOL_Obool)), _931762), _931764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931760, tc_HOL_Obool)), _931762), _931764)))], (9151 ^ _779448) ^ [_932025, _932027, _932029] : [9152 ^ _779448 : [(9153 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932025, tc_HOL_Obool)), _932027), _932029))], (9155 ^ _779448) ^ [] : [_932027 = _932029]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932025, tc_HOL_Obool)), _932027), _932029)))], (9141 ^ _779448) ^ [_931897, _931899, _931901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_931897, tc_HOL_Obool)), _931899), _931901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_931897, tc_HOL_Obool)), _931899), _931901))), -(_931899 = _931901)], (9159 ^ _779448) ^ [_932202, _932204, _932206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932202, tc_HOL_Obool)), _932204), _932206)), 9162 ^ _779448 : [(9163 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932202, tc_HOL_Obool)), _932204), _932206)))], (9165 ^ _779448) ^ [] : [_932204 = _932206]]], (9167 ^ _779448) ^ [_932351, _932353, _932355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932351, tc_HOL_Obool)), _932353), _932355))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932351, tc_HOL_Obool)), _932353), _932355)), -(_932353 = _932355)], (9177 ^ _779448) ^ [_932529, _932531, _932533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932529), _932531)), _932533)), 9180 ^ _779448 : [(9181 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932529), _932533)))], (9183 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932531), _932533)))]]], (9185 ^ _779448) ^ [_932680, _932682, _932684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932680), _932682)), _932684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932680), _932684)))], (9191 ^ _779448) ^ [_932791, _932793, _932795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932791), _932793)), _932795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932793), _932795)))], (9197 ^ _779448) ^ [_932902, _932904, _932906, _932908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932902), _932904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932906), _932908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932902), _932906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932904), _932908))))], (9207 ^ _779448) ^ [_933093, _933095, _933097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933093), _933095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933093), _933097)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933095), _933097))))], (9213 ^ _779448) ^ [_933216, _933218, _933220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933216), _933218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933216), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933220), _933218))))], (9219 ^ _779448) ^ [_933327, _933329, _933331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933327), _933329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933329), _933331))))], (9225 ^ _779448) ^ [_933456, _933458, _933460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933456), _933458)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933456), _933460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933458), _933460)))], (9231 ^ _779448) ^ [_933575, _933577, _933579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933577), _933579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933575), _933577)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933575), _933579))))], (9237 ^ _779448) ^ [_933715, _933717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933715), _933717)), -(_933717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933715), 9240 ^ [_933715, _933717]))], (9244 ^ _779448) ^ [_933822, _933824] : [9245 ^ _779448 : [(9246 ^ _779448) ^ [_933872] : [_933824 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933822), _933872)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933822), _933824)))], (9250 ^ _779448) ^ [_933936, _933938] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933936), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933936), _933938))))], (9252 ^ _779448) ^ [_933972, _933974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _933972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _933974), _933972))))], (9254 ^ _779448) ^ [_934008, _934010, _934012] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934008), _934010)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934012), _934010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934008), _934012))], (9256 ^ _779448) ^ [_934059, _934061, _934063] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934059), _934061)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934059), _934063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934061), _934063))], (9258 ^ _779448) ^ [_934110, _934112, _934114] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934110), _934112)), _934114) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934112), _934114)))], (9260 ^ _779448) ^ [_934161, _934163] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934161), _934163)), _934161) = _934163)], (9262 ^ _779448) ^ [_934198, _934200] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _934198), _934200)), _934200) = _934198)], (9264 ^ _779448) ^ [_934235, _934237, _934239, _934241, _934243] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_934235, _934237, _934239, _934241, c_Orderings_Obot__class_Obot(tc_fun(_934235, tc_HOL_Obool))), _934243)), -(_934243 = _934241)], (9270 ^ _779448) ^ [_934344, _934346, _934348, _934350] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_934344, _934346, _934348, _934350, c_Orderings_Obot__class_Obot(tc_fun(_934344, tc_HOL_Obool))), _934350)))], (9272 ^ _779448) ^ [_934386, _934388, _934390, _934392] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_934386, _934388, _934390, _934392, c_Orderings_Obot__class_Obot(tc_fun(_934386, tc_HOL_Obool))), _934392)))], (9274 ^ _779448) ^ [_934428, _934430, _934432, _934434, _934436, _934438] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_934428, _934430, _934432, _934434, _934436), _934438)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_934428), _934436)))], (9280 ^ _779448) ^ [_934537] : [-(c_Finite__Set_Ofun__left__comm__idem(_934537, tc_fun(_934537, tc_HOL_Obool), c_Set_Oinsert(_934537)))], (9282 ^ _779448) ^ [_934566, _934568, _934570, _934572, _934574] : [class_Groups_Oordered__cancel__ab__semigroup__add(_934566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934566), _934568), _934570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934566), _934572), _934574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934566), _934568), _934572)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934566), _934570), _934574))))], (9296 ^ _779448) ^ [_934837, _934839, _934841, _934843, _934845] : [class_Groups_Oordered__cancel__ab__semigroup__add(_934837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934837), _934839), _934841)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934837), _934843), _934845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934837), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934837), _934839), _934843)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_934837), _934841), _934845))))], (9310 ^ _779448) ^ [_935108, _935110] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935108), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935108), _935110)))))], (9312 ^ _779448) ^ [_935147, _935149] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935147), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935149), _935147)))))], (9314 ^ _779448) ^ [_935201, _935203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935201), _935203)), -(_935203 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935201), 9317 ^ [_935201, _935203])))], (9321 ^ _779448) ^ [_935314, _935316] : [9322 ^ _779448 : [(9323 ^ _779448) ^ [_935367] : [_935316 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935314), _935367))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935314), _935316)))], (9327 ^ _779448) ^ [_935452, _935454, _935456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935454), _935456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935452), _935456)), _935454)))], (9333 ^ _779448) ^ [_935571, _935573, _935575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935571), _935575)), _935573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935571), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935573), _935575))))], (9339 ^ _779448) ^ [_935692, _935694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935692), _935694))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935694), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935692), _935694)) = _935692)], (9345 ^ _779448) ^ [_935745, _935747, _935749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935745), _935747)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935747), _935749)), _935745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935747), _935745)), _935749))], (9351 ^ _779448) ^ [_935882, _935884, _935886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935882), _935884)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935884), _935882)), _935886) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935884), _935886)), _935882))], (9357 ^ _779448) ^ [_936019, _936021, _936023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936019), _936021)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936023), _936021)), _936019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936021), _936019)))], (9363 ^ _779448) ^ [_936156, _936158, _936160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936156), _936158)), 9366 ^ _779448 : [(9367 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936158), _936156) = _936160, -(_936158 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936160), _936156))], (9373 ^ _779448) ^ [] : [_936158 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936160), _936156), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936158), _936156) = _936160)]]], (9379 ^ _779448) ^ [_936415, _936417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936415), _936417)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936417), _936415)), _936415) = _936417)], (9385 ^ _779448) ^ [_936526, _936528, _936530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936526), _936528)), 9388 ^ _779448 : [(9389 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936528), _936526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936530), _936526)), _936528)))], (9395 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936530), _936526)), _936528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936528), _936526))))]]], (9401 ^ _779448) ^ [_936815, _936817, _936819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936815), _936817)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936817), _936815)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936819), _936817)), _936815))], (9407 ^ _779448) ^ [_936952, _936954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _936952), _936954)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936952), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936954), _936952)) = _936954)], (9413 ^ _779448) ^ [_937063, _937065, _937067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937063), _937065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937065), _937067)), _937063))))], (9419 ^ _779448) ^ [_937204, _937206, _937208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _937204), _937206)), _937208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937204), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937208), _937206))))], (9425 ^ _779448) ^ [_937323, _937325, _937327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937327), _937325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _937323), _937325)), _937327)))], (9431 ^ _779448) ^ [_937448, _937450, _937452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _937448), _937450)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _937452), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _937450), _937448)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937452), _937448)), _937450))], (9437 ^ _779448) ^ [_937585] : [-(hAPP(c_Nat_OSuc, _937585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _937585))], (9439 ^ _779448) ^ [_937614] : [-(hAPP(c_Nat_OSuc, _937614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937614), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9441 ^ _779448) ^ [_937645, _937647, _937649, _937651, _937653, _937655, _937657] : [-(hBOOL(hAPP(hAPP(c_member(_937645), _937647), _937649))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_937645, _937651, _937653, _937655, _937649), _937657)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_937645, _937651, _937653, _937655, hAPP(hAPP(c_Set_Oinsert(_937645), _937647), _937649)), hAPP(hAPP(_937653, _937647), _937657))))], (9451 ^ _779448) ^ [_937859, _937861, _937863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_937859), _937861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937859, tc_HOL_Obool)), _937863), _937861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_937859), _937863)), hAPP(c_Finite__Set_Ocard(_937859), _937861))))], (9461 ^ _779448) ^ [_938050, _938052, _938054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938050), _938052)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _938052), _938050))), _938054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _938052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938050), _938054)))], (9467 ^ _779448) ^ [_938199, _938201, _938203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _938199), _938201)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _938203), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _938201), _938199))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938203), _938199)), hAPP(c_Nat_OSuc, _938201)))], (9473 ^ _779448) ^ [_938348, _938350, _938352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_938348), _938350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938348, tc_HOL_Obool)), _938352), _938350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_938348), _938352)), hAPP(c_Finite__Set_Ocard(_938348), _938350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_938348, tc_HOL_Obool)), _938352), _938350)))], (9487 ^ _779448) ^ [_938613, _938615] : [class_Rings_Olinordered__semidom(_938613), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938613), _938615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938613), _938615), c_Groups_Oone__class_Oone(_938613)))))], (9493 ^ _779448) ^ [_938722, _938724, _938726, _938728, _938730] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_938722, _938722, _938724, _938726, _938728), _938730)), -(hBOOL(hAPP(hAPP(c_member(_938722), _938726), _938728))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_938722, _938724, hAPP(hAPP(c_Set_Oinsert(_938722), _938726), _938728)), _938730)))], (9503 ^ _779448) ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920] : [c_Nitpick_Ofold__graph_H(_938908, _938910, _938912, _938914, _938916, hAPP(hAPP(_938912, _938918), _938920)), 9508 ^ _779448 : [(9509 ^ _779448) ^ [] : [-(_938916 = c_Orderings_Obot__class_Obot(tc_fun(_938908, tc_HOL_Obool)))], (9511 ^ _779448) ^ [] : [-(hAPP(hAPP(_938912, _938918), _938920) = _938914)]], 9514 ^ _779448 : [(9515 ^ _779448) ^ [] : [-(hAPP(hAPP(_938912, _938918), _938920) = hAPP(hAPP(_938912, 9512 ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920]), 9513 ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920]))], (9517 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_938908), 9512 ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920]), _938916)))], (9519 ^ _779448) ^ [] : [-(c_Nitpick_Ofold__graph_H(_938908, _938910, _938912, _938914, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938908, tc_HOL_Obool)), _938916), hAPP(hAPP(c_Set_Oinsert(_938908), 9512 ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920]), c_Orderings_Obot__class_Obot(tc_fun(_938908, tc_HOL_Obool)))), 9513 ^ [_938908, _938910, _938912, _938914, _938916, _938918, _938920]))]]], (9521 ^ _779448) ^ [_939345, _939347, _939349, _939351, _939353, _939355, _939357] : [-(c_Nitpick_Ofold__graph_H(_939345, _939347, _939349, _939351, _939353, hAPP(hAPP(_939349, _939355), _939357))), 9522 ^ _779448 : [(9523 ^ _779448) ^ [] : [_939353 = c_Orderings_Obot__class_Obot(tc_fun(_939345, tc_HOL_Obool)), hAPP(hAPP(_939349, _939355), _939357) = _939351], (9529 ^ _779448) ^ [_939574, _939576] : [hAPP(hAPP(_939349, _939355), _939357) = hAPP(hAPP(_939349, _939576), _939574), hBOOL(hAPP(hAPP(c_member(_939345), _939576), _939353)), c_Nitpick_Ofold__graph_H(_939345, _939347, _939349, _939351, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939345, tc_HOL_Obool)), _939353), hAPP(hAPP(c_Set_Oinsert(_939345), _939576), c_Orderings_Obot__class_Obot(tc_fun(_939345, tc_HOL_Obool)))), _939574)]]], (9541 ^ _779448) ^ [_939866, _939868, _939870, _939872, _939874] : [class_Groups_Oab__semigroup__mult(_939866), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_939866, _939866, c_Groups_Otimes__class_Otimes(_939866), _939868, _939870), _939872)), hBOOL(hAPP(hAPP(c_member(_939866), _939874), _939870)), -(hBOOL(hAPP(hAPP(c_member(_939866), _939868), _939870))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_939866, _939866, c_Groups_Otimes__class_Otimes(_939866), _939874, hAPP(hAPP(c_Set_Oinsert(_939866), _939868), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939866, tc_HOL_Obool)), _939870), hAPP(hAPP(c_Set_Oinsert(_939866), _939874), c_Orderings_Obot__class_Obot(tc_fun(_939866, tc_HOL_Obool)))))), _939872)))], (9559 ^ _779448) ^ [_940210, _940212, _940214, _940216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_940210), _940212)), hBOOL(hAPP(c_Finite__Set_Ofinite(_940214), _940216)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_940210, _940214)), c_Sum__Type_OPlus(_940210, _940214, _940212, _940216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_940210), _940212)), hAPP(c_Finite__Set_Ocard(_940214), _940216)))], (9569 ^ _779448) ^ [_940421, _940423] : [-(hAPP(c_Set_Oimage(_940421, _940421, c_COMBI(_940421)), _940423) = _940423)], (9571 ^ _779448) ^ [_940455, _940457, _940459, _940461, _940463] : [c_Fun_Oinj__on(_940455, _940457, _940459, _940461), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940457, tc_HOL_Obool)), hAPP(c_Set_Oimage(_940455, _940457, _940459), _940461)), _940463)), hBOOL(hAPP(c_Finite__Set_Ofinite(_940457), _940463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_940455), _940461)), hAPP(c_Finite__Set_Ocard(_940457), _940463))))], (9585 ^ _779448) ^ [_940739, _940741] : [_940739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940739), _940741) = _940741)], (9591 ^ _779448) ^ [_940822, _940824] : [-(_940822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940822), _940824) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _940822), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _940824)))], (9597 ^ _779448) ^ [_940881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _940881)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _940881), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _940881)], (9603 ^ _779448) ^ [_940978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _940978)), -(_940978 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _940978), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9609 ^ _779448) ^ [_941084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941084), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9611 ^ _779448) ^ [_941112] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _941112)))], (9613 ^ _779448) ^ [_941137, _941139, _941141] : [-(c_Fun_Oinj__on(_941137, _941139, _941141, c_Orderings_Obot__class_Obot(tc_fun(_941137, tc_HOL_Obool))))], (9615 ^ _779448) ^ [_941171] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _941171))))], (9617 ^ _779448) ^ [_941199, _941201, _941203, _941205] : [class_Rings_Olinordered__ring__strict(_941199), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941199), _941201), _941203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941199), _941205), c_Groups_Ozero__class_Ozero(_941199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941199), _941205), _941203)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941199), _941205), _941201))))], (9631 ^ _779448) ^ [_941468, _941470, _941472, _941474] : [class_Rings_Olinordered__ring__strict(_941468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941468), _941470), _941472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941468), _941474), c_Groups_Ozero__class_Ozero(_941468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941468), _941472), _941474)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941468), _941470), _941474))))], (9645 ^ _779448) ^ [_941737, _941739, _941741, _941743] : [class_Rings_Olinordered__comm__semiring__strict(_941737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941737), _941739), _941741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941737), c_Groups_Ozero__class_Ozero(_941737)), _941743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941737), _941743), _941739)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_941737), _941743), _941741))))], (9659 ^ _779448) ^ [_942006, _942008, _942010, _942012] : [class_Rings_Olinordered__semiring__strict(_942006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942006), _942008), _942010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942006), c_Groups_Ozero__class_Ozero(_942006)), _942012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942006), _942012), _942008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942006), _942012), _942010))))], (9673 ^ _779448) ^ [_942275, _942277, _942279, _942281] : [class_Rings_Olinordered__semiring__strict(_942275), 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c_Groups_Ozero__class_Ozero(_948212))))], (10015 ^ _779448) ^ [_948467, _948469, _948471] : [class_Rings_Oordered__cancel__semiring(_948467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948467), _948469), c_Groups_Ozero__class_Ozero(_948467))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948467), c_Groups_Ozero__class_Ozero(_948467)), _948471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948467), _948469), _948471)), c_Groups_Ozero__class_Ozero(_948467))))], (10029 ^ _779448) ^ [_948722, _948724, _948726] : [class_Rings_Oordered__ring(_948722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948722), _948724), c_Groups_Ozero__class_Ozero(_948722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948722), _948726), c_Groups_Ozero__class_Ozero(_948722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948722), c_Groups_Ozero__class_Ozero(_948722)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948722), _948724), _948726))))], (10043 ^ _779448) ^ [_948977, _948979, _948981, _948983] : [class_Rings_Oordered__semiring(_948977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948977), _948979), _948981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948977), c_Groups_Ozero__class_Ozero(_948977)), _948983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948977), _948979), _948983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948977), _948981), _948983))))], (10057 ^ _779448) ^ [_949246, _949248, _949250, _949252] : [class_Rings_Oordered__semiring(_949246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949246), _949248), _949250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949246), c_Groups_Ozero__class_Ozero(_949246)), _949252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949246), _949252), _949248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949246), _949252), _949250))))], (10071 ^ _779448) ^ [_949515, _949517, _949519, _949521] : [class_Rings_Oordered__comm__semiring(_949515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949515), _949517), _949519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949515), c_Groups_Ozero__class_Ozero(_949515)), _949521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949515), _949521), _949517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949515), _949521), _949519))))], (10085 ^ _779448) ^ [_949784, _949786, _949788, _949790] : [class_Rings_Oordered__ring(_949784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949784), _949786), _949788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949784), _949790), c_Groups_Ozero__class_Ozero(_949784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949784), _949788), _949790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949784), _949786), _949790))))], (10099 ^ _779448) ^ [_950053, _950055, _950057, _950059] : [class_Rings_Oordered__ring(_950053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950053), _950055), _950057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950053), _950059), c_Groups_Ozero__class_Ozero(_950053))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950053), _950059), _950057)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950053), _950059), _950055))))], (10113 ^ _779448) ^ [_950322, _950324, _950326, _950328, _950330] : [class_Rings_Oordered__semiring(_950322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950322), _950324), _950326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950322), _950328), _950330)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950322), c_Groups_Ozero__class_Ozero(_950322)), _950324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950322), c_Groups_Ozero__class_Ozero(_950322)), _950328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950322), _950324), _950328)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950322), _950326), _950330))))], (10135 ^ _779448) ^ [_950745, _950747, _950749, _950751, _950753] : [class_Rings_Oordered__semiring(_950745), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950745), _950747), _950749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950745), _950751), _950753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950745), c_Groups_Ozero__class_Ozero(_950745)), _950749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950745), c_Groups_Ozero__class_Ozero(_950745)), _950751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950745), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950745), _950747), _950751)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950745), _950749), _950753))))], (10157 ^ _779448) ^ [_951168, _951170, _951172] : [class_Rings_Oordered__ring(_951168), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951168), c_Groups_Ozero__class_Ozero(_951168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951168), _951170), _951172)))), 10162 ^ _779448 : [(10163 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951168), c_Groups_Ozero__class_Ozero(_951168)), _951170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951168), c_Groups_Ozero__class_Ozero(_951168)), _951172))], (10169 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951168), _951170), c_Groups_Ozero__class_Ozero(_951168))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951168), _951172), c_Groups_Ozero__class_Ozero(_951168)))]]], (10177 ^ _779448) ^ [_951544, _951546, _951548] : [class_Rings_Oordered__cancel__semiring(_951544), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951544), _951546), _951548)), c_Groups_Ozero__class_Ozero(_951544)))), 10182 ^ _779448 : [(10183 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951544), c_Groups_Ozero__class_Ozero(_951544)), _951546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951544), _951548), c_Groups_Ozero__class_Ozero(_951544)))], (10189 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951544), _951546), c_Groups_Ozero__class_Ozero(_951544))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951544), c_Groups_Ozero__class_Ozero(_951544)), _951548))]]], (10197 ^ _779448) ^ [_951920, _951922] : [class_Groups_Ozero(_951920), 10200 ^ _779448 : [(10201 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_951920) = _951922, -(_951922 = c_Groups_Ozero__class_Ozero(_951920))], (10207 ^ _779448) ^ [] : [_951922 = c_Groups_Ozero__class_Ozero(_951920), -(c_Groups_Ozero__class_Ozero(_951920) = _951922)]]], (10213 ^ _779448) ^ [_952137, _952139, _952141, _952143] : [class_Groups_Oab__semigroup__mult(_952137), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952137), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952137), _952139), _952141)), _952143) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952137), _952139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952137), _952141), _952143)))], (10219 ^ _779448) ^ [_952280, _952282, _952284] : [class_Rings_Ono__zero__divisors(_952280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952280), _952282), _952284) = c_Groups_Ozero__class_Ozero(_952280), -(_952282 = c_Groups_Ozero__class_Ozero(_952280)), -(_952284 = c_Groups_Ozero__class_Ozero(_952280))], (10233 ^ _779448) ^ [_952452, _952454, _952456] : [class_Rings_Ono__zero__divisors(_952452), -(_952454 = c_Groups_Ozero__class_Ozero(_952452)), -(_952456 = c_Groups_Ozero__class_Ozero(_952452)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952452), _952454), _952456) = c_Groups_Ozero__class_Ozero(_952452)], (10247 ^ _779448) ^ [_952672, _952674, _952676] : [class_Rings_Oring__no__zero__divisors(_952672), 10250 ^ _779448 : [(10261 ^ _779448) ^ [] : [10262 ^ _779448 : [(10263 ^ _779448) ^ [] : [_952674 = c_Groups_Ozero__class_Ozero(_952672)], (10265 ^ _779448) ^ [] : [_952676 = c_Groups_Ozero__class_Ozero(_952672)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952672), _952674), _952676) = c_Groups_Ozero__class_Ozero(_952672))], (10251 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952672), _952674), _952676) = c_Groups_Ozero__class_Ozero(_952672), -(_952674 = c_Groups_Ozero__class_Ozero(_952672)), -(_952676 = c_Groups_Ozero__class_Ozero(_952672))]]], (10287 ^ _779448) ^ [_953376, _953378, _953380, _953382] : [10289 ^ _779448 : [(10290 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953376), 10288 ^ [_953376, _953378, _953380, _953382]), _953382)))], (10293 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953376), 10291 ^ [_953376, _953378, _953380, _953382]), _953382)))], (10295 ^ _779448) ^ [] : [-(hAPP(_953380, 10288 ^ [_953376, _953378, _953380, _953382]) = hAPP(_953380, 10291 ^ [_953376, _953378, _953380, _953382]))], (10297 ^ _779448) ^ [] : [10288 ^ [_953376, _953378, _953380, _953382] = 10291 ^ [_953376, _953378, _953380, _953382]]], -(c_Fun_Oinj__on(_953376, _953378, _953380, _953382))], (10269 ^ _779448) ^ [_952991, _952993, _952995, _952997] : [c_Fun_Oinj__on(_952991, _952993, _952995, _952997), 10272 ^ _779448 : [(10273 ^ _779448) ^ [_953099] : [hBOOL(hAPP(hAPP(c_member(_952991), _953099), _952997)), 10276 ^ _779448 : [(10277 ^ _779448) ^ [_953201] : [hBOOL(hAPP(hAPP(c_member(_952991), _953201), _952997)), hAPP(_952995, _953099) = hAPP(_952995, _953201), -(_953099 = _953201)]]]]], (10301 ^ _779448) ^ [_953768, _953770] : [class_Rings_Omult__zero(_953768), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953768), _953770), c_Groups_Ozero__class_Ozero(_953768)) = c_Groups_Ozero__class_Ozero(_953768))], (10307 ^ _779448) ^ [_953867, _953869] : [class_Rings_Omult__zero(_953867), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953867), c_Groups_Ozero__class_Ozero(_953867)), _953869) = c_Groups_Ozero__class_Ozero(_953867))], (10313 ^ _779448) ^ [_953966, _953968] : [-(c_Fun_Oinj__on(_953966, _953966, c_COMBI(_953966), _953968))], (10315 ^ _779448) ^ [_953995] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _953995) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10317 ^ _779448) ^ [_954021] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954021), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10329 ^ _779448) ^ [_954163, _954165] : [10330 ^ _779448 : [(10331 ^ _779448) ^ [] : [_954163 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10333 ^ _779448) ^ [] : [_954165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954163), _954165) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10319 ^ _779448) ^ [_954065, _954067] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954065), _954067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_954065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_954067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10347 ^ _779448) ^ [_954422, _954424, _954426] : [10348 ^ _779448 : [(10349 ^ _779448) ^ [] : [_954424 = _954426], (10351 ^ _779448) ^ [] : [_954422 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954422), _954424) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954422), _954426))], (10337 ^ _779448) ^ [_954310, _954312, _954314] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954310), _954312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954310), _954314), -(_954312 = _954314), -(_954310 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10365 ^ _779448) ^ [_954695, _954697, _954699] : [10366 ^ _779448 : [(10367 ^ _779448) ^ [] : [_954695 = _954699], (10369 ^ _779448) ^ [] : [_954697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954695), _954697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954699), _954697))], (10355 ^ _779448) ^ [_954583, _954585, _954587] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954583), _954585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _954587), _954585), -(_954583 = _954587), -(_954585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10373 ^ _779448) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10375 ^ _779448) ^ [_954856, _954858] : [class_Lattices_Oab__semigroup__idem__mult(_954856), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954856), _954858), _954858) = _954858)], (10381 ^ _779448) ^ [_954947, _954949] : [class_Lattices_Oab__semigroup__idem__mult(_954947), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954947), _954949), _954949) = _954949)], (10387 ^ _779448) ^ [_955038, _955040, _955042] : [class_Lattices_Oab__semigroup__idem__mult(_955038), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955038), _955040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955038), _955040), _955042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_955038), _955040), _955042))], (10393 ^ _779448) ^ [_955163, _955165, _955167, _955169, _955171, _955173] : [c_Fun_Oinj__on(_955163, _955165, _955167, _955169), -(_955171 = _955173), hBOOL(hAPP(hAPP(c_member(_955163), _955171), _955169)), hBOOL(hAPP(hAPP(c_member(_955163), _955173), _955169)), hAPP(_955167, _955171) = hAPP(_955167, _955173)], (10411 ^ _779448) ^ [_955476, _955478, _955480, _955482, _955484, _955486] : [c_Fun_Oinj__on(_955476, _955478, _955480, _955482), hBOOL(hAPP(hAPP(c_member(_955476), _955484), _955482)), hBOOL(hAPP(hAPP(c_member(_955476), _955486), _955482)), 10422 ^ _779448 : [(10423 ^ _779448) ^ [] : [hAPP(_955480, _955484) = hAPP(_955480, _955486), -(_955484 = _955486)], (10429 ^ _779448) ^ [] : [_955484 = _955486, -(hAPP(_955480, _955484) = hAPP(_955480, _955486))]]], (10435 ^ _779448) ^ [_955877, _955879, _955881, _955883, _955885, _955887] : [c_Fun_Oinj__on(_955877, _955879, _955881, _955883), hAPP(_955881, _955885) = hAPP(_955881, _955887), hBOOL(hAPP(hAPP(c_member(_955877), _955885), _955883)), hBOOL(hAPP(hAPP(c_member(_955877), _955887), _955883)), -(_955885 = _955887)], (10453 ^ _779448) ^ [_956186, _956188, _956190] : [class_Rings_Olinordered__ring__strict(_956186), 10456 ^ _779448 : [(10457 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956186), _956188), _956188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956186), _956190), _956190)) = c_Groups_Ozero__class_Ozero(_956186), 10460 ^ _779448 : [(10461 ^ _779448) ^ [] : [-(_956188 = c_Groups_Ozero__class_Ozero(_956186))], (10463 ^ _779448) ^ [] : [-(_956190 = c_Groups_Ozero__class_Ozero(_956186))]]], (10465 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956186), _956188), _956188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956186), _956190), _956190)) = c_Groups_Ozero__class_Ozero(_956186)), _956188 = c_Groups_Ozero__class_Ozero(_956186), _956190 = c_Groups_Ozero__class_Ozero(_956186)]]], (10475 ^ _779448) ^ [_956576, _956578] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956576), _956578) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10478 ^ _779448 : [(10479 ^ _779448) ^ [] : [-(_956576 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10481 ^ _779448) ^ [] : [-(_956578 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10483 ^ _779448) ^ [_956687, _956689] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _956687), _956689) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _956687 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956689 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10493 ^ _779448) ^ [_956845, _956847] : [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), _956845), _956847))), 10496 ^ _779448 : [(10497 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956845)))], (10499 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956847)))]]], (10501 ^ _779448) ^ [_956968, _956970] : [-(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), _956968), _956970)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _956970))], (10511 ^ _779448) ^ [_957141, _957143, _957145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957141), _957143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957141), _957145))), 10514 ^ _779448 : [(10515 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957141)))], (10517 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957143), _957145)))]]], (10519 ^ _779448) ^ [_957290, _957292, _957294] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957290), _957292)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957290), _957294)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957292), _957294))], (10529 ^ _779448) ^ [_957491, _957493, _957495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957491), _957493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957495), _957493))), 10532 ^ _779448 : [(10533 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957493)))], (10535 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957491), _957495)))]]], (10537 ^ _779448) ^ [_957640, _957642, _957644] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957640), _957642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957644), _957642)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957642)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957640), _957644))], (10547 ^ _779448) ^ [_957823, _957825, _957827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957823), _957825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _957827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957823), _957827)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _957825), _957827))))], (10557 ^ _779448) ^ [_958004, _958006, _958008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _958004), _958006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _958008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _958008), _958004)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _958008), _958006))))], (10567 ^ _779448) ^ [_958185, _958187, _958189, _958191, _958193] : [c_Fun_Oinj__on(_958185, _958187, _958189, _958191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958185, tc_HOL_Obool)), _958193), _958191)), -(c_Fun_Oinj__on(_958185, _958187, _958189, _958193))], (10577 ^ _779448) ^ [_958354, _958356, _958358, _958360, _958362] : [c_Fun_Oinj__on(_958354, _958356, _958358, _958360), -(c_Fun_Oinj__on(_958354, _958356, _958358, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958354, tc_HOL_Obool)), _958360), _958362)))], (10583 ^ _779448) ^ [_958467, _958469] : [_958467 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _958467), _958469), -(_958469 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_958467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10593 ^ _779448) ^ [_958569, _958571, _958573, _958575, _958577] : [class_Rings_Osemiring(_958569), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958569), _958571), _958573)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958569), _958575), _958573)), _958577)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958569), _958571), _958575)), _958573)), _958577))], (10599 ^ _779448) ^ [_958762, _958764, _958766, _958768] : [class_Rings_Ocomm__semiring(_958762), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958762), _958764), _958766)), _958768) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958762), _958764), _958768)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958762), _958766), _958768)))], (10605 ^ _779448) ^ [_958921] : [class_Rings_Ozero__neq__one(_958921), c_Groups_Ozero__class_Ozero(_958921) = c_Groups_Oone__class_Oone(_958921)], (10611 ^ _779448) ^ [_959003] : [class_Rings_Ozero__neq__one(_959003), c_Groups_Oone__class_Oone(_959003) = c_Groups_Ozero__class_Ozero(_959003)], (10617 ^ _779448) ^ [_959085, _959087, _959089, _959091] : [class_Rings_Olinordered__ring__strict(_959085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959085), c_Groups_Ozero__class_Ozero(_959085)), _959087)), 10624 ^ _779448 : [(10625 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959085), _959087), _959089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959085), _959087), _959091))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959085), _959089), _959091)))], (10631 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959085), _959089), _959091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959085), _959087), _959089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959085), _959087), _959091))))]]], (10637 ^ _779448) ^ [_959466, _959468, _959470, _959472] : [class_Rings_Olinordered__ring__strict(_959466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959466), _959468), c_Groups_Ozero__class_Ozero(_959466))), 10644 ^ _779448 : [(10645 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959466), _959468), _959470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959466), _959468), _959472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959466), _959472), _959470)))], (10651 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959466), _959472), _959470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959466), _959468), _959470)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959466), _959468), _959472))))]]], (10657 ^ _779448) ^ [_959847, _959849, _959851, _959853, _959855] : [class_Rings_Olinordered__semiring__strict(_959847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959847), _959849), _959851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959847), _959853), _959855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959847), c_Groups_Ozero__class_Ozero(_959847)), _959851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959847), c_Groups_Ozero__class_Ozero(_959847)), _959853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959847), _959849), _959853)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959847), _959851), _959855))))], (10679 ^ _779448) ^ [_960270, _960272, _960274, _960276, _960278] : [class_Rings_Olinordered__semiring__strict(_960270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960270), _960272), _960274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960270), _960276), _960278)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960270), c_Groups_Ozero__class_Ozero(_960270)), _960272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960270), c_Groups_Ozero__class_Ozero(_960270)), _960276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960270), _960272), _960276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960270), _960274), _960278))))], (10701 ^ _779448) ^ [_960693, _960695, _960697, _960699, _960701] : [class_Rings_Olinordered__semiring__strict(_960693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960693), _960695), _960697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960693), _960699), _960701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960693), c_Groups_Ozero__class_Ozero(_960693)), _960695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960693), c_Groups_Ozero__class_Ozero(_960693)), _960699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_960693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960693), _960695), _960699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960693), _960697), _960701))))], (10723 ^ _779448) ^ [_961116, _961118, _961120, _961122, _961124] : [class_Rings_Olinordered__semiring__strict(_961116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961116), _961118), _961120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961116), _961122), _961124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961116), c_Groups_Ozero__class_Ozero(_961116)), _961118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961116), c_Groups_Ozero__class_Ozero(_961116)), _961122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961116), _961118), _961122)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961116), _961120), _961124))))], (10745 ^ _779448) ^ [_961539, _961541, _961543, _961545] : [class_Rings_Olinordered__semiring(_961539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961539), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961539), _961541), _961543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961539), _961545), _961543))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961539), c_Groups_Ozero__class_Ozero(_961539)), _961543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961539), _961541), _961545)))], (10759 ^ _779448) ^ [_961808, _961810, _961812, _961814] : [class_Rings_Olinordered__semiring__strict(_961808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961808), _961810), _961812)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961808), _961814), _961812))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961808), c_Groups_Ozero__class_Ozero(_961808)), _961812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_961808), _961810), _961814)))], (10773 ^ _779448) ^ [_962077, _962079, _962081, _962083] : [class_Rings_Olinordered__semiring(_962077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962077), _962079), _962081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962077), _962079), _962083))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962077), c_Groups_Ozero__class_Ozero(_962077)), _962079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962077), _962081), _962083)))], (10787 ^ _779448) ^ [_962346, _962348, _962350, _962352] : [class_Rings_Olinordered__semiring__strict(_962346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962346), _962348), _962350)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962346), _962348), _962352))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962346), c_Groups_Ozero__class_Ozero(_962346)), _962348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962346), _962350), _962352)))], (10801 ^ _779448) ^ [_962615, _962617, _962619, _962621] : [class_Rings_Olinordered__semiring__strict(_962615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962615), _962617), _962619)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962615), _962621), _962619))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962615), c_Groups_Ozero__class_Ozero(_962615)), _962619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962615), _962617), _962621)))], (10815 ^ _779448) ^ [_962884, _962886, _962888, _962890] : [class_Rings_Olinordered__semiring__strict(_962884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962884), _962886), _962888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962884), _962886), _962890))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962884), c_Groups_Ozero__class_Ozero(_962884)), _962886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962884), _962888), _962890)))], (10829 ^ _779448) ^ [_963153, _963155, _963157] : [class_Rings_Olinordered__idom(_963153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963153), c_Groups_Ozero__class_Ozero(_963153)), _963155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963153), c_Groups_Ozero__class_Ozero(_963153)), _963157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963153), _963157), c_Groups_Oone__class_Oone(_963153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963153), _963155), _963157)), _963155)))], (10847 ^ _779448) ^ [_963476, _963478, _963480] : [class_Rings_Olinordered__idom(_963476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963476), c_Groups_Ozero__class_Ozero(_963476)), _963478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963476), c_Groups_Ozero__class_Ozero(_963476)), _963480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963476), _963480), c_Groups_Oone__class_Oone(_963476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963476), _963480), _963478)), _963478)))], (10865 ^ _779448) ^ [_963799, _963801, _963803] : [class_Rings_Olinordered__ring(_963799), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963799), c_Groups_Ozero__class_Ozero(_963799)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963799), _963801), _963801)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963799), _963803), _963803)))))], (10871 ^ _779448) ^ [_963942, _963944, _963946] : [class_Rings_Olinordered__ring__strict(_963942), 10874 ^ _779448 : [(10875 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963942), _963944), _963944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963942), _963946), _963946))), c_Groups_Ozero__class_Ozero(_963942))), 10878 ^ _779448 : [(10879 ^ _779448) ^ [] : [-(_963944 = c_Groups_Ozero__class_Ozero(_963942))], (10881 ^ _779448) ^ [] : [-(_963946 = c_Groups_Ozero__class_Ozero(_963942))]]], (10883 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963942), _963944), _963944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_963942), _963946), _963946))), c_Groups_Ozero__class_Ozero(_963942)))), _963944 = c_Groups_Ozero__class_Ozero(_963942), _963946 = c_Groups_Ozero__class_Ozero(_963942)]]], (10893 ^ _779448) ^ [_964338, _964340, _964342] : [class_Rings_Olinordered__ring__strict(_964338), 10896 ^ _779448 : [(10907 ^ _779448) ^ [] : [10908 ^ _779448 : [(10909 ^ _779448) ^ [] : [-(_964340 = c_Groups_Ozero__class_Ozero(_964338))], (10911 ^ _779448) ^ [] : [-(_964342 = c_Groups_Ozero__class_Ozero(_964338))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964338), c_Groups_Ozero__class_Ozero(_964338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964338), _964340), _964340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964338), _964342), _964342)))))], (10897 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964338), c_Groups_Ozero__class_Ozero(_964338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964338), _964340), _964340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964338), _964342), _964342)))), _964340 = c_Groups_Ozero__class_Ozero(_964338), _964342 = c_Groups_Ozero__class_Ozero(_964338)]]], (10915 ^ _779448) ^ [_964713, _964715, _964717] : [class_Rings_Olinordered__ring(_964713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964713), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964713), _964715), _964715)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_964713), _964717), _964717))), c_Groups_Ozero__class_Ozero(_964713)))], (10921 ^ _779448) ^ [_964857] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _964857))], (10923 ^ _779448) ^ [_964882, _964884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _964882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _964884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _964884), _964882))))], (10933 ^ _779448) ^ [_965041, _965043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965041), _965043))))], (10943 ^ _779448) ^ [_965200, _965202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965202), _965200))))], (10953 ^ _779448) ^ [_965368, _965370] : [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), _965368), _965370))), 10956 ^ _779448 : [(10957 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965368)))], (10959 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965370)))]]], (10961 ^ _779448) ^ [_965491, _965493] : [-(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), _965491), _965493)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _965493))], (10981 ^ _779448) ^ [_965841, _965843, _965845] : [10982 ^ _779448 : [(10983 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965841)))], (10985 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965843), _965845))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965841), _965843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965841), _965845))))], (10971 ^ _779448) ^ [_965664, _965666, _965668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965664), _965666)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _965664), _965668))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965666), _965668)))], (10999 ^ _779448) ^ [_966198, _966200, _966202] : [11000 ^ _779448 : [(11001 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966200)))], (11003 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966198), _966202))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966198), _966200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966202), _966200))))], (10989 ^ _779448) ^ [_966021, _966023, _966025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966021), _966023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _966025), _966023))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _966023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _966021), _966025)))], (11007 ^ _779448) ^ [_966360, _966362, _966364, _966366, _966368, _966370] : [class_Rings_Olinordered__semiring__1(_966360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966360), _966362), _966364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966360), _966366), _966364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966360), c_Groups_Ozero__class_Ozero(_966360)), _966368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966360), c_Groups_Ozero__class_Ozero(_966360)), _966370)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966360), _966368), _966370) = c_Groups_Oone__class_Oone(_966360), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966360), _966368), _966362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966360), _966370), _966366))), _966364)))], (11033 ^ _779448) ^ [_966889, _966891] : [class_Groups_Omonoid__mult(_966889), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966889), c_Groups_Oone__class_Oone(_966889)), _966891) = _966891)], (11039 ^ _779448) ^ [_966984, _966986] : [class_Groups_Ocomm__monoid__mult(_966984), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966984), c_Groups_Oone__class_Oone(_966984)), _966986) = _966986)], (11045 ^ _779448) ^ [_967079, _967081] : [class_Groups_Omonoid__mult(_967079), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967079), _967081), c_Groups_Oone__class_Oone(_967079)) = _967081)], (11051 ^ _779448) ^ [_967174, _967176] : [class_Groups_Ocomm__monoid__mult(_967174), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967174), _967176), c_Groups_Oone__class_Oone(_967174)) = _967176)], (11057 ^ _779448) ^ [_967287, _967289, _967291] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967287)), _967289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967287)), _967291), -(_967289 = _967291)], (11063 ^ _779448) ^ [_967398, _967400, _967402] : [_967400 = _967402, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967398)), _967400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _967398)), _967402))], (11069 ^ _779448) ^ [_967515, _967517, _967519] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967517), _967519)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967515), _967517)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967515), _967519)))], (11071 ^ _779448) ^ [_967572, _967574, _967576] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _967572), _967574)), _967576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967572), _967576)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967574), _967576)))], (11073 ^ _779448) ^ [_967629] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967629), _967629))))], (11075 ^ _779448) ^ [_967663] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967663), _967663)))))], (11077 ^ _779448) ^ [_967703, _967705, _967707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967703), _967705)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967703), _967707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967705), _967707))))], (11083 ^ _779448) ^ [_967826, _967828, _967830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967826), _967828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967830), _967826)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967830), _967828))))], (11089 ^ _779448) ^ [_967949, _967951, _967953, _967955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967949), _967951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _967953), _967955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967949), _967953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _967951), _967955))))], (11099 ^ _779448) ^ [_968140, _968142] : [class_Groups_Omonoid__add(_968140), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968140), c_Groups_Ozero__class_Ozero(_968140)), _968142) = _968142)], (11105 ^ _779448) ^ [_968235, _968237] : [class_Groups_Ocomm__monoid__add(_968235), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968235), c_Groups_Ozero__class_Ozero(_968235)), _968237) = _968237)], (11111 ^ _779448) ^ [_968330, _968332] : [class_Groups_Olinordered__ab__group__add(_968330), 11114 ^ _779448 : [(11115 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_968330) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968330), _968332), _968332), -(_968332 = c_Groups_Ozero__class_Ozero(_968330))], (11121 ^ _779448) ^ [] : [_968332 = c_Groups_Ozero__class_Ozero(_968330), -(c_Groups_Ozero__class_Ozero(_968330) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968330), _968332), _968332))]]], (11127 ^ _779448) ^ [_968571, _968573] : [class_Groups_Omonoid__add(_968571), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968571), _968573), c_Groups_Ozero__class_Ozero(_968571)) = _968573)], (11133 ^ _779448) ^ [_968666, _968668] : [class_Groups_Ocomm__monoid__add(_968666), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968666), _968668), c_Groups_Ozero__class_Ozero(_968666)) = _968668)], (11139 ^ _779448) ^ [_968761, _968763, _968765] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968761), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968763), _968765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968761), _968763)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968761), _968765)))], (11141 ^ _779448) ^ [_968818, _968820, _968822] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _968818), _968820)), _968822) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968818), _968822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _968820), _968822)))], (11143 ^ _779448) ^ [_968875, _968877] : [class_Groups_Ogroup__add(_968875), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_968875), _968877), c_Groups_Ozero__class_Ozero(_968875)) = _968877)], (11149 ^ _779448) ^ [_968970, _968972] : [class_Groups_Ogroup__add(_968970), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_968970), _968972), _968972) = c_Groups_Ozero__class_Ozero(_968970))], (11155 ^ _779448) ^ [_969065, _969067, _969069] : [class_Groups_Oab__group__add(_969065), 11158 ^ _779448 : [(11159 ^ _779448) ^ [] : [_969067 = _969069, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969065), _969067), _969069) = c_Groups_Ozero__class_Ozero(_969065))], (11165 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969065), _969067), _969069) = c_Groups_Ozero__class_Ozero(_969065), -(_969067 = _969069)]]], (11171 ^ _779448) ^ [_969306, _969308, _969310] : [class_Groups_Ogroup__add(_969306), 11174 ^ _779448 : [(11175 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969306), _969308), _969310) = c_Groups_Ozero__class_Ozero(_969306), -(_969308 = _969310)], (11181 ^ _779448) ^ [] : [_969308 = _969310, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_969306), _969308), _969310) = c_Groups_Ozero__class_Ozero(_969306))]]], (11187 ^ _779448) ^ [_969547] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _969547) = _969547)], (11189 ^ _779448) ^ [_969588, _969590] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969588), _969590), 11192 ^ _779448 : [(11193 ^ _779448) ^ [] : [-(_969588 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11195 ^ _779448) ^ [] : [-(_969590 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11197 ^ _779448) ^ [_969699, _969701] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969699), _969701)), _969699 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _969701 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11207 ^ _779448) ^ [_969842] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969842), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _969842)], (11209 ^ _779448) ^ [_969886, _969888] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969886), _969888) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 11212 ^ _779448 : [(11213 ^ _779448) ^ [] : [-(_969886 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11215 ^ _779448) ^ [] : [-(_969888 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11217 ^ _779448) ^ [_969997, _969999] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969997), _969999) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _969997 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _969999 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11227 ^ _779448) ^ [_970149] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _970149)], (11229 ^ _779448) ^ [_970184] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _970184)], (11231 ^ _779448) ^ [_970219] : [hAPP(c_Nat_OSuc, _970219) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11233 ^ _779448) ^ [_970254] : [hAPP(c_Nat_OSuc, _970254) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11235 ^ _779448) ^ [_970289] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _970289)], (11237 ^ _779448) ^ [_970324] : [hAPP(c_Nat_OSuc, _970324) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11239 ^ _779448) ^ [_970359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970359), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11241 ^ _779448) ^ [_970393] : [-(_970393 = 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)), _970393)))], (11247 ^ _779448) ^ [_970425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970425)), _970425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11253 ^ _779448) ^ [_970516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970516), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11255 ^ _779448) ^ [_970544, _970546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _970544), _970546)), _970546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11261 ^ _779448) ^ [_970628] : [-(_970628 = 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)), _970628)))], (11267 ^ _779448) ^ [_970664] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970664) = _970664)], (11269 ^ _779448) ^ [_970690] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970690), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _970690)], (11271 ^ _779448) ^ [_970734, _970736] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970734), _970736) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11274 ^ _779448 : [(11275 ^ _779448) ^ [] : [-(_970734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11277 ^ _779448) ^ [] : [-(_970736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11279 ^ _779448) ^ [_970845, _970847] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970845), _970847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _970847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11289 ^ _779448) ^ [_970988, _970990] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _970988), _970990) = _970988, -(_970990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11295 ^ _779448) ^ [_971077] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971077)))], (11297 ^ _779448) ^ [_971114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971114), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_971114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11303 ^ _779448) ^ [_971195] : [_971195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _971195), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11309 ^ _779448) ^ [_971282] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _971282) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11311 ^ _779448) ^ [_971308] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971308), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _971308)], (11313 ^ _779448) ^ [_971337] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971337), _971337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11315 ^ _779448) ^ [_971366, _971368] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971366), _971368) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _971368), _971366) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_971366 = _971368)], (11325 ^ _779448) ^ [_971519, _971521, _971523] : [class_Rings_Olinordered__semidom(_971519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971519), c_Groups_Oone__class_Oone(_971519)), _971521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971519), c_Groups_Oone__class_Oone(_971519)), _971523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971519), c_Groups_Oone__class_Oone(_971519)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971519), _971521), _971523))))], (11339 ^ _779448) ^ [_971774, _971776, _971778, _971780, _971782, _971784] : [class_Rings_Oring(_971774), 11342 ^ _779448 : [(11343 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), _971776), _971778)), _971780) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), _971782), _971778)), _971784), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971774), _971776), _971782)), _971778)), _971780) = _971784)], (11349 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_971774), _971776), _971782)), _971778)), _971780) = _971784, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), _971776), _971778)), _971780) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_971774), _971782), _971778)), _971784))]]], (11355 ^ _779448) ^ [_972171, _972173, _972175, _972177, _972179, _972181] : [class_Rings_Oring(_972171), 11358 ^ _779448 : [(11359 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), _972173), _972175)), _972177) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), _972179), _972175)), _972181), -(_972177 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972171), _972179), _972173)), _972175)), _972181))], (11365 ^ _779448) ^ [] : [_972177 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972171), _972179), _972173)), _972175)), _972181), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), _972173), _972175)), _972177) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972171), _972179), _972175)), _972181))]]], (11371 ^ _779448) ^ [_972568, _972570, _972572, _972574, _972576] : [c_Fun_Oinj__on(_972568, _972570, _972572, _972574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_972568, tc_HOL_Obool)), _972576), _972574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_972570, tc_HOL_Obool)), hAPP(c_Set_Oimage(_972568, _972570, _972572), _972576)), hAPP(c_Set_Oimage(_972568, _972570, _972572), _972574))))], (11381 ^ _779448) ^ [_972781, _972783] : [-(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)), _972781), _972783))], (11383 ^ _779448) ^ [_972811, _972813, _972815, _972817] : [class_Rings_Olinordered__semidom(_972811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972811), c_Groups_Ozero__class_Ozero(_972811)), _972813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972811), _972815), _972817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972811), _972815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972811), _972813), _972817))))], (11397 ^ _779448) ^ [_973064] : [class_Rings_Olinordered__semidom(_973064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973064), c_Groups_Oone__class_Oone(_973064)), c_Groups_Ozero__class_Ozero(_973064)))], (11403 ^ _779448) ^ [_973160] : [class_Rings_Olinordered__semidom(_973160), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973160), c_Groups_Ozero__class_Ozero(_973160)), c_Groups_Oone__class_Oone(_973160))))], (11409 ^ _779448) ^ [_973255] : [class_Rings_Olinordered__semidom(_973255), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973255), c_Groups_Ozero__class_Ozero(_973255)), c_Groups_Oone__class_Oone(_973255))))], (11415 ^ _779448) ^ [_973350] : [class_Rings_Olinordered__semidom(_973350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973350), c_Groups_Oone__class_Oone(_973350)), c_Groups_Ozero__class_Ozero(_973350)))], (11421 ^ _779448) ^ [_973446] : [class_Lattices_Oab__semigroup__idem__mult(_973446), -(c_Finite__Set_Ofun__left__comm__idem(_973446, _973446, c_Groups_Otimes__class_Otimes(_973446)))], (11427 ^ _779448) ^ [_973525, _973527, _973529, _973531, _973533, _973535] : [class_Rings_Olinordered__semiring__1__strict(_973525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973525), _973527), _973529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973525), _973531), _973529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973525), c_Groups_Ozero__class_Ozero(_973525)), _973533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973525), c_Groups_Ozero__class_Ozero(_973525)), _973535)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973525), _973533), _973535) = c_Groups_Oone__class_Oone(_973525), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973525), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973525), _973533), _973527)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973525), _973535), _973531))), _973529)))], (11453 ^ _779448) ^ [_974054, _974056, _974058] : [-(c_Nat_Onat_Onat__case(_974054, _974056, _974058, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _974056)], (11455 ^ _779448) ^ [_974095, _974097] : [_974095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974095), _974097) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11461 ^ _779448) ^ [_974178, _974180] : [-(_974178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _974178), _974180) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _974180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _974178), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _974180)))], (11467 ^ _779448) ^ [_974240, _974242, _974244, _974246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974240), hAPP(c_Set_Oimage(_974242, _974240, _974244), _974246))), c_Fun_Oinj__on(_974242, _974240, _974244, _974246), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_974242), _974246)))], (11477 ^ _779448) ^ [_974411, _974413, _974415, _974417] : [c_Fun_Oinj__on(_974411, _974413, _974415, _974417), -(hAPP(c_Finite__Set_Ocard(_974413), hAPP(c_Set_Oimage(_974411, _974413, _974415), _974417)) = hAPP(c_Finite__Set_Ocard(_974411), _974417))], (11483 ^ _779448) ^ [_974551, _974553, _974555, _974557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_974551, _974553)), c_Sum__Type_OPlus(_974551, _974553, _974555, _974557))), 11486 ^ _779448 : [(11487 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974551), _974555)))], (11489 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_974553), _974557)))]]], (11491 ^ _779448) ^ [_974694, _974696, _974698, _974700] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_974694, _974696)), c_Sum__Type_OPlus(_974694, _974696, _974698, _974700)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_974694), _974698)), hBOOL(hAPP(c_Finite__Set_Ofinite(_974696), _974700))], (11501 ^ _779448) ^ [_974873, _974875, _974877, _974879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974873), _974875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_974877), _974879)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_974873, _974877)), c_Sum__Type_OPlus(_974873, _974877, _974875, _974879))))], (11511 ^ _779448) ^ [_975050, _975052, _975054, _975056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_975050, _975052)), c_Sum__Type_OPlus(_975050, _975052, _975054, _975056))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975050), _975054)))], (11517 ^ _779448) ^ [_975163, _975165, _975167, _975169] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_975163, _975165)), c_Sum__Type_OPlus(_975163, _975165, _975167, _975169))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_975165), _975169)))], (11523 ^ _779448) ^ [_975276, _975278, _975280, _975282, _975284, _975286] : [c_Fun_Oinj__on(_975276, _975278, _975280, _975282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975276, tc_HOL_Obool)), _975284), _975282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975276, tc_HOL_Obool)), _975286), _975282)), -(hAPP(c_Set_Oimage(_975276, _975278, _975280), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975276, tc_HOL_Obool)), _975284), _975286)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975278, tc_HOL_Obool)), hAPP(c_Set_Oimage(_975276, _975278, _975280), _975284)), hAPP(c_Set_Oimage(_975276, _975278, _975280), _975286)))], (11547 ^ _779448) ^ [_975831, _975833, _975835, _975837] : [11548 ^ _779448 : [(11549 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_975831), _975833)))], (11551 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_975835), _975837)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_975831, _975835)), c_Sum__Type_OPlus(_975831, _975835, _975833, _975837)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11537 ^ _779448) ^ [_975626, _975628, _975630, _975632] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_975626, _975630)), c_Sum__Type_OPlus(_975626, _975630, _975628, _975632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_975626), _975628)), hAPP(c_Finite__Set_Ocard(_975630), _975632))), hBOOL(hAPP(c_Finite__Set_Ofinite(_975626), _975628)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975630), _975632))], (11555 ^ _779448) ^ [_975931, _975933, _975935, _975937, _975939, _975941] : [class_Rings_Oordered__ring(_975931), 11558 ^ _779448 : [(11559 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), _975933), _975935)), _975937)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), _975939), _975935)), _975941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975931), _975937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_975931), _975939), _975933)), _975935)), _975941))))], (11565 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975931), _975937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_975931), _975939), _975933)), _975935)), _975941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), _975933), _975935)), _975937)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_975931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975931), _975939), _975935)), _975941))))]]], (11571 ^ _779448) ^ [_976370, _976372, _976374, _976376, _976378, _976380] : [class_Rings_Oordered__ring(_976370), 11574 ^ _779448 : [(11575 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), _976372), _976374)), _976376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), _976378), _976374)), _976380))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_976370), _976372), _976378)), _976374)), _976376)), _976380)))], (11581 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_976370), _976372), _976378)), _976374)), _976376)), _976380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), _976372), _976374)), _976376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976370), _976378), _976374)), _976380))))]]], (11587 ^ _779448) ^ [_976809, _976811, _976813, _976815, _976817, _976819] : [class_Rings_Oordered__ring(_976809), 11590 ^ _779448 : [(11591 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), _976811), _976813)), _976815)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), _976817), _976813)), _976819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976809), _976815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_976809), _976817), _976811)), _976813)), _976819))))], (11597 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976809), _976815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_976809), _976817), _976811)), _976813)), _976819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_976809), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), _976811), _976813)), _976815)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_976809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976809), _976817), _976813)), _976819))))]]], (11603 ^ _779448) ^ [_977248, _977250, _977252, _977254, _977256, _977258] : [class_Rings_Oordered__ring(_977248), 11606 ^ _779448 : [(11607 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), _977250), _977252)), _977254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), _977256), _977252)), _977258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977248), _977250), _977256)), _977252)), _977254)), _977258)))], (11613 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977248), _977250), _977256)), _977252)), _977254)), _977258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977248), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), _977250), _977252)), _977254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977248), _977256), _977252)), _977258))))]]], (11619 ^ _779448) ^ [_977702, _977704, _977706] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_977702, _977704, c_Orderings_Obot__class_Obot(tc_fun(_977702, tc_HOL_Obool))), _977706))], (11621 ^ _779448) ^ [_977740, _977742, _977744, _977746] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_977740, _977742, _977744), _977746)), _977744 = c_Orderings_Obot__class_Obot(tc_fun(_977740, tc_HOL_Obool))], (11627 ^ _779448) ^ [_977862, _977864, _977866] : [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, _977862)), _977864)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _977862)), _977866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977864), _977866)))], (11633 ^ _779448) ^ [_977993, _977995, _977997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _977995), _977997)), -(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, _977993)), _977995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _977993)), _977997))))], (11639 ^ _779448) ^ [_978130] : [class_Rings_Olinordered__semidom(_978130), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_978130), c_Groups_Ozero__class_Ozero(_978130)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978130), c_Groups_Oone__class_Oone(_978130)), c_Groups_Oone__class_Oone(_978130)))))], (11645 ^ _779448) ^ [_978245, _978247] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978245)), _978247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978245), _978247)))], (11647 ^ _779448) ^ [_978291, _978293] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978291), hAPP(c_Nat_OSuc, _978293)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _978291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _978291), _978293)))], (11649 ^ _779448) ^ [_978355, _978357, _978359] : [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, _978355)), _978357)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978355)), _978359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978357), _978359)))], (11655 ^ _779448) ^ [_978486, _978488, _978490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _978488), _978490)), -(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, _978486)), _978488)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _978486)), _978490))))], (11661 ^ _779448) ^ [_978623, _978625, _978627] : [class_Groups_Oordered__comm__monoid__add(_978623), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978623), _978625), c_Groups_Ozero__class_Ozero(_978623))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978623), _978627), c_Groups_Ozero__class_Ozero(_978623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978623), _978625), _978627)), c_Groups_Ozero__class_Ozero(_978623))))], (11675 ^ _779448) ^ [_978878, _978880, _978882, _978884] : [class_Groups_Oordered__comm__monoid__add(_978878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978878), c_Groups_Ozero__class_Ozero(_978878)), _978880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978878), _978882), _978884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978878), _978882), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978878), _978884), _978880))))], (11689 ^ _779448) ^ [_979131, _979133, _979135, _979137] : [class_Groups_Oordered__comm__monoid__add(_979131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979131), c_Groups_Ozero__class_Ozero(_979131)), _979133)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979131), _979135), _979137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979131), _979135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979131), _979133), _979137))))], (11703 ^ _779448) ^ [_979384, _979386, _979388] : [class_Groups_Oordered__comm__monoid__add(_979384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979384), c_Groups_Ozero__class_Ozero(_979384)), _979386)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979384), c_Groups_Ozero__class_Ozero(_979384)), _979388)), 11714 ^ _779448 : [(11715 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979384), _979386), _979388) = c_Groups_Ozero__class_Ozero(_979384), 11718 ^ _779448 : [(11719 ^ _779448) ^ [] : [-(_979386 = c_Groups_Ozero__class_Ozero(_979384))], (11721 ^ _779448) ^ [] : [-(_979388 = c_Groups_Ozero__class_Ozero(_979384))]]], (11723 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979384), _979386), _979388) = c_Groups_Ozero__class_Ozero(_979384)), _979386 = c_Groups_Ozero__class_Ozero(_979384), _979388 = c_Groups_Ozero__class_Ozero(_979384)]]], (11733 ^ _779448) ^ [_979855, _979857, _979859] : [class_Groups_Oordered__comm__monoid__add(_979855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979855), c_Groups_Ozero__class_Ozero(_979855)), _979857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979855), c_Groups_Ozero__class_Ozero(_979855)), _979859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979855), c_Groups_Ozero__class_Ozero(_979855)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979855), _979857), _979859))))], (11747 ^ _779448) ^ [_980110, _980112] : [class_Groups_Olinordered__ab__group__add(_980110), 11750 ^ _779448 : [(11751 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980110), _980112), _980112)), c_Groups_Ozero__class_Ozero(_980110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980110), _980112), c_Groups_Ozero__class_Ozero(_980110))))], (11757 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980110), _980112), c_Groups_Ozero__class_Ozero(_980110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980110), _980112), _980112)), c_Groups_Ozero__class_Ozero(_980110))))]]], (11763 ^ _779448) ^ [_980393, _980395] : [class_Groups_Olinordered__ab__group__add(_980393), 11766 ^ _779448 : [(11767 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980393), c_Groups_Ozero__class_Ozero(_980393)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980393), _980395), _980395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980393), c_Groups_Ozero__class_Ozero(_980393)), _980395)))], (11773 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980393), c_Groups_Ozero__class_Ozero(_980393)), _980395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980393), c_Groups_Ozero__class_Ozero(_980393)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980393), _980395), _980395))))]]], (11779 ^ _779448) ^ [_980676, _980678] : [class_Groups_Olinordered__ab__group__add(_980676), 11782 ^ _779448 : [(11783 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980676), c_Groups_Ozero__class_Ozero(_980676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980676), _980678), _980678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980676), c_Groups_Ozero__class_Ozero(_980676)), _980678)))], (11789 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980676), c_Groups_Ozero__class_Ozero(_980676)), _980678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980676), c_Groups_Ozero__class_Ozero(_980676)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980676), _980678), _980678))))]]], (11795 ^ _779448) ^ [_980959, _980961] : [class_Groups_Olinordered__ab__group__add(_980959), 11798 ^ _779448 : [(11799 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980959), _980961), _980961)), c_Groups_Ozero__class_Ozero(_980959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980959), _980961), c_Groups_Ozero__class_Ozero(_980959))))], (11805 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980959), _980961), c_Groups_Ozero__class_Ozero(_980959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980959), _980961), _980961)), c_Groups_Ozero__class_Ozero(_980959))))]]], (11811 ^ _779448) ^ [_981242, _981244, _981246] : [class_Groups_Oordered__comm__monoid__add(_981242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981242), c_Groups_Ozero__class_Ozero(_981242)), _981244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981242), c_Groups_Ozero__class_Ozero(_981242)), _981246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981242), c_Groups_Ozero__class_Ozero(_981242)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981242), _981244), _981246))))], (11825 ^ _779448) ^ [_981497, _981499, _981501] : [class_Groups_Oordered__comm__monoid__add(_981497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981497), _981499), c_Groups_Ozero__class_Ozero(_981497))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981497), _981501), c_Groups_Ozero__class_Ozero(_981497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981497), _981499), _981501)), c_Groups_Ozero__class_Ozero(_981497))))], (11839 ^ _779448) ^ [_981752, _981754, _981756] : [class_Groups_Oordered__ab__group__add(_981752), 11842 ^ _779448 : [(11843 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981752), _981754), _981756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_981752), _981754), _981756)), c_Groups_Ozero__class_Ozero(_981752))))], (11849 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_981752), _981754), _981756)), c_Groups_Ozero__class_Ozero(_981752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981752), _981754), _981756)))]]], (11855 ^ _779448) ^ [_982035, _982037, _982039] : [class_Groups_Oordered__ab__group__add(_982035), 11858 ^ _779448 : [(11859 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982035), _982037), _982039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982035), _982037), _982039)), c_Groups_Ozero__class_Ozero(_982035))))], (11865 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_982035), _982037), _982039)), c_Groups_Ozero__class_Ozero(_982035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982035), _982037), _982039)))]]], (11871 ^ _779448) ^ [_982333, _982335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982333), hAPP(c_Nat_OSuc, _982335))), -(_982333 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11879 ^ _779448 : [(11880 ^ _779448) ^ [] : [-(_982333 = hAPP(c_Nat_OSuc, 11878 ^ [_982333, _982335]))], (11882 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11878 ^ [_982333, _982335]), _982335)))]]], (11884 ^ _779448) ^ [_982513, _982515] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982513), hAPP(c_Nat_OSuc, _982515)))), 11885 ^ _779448 : [(11886 ^ _779448) ^ [] : [_982513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11888 ^ _779448) ^ [_982601] : [_982513 = hAPP(c_Nat_OSuc, _982601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982601), _982515))]]], (11896 ^ _779448) ^ [_982747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982747), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_982747 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11902 ^ _779448) ^ [_982828] : [_982828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _982828), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (11908 ^ _779448) ^ [_982927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _982927)), -(_982927 = hAPP(c_Nat_OSuc, 11911 ^ [_982927]))], (11915 ^ _779448) ^ [_983018] : [11916 ^ _779448 : [(11917 ^ _779448) ^ [_983060] : [_983018 = hAPP(c_Nat_OSuc, _983060)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983018)))], (11921 ^ _779448) ^ [_983133, _983135] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983133), _983135) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11926 ^ _779448 : [(11927 ^ _779448) ^ [] : [-(_983133 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11929 ^ _779448) ^ [] : [-(_983135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 11930 ^ _779448 : [(11931 ^ _779448) ^ [] : [-(_983133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11933 ^ _779448) ^ [] : [-(_983135 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (11935 ^ _779448) ^ [_983317, _983319] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983317), _983319) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 11936 ^ _779448 : [(11937 ^ _779448) ^ [] : [_983317 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983319 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11943 ^ _779448) ^ [] : [_983317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _983319 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11951 ^ _779448) ^ [_983558, _983560] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983558), _983560), 11956 ^ _779448 : [(11957 ^ _779448) ^ [] : [-(_983558 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11959 ^ _779448) ^ [] : [-(_983560 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 11960 ^ _779448 : [(11961 ^ _779448) ^ [] : [-(_983558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11963 ^ _779448) ^ [] : [-(_983560 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (11965 ^ _779448) ^ [_983742, _983744] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _983742), _983744)), 11966 ^ _779448 : [(11967 ^ _779448) ^ [] : [_983742 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11973 ^ _779448) ^ [] : [_983742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _983744 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (11991 ^ _779448) ^ [_984093, _984095] : [11992 ^ _779448 : [(11993 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984093))], (11995 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984095))]], -(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), _984093), _984095))))], (11981 ^ _779448) ^ [_983983, _983985] : [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), _983983), _983985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _983985)))], (11999 ^ _779448) ^ [_984234] : [-(hAPP(c_Finite__Set_Ocard(_984234), c_Orderings_Obot__class_Obot(tc_fun(_984234, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12001 ^ _779448) ^ [_984263, _984265] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_984263), _984265))), -(hAPP(c_Finite__Set_Ocard(_984263), _984265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12007 ^ _779448) ^ [_984308, _984310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984310), _984308)), _984310)))], (12017 ^ _779448) ^ [_984482, _984484] : [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), _984482), _984484))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984484), _984482)))], (12023 ^ _779448) ^ [_984581, _984583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _984583), _984581)), -(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), _984581), _984583))))], (12029 ^ _779448) ^ [_984686, _984688] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _984686), _984688)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12031 ^ _779448) ^ [_984738, _984740] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984738), _984740) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984738), _984740)))], (12037 ^ _779448) ^ [_984833, _984835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984833), _984835)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984833), _984835) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12043 ^ _779448) ^ [_984934, _984936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _984934), _984936)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _984934), _984936) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12049 ^ _779448) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12051 ^ _779448) ^ [_985051, _985053] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _985051), hAPP(c_Nat_OSuc, _985053)) = 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), _985051), _985053)))], (12053 ^ _779448) ^ [_985096, _985098, _985100] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_985096), _985098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985096, tc_HOL_Obool)), _985098), hAPP(c_Set_Oimage(_985096, _985096, _985100), _985098))), -(c_Fun_Oinj__on(_985096, _985096, _985100, _985098))], (12063 ^ _779448) ^ [_985275, _985277, _985279] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_985275), _985277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_985275, _985275, _985279), _985277)), _985277)), c_Fun_Oinj__on(_985275, _985275, _985279, _985277), -(hAPP(c_Set_Oimage(_985275, _985275, _985279), _985277) = _985277)], (12077 ^ _779448) ^ [_985522, _985524, _985526, _985528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_985522), _985524)), 12080 ^ _779448 : [(12081 ^ _779448) ^ [] : [c_Fun_Oinj__on(_985522, _985526, _985528, _985524), -(hAPP(c_Finite__Set_Ocard(_985526), hAPP(c_Set_Oimage(_985522, _985526, _985528), _985524)) = hAPP(c_Finite__Set_Ocard(_985522), _985524))], (12087 ^ _779448) ^ [] : [hAPP(c_Finite__Set_Ocard(_985526), hAPP(c_Set_Oimage(_985522, _985526, _985528), _985524)) = hAPP(c_Finite__Set_Ocard(_985522), _985524), -(c_Fun_Oinj__on(_985522, _985526, _985528, _985524))]]], (12093 ^ _779448) ^ [_985806, _985808, _985810, _985812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_985806), _985808)), hAPP(c_Finite__Set_Ocard(_985810), hAPP(c_Set_Oimage(_985806, _985810, _985812), _985808)) = hAPP(c_Finite__Set_Ocard(_985806), _985808), -(c_Fun_Oinj__on(_985806, _985810, _985812, _985808))], (12103 ^ _779448) ^ [_985989, _985991, _985993, _985995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_985989), hAPP(c_Set_Oimage(_985991, _985989, _985993), _985995))), hAPP(c_Finite__Set_Ocard(_985991), _985995))), c_Fun_Oinj__on(_985991, _985989, _985993, _985995)], (12109 ^ _779448) ^ [_986119, _986121, _986123] : [class_Groups_Oordered__comm__monoid__add(_986119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986119), c_Groups_Ozero__class_Ozero(_986119)), _986121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986119), c_Groups_Ozero__class_Ozero(_986119)), _986123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986119), c_Groups_Ozero__class_Ozero(_986119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986119), _986121), _986123))))], (12123 ^ _779448) ^ [_986374, _986376, _986378] : [class_Groups_Oordered__comm__monoid__add(_986374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986374), c_Groups_Ozero__class_Ozero(_986374)), _986376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986374), c_Groups_Ozero__class_Ozero(_986374)), _986378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986374), c_Groups_Ozero__class_Ozero(_986374)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986374), _986376), _986378))))], (12137 ^ _779448) ^ [_986629, _986631, _986633, _986635] : [class_Groups_Oordered__comm__monoid__add(_986629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986629), c_Groups_Ozero__class_Ozero(_986629)), _986631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986629), _986633), _986635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986629), _986633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986629), _986631), _986635))))], (12151 ^ _779448) ^ [_986882, _986884, _986886, _986888] : [class_Groups_Oordered__comm__monoid__add(_986882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986882), c_Groups_Ozero__class_Ozero(_986882)), _986884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986882), _986886), _986888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986882), _986886), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986882), _986884), _986888))))], (12165 ^ _779448) ^ [_987135, _987137, _987139] : [class_Groups_Oordered__comm__monoid__add(_987135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987135), _987137), c_Groups_Ozero__class_Ozero(_987135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987135), _987139), c_Groups_Ozero__class_Ozero(_987135))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987135), _987137), _987139)), c_Groups_Ozero__class_Ozero(_987135))))], (12179 ^ _779448) ^ [_987390, _987392, _987394] : [class_Groups_Oordered__comm__monoid__add(_987390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987390), _987392), c_Groups_Ozero__class_Ozero(_987390))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987390), _987394), c_Groups_Ozero__class_Ozero(_987390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987390), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987390), _987392), _987394)), c_Groups_Ozero__class_Ozero(_987390))))], (12193 ^ _779448) ^ [_987645, _987647, _987649, _987651, _987653] : [class_Groups_Oab__semigroup__mult(_987645), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_987645, _987645, c_Groups_Otimes__class_Otimes(_987645), _987647, _987649), _987651)), -(hBOOL(hAPP(hAPP(c_member(_987645), _987647), _987649))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_987645, _987645, c_Groups_Otimes__class_Otimes(_987645), _987653, hAPP(hAPP(c_Set_Oinsert(_987645), _987647), _987649)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987645), _987653), _987651))))], (12207 ^ _779448) ^ [_987885, _987887, _987889] : [class_Rings_Olinordered__idom(_987885), -(_987887 = _987889), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987885), _987887), _987889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987885), _987889), _987887)))], (12221 ^ _779448) ^ [_988044, _988046, _988048, _988050, _988052] : [c_Fun_Oinj__on(_988044, _988046, _988048, hAPP(hAPP(c_Set_Oinsert(_988044), _988050), _988052)), 12224 ^ _779448 : [(12225 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_988044, _988046, _988048, _988052))], (12227 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_988046), hAPP(_988048, _988050)), hAPP(c_Set_Oimage(_988044, _988046, _988048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988044, tc_HOL_Obool)), _988052), hAPP(hAPP(c_Set_Oinsert(_988044), _988050), c_Orderings_Obot__class_Obot(tc_fun(_988044, tc_HOL_Obool)))))))]]], (12229 ^ _779448) ^ [_988263, _988265, _988267, _988269, _988271] : [-(c_Fun_Oinj__on(_988263, _988265, _988267, hAPP(hAPP(c_Set_Oinsert(_988263), _988269), _988271))), c_Fun_Oinj__on(_988263, _988265, _988267, _988271), -(hBOOL(hAPP(hAPP(c_member(_988265), hAPP(_988267, _988269)), hAPP(c_Set_Oimage(_988263, _988265, _988267), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988263, tc_HOL_Obool)), _988271), hAPP(hAPP(c_Set_Oinsert(_988263), _988269), c_Orderings_Obot__class_Obot(tc_fun(_988263, tc_HOL_Obool))))))))], (12249 ^ _779448) ^ [_988685, _988687] : [12250 ^ _779448 : [(12251 ^ _779448) ^ [] : [_988687 = c_Orderings_Obot__class_Obot(tc_fun(_988685, tc_HOL_Obool))], (12253 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_988685), _988687)))]], -(hAPP(c_Finite__Set_Ocard(_988685), _988687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12239 ^ _779448) ^ [_988530, _988532] : [hAPP(c_Finite__Set_Ocard(_988530), _988532) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_988532 = c_Orderings_Obot__class_Obot(tc_fun(_988530, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_988530), _988532))], (12257 ^ _779448) ^ [_988829, _988831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_988829), _988831))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988829), _988831)))], (12263 ^ _779448) ^ [_988928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _988928)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _988928), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _988928)], (12269 ^ _779448) ^ [_989025, _989027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _989025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989025), hAPP(c_Nat_OSuc, _989027))), _989025)))], (12291 ^ _779448) ^ [_989436, _989438, _989440] : [-(hBOOL(hAPP(_989436, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989438), _989440)))), 12294 ^ _779448 : [(12295 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989438), _989440)))], (12297 ^ _779448) ^ [] : [hBOOL(hAPP(_989436, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12299 ^ _779448 : [(12300 ^ _779448) ^ [] : [-(_989438 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989440), 12298 ^ [_989436, _989438, _989440]))], (12302 ^ _779448) ^ [] : [hBOOL(hAPP(_989436, 12298 ^ [_989436, _989438, _989440]))]]], (12275 ^ _779448) ^ [_989152, _989154, _989156] : [hBOOL(hAPP(_989152, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989154), _989156))), 12278 ^ _779448 : [(12279 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989154), _989156)), -(hBOOL(hAPP(_989152, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12285 ^ _779448) ^ [_989337] : [_989154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989156), _989337), -(hBOOL(hAPP(_989152, _989337)))]]], (12322 ^ _779448) ^ [_990031, _990033, _990035] : [-(hBOOL(hAPP(_990031, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _990033), _990035)))), 12325 ^ _779448 : [(12326 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990033), _990035)))], (12328 ^ _779448) ^ [] : [hBOOL(hAPP(_990031, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12330 ^ _779448 : [(12331 ^ _779448) ^ [] : [-(_990033 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990035), 12329 ^ [_990031, _990033, _990035]))], (12333 ^ _779448) ^ [] : [hBOOL(hAPP(_990031, 12329 ^ [_990031, _990033, _990035]))]]], (12306 ^ _779448) ^ [_989739, _989741, _989743] : [hBOOL(hAPP(_989739, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _989741), _989743))), 12309 ^ _779448 : [(12310 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989741), _989743)), -(hBOOL(hAPP(_989739, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12316 ^ _779448) ^ [_989930] : [_989741 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989743), _989930), -(hBOOL(hAPP(_989739, _989930)))]]], (12337 ^ _779448) ^ [_990324, _990326, _990328, _990330, _990332, _990334] : [c_Fun_Oinj__on(_990324, _990326, _990328, _990330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990326, tc_HOL_Obool)), hAPP(c_Set_Oimage(_990324, _990326, _990328), _990330)), _990332)), c_Fun_Oinj__on(_990326, _990324, _990334, _990332), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990324, tc_HOL_Obool)), hAPP(c_Set_Oimage(_990326, _990324, _990334), _990332)), _990330)), hBOOL(hAPP(c_Finite__Set_Ofinite(_990324), _990330)), hBOOL(hAPP(c_Finite__Set_Ofinite(_990326), _990332)), -(hAPP(c_Finite__Set_Ocard(_990324), _990330) = hAPP(c_Finite__Set_Ocard(_990326), _990332))], (12363 ^ _779448) ^ [_990842, _990844, _990846, _990848] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_990842, _990844, hAPP(hAPP(c_Set_Oinsert(_990842), _990846), c_Orderings_Obot__class_Obot(tc_fun(_990842, tc_HOL_Obool)))), _990848)), -(_990846 = _990848)], (12369 ^ _779448) ^ [_990957, _990959, _990961, _990963] : [_990961 = _990963, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_990957, _990959, hAPP(hAPP(c_Set_Oinsert(_990957), _990961), c_Orderings_Obot__class_Obot(tc_fun(_990957, tc_HOL_Obool)))), _990963)))], (12375 ^ _779448) ^ [_991093, _991095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_991093), _991095))), 12378 ^ _779448 : [(12379 ^ _779448) ^ [] : [_991095 = c_Orderings_Obot__class_Obot(tc_fun(_991093, tc_HOL_Obool))], (12381 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_991093), _991095)))]]], (12383 ^ _779448) ^ [_991234, _991236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_991234), _991236)))), -(_991236 = c_Orderings_Obot__class_Obot(tc_fun(_991234, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_991234), _991236))], (12393 ^ _779448) ^ [_991400, _991402, _991404, _991406] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_991400), _991402)), hBOOL(hAPP(c_Finite__Set_Ofinite(_991404), _991406)), 12400 ^ _779448 : [(12411 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_991400), _991402)), hAPP(c_Finite__Set_Ocard(_991404), _991406))), 12415 ^ _779448 : [(12416 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_991400, _991404, 12414 ^ [_991400, _991402, _991404, _991406], _991402))], (12418 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991404, tc_HOL_Obool)), hAPP(c_Set_Oimage(_991400, _991404, 12414 ^ [_991400, _991402, _991404, _991406]), _991402)), _991406)))]]], (12401 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_991400), _991402)), hAPP(c_Finite__Set_Ocard(_991404), _991406)))), 12402 ^ _779448 : [(12403 ^ _779448) ^ [_991611] : [c_Fun_Oinj__on(_991400, _991404, _991611, _991402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991404, tc_HOL_Obool)), hAPP(c_Set_Oimage(_991400, _991404, _991611), _991402)), _991406))]]]]], (12420 ^ _779448) ^ [_991927, _991929, _991931, _991933, _991935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _991927), _991929)), 12423 ^ _779448 : [(12424 ^ _779448) ^ [] : [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), _991927), _991931)), _991933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991929), _991931)), _991935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991933), 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), _991929), _991927)), _991931)), _991935))))], (12430 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991933), 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), _991929), _991927)), _991931)), _991935))), -(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), _991927), _991931)), _991933)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991929), _991931)), _991935))))]]], (12436 ^ _779448) ^ [_992318, _992320, _992322, _992324, _992326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992318), _992320)), 12439 ^ _779448 : [(12440 ^ _779448) ^ [] : [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), _992320), _992322)), _992324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992318), _992322)), _992326))), -(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), _992320), _992318)), _992322)), _992324)), _992326)))], (12446 ^ _779448) ^ [] : [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), _992320), _992318)), _992322)), _992324)), _992326)), -(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), _992320), _992322)), _992324)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992318), _992322)), _992326))))]]], (12452 ^ _779448) ^ [_992708, _992710, _992712, _992714] : [-(_992708 = c_Orderings_Obot__class_Obot(tc_fun(_992710, tc_HOL_Obool))), 12455 ^ _779448 : [(12467 ^ _779448) ^ [] : [12468 ^ _779448 : [(12469 ^ _779448) ^ [_993041] : [hAPP(c_Set_Oimage(_992712, _992710, _993041), _992714) = _992708]], 12471 ^ _779448 : [(12472 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_992710, _992712, 12470 ^ [_992708, _992710, _992712, _992714], _992708))], (12474 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992712, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992710, _992712, 12470 ^ [_992708, _992710, _992712, _992714]), _992708)), _992714)))]]], (12456 ^ _779448) ^ [] : [-(hAPP(c_Set_Oimage(_992712, _992710, 12463 ^ [_992708, _992710, _992712, _992714]), _992714) = _992708), 12457 ^ _779448 : [(12458 ^ _779448) ^ [_992849] : [c_Fun_Oinj__on(_992710, _992712, _992849, _992708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_992712, tc_HOL_Obool)), hAPP(c_Set_Oimage(_992710, _992712, _992849), _992708)), _992714))]]]]], (12476 ^ _779448) ^ [_993166, _993168, _993170, _993172, _993174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993166), _993168)), 12479 ^ _779448 : [(12480 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993166), _993170)), _993172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993168), _993170)), _993174), -(_993172 = 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), _993168), _993166)), _993170)), _993174))], (12486 ^ _779448) ^ [] : [_993172 = 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), _993168), _993166)), _993170)), _993174), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993166), _993170)), _993172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993168), _993170)), _993174))]]], (12492 ^ _779448) ^ [_993527, _993529, _993531, _993533, _993535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993527), _993529)), -(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), _993527), _993531)), _993533)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993529), _993531)), _993535)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _993533), 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), _993529), _993527)), _993531)), _993535)))], (12498 ^ _779448) ^ [_993728, _993730, _993732, _993734, _993736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993728), _993730)), 12501 ^ _779448 : [(12502 ^ _779448) ^ [] : [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), _993728), _993732)), _993734)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993730), _993732)), _993736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993734), 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), _993730), _993728)), _993732)), _993736))))], (12508 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993734), 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), _993730), _993728)), _993732)), _993736))), -(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), _993728), _993732)), _993734)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993730), _993732)), _993736))))]]], (12514 ^ _779448) ^ [_994119, _994121, _994123, _994125, _994127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994119), _994121)), 12517 ^ _779448 : [(12518 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994121), _994123)), _994125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994119), _994123)), _994127), -(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), _994121), _994119)), _994123)), _994125) = _994127)], (12524 ^ _779448) ^ [] : [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), _994121), _994119)), _994123)), _994125) = _994127, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994121), _994123)), _994125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994119), _994123)), _994127))]]], (12530 ^ _779448) ^ [_994480, _994482, _994484, _994486, _994488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994480), _994482)), -(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), _994482), _994484)), _994486)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994480), _994484)), _994488)) = 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), _994482), _994480)), _994484)), _994486)), _994488))], (12536 ^ _779448) ^ [_994681, _994683, _994685, _994687, _994689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994681), _994683)), 12539 ^ _779448 : [(12540 ^ _779448) ^ [] : [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), _994683), _994685)), _994687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994681), _994685)), _994689))), -(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), _994683), _994681)), _994685)), _994687)), _994689)))], (12546 ^ _779448) ^ [] : [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), _994683), _994681)), _994685)), _994687)), _994689)), -(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), _994683), _994685)), _994687)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994681), _994685)), _994689))))]]], (12552 ^ _779448) ^ [_995072, _995074] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995072), _995074) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995074), _995072))], (12554 ^ _779448) ^ [_995109, _995111, _995113] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995109), _995111)), _995113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995111), _995113)))], (12566 ^ _779448) ^ [_995290, _995292, _995294] : [12567 ^ _779448 : [(12568 ^ _779448) ^ [] : [_995290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12570 ^ _779448) ^ [] : [_995292 = _995294]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995290), _995292) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995290), _995294))], (12556 ^ _779448) ^ [_995178, _995180, _995182] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995178), _995180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995178), _995182), -(_995178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_995180 = _995182)], (12585 ^ _779448) ^ [_995632] : [12587 ^ _779448 : [(12588 ^ _779448) ^ [_995708] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 12586 ^ [_995632, _995708]), _995632)))], (12590 ^ _779448) ^ [_995742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12586 ^ [_995632, _995742]), _995742))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _995632)))], (12574 ^ _779448) ^ [_995445] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _995445)), 12578 ^ _779448 : [(12579 ^ _779448) ^ [_995525] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _995525), _995445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995525), 12577 ^ [_995445])))]]], (12594 ^ _779448) ^ [_995811, _995813, _995815, _995817] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995811), _995813)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _995815), _995813)), _995817)) = 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), _995811), _995815)), _995813)), _995817))], (12607 ^ _779448) ^ [_996081] : [12609 ^ _779448 : [(12610 ^ _779448) ^ [_996157] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 12608 ^ [_996081, _996157]), _996081)))], (12612 ^ _779448) ^ [_996191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 12608 ^ [_996081, _996191]), _996191))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _996081)))], (12596 ^ _779448) ^ [_995894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _995894)), 12600 ^ _779448 : [(12601 ^ _779448) ^ [_995974] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _995974), _995894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995974), 12599 ^ [_995894])))]]], (12616 ^ _779448) ^ [_996260, _996262, _996264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _996260)), 12619 ^ _779448 : [(12620 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996260), _996262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996260), _996264), -(_996262 = _996264)], (12626 ^ _779448) ^ [] : [_996262 = _996264, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996260), _996262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996260), _996264))]]], (12632 ^ _779448) ^ [_996513, _996515, _996517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _996513)), 12635 ^ _779448 : [(12636 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996513), _996515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996513), _996517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996515), _996517)))], (12642 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996515), _996517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996513), _996515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996513), _996517))))]]], (12648 ^ _779448) ^ [_996796, _996798, _996800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _996796)), 12651 ^ _779448 : [(12652 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996796), _996798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996796), _996800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996798), _996800)))], (12658 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996798), _996800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996796), _996798)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _996796), _996800))))]]], (12664 ^ _779448) ^ [_997079, _997081, _997083] : [class_Rings_Ocomm__semiring__1(_997079), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997079), _997081), _997083)), _997083) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997079), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997079), _997081), c_Groups_Oone__class_Oone(_997079))), _997083))], (12670 ^ _779448) ^ [_997224, _997226, _997228] : [class_Rings_Ocomm__semiring__1(_997224), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997224), _997226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997224), _997228), _997226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997224), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997224), _997228), c_Groups_Oone__class_Oone(_997224))), _997226))], (12676 ^ _779448) ^ [_997369, _997371] : [class_Rings_Ocomm__semiring__1(_997369), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997369), _997371), _997371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997369), c_Groups_Oone__class_Oone(_997369)), c_Groups_Oone__class_Oone(_997369))), _997371))], (12682 ^ _779448) ^ [_997500, _997502, _997504, _997506, _997508, _997510] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_997500), -(_997502 = c_Groups_Ozero__class_Ozero(_997500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997500), _997504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997500), _997502), _997508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997500), _997506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997500), _997502), _997510)), _997504 = _997506, -(_997508 = _997510)], (12700 ^ _779448) ^ [_997838, _997840] : [class_Rings_Olinordered__idom(_997838), 12703 ^ _779448 : [(12704 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997838), _997840), _997840)), c_Groups_Ozero__class_Ozero(_997838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997838), _997840), c_Groups_Ozero__class_Ozero(_997838))))], (12710 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997838), _997840), c_Groups_Ozero__class_Ozero(_997838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997838), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997838), _997840), _997840)), c_Groups_Ozero__class_Ozero(_997838))))]]], (12716 ^ _779448) ^ [_998142, _998144, _998146, _998148] : [c_Sum__Type_OPlus(_998142, _998144, _998146, _998148) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_998142, _998144), tc_HOL_Obool)), 12719 ^ _779448 : [(12720 ^ _779448) ^ [] : [-(_998146 = c_Orderings_Obot__class_Obot(tc_fun(_998142, tc_HOL_Obool)))], (12722 ^ _779448) ^ [] : [-(_998148 = c_Orderings_Obot__class_Obot(tc_fun(_998144, tc_HOL_Obool)))]]], (12724 ^ _779448) ^ [_998291, _998293, _998295, _998297] : [-(c_Sum__Type_OPlus(_998291, _998293, _998295, _998297) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_998291, _998293), tc_HOL_Obool))), _998295 = c_Orderings_Obot__class_Obot(tc_fun(_998291, tc_HOL_Obool)), _998297 = c_Orderings_Obot__class_Obot(tc_fun(_998293, tc_HOL_Obool))], (12734 ^ _779448) ^ [_998494, _998496, _998498] : [hAPP(c_Finite__Set_Ocard(_998494), _998496) = hAPP(c_Nat_OSuc, _998498), 12739 ^ _779448 : [(12740 ^ _779448) ^ [] : [-(_998496 = hAPP(hAPP(c_Set_Oinsert(_998494), 12737 ^ [_998494, _998496, _998498]), 12738 ^ [_998494, _998496, _998498]))], (12742 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_998494), 12737 ^ [_998494, _998496, _998498]), 12738 ^ [_998494, _998496, _998498]))], (12744 ^ _779448) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_998494), 12738 ^ [_998494, _998496, _998498]) = _998498)], (12746 ^ _779448) ^ [] : [_998498 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(12738 ^ [_998494, _998496, _998498] = c_Orderings_Obot__class_Obot(tc_fun(_998494, tc_HOL_Obool)))]]], (12752 ^ _779448) ^ [_998912, _998914, _998916] : [-(hAPP(c_Finite__Set_Ocard(_998912), _998914) = hAPP(c_Nat_OSuc, _998916)), 12753 ^ _779448 : [(12754 ^ _779448) ^ [_999012, _999014] : [_998914 = hAPP(hAPP(c_Set_Oinsert(_998912), _999014), _999012), -(hBOOL(hAPP(hAPP(c_member(_998912), _999014), _999012))), hAPP(c_Finite__Set_Ocard(_998912), _999012) = _998916, 12765 ^ _779448 : [(12766 ^ _779448) ^ [] : [-(_998916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12768 ^ _779448) ^ [] : [_999012 = c_Orderings_Obot__class_Obot(tc_fun(_998912, tc_HOL_Obool))]]]]], (12772 ^ _779448) ^ [_999361, _999363, _999365, _999367, _999369, _999371] : [hBOOL(hAPP(hAPP(c_member(_999361), _999363), c_SetInterval_Oord_OgreaterThanAtMost(_999361, _999365, _999367, _999369, _999371))), 12775 ^ _779448 : [(12776 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_999367, _999369), _999363)))], (12778 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_999365, _999363), _999371)))]]], (12780 ^ _779448) ^ [_999514, _999516, _999518, _999520, _999522, _999524] : [-(hBOOL(hAPP(hAPP(c_member(_999514), _999516), c_SetInterval_Oord_OgreaterThanAtMost(_999514, _999518, _999520, _999522, _999524)))), hBOOL(hAPP(hAPP(_999520, _999522), _999516)), hBOOL(hAPP(hAPP(_999518, _999516), _999524))], (12790 ^ _779448) ^ [_999734, _999736, _999738, _999740, _999742, _999744] : [hBOOL(hAPP(hAPP(c_member(_999734), _999736), c_SetInterval_Oord_OatLeastLessThan(_999734, _999738, _999740, _999742, _999744))), 12793 ^ _779448 : [(12794 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_999738, _999742), _999736)))], (12796 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_999740, _999736), _999744)))]]], (12798 ^ _779448) ^ [_999887, _999889, _999891, _999893, _999895, _999897] : [-(hBOOL(hAPP(hAPP(c_member(_999887), _999889), c_SetInterval_Oord_OatLeastLessThan(_999887, _999891, _999893, _999895, _999897)))), hBOOL(hAPP(hAPP(_999891, _999895), _999889)), hBOOL(hAPP(hAPP(_999893, _999889), _999897))], (12808 ^ _779448) ^ [_1000080, _1000082, _1000084, _1000086, _1000088] : [class_Rings_Ocomm__semiring__1(_1000080), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), _1000082), _1000084)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), _1000086), _1000088)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), _1000082), _1000086)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000080), _1000084), _1000088)))], (12814 ^ _779448) ^ [_1000257, _1000259, _1000261, _1000263] : [class_Rings_Ocomm__semiring__1(_1000257), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000257), _1000259), _1000261)), _1000263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000257), _1000259), _1000263)), _1000261))], (12820 ^ _779448) ^ [_1000400, _1000402, _1000404, _1000406] : [class_Rings_Ocomm__semiring__1(_1000400), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000400), _1000402), _1000404)), _1000406) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000400), _1000402), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000400), _1000404), _1000406)))], (12826 ^ _779448) ^ [_1000543, _1000545, _1000547, _1000549] : [class_Rings_Ocomm__semiring__1(_1000543), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000543), _1000545), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000543), _1000547), _1000549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000543), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000543), _1000545), _1000547)), _1000549))], (12832 ^ _779448) ^ [_1000686, _1000688, _1000690, _1000692] : [class_Rings_Ocomm__semiring__1(_1000686), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000686), _1000688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000686), _1000690), _1000692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000686), _1000690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000686), _1000688), _1000692)))], (12838 ^ _779448) ^ [_1000829, _1000831, _1000833] : [class_Rings_Ocomm__semiring__1(_1000829), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000829), _1000831), _1000833) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000829), _1000833), _1000831))], (12844 ^ _779448) ^ [_1000938, _1000940, _1000942, _1000944, _1000946] : [class_Rings_Ocomm__semiring__1(_1000938), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), _1000940), _1000942)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), _1000944), _1000946)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), _1000940), _1000944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000938), _1000942), _1000946)))], (12850 ^ _779448) ^ [_1001115, _1001117, _1001119, _1001121, _1001123] : [class_Rings_Ocomm__semiring__1(_1001115), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), _1001117), _1001119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), _1001121), _1001123)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), _1001121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001115), _1001117), _1001119)), _1001123)))], (12856 ^ _779448) ^ [_1001292, _1001294, _1001296, _1001298, _1001300] : [class_Rings_Ocomm__semiring__1(_1001292), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), _1001294), _1001296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), _1001298), _1001300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), _1001294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), _1001296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001292), _1001298), _1001300))))], (12862 ^ _779448) ^ [_1001469, _1001471, _1001473, _1001475] : [class_Rings_Ocomm__semiring__1(_1001469), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001469), _1001471), _1001473)), _1001475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001469), _1001471), _1001475)), _1001473))], (12868 ^ _779448) ^ [_1001612, _1001614, _1001616, _1001618] : [class_Rings_Ocomm__semiring__1(_1001612), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001612), _1001614), _1001616)), _1001618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001612), _1001614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001612), _1001616), _1001618)))], (12874 ^ _779448) ^ [_1001755, _1001757, _1001759, _1001761] : [class_Rings_Ocomm__semiring__1(_1001755), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001755), _1001757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001755), _1001759), _1001761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001755), _1001757), _1001759)), _1001761))], (12880 ^ _779448) ^ [_1001898, _1001900, _1001902, _1001904] : [class_Rings_Ocomm__semiring__1(_1001898), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001898), _1001900), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001898), _1001902), _1001904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001898), _1001902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001898), _1001900), _1001904)))], (12886 ^ _779448) ^ [_1002041, _1002043, _1002045] : [class_Rings_Ocomm__semiring__1(_1002041), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002041), _1002043), _1002045) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002041), _1002045), _1002043))], (12892 ^ _779448) ^ [_1002150, _1002152] : [class_Groups_Olinordered__ab__group__add(_1002150), 12895 ^ _779448 : [(12896 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002150), _1002152), _1002152) = c_Groups_Ozero__class_Ozero(_1002150), -(_1002152 = c_Groups_Ozero__class_Ozero(_1002150))], (12902 ^ _779448) ^ [] : [_1002152 = c_Groups_Ozero__class_Ozero(_1002150), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002150), _1002152), _1002152) = c_Groups_Ozero__class_Ozero(_1002150))]]], (12908 ^ _779448) ^ [_1002391, _1002393, _1002395] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1002391), 12911 ^ _779448 : [(12912 ^ _779448) ^ [] : [_1002393 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002391), _1002393), _1002395), -(_1002395 = c_Groups_Ozero__class_Ozero(_1002391))], (12918 ^ _779448) ^ [] : [_1002395 = c_Groups_Ozero__class_Ozero(_1002391), -(_1002393 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002391), _1002393), _1002395))]]], (12924 ^ _779448) ^ [_1002632, _1002634] : [class_Rings_Ocomm__semiring__1(_1002632), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002632), _1002634), c_Groups_Ozero__class_Ozero(_1002632)) = _1002634)], (12930 ^ _779448) ^ [_1002727, _1002729] : [class_Rings_Ocomm__semiring__1(_1002727), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002727), c_Groups_Ozero__class_Ozero(_1002727)), _1002729) = _1002729)], (12936 ^ _779448) ^ [_1002822, _1002824] : [class_Rings_Ocomm__semiring__1(_1002822), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002822), _1002824), c_Groups_Ozero__class_Ozero(_1002822)) = c_Groups_Ozero__class_Ozero(_1002822))], (12942 ^ _779448) ^ [_1002921, _1002923] : [class_Rings_Ocomm__semiring__1(_1002921), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002921), c_Groups_Ozero__class_Ozero(_1002921)), _1002923) = c_Groups_Ozero__class_Ozero(_1002921))], (12948 ^ _779448) ^ [_1003020, _1003022, _1003024, _1003026, _1003028] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1003020), 12951 ^ _779448 : [(12962 ^ _779448) ^ [] : [12963 ^ _779448 : [(12964 ^ _779448) ^ [] : [_1003022 = _1003026], (12966 ^ _779448) ^ [] : [_1003024 = _1003028]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003022), _1003024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003026), _1003028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003022), _1003028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003026), _1003024)))], (12952 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003022), _1003024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003026), _1003028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003022), _1003028)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003020), _1003026), _1003024)), -(_1003022 = _1003026), -(_1003024 = _1003028)]]], (12970 ^ _779448) ^ [_1003432, _1003434, _1003436, _1003438] : [class_Rings_Ocomm__semiring__1(_1003432), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003432), _1003434), _1003436)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003432), _1003438), _1003436)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003432), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003432), _1003434), _1003438)), _1003436))], (12976 ^ _779448) ^ [_1003591, _1003593, _1003595, _1003597] : [class_Rings_Ocomm__semiring__1(_1003591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003591), _1003593), _1003595)), _1003597) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003591), _1003593), _1003597)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003591), _1003595), _1003597)))], (12982 ^ _779448) ^ [_1003750, _1003752, _1003754, _1003756, _1003758] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1003750), 12985 ^ _779448 : [(12996 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003752), _1003756)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003754), _1003758)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003752), _1003758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003754), _1003756))), 12999 ^ _779448 : [(13000 ^ _779448) ^ [] : [_1003752 = _1003754], (13002 ^ _779448) ^ [] : [_1003756 = _1003758]]], (12986 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003752), _1003756)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003754), _1003758)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1003750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003752), _1003758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003750), _1003754), _1003756)), -(_1003752 = _1003754), -(_1003756 = _1003758)]]], (13004 ^ _779448) ^ [_1004168, _1004170, _1004172, _1004174] : [class_Rings_Ocomm__semiring__1(_1004168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004168), _1004170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004168), _1004172), _1004174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1004168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004168), _1004170), _1004172)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004168), _1004170), _1004174)))], (13010 ^ _779448) ^ [_1004327, _1004329] : [class_Rings_Ocomm__semiring__1(_1004327), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004327), _1004329), c_Groups_Oone__class_Oone(_1004327)) = _1004329)], (13016 ^ _779448) ^ [_1004422, _1004424] : [class_Rings_Ocomm__semiring__1(_1004422), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004422), c_Groups_Oone__class_Oone(_1004422)), _1004424) = _1004424)], (13022 ^ _779448) ^ [_1004538, _1004540, _1004542, _1004544] : [hBOOL(hAPP(hAPP(c_member(_1004538), _1004540), c_SetInterval_Oord_OatMost(_1004538, _1004542, _1004544))), -(hBOOL(hAPP(hAPP(_1004542, _1004540), _1004544)))], (13028 ^ _779448) ^ [_1004647, _1004649, _1004651, _1004653] : [hBOOL(hAPP(hAPP(_1004651, _1004649), _1004653)), -(hBOOL(hAPP(hAPP(c_member(_1004647), _1004649), c_SetInterval_Oord_OatMost(_1004647, _1004651, _1004653))))], (13034 ^ _779448) ^ [_1004783, _1004785, _1004787, _1004789] : [hBOOL(hAPP(hAPP(c_member(_1004783), _1004785), c_SetInterval_Oord_OatLeast(_1004783, _1004787, _1004789))), -(hBOOL(hAPP(hAPP(_1004787, _1004789), _1004785)))], (13040 ^ _779448) ^ [_1004892, _1004894, _1004896, _1004898] : [hBOOL(hAPP(hAPP(_1004896, _1004898), _1004894)), -(hBOOL(hAPP(hAPP(c_member(_1004892), _1004894), c_SetInterval_Oord_OatLeast(_1004892, _1004896, _1004898))))], (13046 ^ _779448) ^ [_1005028, _1005030, _1005032, _1005034] : [hBOOL(hAPP(hAPP(c_member(_1005028), _1005030), c_SetInterval_Oord_OlessThan(_1005028, _1005032, _1005034))), -(hBOOL(hAPP(hAPP(_1005032, _1005030), _1005034)))], (13052 ^ _779448) ^ [_1005137, _1005139, _1005141, _1005143] : [hBOOL(hAPP(hAPP(_1005141, _1005139), _1005143)), -(hBOOL(hAPP(hAPP(c_member(_1005137), _1005139), c_SetInterval_Oord_OlessThan(_1005137, _1005141, _1005143))))], (13058 ^ _779448) ^ [_1005273, _1005275, _1005277, _1005279] : [hBOOL(hAPP(hAPP(c_member(_1005273), _1005275), c_SetInterval_Oord_OgreaterThan(_1005273, _1005277, _1005279))), -(hBOOL(hAPP(hAPP(_1005277, _1005279), _1005275)))], (13064 ^ _779448) ^ [_1005382, _1005384, _1005386, _1005388] : [hBOOL(hAPP(hAPP(_1005386, _1005388), _1005384)), -(hBOOL(hAPP(hAPP(c_member(_1005382), _1005384), c_SetInterval_Oord_OgreaterThan(_1005382, _1005386, _1005388))))], (13070 ^ _779448) ^ [_1005521, _1005523, _1005525, _1005527, _1005529] : [hBOOL(hAPP(hAPP(c_member(_1005521), _1005523), c_SetInterval_Oord_OatLeastAtMost(_1005521, _1005525, _1005527, _1005529))), 13073 ^ _779448 : [(13074 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1005525, _1005527), _1005523)))], (13076 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1005525, _1005523), _1005529)))]]], (13078 ^ _779448) ^ [_1005670, _1005672, _1005674, _1005676, _1005678] : [-(hBOOL(hAPP(hAPP(c_member(_1005670), _1005672), c_SetInterval_Oord_OatLeastAtMost(_1005670, _1005674, _1005676, _1005678)))), hBOOL(hAPP(hAPP(_1005674, _1005676), _1005672)), hBOOL(hAPP(hAPP(_1005674, _1005672), _1005678))], (13088 ^ _779448) ^ [_1005881, _1005883, _1005885, _1005887, _1005889] : [hBOOL(hAPP(hAPP(c_member(_1005881), _1005883), c_SetInterval_Oord_OgreaterThanLessThan(_1005881, _1005885, _1005887, _1005889))), 13091 ^ _779448 : [(13092 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1005885, _1005887), _1005883)))], (13094 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1005885, _1005883), _1005889)))]]], (13096 ^ _779448) ^ [_1006030, _1006032, _1006034, _1006036, _1006038] : [-(hBOOL(hAPP(hAPP(c_member(_1006030), _1006032), c_SetInterval_Oord_OgreaterThanLessThan(_1006030, _1006034, _1006036, _1006038)))), hBOOL(hAPP(hAPP(_1006034, _1006036), _1006032)), hBOOL(hAPP(hAPP(_1006034, _1006032), _1006038))], (13106 ^ _779448) ^ [_1006217, _1006219] : [class_Rings_Olinordered__idom(_1006217), hBOOL(hAPP(hAPP(c_member(_1006217), _1006219), c_Int_Oring__1__class_OInts(_1006217))), 13113 ^ _779448 : [(13114 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006217), c_Groups_Oone__class_Oone(_1006217)), _1006219)), _1006219)), c_Groups_Ozero__class_Ozero(_1006217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006217), _1006219), c_Groups_Ozero__class_Ozero(_1006217))))], (13120 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006217), _1006219), c_Groups_Ozero__class_Ozero(_1006217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1006217), c_Groups_Oone__class_Oone(_1006217)), _1006219)), _1006219)), c_Groups_Ozero__class_Ozero(_1006217))))]]], (13126 ^ _779448) ^ [_1006621, _1006623, _1006625, _1006627, _1006629, _1006631] : [hBOOL(hAPP(hAPP(c_member(_1006621), _1006623), _1006625)), -(hAPP(c_Set_Oimage(_1006621, _1006627, c_Fun_Ofun__upd(_1006621, _1006627, _1006629, _1006623, _1006631)), _1006625) = hAPP(hAPP(c_Set_Oinsert(_1006627), _1006631), hAPP(c_Set_Oimage(_1006621, _1006627, _1006629), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006621, tc_HOL_Obool)), _1006625), hAPP(hAPP(c_Set_Oinsert(_1006621), _1006623), c_Orderings_Obot__class_Obot(tc_fun(_1006621, tc_HOL_Obool)))))))], (13132 ^ _779448) ^ [_1006818, _1006820, _1006822, _1006824, _1006826, _1006828] : [-(hBOOL(hAPP(hAPP(c_member(_1006818), _1006820), _1006822))), -(hAPP(c_Set_Oimage(_1006818, _1006824, c_Fun_Ofun__upd(_1006818, _1006824, _1006826, _1006820, _1006828)), _1006822) = hAPP(c_Set_Oimage(_1006818, _1006824, _1006826), _1006822))], (13138 ^ _779448) ^ [_1006891, _1006893, _1006895, _1006897, _1006899, _1006901] : [c_Fun_Oinj__on(_1006891, _1006893, _1006895, _1006897), hBOOL(hAPP(hAPP(c_member(_1006893), _1006899), hAPP(c_Set_Oimage(_1006891, _1006893, _1006895), _1006897))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006891, tc_HOL_Obool)), _1006897), _1006901)), -(hBOOL(hAPP(hAPP(c_member(_1006891), hAPP(c_Fun_Othe__inv__into(_1006891, _1006893, _1006897, _1006895), _1006899)), _1006901)))], (13152 ^ _779448) ^ [_1007178, _1007180, _1007182, _1007184] : [-(c_Fun_Ofun__upd(_1007178, _1007180, _1007182, _1007184, hAPP(_1007182, _1007184)) = _1007182)], (13154 ^ _779448) ^ [_1007216, _1007218, _1007220, _1007222, _1007224] : [hAPP(_1007216, _1007218) = _1007220, -(c_Fun_Ofun__upd(_1007222, _1007224, _1007216, _1007218, _1007220) = _1007216)], (13160 ^ _779448) ^ [_1007313, _1007315, _1007317, _1007319, _1007321, _1007323] : [-(_1007313 = _1007315), -(hAPP(c_Fun_Ofun__upd(_1007317, _1007319, _1007321, _1007315, _1007323), _1007313) = hAPP(_1007321, _1007313))], (13166 ^ _779448) ^ [_1007365, _1007367, _1007369, _1007371, _1007373, _1007375, _1007377] : [-(_1007365 = _1007367), -(c_Fun_Ofun__upd(_1007369, _1007371, c_Fun_Ofun__upd(_1007369, _1007371, _1007373, _1007365, _1007375), _1007367, _1007377) = c_Fun_Ofun__upd(_1007369, _1007371, c_Fun_Ofun__upd(_1007369, _1007371, _1007373, _1007367, _1007377), _1007365, _1007375))], (13172 ^ _779448) ^ [_1007456, _1007458, _1007460, _1007462, _1007464, _1007466] : [_1007456 = _1007458, -(hAPP(c_Fun_Ofun__upd(_1007460, _1007462, _1007464, _1007458, _1007466), _1007456) = _1007466)], (13178 ^ _779448) ^ [_1007553, _1007555, _1007557, _1007559, _1007561, _1007563] : [-(_1007553 = _1007555), -(hAPP(c_Fun_Ofun__upd(_1007557, _1007559, _1007561, _1007555, _1007563), _1007553) = hAPP(_1007561, _1007553))], (13184 ^ _779448) ^ [_1007611, _1007613, _1007615, _1007617, _1007619] : [-(hAPP(c_Fun_Ofun__upd(_1007611, _1007613, _1007615, _1007617, _1007619), _1007617) = _1007619)], (13186 ^ _779448) ^ [_1007651, _1007653, _1007655, _1007657, _1007659, _1007661] : [-(c_Fun_Ofun__upd(_1007651, _1007653, c_Fun_Ofun__upd(_1007651, _1007653, _1007655, _1007657, _1007659), _1007657, _1007661) = c_Fun_Ofun__upd(_1007651, _1007653, _1007655, _1007657, _1007661))], (13188 ^ _779448) ^ [_1007726, _1007728, _1007730, _1007732, _1007734] : [c_Fun_Ofun__upd(_1007726, _1007728, _1007730, _1007732, _1007734) = _1007730, -(hAPP(_1007730, _1007732) = _1007734)], (13194 ^ _779448) ^ [_1007823, _1007825, _1007827, _1007829, _1007831] : [hAPP(_1007827, _1007829) = _1007831, -(c_Fun_Ofun__upd(_1007823, _1007825, _1007827, _1007829, _1007831) = _1007827)], (13200 ^ _779448) ^ [_1007947, _1007949, _1007951, _1007953, _1007955, _1007957] : [_1007947 = _1007949, -(hAPP(c_Fun_Ofun__upd(_1007951, _1007953, _1007955, _1007949, _1007957), _1007947) = _1007957)], (13206 ^ _779448) ^ [_1008044, _1008046, _1008048, _1008050, _1008052, _1008054] : [-(_1008044 = _1008046), -(hAPP(c_Fun_Ofun__upd(_1008048, _1008050, _1008052, _1008046, _1008054), _1008044) = hAPP(_1008052, _1008044))], (13212 ^ _779448) ^ [_1008102] : [class_Rings_Oring__1(_1008102), -(hBOOL(hAPP(hAPP(c_member(_1008102), c_Groups_Ozero__class_Ozero(_1008102)), c_Int_Oring__1__class_OInts(_1008102))))], (13218 ^ _779448) ^ [_1008197, _1008199, _1008201] : [class_Rings_Oring__1(_1008197), hBOOL(hAPP(hAPP(c_member(_1008197), _1008199), c_Int_Oring__1__class_OInts(_1008197))), hBOOL(hAPP(hAPP(c_member(_1008197), _1008201), c_Int_Oring__1__class_OInts(_1008197))), -(hBOOL(hAPP(hAPP(c_member(_1008197), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008197), _1008199), _1008201)), c_Int_Oring__1__class_OInts(_1008197))))], (13232 ^ _779448) ^ [_1008452, _1008454, _1008456] : [class_Rings_Oring__1(_1008452), hBOOL(hAPP(hAPP(c_member(_1008452), _1008454), c_Int_Oring__1__class_OInts(_1008452))), hBOOL(hAPP(hAPP(c_member(_1008452), _1008456), c_Int_Oring__1__class_OInts(_1008452))), -(hBOOL(hAPP(hAPP(c_member(_1008452), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1008452), _1008454), _1008456)), c_Int_Oring__1__class_OInts(_1008452))))], (13246 ^ _779448) ^ [_1008707, _1008709, _1008711] : [class_Rings_Oring__1(_1008707), hBOOL(hAPP(hAPP(c_member(_1008707), _1008709), c_Int_Oring__1__class_OInts(_1008707))), hBOOL(hAPP(hAPP(c_member(_1008707), _1008711), c_Int_Oring__1__class_OInts(_1008707))), -(hBOOL(hAPP(hAPP(c_member(_1008707), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1008707), _1008709), _1008711)), c_Int_Oring__1__class_OInts(_1008707))))], (13260 ^ _779448) ^ [_1008962] : [class_Rings_Oring__1(_1008962), -(hBOOL(hAPP(hAPP(c_member(_1008962), c_Groups_Oone__class_Oone(_1008962)), c_Int_Oring__1__class_OInts(_1008962))))], (13266 ^ _779448) ^ [_1009057, _1009059, _1009061, _1009063, _1009065, _1009067] : [c_Fun_Oinj__on(_1009057, _1009059, _1009061, _1009063), hAPP(_1009061, _1009065) = _1009067, hBOOL(hAPP(hAPP(c_member(_1009057), _1009065), _1009063)), -(hAPP(c_Fun_Othe__inv__into(_1009057, _1009059, _1009063, _1009061), _1009067) = _1009065)], (13280 ^ _779448) ^ [_1009302, _1009304, _1009306, _1009308, _1009310] : [c_Fun_Oinj__on(_1009302, _1009304, _1009306, _1009308), hBOOL(hAPP(hAPP(c_member(_1009302), _1009310), _1009308)), -(hAPP(c_Fun_Othe__inv__into(_1009302, _1009304, _1009308, _1009306), hAPP(_1009306, _1009310)) = _1009310)], (13290 ^ _779448) ^ [_1009483, _1009485, _1009487, _1009489] : [c_Fun_Oinj__on(_1009483, _1009485, _1009487, _1009489), -(hAPP(c_Set_Oimage(_1009485, _1009483, c_Fun_Othe__inv__into(_1009483, _1009485, _1009489, _1009487)), hAPP(c_Set_Oimage(_1009483, _1009485, _1009487), _1009489)) = _1009489)], (13296 ^ _779448) ^ [_1009606, _1009608, _1009610, _1009612] : [c_Fun_Oinj__on(_1009606, _1009608, _1009610, _1009612), -(c_Fun_Oinj__on(_1009608, _1009606, c_Fun_Othe__inv__into(_1009606, _1009608, _1009612, _1009610), hAPP(c_Set_Oimage(_1009606, _1009608, _1009610), _1009612)))], (13302 ^ _779448) ^ [_1009719, _1009721, _1009723, _1009725, _1009727, _1009729] : [c_Fun_Oinj__on(_1009719, _1009721, _1009723, _1009725), -(hBOOL(hAPP(hAPP(c_member(_1009721), _1009727), hAPP(c_Set_Oimage(_1009719, _1009721, _1009723), _1009725)))), -(c_Fun_Oinj__on(_1009719, _1009721, c_Fun_Ofun__upd(_1009719, _1009721, _1009723, _1009729, _1009727), _1009725))], (13312 ^ _779448) ^ [_1009867, _1009869] : [class_Int_Oring__char__0(_1009867), hBOOL(hAPP(hAPP(c_member(_1009867), _1009869), c_Int_Oring__1__class_OInts(_1009867))), 13319 ^ _779448 : [(13320 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009867), _1009869), _1009869) = c_Groups_Ozero__class_Ozero(_1009867), -(_1009869 = c_Groups_Ozero__class_Ozero(_1009867))], (13326 ^ _779448) ^ [] : [_1009869 = c_Groups_Ozero__class_Ozero(_1009867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009867), _1009869), _1009869) = c_Groups_Ozero__class_Ozero(_1009867))]]], (13332 ^ _779448) ^ [_1010178, _1010180, _1010182, _1010184, _1010186] : [-(hAPP(c_Fun_Othe__inv__into(_1010178, _1010180, _1010182, _1010184), _1010186) = c_HOL_OThe(_1010178, hAPP(hAPP(c_COMBS(_1010178, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1010178), c_fconj), hAPP(hAPP(c_COMBC(_1010178, tc_fun(_1010178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1010178)), _1010182))), hAPP(hAPP(c_COMBC(_1010178, _1010180, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1010180, tc_fun(_1010180, tc_HOL_Obool), _1010178), c_fequal), _1010184)), _1010186))))], (13334 ^ _779448) ^ [_1010278, _1010280, _1010282, _1010284, _1010286] : [c_Fun_Oinj__on(_1010278, _1010280, _1010282, _1010284), hBOOL(hAPP(hAPP(c_member(_1010280), _1010286), hAPP(c_Set_Oimage(_1010278, _1010280, _1010282), _1010284))), -(hAPP(_1010282, hAPP(c_Fun_Othe__inv__into(_1010278, _1010280, _1010284, _1010282), _1010286)) = _1010286)], (13344 ^ _779448) ^ [_1010473, _1010475] : [class_Int_Oring__char__0(_1010473), hBOOL(hAPP(hAPP(c_member(_1010473), _1010475), c_Int_Oring__1__class_OInts(_1010473))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010473), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010473), c_Groups_Oone__class_Oone(_1010473)), _1010475)), _1010475) = c_Groups_Ozero__class_Ozero(_1010473)], (13354 ^ _779448) ^ [_1010658, _1010660] : [-(hBOOL(hAPP(_1010658, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1010658, _1010660)), 13362 ^ _779448 : [(13363 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 13361 ^ [_1010658, _1010660]), _1010660)))], (13371 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1010658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 13361 ^ [_1010658, _1010660]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (13365 ^ _779448) ^ [_1010896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1010896), 13361 ^ [_1010658, _1010660])), hBOOL(hAPP(_1010658, _1010896))]]], (13373 ^ _779448) ^ [_1011048, _1011050] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011048), _1011050)), -(hAPP(c_Finite__Set_Ocard(_1011048), _1011050) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1011048, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1011048), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011050))], (13379 ^ _779448) ^ [_1011190, _1011192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011190), _1011192)), -(hAPP(c_Finite__Set_Ocard(_1011190), _1011192) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1011190, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1011190), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011192))], (13385 ^ _779448) ^ [_1011317, _1011319] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1011317), _1011319))), -(hAPP(c_Finite__Set_Ocard(_1011317), _1011319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13391 ^ _779448) ^ [_1011364, _1011366, _1011368, _1011370, _1011372] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1011364, _1011366, hAPP(hAPP(c_Set_Oinsert(_1011364), _1011368), _1011370)), _1011372)), 13396 ^ _779448 : [(13397 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1011364), _1011368), _1011370) = hAPP(hAPP(c_Set_Oinsert(_1011364), 13394 ^ [_1011364, _1011366, _1011368, _1011370, _1011372]), 13395 ^ [_1011364, _1011366, _1011368, _1011370, _1011372]))], (13399 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1011364, _1011364, _1011366, 13394 ^ [_1011364, _1011366, _1011368, _1011370, _1011372], 13395 ^ [_1011364, _1011366, _1011368, _1011370, _1011372]), _1011372)))], (13401 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011364), 13394 ^ [_1011364, _1011366, _1011368, _1011370, _1011372]), 13395 ^ [_1011364, _1011366, _1011368, _1011370, _1011372]))]]], (13403 ^ _779448) ^ [_1011781, _1011783, _1011785, _1011787, _1011789] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1011781, _1011783, hAPP(hAPP(c_Set_Oinsert(_1011781), _1011785), _1011787)), _1011789)), 13408 ^ _779448 : [(13409 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1011781), _1011785), _1011787) = hAPP(hAPP(c_Set_Oinsert(_1011781), 13406 ^ [_1011781, _1011783, _1011785, _1011787, _1011789]), 13407 ^ [_1011781, _1011783, _1011785, _1011787, _1011789]))], (13411 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1011781, _1011781, _1011783, 13406 ^ [_1011781, _1011783, _1011785, _1011787, _1011789], 13407 ^ [_1011781, _1011783, _1011785, _1011787, _1011789]), _1011789)))], (13413 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011781), 13406 ^ [_1011781, _1011783, _1011785, _1011787, _1011789]), 13407 ^ [_1011781, _1011783, _1011785, _1011787, _1011789]))]]], (13415 ^ _779448) ^ [_1012172, _1012174, _1012176, _1012178, _1012180] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1012172, _1012174, hAPP(hAPP(c_Set_Oinsert(_1012172), _1012176), _1012178)), _1012180))), 13416 ^ _779448 : [(13417 ^ _779448) ^ [_1012276, _1012278] : [hAPP(hAPP(c_Set_Oinsert(_1012172), _1012176), _1012178) = hAPP(hAPP(c_Set_Oinsert(_1012172), _1012278), _1012276), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1012172, _1012172, _1012174, _1012278, _1012276), _1012180)), -(hBOOL(hAPP(hAPP(c_member(_1012172), _1012278), _1012276)))]]], (13429 ^ _779448) ^ [_1012533, _1012535, _1012537] : [class_Groups_Oab__semigroup__mult(_1012533), -(_1012535 = c_Orderings_Obot__class_Obot(tc_fun(_1012533, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012533), _1012535)), -(hBOOL(hAPP(hAPP(c_member(_1012533), _1012537), _1012535))), -(hAPP(c_Finite__Set_Ofold1(_1012533, c_Groups_Otimes__class_Otimes(_1012533)), hAPP(hAPP(c_Set_Oinsert(_1012533), _1012537), _1012535)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012533), _1012537), hAPP(c_Finite__Set_Ofold1(_1012533, c_Groups_Otimes__class_Otimes(_1012533)), _1012535)))], (13447 ^ _779448) ^ [_1012832, _1012834] : [13449 ^ _779448 : [(13450 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13448 ^ [_1012832, _1012834]), _1012832)))], (13452 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1012834), 13448 ^ [_1012832, _1012834]))]], -(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)), _1012834), _1012832))], (13456 ^ _779448) ^ [_1013007, _1013009] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1013007), _1013009)), 13462 ^ _779448 : [(13463 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013007), 13461 ^ [_1013007, _1013009]), _1013009)))], (13465 ^ _779448) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1013007), _1013009) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13469 ^ _779448) ^ [_1013207] : [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), _1013207))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1013207) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1013207)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (13475 ^ _779448) ^ [_1013322, _1013324, _1013326] : [class_Int_Onumber(_1013322), 13478 ^ _779448 : [(13479 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1013322), _1013324) = _1013326, -(_1013326 = hAPP(c_Int_Onumber__class_Onumber__of(_1013322), _1013324))], (13485 ^ _779448) ^ [] : [_1013326 = hAPP(c_Int_Onumber__class_Onumber__of(_1013322), _1013324), -(hAPP(c_Int_Onumber__class_Onumber__of(_1013322), _1013324) = _1013326)]]], (13491 ^ _779448) ^ [_1013563, _1013565, _1013567] : [class_Int_Onumber__ring(_1013563), class_Int_Oring__char__0(_1013563), 13498 ^ _779448 : [(13499 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1013563), _1013565) = hAPP(c_Int_Onumber__class_Onumber__of(_1013563), _1013567), -(_1013565 = _1013567)], (13505 ^ _779448) ^ [] : [_1013565 = _1013567, -(hAPP(c_Int_Onumber__class_Onumber__of(_1013563), _1013565) = hAPP(c_Int_Onumber__class_Onumber__of(_1013563), _1013567))]]], (13511 ^ _779448) ^ [_1013858, _1013860, _1013862] : [class_Int_Onumber__ring(_1013858), class_Rings_Olinordered__idom(_1013858), 13518 ^ _779448 : [(13519 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013858), hAPP(c_Int_Onumber__class_Onumber__of(_1013858), _1013860)), hAPP(c_Int_Onumber__class_Onumber__of(_1013858), _1013862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1013860), _1013862)))], (13525 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1013860), _1013862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013858), hAPP(c_Int_Onumber__class_Onumber__of(_1013858), _1013860)), hAPP(c_Int_Onumber__class_Onumber__of(_1013858), _1013862))))]]], (13531 ^ _779448) ^ [_1014189, _1014191, _1014193] : [class_Int_Onumber__ring(_1014189), class_Rings_Olinordered__idom(_1014189), 13538 ^ _779448 : [(13539 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1014189), hAPP(c_Int_Onumber__class_Onumber__of(_1014189), _1014191)), hAPP(c_Int_Onumber__class_Onumber__of(_1014189), _1014193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014191), _1014193)))], (13545 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1014191), _1014193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1014189), hAPP(c_Int_Onumber__class_Onumber__of(_1014189), _1014191)), hAPP(c_Int_Onumber__class_Onumber__of(_1014189), _1014193))))]]], (13551 ^ _779448) ^ [_1014520, _1014522, _1014524] : [class_Int_Onumber__ring(_1014520), -(hAPP(c_Int_Onumber__class_Onumber__of(_1014520), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1014522), _1014524)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014520), hAPP(c_Int_Onumber__class_Onumber__of(_1014520), _1014522)), hAPP(c_Int_Onumber__class_Onumber__of(_1014520), _1014524)))], (13557 ^ _779448) ^ [_1014655, _1014657, _1014659] : [class_Int_Onumber__ring(_1014655), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014655), hAPP(c_Int_Onumber__class_Onumber__of(_1014655), _1014657)), hAPP(c_Int_Onumber__class_Onumber__of(_1014655), _1014659)) = hAPP(c_Int_Onumber__class_Onumber__of(_1014655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1014657), _1014659)))], (13563 ^ _779448) ^ [_1014790, _1014792, _1014794, _1014796] : [class_Int_Onumber__ring(_1014790), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014790), hAPP(c_Int_Onumber__class_Onumber__of(_1014790), _1014792)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014790), hAPP(c_Int_Onumber__class_Onumber__of(_1014790), _1014794)), _1014796)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014790), hAPP(c_Int_Onumber__class_Onumber__of(_1014790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1014792), _1014794))), _1014796))], (13569 ^ _779448) ^ [_1014959, _1014961, _1014963] : [class_Int_Onumber__ring(_1014959), -(hAPP(c_Int_Onumber__class_Onumber__of(_1014959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1014961), _1014963)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1014959), hAPP(c_Int_Onumber__class_Onumber__of(_1014959), _1014961)), hAPP(c_Int_Onumber__class_Onumber__of(_1014959), _1014963)))], (13575 ^ _779448) ^ [_1015094, _1015096, _1015098] : [class_Int_Onumber__ring(_1015094), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015094), hAPP(c_Int_Onumber__class_Onumber__of(_1015094), _1015096)), hAPP(c_Int_Onumber__class_Onumber__of(_1015094), _1015098)) = hAPP(c_Int_Onumber__class_Onumber__of(_1015094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015096), _1015098)))], (13581 ^ _779448) ^ [_1015229, _1015231, _1015233, _1015235] : [class_Int_Onumber__ring(_1015229), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015229), hAPP(c_Int_Onumber__class_Onumber__of(_1015229), _1015231)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015229), hAPP(c_Int_Onumber__class_Onumber__of(_1015229), _1015233)), _1015235)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015229), hAPP(c_Int_Onumber__class_Onumber__of(_1015229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1015231), _1015233))), _1015235))], (13587 ^ _779448) ^ [_1015398, _1015400, _1015402] : [class_Int_Onumber__ring(_1015398), -(hAPP(c_Int_Onumber__class_Onumber__of(_1015398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1015400), _1015402)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1015398), hAPP(c_Int_Onumber__class_Onumber__of(_1015398), _1015400)), hAPP(c_Int_Onumber__class_Onumber__of(_1015398), _1015402)))], (13593 ^ _779448) ^ [_1015533, _1015535, _1015537, _1015539, _1015541] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1015533, _1015535, _1015537), _1015539), _1015541), c_Orderings_Obot__class_Obot(tc_fun(_1015535, tc_HOL_Obool))) = _1015541)], (13595 ^ _779448) ^ [_1015582, _1015584, _1015586] : [class_Int_Onumber(_1015582), class_Orderings_Olinorder(_1015582), 13602 ^ _779448 : [(13603 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015582), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015584)), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015586))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015582), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015586)), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015584)))], (13609 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1015582), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015586)), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015584)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015582), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015584)), hAPP(c_Int_Onumber__class_Onumber__of(_1015582), _1015586))))]]], (13615 ^ _779448) ^ [_1015909, _1015911, _1015913, _1015915] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015909), hAPP(c_Int_Onumber__class_Onumber__of(_1015909), _1015911)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015909), _1015913), _1015915)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1015909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015909), hAPP(c_Int_Onumber__class_Onumber__of(_1015909), _1015911)), _1015913)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015909), hAPP(c_Int_Onumber__class_Onumber__of(_1015909), _1015911)), _1015915))), class_Int_Onumber(_1015909), class_Rings_Osemiring(_1015909)], (13625 ^ _779448) ^ [_1016152, _1016154, _1016156, _1016158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016152), _1016154), _1016156)), hAPP(c_Int_Onumber__class_Onumber__of(_1016152), _1016158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016152), _1016154), hAPP(c_Int_Onumber__class_Onumber__of(_1016152), _1016158))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016152), _1016156), hAPP(c_Int_Onumber__class_Onumber__of(_1016152), _1016158)))), class_Int_Onumber(_1016152), class_Rings_Osemiring(_1016152)], (13635 ^ _779448) ^ [_1016395, _1016397, _1016399, _1016401] : [class_Int_Onumber__ring(_1016395), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1016395), hAPP(c_Int_Onumber__class_Onumber__of(_1016395), _1016397)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016395), hAPP(c_Int_Onumber__class_Onumber__of(_1016395), _1016399)), _1016401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016395), hAPP(c_Int_Onumber__class_Onumber__of(_1016395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1016397), _1016399))), _1016401))], (13641 ^ _779448) ^ [_1016564, _1016566, _1016568, _1016570] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016564), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016564), _1016566), _1016568)), hAPP(c_Int_Onumber__class_Onumber__of(_1016564), _1016570)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016564), _1016566), hAPP(c_Int_Onumber__class_Onumber__of(_1016564), _1016570))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016564), _1016568), hAPP(c_Int_Onumber__class_Onumber__of(_1016564), _1016570)))), class_Int_Onumber(_1016564), class_Rings_Oring(_1016564)], (13651 ^ _779448) ^ [_1016807, _1016809, _1016811, _1016813] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016807), hAPP(c_Int_Onumber__class_Onumber__of(_1016807), _1016809)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016807), _1016811), _1016813)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1016807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016807), hAPP(c_Int_Onumber__class_Onumber__of(_1016807), _1016809)), _1016811)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016807), hAPP(c_Int_Onumber__class_Onumber__of(_1016807), _1016809)), _1016813))), class_Int_Onumber(_1016807), class_Rings_Oring(_1016807)], (13661 ^ _779448) ^ [_1017050, _1017052] : [class_Int_Onumber__ring(_1017050), -(hBOOL(hAPP(hAPP(c_member(_1017050), hAPP(c_Int_Onumber__class_Onumber__of(_1017050), _1017052)), c_Int_Oring__1__class_OInts(_1017050))))], (13667 ^ _779448) ^ [_1017153, _1017155, _1017157] : [-(hAPP(c_Finite__Set_Ofold1(_1017153, _1017155), hAPP(hAPP(c_Set_Oinsert(_1017153), _1017157), c_Orderings_Obot__class_Obot(tc_fun(_1017153, tc_HOL_Obool)))) = _1017157)], (13669 ^ _779448) ^ [_1017199, _1017201, _1017203, _1017205] : [_1017199 = c_Finite__Set_Ofold1(_1017201, _1017203), -(hAPP(_1017199, hAPP(hAPP(c_Set_Oinsert(_1017201), _1017205), c_Orderings_Obot__class_Obot(tc_fun(_1017201, tc_HOL_Obool)))) = _1017205)], (13675 ^ _779448) ^ [_1017318, _1017320, _1017322, _1017324, _1017326, _1017328, _1017330] : [c_Finite__Set_Ofolding__image__simple(_1017318, _1017320, _1017322, _1017324, _1017326, _1017328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017320), _1017330)), -(hAPP(_1017328, _1017330) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1017318, _1017320, _1017322), _1017326), _1017324), _1017330))], (13685 ^ _779448) ^ [_1017515, _1017517, _1017519, _1017521] : [c_Finite__Set_Ofolding__one(_1017515, _1017517, _1017519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017515), _1017521)), -(hAPP(_1017519, _1017521) = hAPP(c_Finite__Set_Ofold1(_1017515, _1017517), _1017521))], (13695 ^ _779448) ^ [_1017680, _1017682, _1017684] : [-(hAPP(c_Finite__Set_Ofold1(_1017680, _1017682), _1017684) = c_HOL_OThe(_1017680, c_Finite__Set_Ofold1Set(_1017680, _1017682, _1017684)))], (13697 ^ _779448) ^ [_1017720, _1017722, _1017724, _1017726, _1017728] : [class_Groups_Ocomm__monoid__mult(_1017720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1017722), _1017724)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1017720, _1017722, c_Groups_Otimes__class_Otimes(_1017720)), hAPP(hAPP(c_COMBS(_1017722, _1017720, _1017720), hAPP(hAPP(c_COMBB(_1017720, tc_fun(_1017720, _1017720), _1017722), c_Groups_Otimes__class_Otimes(_1017720)), _1017726)), _1017728)), c_Groups_Oone__class_Oone(_1017720)), _1017724) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017720), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1017720, _1017722, c_Groups_Otimes__class_Otimes(_1017720)), _1017726), c_Groups_Oone__class_Oone(_1017720)), _1017724)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1017720, _1017722, c_Groups_Otimes__class_Otimes(_1017720)), _1017728), c_Groups_Oone__class_Oone(_1017720)), _1017724)))], (13707 ^ _779448) ^ [_1018035, _1018037, _1018039, _1018041, _1018043, _1018045] : [class_Groups_Oab__semigroup__mult(_1018035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018037), _1018039)), -(hBOOL(hAPP(hAPP(c_member(_1018037), _1018041), _1018039))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1018035, _1018037, c_Groups_Otimes__class_Otimes(_1018035)), _1018043), _1018045), hAPP(hAPP(c_Set_Oinsert(_1018037), _1018041), _1018039)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018035), hAPP(_1018043, _1018041)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1018035, _1018037, c_Groups_Otimes__class_Otimes(_1018035)), _1018043), _1018045), _1018039)))], (13721 ^ _779448) ^ [_1018313, _1018315, _1018317] : [class_Lattices_Oab__semigroup__idem__mult(_1018313), -(_1018315 = c_Orderings_Obot__class_Obot(tc_fun(_1018313, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018313), _1018315)), -(hAPP(c_Finite__Set_Ofold1(_1018313, c_Groups_Otimes__class_Otimes(_1018313)), hAPP(hAPP(c_Set_Oinsert(_1018313), _1018317), _1018315)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018313), _1018317), hAPP(c_Finite__Set_Ofold1(_1018313, c_Groups_Otimes__class_Otimes(_1018313)), _1018315)))], (13735 ^ _779448) ^ [_1018583, _1018585] : [class_Groups_Oab__semigroup__mult(_1018583), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018583), _1018585)), -(_1018585 = c_Orderings_Obot__class_Obot(tc_fun(_1018583, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1018583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018583), 13748 ^ [_1018583, _1018585]), 13749 ^ [_1018583, _1018585])), hAPP(hAPP(c_Set_Oinsert(_1018583), 13748 ^ [_1018583, _1018585]), hAPP(hAPP(c_Set_Oinsert(_1018583), 13749 ^ [_1018583, _1018585]), c_Orderings_Obot__class_Obot(tc_fun(_1018583, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1018583), hAPP(c_Finite__Set_Ofold1(_1018583, c_Groups_Otimes__class_Otimes(_1018583)), _1018585)), _1018585)))], (13755 ^ _779448) ^ [_1019037, _1019039, _1019041] : [class_Lattices_Oab__semigroup__idem__mult(_1019037), hAPP(_1019039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019037), 13760 ^ [_1019037, _1019039, _1019041]), 13761 ^ [_1019037, _1019039, _1019041])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019037), hAPP(_1019039, 13760 ^ [_1019037, _1019039, _1019041])), hAPP(_1019039, 13761 ^ [_1019037, _1019039, _1019041])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019037), _1019041)), -(_1019041 = c_Orderings_Obot__class_Obot(tc_fun(_1019037, tc_HOL_Obool))), -(hAPP(_1019039, hAPP(c_Finite__Set_Ofold1(_1019037, c_Groups_Otimes__class_Otimes(_1019037)), _1019041)) = hAPP(c_Finite__Set_Ofold1(_1019037, c_Groups_Otimes__class_Otimes(_1019037)), hAPP(c_Set_Oimage(_1019037, _1019037, _1019039), _1019041)))], (13775 ^ _779448) ^ [_1019460, _1019462, _1019464, _1019466] : [class_Groups_Ocomm__monoid__mult(_1019460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019462), _1019464)), 13785 ^ _779448 : [(13786 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019462), 13784 ^ [_1019460, _1019462, _1019464, _1019466]), _1019464)))], (13788 ^ _779448) ^ [] : [hAPP(_1019466, 13784 ^ [_1019460, _1019462, _1019464, _1019466]) = c_Groups_Oone__class_Oone(_1019460)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019460, _1019462, c_Groups_Otimes__class_Otimes(_1019460)), _1019466), c_Groups_Oone__class_Oone(_1019460)), _1019464) = c_Groups_Oone__class_Oone(_1019460))], (13792 ^ _779448) ^ [_1019801, _1019803, _1019805, _1019807, _1019809, _1019811] : [class_Groups_Oab__semigroup__mult(_1019801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019803), _1019805)), 13802 ^ _779448 : [(13803 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019803), 13801 ^ [_1019801, _1019803, _1019805, _1019807, _1019809, _1019811]), _1019805)))], (13805 ^ _779448) ^ [] : [hAPP(_1019807, 13801 ^ [_1019801, _1019803, _1019805, _1019807, _1019809, _1019811]) = hAPP(_1019809, 13801 ^ [_1019801, _1019803, _1019805, _1019807, _1019809, _1019811])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019801, _1019803, c_Groups_Otimes__class_Otimes(_1019801)), _1019807), _1019811), _1019805) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019801, _1019803, c_Groups_Otimes__class_Otimes(_1019801)), _1019809), _1019811), _1019805))], (13809 ^ _779448) ^ [_1020206, _1020208, _1020210] : [class_Groups_Oab__semigroup__mult(_1020206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020206), _1020208)), -(hBOOL(hAPP(hAPP(c_member(_1020206), _1020210), _1020208))), -(hAPP(c_Finite__Set_Ofold1(_1020206, c_Groups_Otimes__class_Otimes(_1020206)), hAPP(hAPP(c_Set_Oinsert(_1020206), _1020210), _1020208)) = hAPP(hAPP(c_Finite__Set_Ofold(_1020206, _1020206, c_Groups_Otimes__class_Otimes(_1020206)), _1020210), _1020208))], (13823 ^ _779448) ^ [_1020430, _1020432] : [class_Int_Onumber__ring(_1020430), -(hAPP(c_Int_Onumber__class_Onumber__of(_1020430), c_Int_Osucc(_1020432)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1020430), c_Groups_Oone__class_Oone(_1020430)), hAPP(c_Int_Onumber__class_Onumber__of(_1020430), _1020432)))], (13829 ^ _779448) ^ [_1020549, _1020551, _1020553, _1020555, _1020557, _1020559] : [-(c_Nitpick_Opair__box_Opair__box__size(_1020549, _1020551, _1020553, _1020555, c_Nitpick_Opair__box_OPairBox(_1020549, _1020551, _1020557, _1020559)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1020553, _1020557)), hAPP(_1020555, _1020559))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13831 ^ _779448) ^ [_1020611, _1020613, _1020615, _1020617, _1020619, _1020621, _1020623] : [class_Groups_Oab__semigroup__mult(_1020611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020613), _1020615)), c_Fun_Oinj__on(_1020613, _1020617, _1020619, _1020615), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1020611, _1020617, c_Groups_Otimes__class_Otimes(_1020611)), _1020621), _1020623), hAPP(c_Set_Oimage(_1020613, _1020617, _1020619), _1020615)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1020611, _1020613, c_Groups_Otimes__class_Otimes(_1020611)), hAPP(c_Fun_Ocomp(_1020617, _1020611, _1020613, _1020621), _1020619)), _1020623), _1020615))], (13845 ^ _779448) ^ [_1020922] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1020922)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1020922)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13847 ^ _779448) ^ [_1020973, _1020975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1020973)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1020975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020973), _1020975)))], (13853 ^ _779448) ^ [_1021078, _1021080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021078), _1021080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021078)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021080))))], (13859 ^ _779448) ^ [_1021189, _1021191] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021189)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021191)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021189), _1021191)))], (13861 ^ _779448) ^ [_1021250, _1021252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021250)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021252))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021250), _1021252)))], (13867 ^ _779448) ^ [_1021355, _1021357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021355), _1021357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021355)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021357))))], (13873 ^ _779448) ^ [_1021466, _1021468] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1021468)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1021466), _1021468)))], (13875 ^ _779448) ^ [_1021524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1021524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021524)))], (13881 ^ _779448) ^ [_1021603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1021603)))], (13887 ^ _779448) ^ [_1021688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021688)), -(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)), _1021688))))], (13893 ^ _779448) ^ [_1021792, _1021794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021792), _1021794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1021792), _1021794)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13899 ^ _779448) ^ [_1021897, _1021899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1021897), _1021899)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021897), _1021899)))], (13905 ^ _779448) ^ [_1022008, _1022010, _1022012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022008), _1022010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022012), _1022008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022012), _1022010))))], (13915 ^ _779448) ^ [_1022189, _1022191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022189)), 13918 ^ _779448 : [(13919 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022189), _1022191) = c_Groups_Oone__class_Oone(tc_Int_Oint), 13922 ^ _779448 : [(13923 ^ _779448) ^ [] : [-(_1022189 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (13925 ^ _779448) ^ [] : [-(_1022191 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (13927 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022189), _1022191) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1022189 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1022191 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (13937 ^ _779448) ^ [_1022502] : [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)), _1022502)), _1022502)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022502), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13943 ^ _779448) ^ [_1022611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022611), 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)), _1022611)), _1022611)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13949 ^ _779448) ^ [_1022726] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022726), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1022726)], (13951 ^ _779448) ^ [_1022755] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1022755) = _1022755)], (13953 ^ _779448) ^ [] : [-(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))))], (13955 ^ _779448) ^ [_1022808] : [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)), _1022808)), _1022808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (13957 ^ _779448) ^ [_1022840] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022840) = _1022840)], (13959 ^ _779448) ^ [_1022866] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022866), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1022866)], (13961 ^ _779448) ^ [_1022895, _1022897, _1022899] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022897), _1022899)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022895), _1022897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022895), _1022899)))], (13963 ^ _779448) ^ [_1022952, _1022954, _1022956] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022952), _1022954)), _1022956) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022952), _1022956)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022954), _1022956)))], (13965 ^ _779448) ^ [_1023009, _1023011, _1023013] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023009), _1023011)), _1023013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023009), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023011), _1023013)))], (13967 ^ _779448) ^ [_1023060, _1023062] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023060), _1023062) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023062), _1023060))], (13969 ^ _779448) ^ [_1023097, _1023099, _1023101] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1023097), _1023099)), _1023101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023097), _1023101)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023099), _1023101)))], (13971 ^ _779448) ^ [_1023154, _1023156, _1023158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1023156), _1023158)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023154), _1023156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023154), _1023158)))], (13973 ^ _779448) ^ [_1023211] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023211), _1023211)))], (13975 ^ _779448) ^ [_1023235, _1023237] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023235), _1023237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023237), _1023235)))], (13981 ^ _779448) ^ [_1023281, _1023283, _1023285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023281), _1023283)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023283), _1023285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023281), _1023285)))], (13991 ^ _779448) ^ [_1023444, _1023446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023444), _1023446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023446), _1023444)), -(_1023444 = _1023446)], (14001 ^ _779448) ^ [_1023593, _1023595, _1023597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023593), _1023595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023597), _1023593)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023597), _1023595))))], (14007 ^ _779448) ^ [_1023716, _1023718, _1023720] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023716), _1023718)), _1023720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023718), _1023720)))], (14009 ^ _779448) ^ [_1023767, _1023769, _1023771] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023767), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023769), _1023771)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023767), _1023771)))], (14011 ^ _779448) ^ [_1023818, _1023820] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023818), _1023820) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023820), _1023818))], (14013 ^ _779448) ^ [_1023855] : [-(c_Int_Osucc(_1023855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023855), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14015 ^ _779448) ^ [_1023882, _1023884] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023882), _1023884))), -(_1023882 = _1023884), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023884), _1023882)))], (14035 ^ _779448) ^ [_1024068, _1024070] : [14036 ^ _779448 : [(14037 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024068), _1024070))], (14039 ^ _779448) ^ [] : [_1024068 = _1024070]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024070), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14025 ^ _779448) ^ [_1023950, _1023952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023952), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023950), _1023952))), -(_1023950 = _1023952)], (14043 ^ _779448) ^ [_1024217, _1024219, _1024221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024217), _1024219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024217), _1024221)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024219), _1024221))))], (14049 ^ _779448) ^ [_1024340, _1024342, _1024344, _1024346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024340), _1024342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024344), _1024346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024340), _1024344)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024342), _1024346))))], (14059 ^ _779448) ^ [_1024531, _1024533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024531), _1024533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024531), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1024533)))], (14065 ^ _779448) ^ [_1024655, _1024657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024655), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1024657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024655), _1024657)))], (14071 ^ _779448) ^ [_1024760, _1024762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024760), _1024762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1024760), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1024762)))], (14077 ^ _779448) ^ [_1024886, _1024888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1024888), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024886), _1024888)))], (14083 ^ _779448) ^ [_1024991, _1024993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024991), _1024993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1024993), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14089 ^ _779448) ^ [_1025117, _1025119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025119), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025117), _1025119)))], (14095 ^ _779448) ^ [_1025222, _1025224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025222), _1025224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025222), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025224), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (14101 ^ _779448) ^ [_1025348, _1025350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025348), _1025350)), 14104 ^ _779448 : [(14105 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025348), _1025350)))], (14107 ^ _779448) ^ [] : [_1025348 = _1025350]]], (14109 ^ _779448) ^ [_1025475, _1025477] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1025475), _1025477))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1025475), _1025477)), -(_1025475 = _1025477)], (14119 ^ _779448) ^ [_1025629, _1025631, _1025633, _1025635, _1025637, _1025639, _1025641, _1025643] : [hAPP(c_Fun_Ocomp(_1025629, _1025631, _1025633, _1025635), _1025637) = hAPP(c_Fun_Ocomp(_1025639, _1025631, _1025633, _1025641), _1025643), 14122 ^ _779448 : [(14123 ^ _779448) ^ [_1025744] : [-(hAPP(_1025635, hAPP(_1025637, _1025744)) = hAPP(_1025641, hAPP(_1025643, _1025744)))]]], (14125 ^ _779448) ^ [_1025783, _1025785, _1025787, _1025789, _1025791, _1025793, _1025795, _1025797, _1025799] : [hAPP(c_Fun_Ocomp(_1025783, _1025785, _1025787, _1025789), _1025791) = hAPP(c_Fun_Ocomp(_1025793, _1025785, _1025787, _1025795), _1025797), -(hAPP(_1025789, hAPP(_1025791, _1025799)) = hAPP(_1025795, hAPP(_1025797, _1025799)))], (14131 ^ _779448) ^ [_1025930, _1025932, _1025934, _1025936, _1025938, _1025940] : [-(hAPP(hAPP(c_Fun_Ocomp(_1025930, _1025932, _1025934, _1025936), _1025938), _1025940) = hAPP(_1025936, hAPP(_1025938, _1025940)))], (14133 ^ _779448) ^ [_1025980, _1025982, _1025984, _1025986, _1025988, _1025990, _1025992] : [-(hAPP(c_Fun_Ocomp(_1025980, _1025982, _1025984, _1025986), hAPP(c_Fun_Ocomp(_1025988, _1025980, _1025984, _1025990), _1025992)) = hAPP(c_Fun_Ocomp(_1025988, _1025982, _1025984, hAPP(c_Fun_Ocomp(_1025980, _1025982, _1025988, _1025986), _1025990)), _1025992))], (14135 ^ _779448) ^ [_1026047, _1026049, _1026051, _1026053, _1026055, _1026057] : [-(hAPP(hAPP(c_Fun_Ocomp(_1026047, _1026049, _1026051, _1026053), _1026055), _1026057) = hAPP(_1026053, hAPP(_1026055, _1026057)))], (14137 ^ _779448) ^ [_1026097, _1026099, _1026101, _1026103, _1026105, _1026107, _1026109, _1026111, _1026113, _1026115, _1026117] : [hAPP(_1026097, hAPP(_1026099, _1026101)) = hAPP(_1026103, hAPP(_1026105, _1026107)), -(hAPP(hAPP(c_Fun_Ocomp(_1026109, _1026111, _1026113, _1026097), _1026099), _1026101) = hAPP(hAPP(c_Fun_Ocomp(_1026115, _1026111, _1026117, _1026103), _1026105), _1026107))], (14143 ^ _779448) ^ [_1026287, _1026289, _1026291, _1026293, _1026295, _1026297] : [c_Nitpick_Opair__box_OPairBox(_1026287, _1026289, _1026291, _1026293) = c_Nitpick_Opair__box_OPairBox(_1026287, _1026289, _1026295, _1026297), 14146 ^ _779448 : [(14147 ^ _779448) ^ [] : [-(_1026291 = _1026295)], (14149 ^ _779448) ^ [] : [-(_1026293 = _1026297)]]], (14151 ^ _779448) ^ [_1026414, _1026416, _1026418, _1026420, _1026422, _1026424] : [-(c_Nitpick_Opair__box_OPairBox(_1026414, _1026416, _1026418, _1026420) = c_Nitpick_Opair__box_OPairBox(_1026414, _1026416, _1026422, _1026424)), _1026418 = _1026422, _1026420 = _1026424], (14161 ^ _779448) ^ [_1026581, _1026583, _1026585, _1026587, _1026589, _1026591] : [-(hAPP(c_Set_Oimage(_1026581, _1026583, hAPP(c_Fun_Ocomp(_1026585, _1026583, _1026581, _1026587), _1026589)), _1026591) = hAPP(c_Set_Oimage(_1026585, _1026583, _1026587), hAPP(c_Set_Oimage(_1026581, _1026585, _1026589), _1026591)))], (14163 ^ _779448) ^ [_1026643, _1026645, _1026647, _1026649, _1026651, _1026653] : [c_Fun_Oinj__on(_1026643, _1026645, hAPP(c_Fun_Ocomp(_1026647, _1026645, _1026643, _1026649), _1026651), _1026653), -(c_Fun_Oinj__on(_1026643, _1026647, _1026651, _1026653))], (14169 ^ _779448) ^ [_1026752, _1026754, _1026756, _1026758] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1026752, _1026754, _1026756), _1026758), c_Orderings_Obot__class_Obot(tc_fun(_1026752, tc_HOL_Obool))) = _1026758)], (14171 ^ _779448) ^ [_1026796, _1026798, _1026800, _1026802, _1026804, _1026806, _1026808] : [-(hAPP(c_Fun_Ocomp(_1026796, _1026798, _1026800, _1026802), c_Fun_Ofun__upd(_1026800, _1026796, _1026804, _1026806, _1026808)) = c_Fun_Ofun__upd(_1026800, _1026798, hAPP(c_Fun_Ocomp(_1026796, _1026798, _1026800, _1026802), _1026804), _1026806, hAPP(_1026802, _1026808)))], (14173 ^ _779448) ^ [_1026862, _1026864, _1026866, _1026868] : [c_Finite__Set_Ofun__left__comm__idem(_1026862, _1026864, _1026866), -(hAPP(c_Fun_Ocomp(_1026864, _1026864, _1026864, hAPP(_1026866, _1026868)), hAPP(_1026866, _1026868)) = hAPP(_1026866, _1026868))], (14179 ^ _779448) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14181 ^ _779448) ^ [_1026997, _1026999, _1027001, _1027003] : [-(hAPP(c_Finite__Set_Ofold__image(_1026997, _1026999, _1027001), _1027003) = c_Finite__Set_Ofold(_1026999, _1026997, hAPP(hAPP(c_COMBB(_1026997, tc_fun(_1026997, _1026997), _1026999), _1027001), _1027003)))], (14183 ^ _779448) ^ [_1027050, _1027052, _1027054, _1027056, _1027058, _1027060] : [c_Fun_Oinj__on(_1027050, _1027052, hAPP(c_Fun_Ocomp(_1027054, _1027052, _1027050, _1027056), _1027058), _1027060), -(c_Fun_Oinj__on(_1027054, _1027052, _1027056, hAPP(c_Set_Oimage(_1027050, _1027054, _1027058), _1027060)))], (14189 ^ _779448) ^ [_1027173, _1027175, _1027177, _1027179, _1027181, _1027183] : [c_Fun_Oinj__on(_1027173, _1027175, _1027177, _1027179), c_Fun_Oinj__on(_1027175, _1027181, _1027183, hAPP(c_Set_Oimage(_1027173, _1027175, _1027177), _1027179)), -(c_Fun_Oinj__on(_1027173, _1027181, hAPP(c_Fun_Ocomp(_1027175, _1027181, _1027173, _1027183), _1027177), _1027179))], (14199 ^ _779448) ^ [_1027360, _1027362, _1027364, _1027366, _1027368, _1027370] : [c_Fun_Oinj__on(_1027360, _1027362, _1027364, _1027366), 14202 ^ _779448 : [(14203 ^ _779448) ^ [] : [c_Fun_Oinj__on(_1027362, _1027368, _1027370, hAPP(c_Set_Oimage(_1027360, _1027362, _1027364), _1027366)), -(c_Fun_Oinj__on(_1027360, _1027368, hAPP(c_Fun_Ocomp(_1027362, _1027368, _1027360, _1027370), _1027364), _1027366))], (14209 ^ _779448) ^ [] : [c_Fun_Oinj__on(_1027360, _1027368, hAPP(c_Fun_Ocomp(_1027362, _1027368, _1027360, _1027370), _1027364), _1027366), -(c_Fun_Oinj__on(_1027362, _1027368, _1027370, hAPP(c_Set_Oimage(_1027360, _1027362, _1027364), _1027366)))]]], (14215 ^ _779448) ^ [_1027652, _1027654, _1027656, _1027658, _1027660] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1027652, _1027654, _1027656), _1027658), _1027660) = c_HOL_OThe(_1027654, c_Finite__Set_Ofold__graph(_1027652, _1027654, _1027656, _1027658, _1027660)))], (14217 ^ _779448) ^ [_1027702, _1027704, _1027706, _1027708, _1027710, _1027712] : [c_Finite__Set_Ofun__left__comm__idem(_1027702, _1027704, _1027706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027702), _1027708)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1027702, _1027704, _1027706), _1027710), hAPP(hAPP(c_Set_Oinsert(_1027702), _1027712), _1027708)) = hAPP(hAPP(c_Finite__Set_Ofold(_1027702, _1027704, _1027706), hAPP(hAPP(_1027706, _1027712), _1027710)), _1027708))], (14227 ^ _779448) ^ [_1027925, _1027927, _1027929, _1027931, _1027933, _1027935] : [c_Finite__Set_Ofun__left__comm__idem(_1027925, _1027927, _1027929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1027925), _1027931)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1027925, _1027927, _1027929), _1027933), hAPP(hAPP(c_Set_Oinsert(_1027925), _1027935), _1027931)) = hAPP(hAPP(_1027929, _1027935), hAPP(hAPP(c_Finite__Set_Ofold(_1027925, _1027927, _1027929), _1027933), _1027931)))], (14237 ^ _779448) ^ [_1028148, _1028150, _1028152, _1028154, _1028156] : [c_Finite__Set_Ofolding__one__idem(_1028148, _1028150, _1028152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028148), _1028154)), -(hAPP(_1028152, hAPP(hAPP(c_Set_Oinsert(_1028148), _1028156), _1028154)) = hAPP(hAPP(c_Finite__Set_Ofold(_1028148, _1028148, _1028150), _1028156), _1028154))], (14247 ^ _779448) ^ [_1028341, _1028343, _1028345, _1028347, _1028349, _1028351, _1028353] : [c_Fun_Oinj__on(_1028341, _1028343, _1028345, hAPP(c_Set_Oimage(_1028347, _1028341, _1028349), _1028351)), c_Fun_Oinj__on(_1028347, _1028341, _1028349, _1028351), hBOOL(hAPP(hAPP(c_member(_1028343), _1028353), hAPP(c_Set_Oimage(_1028341, _1028343, _1028345), hAPP(c_Set_Oimage(_1028347, _1028341, _1028349), _1028351)))), -(hAPP(c_Fun_Othe__inv__into(_1028347, _1028343, _1028351, hAPP(c_Fun_Ocomp(_1028341, _1028343, _1028347, _1028345), _1028349)), _1028353) = hAPP(hAPP(c_Fun_Ocomp(_1028341, _1028347, _1028343, c_Fun_Othe__inv__into(_1028347, _1028341, _1028351, _1028349)), c_Fun_Othe__inv__into(_1028341, _1028343, hAPP(c_Set_Oimage(_1028347, _1028341, _1028349), _1028351), _1028345)), _1028353))], (14261 ^ _779448) ^ [_1028704, _1028706, _1028708] : [class_Lattices_Oab__semigroup__idem__mult(_1028704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1028704), _1028706)), -(hAPP(c_Finite__Set_Ofold1(_1028704, c_Groups_Otimes__class_Otimes(_1028704)), hAPP(hAPP(c_Set_Oinsert(_1028704), _1028708), _1028706)) = hAPP(hAPP(c_Finite__Set_Ofold(_1028704, _1028704, c_Groups_Otimes__class_Otimes(_1028704)), _1028708), _1028706))], (14271 ^ _779448) ^ [_1028899, _1028901, _1028903] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1028899), _1028901)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1028899, tc_HOL_Obool)), _1028903), _1028901) = hAPP(hAPP(c_Finite__Set_Ofold(_1028899, tc_fun(_1028899, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1028899, tc_HOL_Obool), tc_fun(tc_fun(_1028899, tc_HOL_Obool), tc_fun(_1028899, tc_HOL_Obool)), _1028899), hAPP(c_COMBC(tc_fun(_1028899, tc_HOL_Obool), tc_fun(_1028899, tc_HOL_Obool), tc_fun(_1028899, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1028899, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1028899, tc_fun(_1028899, tc_HOL_Obool), tc_fun(_1028899, tc_HOL_Obool)), c_Set_Oinsert(_1028899)), c_Orderings_Obot__class_Obot(tc_fun(_1028899, tc_HOL_Obool))))), _1028903), _1028901))], (14277 ^ _779448) ^ [_1029166, _1029168, _1029170, _1029172, _1029174] : [c_Finite__Set_Ofolding__one(_1029166, _1029168, _1029170), hBOOL(hAPP(c_Finite__Set_Ofinite(_1029166), _1029172)), -(hBOOL(hAPP(hAPP(c_member(_1029166), _1029174), _1029172))), -(hAPP(_1029170, hAPP(hAPP(c_Set_Oinsert(_1029166), _1029174), _1029172)) = hAPP(hAPP(c_Finite__Set_Ofold(_1029166, _1029166, _1029168), _1029174), _1029172))], (14291 ^ _779448) ^ [_1029388, _1029390, _1029392, _1029394, _1029396, _1029398] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029388), _1029390)), _1029392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029394), _1029396)), _1029398), 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), _1029394), _1029396)), _1029398)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029392), _1029388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029398)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1029394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029394), _1029388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029396), _1029390)))], (14317 ^ _779448) ^ [_1029893, _1029895, _1029897, _1029899, _1029901] : [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), _1029893), _1029895)), _1029897)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1029893), _1029899)), _1029901))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029901), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029893), _1029901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1029893), _1029897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1029899), _1029895)))], (14335 ^ _779448) ^ [_1030248, _1030250, _1030252, _1030254, _1030256, _1030258] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030248), _1030250)), _1030252) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030254), _1030256)), _1030258), 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), _1030254), _1030256)), _1030258))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030258), _1030254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1030254), _1030248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1030250), _1030256)))], (14361 ^ _779448) ^ [_1030747, _1030749, _1030751, _1030753, _1030755] : [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), _1030747), _1030749)), _1030751)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1030747), _1030753)), _1030755))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1030751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030751), _1030747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030755), _1030747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1030749), _1030753)))], (14379 ^ _779448) ^ [_1031096, _1031098, _1031100] : [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), _1031096), _1031098)), _1031100)), 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)), _1031100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031098), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14393 ^ _779448) ^ [_1031335, _1031337, _1031339] : [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), _1031335), _1031337)), _1031339))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031339), _1031335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031337)))], (14407 ^ _779448) ^ [_1031568, _1031570, _1031572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031568)), _1031568 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1031570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031568), _1031572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031570), _1031568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1031572)))], (14421 ^ _779448) ^ [_1031797, _1031799, _1031801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031797)), _1031797 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1031799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1031797), _1031801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1031799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1031801), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (14435 ^ _779448) ^ [_1032026] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1032026) = _1032026)], (14437 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (14439 ^ _779448) ^ [_1032076, _1032078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032078)), -(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), _1032076), _1032078))))], (14449 ^ _779448) ^ [] : [-(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))))], (14451 ^ _779448) ^ [_1032247, _1032249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1032249)), -(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), _1032247), _1032249))))], (14461 ^ _779448) ^ [_1032400, _1032402, _1032404, _1032406] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1032400, _1032402)), c_Nitpick_Opair__box_OPairBox(_1032400, _1032402, _1032404, _1032406)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14463 ^ _779448) ^ [_1032442, _1032444, _1032446, _1032448, _1032450, _1032452] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1032442, _1032444, _1032446, _1032448, c_Nitpick_Opair__box_OPairBox(_1032442, _1032444, _1032450, _1032452)) = hAPP(hAPP(_1032448, _1032450), _1032452))], (14465 ^ _779448) ^ [_1032492, _1032494, _1032496, _1032498, _1032500, _1032502] : [-(c_Nitpick_Opair__box_Opair__box__case(_1032492, _1032494, _1032496, _1032498, c_Nitpick_Opair__box_OPairBox(_1032492, _1032494, _1032500, _1032502)) = hAPP(hAPP(_1032498, _1032500), _1032502))], (14467 ^ _779448) ^ [_1032542, _1032544, _1032546, _1032548, _1032550, _1032552] : [c_Finite__Set_Ofun__left__comm(_1032542, _1032544, _1032546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032542), _1032548)), hBOOL(hAPP(hAPP(c_member(_1032542), _1032550), _1032548)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1032542, _1032544, _1032546), _1032552), _1032548) = hAPP(hAPP(_1032546, _1032550), hAPP(hAPP(c_Finite__Set_Ofold(_1032542, _1032544, _1032546), _1032552), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032542, tc_HOL_Obool)), _1032548), hAPP(hAPP(c_Set_Oinsert(_1032542), _1032550), c_Orderings_Obot__class_Obot(tc_fun(_1032542, tc_HOL_Obool)))))))], (14481 ^ _779448) ^ [_1032871, _1032873, _1032875, _1032877, _1032879, _1032881] : [c_Finite__Set_Ofolding(_1032871, _1032873, _1032875, _1032877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1032871), _1032879)), hBOOL(hAPP(hAPP(c_member(_1032871), _1032881), _1032879)), -(hAPP(_1032877, _1032879) = hAPP(c_Fun_Ocomp(_1032873, _1032873, _1032873, hAPP(_1032877, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032871, tc_HOL_Obool)), _1032879), hAPP(hAPP(c_Set_Oinsert(_1032871), _1032881), c_Orderings_Obot__class_Obot(tc_fun(_1032871, tc_HOL_Obool)))))), hAPP(_1032875, _1032881)))], (14495 ^ _779448) ^ [_1033184, _1033186, _1033188, _1033190, _1033192, _1033194] : [c_Finite__Set_Ofun__left__comm(_1033184, _1033186, _1033188), -(hAPP(hAPP(_1033188, _1033190), hAPP(hAPP(_1033188, _1033192), _1033194)) = hAPP(hAPP(_1033188, _1033192), hAPP(hAPP(_1033188, _1033190), _1033194)))], (14501 ^ _779448) ^ [_1033319, _1033321, _1033323, _1033325, _1033327] : [c_Finite__Set_Ofun__left__comm(_1033319, _1033321, _1033323), -(c_Finite__Set_Ofun__left__comm(_1033325, _1033321, hAPP(hAPP(c_COMBB(_1033319, tc_fun(_1033321, _1033321), _1033325), _1033323), _1033327)))], (14507 ^ _779448) ^ [_1033432] : [class_Groups_Oab__semigroup__mult(_1033432), -(c_Finite__Set_Ofun__left__comm(_1033432, _1033432, c_Groups_Otimes__class_Otimes(_1033432)))], (14513 ^ _779448) ^ [_1033511, _1033513, _1033515, _1033517, _1033519, _1033521, _1033523, _1033525] : [c_Finite__Set_Ofolding(_1033511, _1033513, _1033515, _1033517), -(hAPP(c_Fun_Ocomp(_1033513, _1033513, _1033519, hAPP(_1033515, _1033521)), hAPP(c_Fun_Ocomp(_1033513, _1033513, _1033519, hAPP(_1033515, _1033523)), _1033525)) = hAPP(c_Fun_Ocomp(_1033513, _1033513, _1033519, hAPP(_1033515, _1033523)), hAPP(c_Fun_Ocomp(_1033513, _1033513, _1033519, hAPP(_1033515, _1033521)), _1033525)))], (14519 ^ _779448) ^ [_1033692, _1033694, _1033696, _1033698, _1033700, _1033702] : [c_Finite__Set_Ofolding(_1033692, _1033694, _1033696, _1033698), -(hAPP(c_Fun_Ocomp(_1033694, _1033694, _1033694, hAPP(_1033696, _1033700)), hAPP(_1033696, _1033702)) = hAPP(c_Fun_Ocomp(_1033694, _1033694, _1033694, hAPP(_1033696, _1033702)), hAPP(_1033696, _1033700)))], (14525 ^ _779448) ^ [_1033837, _1033839, _1033841, _1033843, _1033845, _1033847, _1033849, _1033851, _1033853, _1033855, _1033857] : [c_Finite__Set_Ofolding(_1033837, _1033839, _1033841, _1033843), -(hAPP(c_Fun_Ocomp(_1033845, _1033847, _1033849, _1033851), hAPP(c_Fun_Ocomp(_1033853, _1033845, _1033849, _1033855), _1033857)) = hAPP(c_Fun_Ocomp(_1033853, _1033847, _1033849, hAPP(c_Fun_Ocomp(_1033845, _1033847, _1033853, _1033851), _1033855)), _1033857))], (14531 ^ _779448) ^ [_1034000, _1034002, _1034004, _1034006, _1034008] : [c_Finite__Set_Ofun__left__comm(_1034000, _1034002, _1034004), -(hAPP(c_Fun_Ocomp(_1034002, _1034002, _1034002, hAPP(_1034004, _1034006)), hAPP(_1034004, _1034008)) = hAPP(c_Fun_Ocomp(_1034002, _1034002, _1034002, hAPP(_1034004, _1034008)), hAPP(_1034004, _1034006)))], (14537 ^ _779448) ^ [_1034141, _1034143, _1034145, _1034147, _1034149, _1034151, _1034153] : [c_Finite__Set_Ofun__left__comm(_1034141, _1034143, _1034145), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1034141, _1034143, _1034145, _1034147, _1034149), _1034151)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1034141, _1034143, _1034145, _1034147, _1034149), _1034153)), -(_1034153 = _1034151)], (14551 ^ _779448) ^ [_1034386, _1034388, _1034390, _1034392, _1034394, _1034396] : [c_Finite__Set_Ofolding(_1034386, _1034388, _1034390, _1034392), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034386), _1034394)), -(hAPP(c_Fun_Ocomp(_1034388, _1034388, _1034388, hAPP(_1034390, _1034396)), hAPP(_1034392, _1034394)) = hAPP(c_Fun_Ocomp(_1034388, _1034388, _1034388, hAPP(_1034392, _1034394)), hAPP(_1034390, _1034396)))], (14561 ^ _779448) ^ [_1034599, _1034601, _1034603, _1034605, _1034607, _1034609, _1034611, _1034613] : [c_Finite__Set_Ofolding(_1034599, _1034601, _1034603, _1034605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034599), _1034607)), -(hAPP(c_Fun_Ocomp(_1034601, _1034601, _1034609, hAPP(_1034603, _1034611)), hAPP(c_Fun_Ocomp(_1034601, _1034601, _1034609, hAPP(_1034605, _1034607)), _1034613)) = hAPP(c_Fun_Ocomp(_1034601, _1034601, _1034609, hAPP(_1034605, _1034607)), hAPP(c_Fun_Ocomp(_1034601, _1034601, _1034609, hAPP(_1034603, _1034611)), _1034613)))], (14571 ^ _779448) ^ [_1034852, _1034854, _1034856, _1034858, _1034860, _1034862] : [c_Finite__Set_Ofolding(_1034852, _1034854, _1034856, _1034858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034852), _1034860)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034852), _1034862)), -(hAPP(c_Fun_Ocomp(_1034854, _1034854, _1034854, hAPP(_1034858, _1034862)), hAPP(_1034858, _1034860)) = hAPP(c_Fun_Ocomp(_1034854, _1034854, _1034854, hAPP(_1034858, _1034860)), hAPP(_1034858, _1034862)))], (14585 ^ _779448) ^ [_1035133, _1035135, _1035137, _1035139, _1035141, _1035143, _1035145, _1035147] : [c_Finite__Set_Ofolding(_1035133, _1035135, _1035137, _1035139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035133), _1035141)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035133), _1035143)), -(hAPP(c_Fun_Ocomp(_1035135, _1035135, _1035145, hAPP(_1035139, _1035143)), hAPP(c_Fun_Ocomp(_1035135, _1035135, _1035145, hAPP(_1035139, _1035141)), _1035147)) = hAPP(c_Fun_Ocomp(_1035135, _1035135, _1035145, hAPP(_1035139, _1035141)), hAPP(c_Fun_Ocomp(_1035135, _1035135, _1035145, hAPP(_1035139, _1035143)), _1035147)))], (14599 ^ _779448) ^ [_1035458, _1035460, _1035462, _1035464, _1035466, _1035468] : [c_Finite__Set_Ofolding(_1035458, _1035460, _1035462, _1035464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035458), _1035466)), -(hAPP(hAPP(_1035464, _1035466), _1035468) = hAPP(hAPP(c_Finite__Set_Ofold(_1035458, _1035460, _1035462), _1035468), _1035466))], (14609 ^ _779448) ^ [_1035647, _1035649, _1035651, _1035653, _1035655, _1035657] : [c_Finite__Set_Ofun__left__comm(_1035647, _1035649, _1035651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1035647), _1035653)), -(hAPP(hAPP(_1035651, _1035655), hAPP(hAPP(c_Finite__Set_Ofold(_1035647, _1035649, _1035651), _1035657), _1035653)) = hAPP(hAPP(c_Finite__Set_Ofold(_1035647, _1035649, _1035651), hAPP(hAPP(_1035651, _1035655), _1035657)), _1035653))], (14619 ^ _779448) ^ [_1035866, _1035868, _1035870, _1035872, _1035874, _1035876] : [c_Finite__Set_Ofun__left__comm(_1035866, _1035868, _1035870), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1035866, _1035868, _1035870, _1035872, _1035874), _1035876)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1035866, _1035868, _1035870), _1035872), _1035874) = _1035876)], (14629 ^ _779448) ^ [_1036049, _1036051, _1036053, _1036055, _1036057] : [c_Finite__Set_Ofun__left__comm(_1036049, _1036051, _1036053), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036049), _1036055)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1036049, _1036051, _1036053, _1036057, _1036055), hAPP(hAPP(c_Finite__Set_Ofold(_1036049, _1036051, _1036053), _1036057), _1036055))))], (14639 ^ _779448) ^ [_1036236, _1036238, _1036240, _1036242, _1036244, _1036246] : [c_Finite__Set_Ofolding(_1036236, _1036238, _1036240, _1036242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036236), _1036244)), -(hBOOL(hAPP(hAPP(c_member(_1036236), _1036246), _1036244))), -(hAPP(_1036242, hAPP(hAPP(c_Set_Oinsert(_1036236), _1036246), _1036244)) = hAPP(c_Fun_Ocomp(_1036238, _1036238, _1036238, hAPP(_1036242, _1036244)), hAPP(_1036240, _1036246)))], (14653 ^ _779448) ^ [_1036472, _1036474, _1036476, _1036478, _1036480, _1036482] : [c_Finite__Set_Ofun__left__comm(_1036472, _1036474, _1036476), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036472), _1036478)), -(hBOOL(hAPP(hAPP(c_member(_1036472), _1036480), _1036478))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1036472, _1036474, _1036476), _1036482), hAPP(hAPP(c_Set_Oinsert(_1036472), _1036480), _1036478)) = hAPP(hAPP(c_Finite__Set_Ofold(_1036472, _1036474, _1036476), hAPP(hAPP(_1036476, _1036480), _1036482)), _1036478))], (14667 ^ _779448) ^ [_1036724, _1036726, _1036728, _1036730, _1036732, _1036734] : [c_Finite__Set_Ofun__left__comm(_1036724, _1036726, _1036728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036724), _1036730)), -(hBOOL(hAPP(hAPP(c_member(_1036724), _1036732), _1036730))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1036724, _1036726, _1036728), _1036734), hAPP(hAPP(c_Set_Oinsert(_1036724), _1036732), _1036730)) = hAPP(hAPP(_1036728, _1036732), hAPP(hAPP(c_Finite__Set_Ofold(_1036724, _1036726, _1036728), _1036734), _1036730)))], (14681 ^ _779448) ^ [] : [-(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))))], (14683 ^ _779448) ^ [_1036994, _1036996, _1036998, _1037000, _1037002, _1037004] : [c_Finite__Set_Ofolding(_1036994, _1036996, _1036998, _1037000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036994), _1037002)), -(hAPP(_1037000, hAPP(hAPP(c_Set_Oinsert(_1036994), _1037004), _1037002)) = hAPP(c_Fun_Ocomp(_1036996, _1036996, _1036996, hAPP(_1037000, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036994, tc_HOL_Obool)), _1037002), hAPP(hAPP(c_Set_Oinsert(_1036994), _1037004), c_Orderings_Obot__class_Obot(tc_fun(_1036994, tc_HOL_Obool)))))), hAPP(_1036998, _1037004)))], (14693 ^ _779448) ^ [_1037249, _1037251, _1037253, _1037255, _1037257, _1037259] : [c_Finite__Set_Ofun__left__comm(_1037249, _1037251, _1037253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037249), _1037255)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1037249, _1037251, _1037253), _1037257), hAPP(hAPP(c_Set_Oinsert(_1037249), _1037259), _1037255)) = hAPP(hAPP(_1037253, _1037259), hAPP(hAPP(c_Finite__Set_Ofold(_1037249, _1037251, _1037253), _1037257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037249, tc_HOL_Obool)), _1037255), hAPP(hAPP(c_Set_Oinsert(_1037249), _1037259), c_Orderings_Obot__class_Obot(tc_fun(_1037249, tc_HOL_Obool)))))))], (14703 ^ _779448) ^ [_1037520, _1037522, _1037524, _1037526, _1037528, _1037530, _1037532] : [c_Finite__Set_Ofun__left__comm(_1037520, _1037522, _1037524), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1037520, _1037522, _1037524, _1037526, _1037528), _1037530)), hBOOL(hAPP(hAPP(c_member(_1037520), _1037532), _1037528)), 14715 ^ _779448 : [(14716 ^ _779448) ^ [] : [-(_1037530 = hAPP(hAPP(_1037524, _1037532), 14714 ^ [_1037520, _1037522, _1037524, _1037526, _1037528, _1037530, _1037532]))], (14718 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1037520, _1037522, _1037524, _1037526, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1037520, tc_HOL_Obool)), _1037528), hAPP(hAPP(c_Set_Oinsert(_1037520), _1037532), c_Orderings_Obot__class_Obot(tc_fun(_1037520, tc_HOL_Obool))))), 14714 ^ [_1037520, _1037522, _1037524, _1037526, _1037528, _1037530, _1037532])))]]], (14720 ^ _779448) ^ [_1037904, _1037906, _1037908, _1037910, _1037912, _1037914, _1037916, _1037918] : [c_Finite__Set_Ofolding__image(_1037904, _1037906, _1037908, _1037910, _1037912), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037906), _1037914)), c_Fun_Oinj__on(_1037906, _1037906, _1037916, _1037914), -(hAPP(hAPP(_1037912, _1037918), hAPP(c_Set_Oimage(_1037906, _1037906, _1037916), _1037914)) = hAPP(hAPP(_1037912, hAPP(c_Fun_Ocomp(_1037906, _1037904, _1037906, _1037918), _1037916)), _1037914))], (14734 ^ _779448) ^ [_1038193] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1038193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1038193)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (14736 ^ _779448) ^ [_1038240, _1038242] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038240))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038240)), _1038242)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1038242))], (14742 ^ _779448) ^ [_1038351, _1038353] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038351)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038351)), _1038353)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1038351))), _1038353))], (14748 ^ _779448) ^ [_1038426, _1038428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038426), _1038428)), -(c_Nat__Transfer_Otsub(_1038428, _1038426) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1038428), _1038426))], (14754 ^ _779448) ^ [_1038525, _1038527] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038525), _1038527))), -(c_Nat__Transfer_Otsub(_1038527, _1038525) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14760 ^ _779448) ^ [_1038571, _1038573, _1038575, _1038577, _1038579, _1038581] : [c_Finite__Set_Ofolding__idem(_1038571, _1038573, _1038575, _1038577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038571), _1038579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038571, tc_HOL_Obool)), _1038581), _1038579)), -(hAPP(c_Fun_Ocomp(_1038573, _1038573, _1038573, hAPP(_1038577, _1038579)), hAPP(_1038577, _1038581)) = hAPP(_1038577, _1038579))], (14774 ^ _779448) ^ [_1038842, _1038844, _1038846, _1038848, _1038850, _1038852] : [c_Finite__Set_Ofolding__idem(_1038842, _1038844, _1038846, _1038848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038842), _1038850)), -(hAPP(_1038848, hAPP(hAPP(c_Set_Oinsert(_1038842), _1038852), _1038850)) = hAPP(c_Fun_Ocomp(_1038844, _1038844, _1038844, hAPP(_1038848, _1038850)), hAPP(_1038846, _1038852)))], (14784 ^ _779448) ^ [_1039049, _1039051, _1039053, _1039055, _1039057, _1039059] : [c_Finite__Set_Ofolding__idem(_1039049, _1039051, _1039053, _1039055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039049), _1039057)), hBOOL(hAPP(hAPP(c_member(_1039049), _1039059), _1039057)), -(hAPP(c_Fun_Ocomp(_1039051, _1039051, _1039051, hAPP(_1039055, _1039057)), hAPP(_1039053, _1039059)) = hAPP(_1039055, _1039057))], (14798 ^ _779448) ^ [_1039314] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1039314) = _1039314)], (14800 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14802 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14804 ^ _779448) ^ [_1039394] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1039394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039394)))], (14810 ^ _779448) ^ [_1039428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1039428)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1039428))], (14816 ^ _779448) ^ [_1039526] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1039526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1039526), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14822 ^ _779448) ^ [_1039611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1039611), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1039611)))], (14828 ^ _779448) ^ [_1039702, _1039704, _1039706, _1039708, _1039710] : [c_Finite__Set_Ofolding__idem(_1039702, _1039704, _1039706, _1039708), -(hAPP(c_Fun_Ocomp(_1039704, _1039704, _1039704, hAPP(_1039706, _1039710)), hAPP(_1039706, _1039710)) = hAPP(_1039706, _1039710))], (14834 ^ _779448) ^ [_1039823, _1039825, _1039827, _1039829, _1039831, _1039833, _1039835] : [c_Finite__Set_Ofolding__idem(_1039823, _1039825, _1039827, _1039829), -(hAPP(c_Fun_Ocomp(_1039825, _1039825, _1039831, hAPP(_1039827, _1039833)), hAPP(c_Fun_Ocomp(_1039825, _1039825, _1039831, hAPP(_1039827, _1039833)), _1039835)) = hAPP(c_Fun_Ocomp(_1039825, _1039825, _1039831, hAPP(_1039827, _1039833)), _1039835))], (14840 ^ _779448) ^ [_1039980, _1039982, _1039984, _1039986, _1039988, _1039990, _1039992, _1039994] : [c_Finite__Set_Ofolding__image(_1039980, _1039982, _1039984, _1039986, _1039988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039982), _1039990)), -(hAPP(hAPP(_1039988, hAPP(hAPP(c_COMBS(_1039982, _1039980, _1039980), hAPP(hAPP(c_COMBB(_1039980, tc_fun(_1039980, _1039980), _1039982), _1039984), _1039992)), _1039994)), _1039990) = hAPP(hAPP(_1039984, hAPP(hAPP(_1039988, _1039992), _1039990)), hAPP(hAPP(_1039988, _1039994), _1039990)))], (14850 ^ _779448) ^ [] : [-(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))], (14852 ^ _779448) ^ [_1040259] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040259))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040259) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14858 ^ _779448) ^ [_1040350, _1040352, _1040354, _1040356, _1040358, _1040360, _1040362] : [c_Finite__Set_Ofolding__image(_1040350, _1040352, _1040354, _1040356, _1040358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040352), _1040360)), -(hAPP(hAPP(_1040358, _1040362), _1040360) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1040350, _1040352, _1040354), _1040362), _1040356), _1040360))], (14894 ^ _779448) ^ [_1040951, _1040953] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040951) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040953)), 14897 ^ _779448 : [(14898 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040951))))], (14900 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040953)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 14901 ^ _779448 : [(14902 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040951)))], (14904 ^ _779448) ^ [] : [14905 ^ _779448 : [(14906 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040953))))], (14908 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040951) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 14909 ^ _779448 : [(14910 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040953)))], (14912 ^ _779448) ^ [] : [_1040951 = _1040953]]]]], (14868 ^ _779448) ^ [_1040566, _1040568] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040566) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040568), 14871 ^ _779448 : [(14872 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040568)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14878 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040566)))), 14881 ^ _779448 : [(14882 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040568))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040566) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14888 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040568)))), -(_1040566 = _1040568)]]]]], (14916 ^ _779448) ^ [_1041364, _1041366, _1041368] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041364))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041364)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041366)), _1041368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041366)), _1041368))], (14922 ^ _779448) ^ [_1041502, _1041504, _1041506] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041502)))), 14925 ^ _779448 : [(14926 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041504))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041504)), _1041506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041502)), _1041506))], (14932 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041504)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041504)), _1041506)) = 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), _1041502), _1041504))), _1041506))]]], (14938 ^ _779448) ^ [_1041827, _1041829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1041829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1041827, _1041829))))], (14948 ^ _779448) ^ [_1041974, _1041976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1041974), _1041976)), -(c_Nat__Transfer_Otsub(_1041976, _1041974) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1041976), _1041974))], (14954 ^ _779448) ^ [_1042085] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042085))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042085)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14960 ^ _779448) ^ [_1042176] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042176)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042176)))], (14966 ^ _779448) ^ [_1042234] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042234))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1042234)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14972 ^ _779448) ^ [_1042323] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042323)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1042323)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042323)), 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)))))], (14978 ^ _779448) ^ [_1042378, _1042380] : [class_Int_Onumber__ring(_1042378), 14981 ^ _779448 : [(14982 ^ _779448) ^ [] : [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), _1042380))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1042378), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042380)) = hAPP(c_Int_Onumber__class_Onumber__of(_1042378), _1042380))], (14988 ^ _779448) ^ [] : [-(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), _1042380)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1042378), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042380)) = c_Groups_Ozero__class_Ozero(_1042378))]]], (14994 ^ _779448) ^ [_1042624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042624), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042624)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15000 ^ _779448) ^ [_1042721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042721), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042721)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042721)))], (15006 ^ _779448) ^ [_1042782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042782), 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), _1042782)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15012 ^ _779448) ^ [_1042873] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042873), 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), _1042873)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042873)))], (15018 ^ _779448) ^ [_1042925, _1042927, _1042929, _1042931, _1042933, _1042935, _1042937] : [c_Finite__Set_Ofun__left__comm(_1042925, _1042927, _1042929), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042925, _1042927, _1042929, _1042931, hAPP(hAPP(c_Set_Oinsert(_1042925), _1042933), _1042935)), _1042937)), -(hBOOL(hAPP(hAPP(c_member(_1042925), _1042933), _1042935))), 15030 ^ _779448 : [(15031 ^ _779448) ^ [] : [-(_1042937 = hAPP(hAPP(_1042929, _1042933), 15029 ^ [_1042925, _1042927, _1042929, _1042931, _1042933, _1042935, _1042937]))], (15033 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042925, _1042927, _1042929, _1042931, _1042935), 15029 ^ [_1042925, _1042927, _1042929, _1042931, _1042933, _1042935, _1042937])))]]], (15035 ^ _779448) ^ [_1043251, _1043253] : [class_Int_Onumber__ring(_1043251), 15038 ^ _779448 : [(15039 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043253))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1043251), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043253)) = c_Groups_Ozero__class_Ozero(_1043251))], (15045 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1043253)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1043251), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043253)) = hAPP(c_Int_Onumber__class_Onumber__of(_1043251), _1043253))]]], (15051 ^ _779448) ^ [_1043503] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1043503)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043503) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15057 ^ _779448) ^ [_1043594] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043594) = 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(_1043594)))))], (15063 ^ _779448) ^ [_1043703, _1043705, _1043707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043703), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043703)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043705)), _1043707)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15069 ^ _779448) ^ [_1043822, _1043824, _1043826] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1043822), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043822)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043824)), _1043826)) = 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), _1043822), _1043824))), _1043826))], (15075 ^ _779448) ^ [_1043915, _1043917] : [c_Int_OBit1(_1043915) = c_Int_OBit1(_1043917), -(_1043915 = _1043917)], (15081 ^ _779448) ^ [_1043996, _1043998] : [_1043996 = _1043998, -(c_Int_OBit1(_1043996) = c_Int_OBit1(_1043998))], (15087 ^ _779448) ^ [_1044092] : [c_Int_OBit1(_1044092) = c_Int_OPls], (15089 ^ _779448) ^ [_1044126] : [c_Int_OPls = c_Int_OBit1(_1044126)], (15091 ^ _779448) ^ [_1044151, _1044153, _1044155] : [class_Nat_Osemiring__char__0(_1044151), 15094 ^ _779448 : [(15095 ^ _779448) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1044151), _1044153) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1044151), _1044155), -(_1044153 = _1044155)], (15101 ^ _779448) ^ [] : [_1044153 = _1044155, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1044151), _1044153) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1044151), _1044155))]]], (15107 ^ _779448) ^ [_1044404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1044404)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1044404), c_Int_OPls)))], (15113 ^ _779448) ^ [_1044499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1044499), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1044499)), c_Int_OPls)))], (15119 ^ _779448) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (15121 ^ _779448) ^ [_1044630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1044630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1044630)))], (15127 ^ _779448) ^ [_1044713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1044713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1044713))))], (15133 ^ _779448) ^ [] : [-(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)))))], (15135 ^ _779448) ^ [_1044820, _1044822] : [class_Int_Onumber__ring(_1044820), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044820), hAPP(c_Int_Onumber__class_Onumber__of(_1044820), c_Int_OBit1(c_Int_OPls))), _1044822) = _1044822)], (15141 ^ _779448) ^ [_1044921, _1044923] : [class_Int_Onumber__ring(_1044921), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044921), _1044923), hAPP(c_Int_Onumber__class_Onumber__of(_1044921), c_Int_OBit1(c_Int_OPls))) = _1044923)], (15147 ^ _779448) ^ [_1045022] : [class_Int_Onumber__ring(_1045022), -(hAPP(c_Int_Onumber__class_Onumber__of(_1045022), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1045022))], (15153 ^ _779448) ^ [_1045109] : [class_Int_Onumber__ring(_1045109), -(c_Groups_Oone__class_Oone(_1045109) = hAPP(c_Int_Onumber__class_Onumber__of(_1045109), c_Int_OBit1(c_Int_OPls)))], (15159 ^ _779448) ^ [_1045208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045208)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045208), c_Int_OPls)))], (15165 ^ _779448) ^ [_1045303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1045303), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045303)), c_Int_OPls)))], (15171 ^ _779448) ^ [_1045416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1045416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1045416)))], (15177 ^ _779448) ^ [_1045499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1045499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1045499))))], (15183 ^ _779448) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (15185 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15187 ^ _779448) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (15189 ^ _779448) ^ [_1045657, _1045659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045657)), c_Int_OBit1(_1045659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1045657), _1045659)))], (15195 ^ _779448) ^ [_1045758, _1045760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1045758), _1045760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045758)), c_Int_OBit1(_1045760))))], (15201 ^ _779448) ^ [_1045880, _1045882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045880)), c_Int_OBit1(_1045882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1045880), _1045882)))], (15207 ^ _779448) ^ [_1045981, _1045983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1045981), _1045983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1045981)), c_Int_OBit1(_1045983))))], (15213 ^ _779448) ^ [_1046103, _1046105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1046103)), c_Int_OBit1(_1046105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1046103), _1046105)))], (15219 ^ _779448) ^ [_1046204, _1046206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1046204), _1046206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1046204)), c_Int_OBit1(_1046206))))], (15225 ^ _779448) ^ [_1046326, _1046328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1046326)), c_Int_OBit1(_1046328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1046326), _1046328)))], (15231 ^ _779448) ^ [_1046427, _1046429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1046427), _1046429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1046427)), c_Int_OBit1(_1046429))))], (15237 ^ _779448) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15239 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (15241 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (15243 ^ _779448) ^ [_1046594] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1046594), c_Int_OPls) = _1046594)], (15245 ^ _779448) ^ [_1046623] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1046623) = _1046623)], (15247 ^ _779448) ^ [_1046649] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1046649) = c_Int_OPls)], (15249 ^ _779448) ^ [_1046684] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1046684)))], (15251 ^ _779448) ^ [_1046712] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046712), c_Int_OPls) = _1046712)], (15253 ^ _779448) ^ [_1046753] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1046753)), -(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)), _1046753))))], (15259 ^ _779448) ^ [_1046838] : [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)), _1046838))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1046838)))], (15265 ^ _779448) ^ [] : [-(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)))], (15267 ^ _779448) ^ [] : [-(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)))))], (15269 ^ _779448) ^ [] : [-(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))))))], (15271 ^ _779448) ^ [_1046983] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1046983))) = 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)))), _1046983))], (15273 ^ _779448) ^ [_1047018] : [-(c_Int_Osucc(c_Int_Opred(_1047018)) = _1047018)], (15275 ^ _779448) ^ [_1047045, _1047047] : [class_Int_Onumber__ring(_1047045), class_Rings_Olinordered__idom(_1047045), 15282 ^ _779448 : [(15283 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047045), c_Groups_Oone__class_Oone(_1047045)), hAPP(c_Int_Onumber__class_Onumber__of(_1047045), _1047047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1047047)))], (15289 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1047047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047045), c_Groups_Oone__class_Oone(_1047045)), hAPP(c_Int_Onumber__class_Onumber__of(_1047045), _1047047))))]]], (15295 ^ _779448) ^ [_1047350, _1047352] : [class_Int_Onumber__ring(_1047350), class_Rings_Olinordered__idom(_1047350), 15302 ^ _779448 : [(15303 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047350), hAPP(c_Int_Onumber__class_Onumber__of(_1047350), _1047352)), c_Groups_Oone__class_Oone(_1047350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047352), c_Int_OBit1(c_Int_OPls))))], (15309 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047352), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047350), hAPP(c_Int_Onumber__class_Onumber__of(_1047350), _1047352)), c_Groups_Oone__class_Oone(_1047350))))]]], (15315 ^ _779448) ^ [_1047664, _1047666] : [class_Int_Onumber__ring(_1047664), class_Rings_Olinordered__idom(_1047664), 15322 ^ _779448 : [(15323 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047664), c_Groups_Oone__class_Oone(_1047664)), hAPP(c_Int_Onumber__class_Onumber__of(_1047664), _1047666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1047666)))], (15329 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1047666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047664), c_Groups_Oone__class_Oone(_1047664)), hAPP(c_Int_Onumber__class_Onumber__of(_1047664), _1047666))))]]], (15335 ^ _779448) ^ [_1047969, _1047971] : [class_Int_Onumber__ring(_1047969), class_Rings_Olinordered__idom(_1047969), 15342 ^ _779448 : [(15343 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047969), hAPP(c_Int_Onumber__class_Onumber__of(_1047969), _1047971)), c_Groups_Oone__class_Oone(_1047969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047971), c_Int_OBit1(c_Int_OPls))))], (15349 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1047971), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047969), hAPP(c_Int_Onumber__class_Onumber__of(_1047969), _1047971)), c_Groups_Oone__class_Oone(_1047969))))]]], (15355 ^ _779448) ^ [_1048283, _1048285] : [class_Int_Onumber__ring(_1048283), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048283), c_Groups_Oone__class_Oone(_1048283)), hAPP(c_Int_Onumber__class_Onumber__of(_1048283), _1048285)) = hAPP(c_Int_Onumber__class_Onumber__of(_1048283), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1048285)))], (15361 ^ _779448) ^ [_1048404, _1048406] : [class_Int_Onumber__ring(_1048404), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1048404), hAPP(c_Int_Onumber__class_Onumber__of(_1048404), _1048406)), c_Groups_Oone__class_Oone(_1048404)) = hAPP(c_Int_Onumber__class_Onumber__of(_1048404), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1048406), c_Int_OBit1(c_Int_OPls))))], (15367 ^ _779448) ^ [_1048531, _1048533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1048531)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1048533)), _1048531) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048533), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1048531), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (15373 ^ _779448) ^ [] : [-(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)))], (15375 ^ _779448) ^ [] : [-(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))], (15377 ^ _779448) ^ [_1048702] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1048702) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1048702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15383 ^ _779448) ^ [_1048779] : [_1048779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1048779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15389 ^ _779448) ^ [_1048862] : [-(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), _1048862))))], (15402 ^ _779448) ^ [_1049072] : [15403 ^ _779448 : [(15404 ^ _779448) ^ [_1049129] : [hBOOL(hAPP(_1049072, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049129)))]], 15406 ^ _779448 : [(15407 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15405 ^ [_1049072])))], (15409 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1049072, 15405 ^ [_1049072])))]]], (15391 ^ _779448) ^ [_1048902] : [-(hBOOL(hAPP(_1048902, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 15398 ^ [_1048902])))), 15392 ^ _779448 : [(15393 ^ _779448) ^ [_1048954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048954)), hBOOL(hAPP(_1048902, _1048954))]]], (15411 ^ _779448) ^ [_1049233] : [15413 ^ _779448 : [(15414 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15412 ^ [_1049233])))], (15416 ^ _779448) ^ [] : [hBOOL(hAPP(_1049233, 15412 ^ [_1049233]))]], 15417 ^ _779448 : [(15418 ^ _779448) ^ [_1049360] : [-(hBOOL(hAPP(_1049233, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049360))))]]], (15420 ^ _779448) ^ [_1049390] : [hBOOL(hAPP(_1049390, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 15421 ^ [_1049390]))), 15424 ^ _779448 : [(15425 ^ _779448) ^ [_1049490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049490)), -(hBOOL(hAPP(_1049390, _1049490)))]]], (15431 ^ _779448) ^ [_1049581] : [-(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), _1049581))))], (15433 ^ _779448) ^ [_1049618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049618)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15435 ^ _779448) ^ [_1049664, _1049666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049664)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049666))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049664), _1049666)))], (15441 ^ _779448) ^ [_1049769, _1049771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049769), _1049771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049769)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049771))))], (15447 ^ _779448) ^ [_1049895, _1049897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049895)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1049897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049895), _1049897)))], (15453 ^ _779448) ^ [_1050000, _1050002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1050000), _1050002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050000)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050002))))], (15459 ^ _779448) ^ [_1050123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050123)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050123), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15465 ^ _779448) ^ [_1050218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050218), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050218)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15471 ^ _779448) ^ [_1050334, _1050336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050334)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050334), _1050336)))], (15477 ^ _779448) ^ [_1050439, _1050441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050439), _1050441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050439)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050441))))], (15483 ^ _779448) ^ [_1050565, _1050567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050565)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050565), _1050567)))], (15489 ^ _779448) ^ [_1050670, _1050672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050670), _1050672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050670)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050672))))], (15495 ^ _779448) ^ [_1050781, _1050783] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050781)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050783)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050781), _1050783)))], (15497 ^ _779448) ^ [_1050827, _1050829] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050827)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050829)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050827), _1050829)))], (15499 ^ _779448) ^ [_1050873, _1050875, _1050877] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050873)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1050875)), _1050877)) = 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), _1050873), _1050875))), _1050877))], (15501 ^ _779448) ^ [_1050948, _1050950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1050948), _1050950)), -(_1050950 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1050948), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 15504 ^ [_1050948, _1050950])))], (15508 ^ _779448) ^ [_1051061, _1051063] : [15509 ^ _779448 : [(15510 ^ _779448) ^ [_1051114] : [_1051063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1051061), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051114))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051061), _1051063)))], (15514 ^ _779448) ^ [_1051181, _1051183] : [class_Rings_Olinordered__semidom(_1051181), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051181), c_Groups_Ozero__class_Ozero(_1051181)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051181), _1051183))))], (15520 ^ _779448) ^ [_1051284, _1051286] : [class_Rings_Olinordered__semidom(_1051284), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051284), c_Groups_Ozero__class_Ozero(_1051284)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051284), _1051286))))], (15526 ^ _779448) ^ [_1051387, _1051389] : [class_Rings_Olinordered__semidom(_1051387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051387), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051387), _1051389)), c_Groups_Ozero__class_Ozero(_1051387)))], (15532 ^ _779448) ^ [_1051491] : [class_Int_Onumber__ring(_1051491), -(hAPP(c_Int_Onumber__class_Onumber__of(_1051491), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1051491))], (15538 ^ _779448) ^ [_1051578] : [class_Int_Onumber__ring(_1051578), -(c_Groups_Ozero__class_Ozero(_1051578) = hAPP(c_Int_Onumber__class_Onumber__of(_1051578), c_Int_OPls))], (15544 ^ _779448) ^ [_1051665] : [-(c_Int_OBit1(_1051665) = 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)), _1051665)), _1051665))], (15546 ^ _779448) ^ [_1051699, _1051701] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051699)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051701)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051699), _1051701)))], (15548 ^ _779448) ^ [_1051745, _1051747] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051745), _1051747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051745)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051747)))], (15550 ^ _779448) ^ [_1051791, _1051793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051791)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1051793)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1051791), _1051793)))], (15552 ^ _779448) ^ [_1051837, _1051839] : [class_Int_Onumber__ring(_1051837), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051837), hAPP(c_Int_Onumber__class_Onumber__of(_1051837), c_Int_OPls)), _1051839) = _1051839)], (15558 ^ _779448) ^ [_1051938, _1051940] : [class_Int_Onumber__ring(_1051938), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1051938), _1051940), hAPP(c_Int_Onumber__class_Onumber__of(_1051938), c_Int_OPls)) = _1051940)], (15564 ^ _779448) ^ [_1052039] : [class_Rings_Osemiring__1(_1052039), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052039), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1052039))], (15570 ^ _779448) ^ [_1052126, _1052128, _1052130] : [class_Rings_Olinordered__semidom(_1052126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052126), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052126), _1052128)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052126), _1052130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052128), _1052130)))], (15580 ^ _779448) ^ [_1052301, _1052303, _1052305] : [class_Rings_Olinordered__semidom(_1052301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052303), _1052305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052301), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052301), _1052303)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052301), _1052305))))], (15590 ^ _779448) ^ [_1052476, _1052478, _1052480] : [class_Rings_Olinordered__semidom(_1052476), 15593 ^ _779448 : [(15594 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052476), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052476), _1052478)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052476), _1052480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052478), _1052480)))], (15600 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1052478), _1052480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052476), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052476), _1052478)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052476), _1052480))))]]], (15606 ^ _779448) ^ [] : [-(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)))], (15608 ^ _779448) ^ [] : [-(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))], (15610 ^ _779448) ^ [_1052789, _1052791, _1052793] : [class_Rings_Olinordered__semidom(_1052789), 15613 ^ _779448 : [(15614 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052789), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052789), _1052791)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052789), _1052793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052791), _1052793)))], (15620 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052791), _1052793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052789), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052789), _1052791)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1052789), _1052793))))]]], (15626 ^ _779448) ^ [_1053066, _1053068, _1053070] : [class_Rings_Osemiring__1(_1053066), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1053068), _1053070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053066), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053066), _1053068)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053066), _1053070)))], (15632 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15634 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15636 ^ _779448) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (15638 ^ _779448) ^ [_1053261, _1053263, _1053265] : [class_Rings_Osemiring__1(_1053261), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1053263), _1053265)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053261), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053261), _1053263)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053261), _1053265)))], (15644 ^ _779448) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (15646 ^ _779448) ^ [_1053426] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1053426)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1053426))))], (15652 ^ _779448) ^ [_1053521] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1053521))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1053521)))))], (15658 ^ _779448) ^ [_1053622, _1053624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1053622)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1053624)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1053622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053624), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1053622))))], (15664 ^ _779448) ^ [_1053749] : [class_Rings_Osemiring__1(_1053749), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053749), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1053749))], (15670 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (15672 ^ _779448) ^ [_1053860, _1053862] : [class_Rings_Oring__1(_1053860), -(hBOOL(hAPP(hAPP(c_member(_1053860), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1053860), _1053862)), c_Int_Oring__1__class_OInts(_1053860))))], (15678 ^ _779448) ^ [_1053963, _1053965] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053963), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053965)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1053963), _1053965)))], (15680 ^ _779448) ^ [_1054021, _1054023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1054021), _1054023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1054021)), _1054023)))], (15686 ^ _779448) ^ [_1054118, _1054120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1054118)), _1054120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1054118), _1054120)))], (15692 ^ _779448) ^ [_1054221] : [-(c_Int_Opred(_1054221) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1054221), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15694 ^ _779448) ^ [_1054258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1054258), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054258)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15700 ^ _779448) ^ [_1054355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1054355), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1054355)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1054355)))], (15706 ^ _779448) ^ [_1054410, _1054412] : [class_Int_Onumber__ring(_1054410), -(hAPP(c_Int_Onumber__class_Onumber__of(_1054410), c_Int_OBit1(_1054412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1054410), c_Groups_Oone__class_Oone(_1054410)), hAPP(c_Int_Onumber__class_Onumber__of(_1054410), _1054412))), hAPP(c_Int_Onumber__class_Onumber__of(_1054410), _1054412)))], (15712 ^ _779448) ^ [_1054567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1054567)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1054567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15718 ^ _779448) ^ [_1054654] : [_1054654 = 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), _1054654)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15724 ^ _779448) ^ [] : [-(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))], (15726 ^ _779448) ^ [_1054780, _1054782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054780), _1054782)), -(_1054782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1054780), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 15729 ^ [_1054780, _1054782]))))], (15733 ^ _779448) ^ [_1054899, _1054901] : [15734 ^ _779448 : [(15735 ^ _779448) ^ [_1054955] : [_1054901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1054899), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1054955)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054899), _1054901)))], (15739 ^ _779448) ^ [_1055025] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1055025)) = 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), _1055025)))], (15741 ^ _779448) ^ [_1055060, _1055062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055060), _1055062)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055062)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055060)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1055062), _1055060)))], (15747 ^ _779448) ^ [_1055189, _1055191] : [class_Rings_Osemiring__1(_1055189), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1055189), hAPP(c_Nat_OSuc, _1055191)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055189), c_Groups_Oone__class_Oone(_1055189)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1055189), _1055191)))], (15753 ^ _779448) ^ [_1055322] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055322), c_Int_OPls)))], (15759 ^ _779448) ^ [_1055409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055409), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055409) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15765 ^ _779448) ^ [_1055514] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055514), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055514), c_Int_OPls)))], (15771 ^ _779448) ^ [_1055601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055601), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055601))], (15777 ^ _779448) ^ [_1055709, _1055711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055709)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055711))), 15780 ^ _779448 : [(15787 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055709), _1055711)))], (15781 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055709), _1055711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1055711)))]]], (15789 ^ _779448) ^ [_1055912, _1055914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055912)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1055914)))), 15792 ^ _779448 : [(15793 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055912), _1055914)))], (15795 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1055914))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055912), _1055914))], (15801 ^ _779448) ^ [_1056122, _1056124, _1056126] : [class_Rings_Oring__1(_1056122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1056124), _1056126)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1056126), _1056124)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1056122), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056122), _1056126)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1056122), _1056124)))], (15821 ^ _779448) ^ [_1056466, _1056468] : [15822 ^ _779448 : [(15823 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056466), _1056468))], (15825 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056466), 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), _1056466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056468))))], (15811 ^ _779448) ^ [_1056336, _1056338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056336)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1056338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056336), _1056338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1056336), c_Int_OPls)))], (15829 ^ _779448) ^ [_1056639] : [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), _1056639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1056639)))], (15835 ^ _779448) ^ [_1056724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1056724)), -(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), _1056724))))], (15841 ^ _779448) ^ [_1056815, _1056817, _1056819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056815), _1056817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1056819)), -(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), _1056819)), _1056815)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056819)), _1056817))))], (15851 ^ _779448) ^ [_1057008, _1057010] : [class_Int_Onumber__ring(_1057008), class_Rings_Olinordered__idom(_1057008), 15858 ^ _779448 : [(15859 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057008), hAPP(c_Int_Onumber__class_Onumber__of(_1057008), _1057010)), c_Groups_Ozero__class_Ozero(_1057008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057010), c_Int_OPls)))], (15865 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057010), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057008), hAPP(c_Int_Onumber__class_Onumber__of(_1057008), _1057010)), c_Groups_Ozero__class_Ozero(_1057008))))]]], (15871 ^ _779448) ^ [_1057322, _1057324] : [class_Int_Onumber__ring(_1057322), class_Rings_Olinordered__idom(_1057322), 15878 ^ _779448 : [(15879 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), c_Groups_Ozero__class_Ozero(_1057322)), hAPP(c_Int_Onumber__class_Onumber__of(_1057322), _1057324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1057324)))], (15885 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1057324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), c_Groups_Ozero__class_Ozero(_1057322)), hAPP(c_Int_Onumber__class_Onumber__of(_1057322), _1057324))))]]], (15891 ^ _779448) ^ [_1057627, _1057629] : [class_Int_Onumber__ring(_1057627), class_Rings_Olinordered__idom(_1057627), 15898 ^ _779448 : [(15899 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057627), c_Groups_Ozero__class_Ozero(_1057627)), hAPP(c_Int_Onumber__class_Onumber__of(_1057627), _1057629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1057629)))], (15905 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1057629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057627), c_Groups_Ozero__class_Ozero(_1057627)), hAPP(c_Int_Onumber__class_Onumber__of(_1057627), _1057629))))]]], (15911 ^ _779448) ^ [_1057932, _1057934] : [class_Int_Onumber__ring(_1057932), class_Rings_Olinordered__idom(_1057932), 15918 ^ _779448 : [(15919 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057932), hAPP(c_Int_Onumber__class_Onumber__of(_1057932), _1057934)), c_Groups_Ozero__class_Ozero(_1057932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057934), c_Int_OPls)))], (15925 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057934), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057932), hAPP(c_Int_Onumber__class_Onumber__of(_1057932), _1057934)), c_Groups_Ozero__class_Ozero(_1057932))))]]], (15931 ^ _779448) ^ [_1058246, _1058248] : [class_Rings_Olinordered__semidom(_1058246), 15934 ^ _779448 : [(15935 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058246), c_Groups_Ozero__class_Ozero(_1058246)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058246), _1058248))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058248)))], (15941 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1058248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058246), c_Groups_Ozero__class_Ozero(_1058246)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1058246), _1058248))))]]], (15947 ^ _779448) ^ [_1058505] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1058505))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058505)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15953 ^ _779448) ^ [_1058596] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1058596)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058596)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1058596))], (15959 ^ _779448) ^ [_1058658] : [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), _1058658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1058658)))], (15965 ^ _779448) ^ [_1058743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1058743)), -(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), _1058743))))], (15971 ^ _779448) ^ [_1058843, _1058845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058843), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058843)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058845)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058845))], (15977 ^ _779448) ^ [_1058955, _1058957] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058955), c_Int_OPls))), 15980 ^ _779448 : [(15981 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058957), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058955)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058957)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058955))], (15987 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058957), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058955)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1058957)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058955), _1058957)))]]], (15993 ^ _779448) ^ [_1059237, _1059239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059237), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1059237)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1059239)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15999 ^ _779448) ^ [_1059342, _1059344] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059342), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1059342)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1059344)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059342), _1059344)))], (16021 ^ _779448) ^ [_1059713, _1059715, _1059717] : [-(hBOOL(hAPP(_1059713, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059715), _1059717))))), 16024 ^ _779448 : [(16025 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059717), _1059715)))], (16027 ^ _779448) ^ [] : [hBOOL(hAPP(_1059713, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059715)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059717))))]], 16028 ^ _779448 : [(16029 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1059715), _1059717)))], (16031 ^ _779448) ^ [] : [hBOOL(hAPP(_1059713, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (16005 ^ _779448) ^ [_1059424, _1059426, _1059428] : [hBOOL(hAPP(_1059424, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1059426), _1059428)))), 16008 ^ _779448 : [(16009 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1059428), _1059426)), -(hBOOL(hAPP(_1059424, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059426)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1059428)))))], (16015 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1059426), _1059428)), -(hBOOL(hAPP(_1059424, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (16035 ^ _779448) ^ [] : [-(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))))], (16037 ^ _779448) ^ [_1060006, _1060008] : [class_Rings_Osemiring__1(_1060006), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060006), _1060008) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1060006, hAPP(hAPP(c_COMBC(_1060006, _1060006, _1060006), c_Groups_Oplus__class_Oplus(_1060006)), c_Groups_Oone__class_Oone(_1060006)), _1060008, c_Groups_Ozero__class_Ozero(_1060006)))], (16043 ^ _779448) ^ [_1060133, _1060135, _1060137] : [class_Int_Onumber__ring(_1060133), 16046 ^ _779448 : [(16047 ^ _779448) ^ [] : [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), _1060135))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1060133), hAPP(c_Int_Onumber__class_Onumber__of(_1060133), _1060137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060135))) = hAPP(hAPP(c_HOL_OLet(_1060133, _1060133), hAPP(hAPP(c_Power_Opower__class_Opower(_1060133), hAPP(c_Int_Onumber__class_Onumber__of(_1060133), _1060137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060135))), hAPP(hAPP(c_COMBS(_1060133, _1060133, _1060133), hAPP(hAPP(c_COMBB(_1060133, tc_fun(_1060133, _1060133), _1060133), c_Groups_Otimes__class_Otimes(_1060133)), hAPP(c_Groups_Otimes__class_Otimes(_1060133), hAPP(c_Int_Onumber__class_Onumber__of(_1060133), _1060137)))), c_COMBI(_1060133))))], (16053 ^ _779448) ^ [] : [-(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), _1060135)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1060133), hAPP(c_Int_Onumber__class_Onumber__of(_1060133), _1060137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060135))) = c_Groups_Oone__class_Oone(_1060133))]]], (16059 ^ _779448) ^ [_1060540, _1060542] : [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), _1060540))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1060542), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060540))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1060542), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060540))), 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), _1060542))), c_COMBI(tc_Int_Oint))))], (16065 ^ _779448) ^ [_1060697, _1060699] : [-(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), _1060697)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1060699), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060697))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (16071 ^ _779448) ^ [_1060751, _1060753] : [class_Int_Onumber__ring(_1060751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1060753)), -(hBOOL(hAPP(hAPP(c_member(_1060751), hAPP(c_Int_Onumber__class_Onumber__of(_1060751), _1060753)), c_Nat_Osemiring__1__class_ONats(_1060751))))], (16081 ^ _779448) ^ [] : [-(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)))], (16083 ^ _779448) ^ [_1060928, _1060930, _1060932] : [class_Int_Onumber__ring(_1060928), 16086 ^ _779448 : [(16087 ^ _779448) ^ [] : [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), _1060930))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1060928), _1060932), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060930))) = hAPP(hAPP(c_HOL_OLet(_1060928, _1060928), hAPP(hAPP(c_Power_Opower__class_Opower(_1060928), _1060932), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060930))), hAPP(hAPP(c_COMBS(_1060928, _1060928, _1060928), hAPP(hAPP(c_COMBB(_1060928, tc_fun(_1060928, _1060928), _1060928), c_Groups_Otimes__class_Otimes(_1060928)), hAPP(c_Groups_Otimes__class_Otimes(_1060928), _1060932))), c_COMBI(_1060928))))], (16093 ^ _779448) ^ [] : [-(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), _1060930)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1060928), _1060932), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1060930))) = c_Groups_Oone__class_Oone(_1060928))]]], (16099 ^ _779448) ^ [_1061301, _1061303] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061301) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061303), -(_1061301 = _1061303)], (16105 ^ _779448) ^ [_1061386, _1061388] : [_1061386 = _1061388, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061386) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061388))], (16111 ^ _779448) ^ [_1061477, _1061479] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061477)), _1061479) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1061477), _1061479)))], (16113 ^ _779448) ^ [_1061520, _1061522] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1061520), _1061522)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1061520)), _1061522))], (16115 ^ _779448) ^ [_1061578, _1061580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1061578), _1061580)), -(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)), _1061578)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1061580))))], (16121 ^ _779448) ^ [_1061683, _1061685] : [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)), _1061683)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1061685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1061683), _1061685)))], (16127 ^ _779448) ^ [_1061809, _1061811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1061809), _1061811)), -(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)), _1061809)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1061811))))], (16133 ^ _779448) ^ [_1061914, _1061916] : [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)), _1061914)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1061916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1061914), _1061916)))], (16139 ^ _779448) ^ [_1062040, _1062042] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1062040), _1062042)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062040)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062042))))], (16145 ^ _779448) ^ [_1062145, _1062147] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062145)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062147))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1062145), _1062147)))], (16151 ^ _779448) ^ [_1062271, _1062273] : [_1062271 = _1062273, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062271) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062273))], (16157 ^ _779448) ^ [_1062356, _1062358] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062356) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1062358), -(_1062356 = _1062358)], (16163 ^ _779448) ^ [_1062462, _1062464] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062462) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062464), -(_1062462 = _1062464)], (16169 ^ _779448) ^ [_1062547, _1062549] : [_1062547 = _1062549, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062547) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062549))], (16175 ^ _779448) ^ [_1062638, _1062640] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062638)), _1062640) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1062638), _1062640)))], (16177 ^ _779448) ^ [_1062681] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1062681) = 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)), _1062681)))], (16179 ^ _779448) ^ [] : [-(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))))], (16181 ^ _779448) ^ [] : [-(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))], (16183 ^ _779448) ^ [_1062749, _1062751, _1062753, _1062755] : [class_Rings_Ocomm__semiring__1(_1062749), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062749), _1062751), _1062753)), _1062755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062749), hAPP(hAPP(c_Power_Opower__class_Opower(_1062749), _1062751), _1062755)), hAPP(hAPP(c_Power_Opower__class_Opower(_1062749), _1062753), _1062755)))], (16189 ^ _779448) ^ [_1062908, _1062910, _1062912, _1062914] : [class_Rings_Ocomm__semiring__1(_1062908), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1062908), hAPP(hAPP(c_Power_Opower__class_Opower(_1062908), _1062910), _1062912)), _1062914) = hAPP(hAPP(c_Power_Opower__class_Opower(_1062908), _1062910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062912), _1062914)))], (16195 ^ _779448) ^ [_1063047, _1063049, _1063051] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063047), _1063049)), _1063051) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063049), _1063051)))], (16197 ^ _779448) ^ [_1063098, _1063100] : [class_Rings_Ocomm__semiring__1(_1063098), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1063098), _1063100), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1063100)], (16203 ^ _779448) ^ [_1063189, _1063191, _1063193] : [class_Rings_Ocomm__semiring__1(_1063189), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063189), hAPP(hAPP(c_Power_Opower__class_Opower(_1063189), _1063191), _1063193)), _1063191) = hAPP(hAPP(c_Power_Opower__class_Opower(_1063189), _1063191), hAPP(c_Nat_OSuc, _1063193)))], (16209 ^ _779448) ^ [_1063320, _1063322, _1063324] : [class_Rings_Ocomm__semiring__1(_1063320), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063320), _1063322), hAPP(hAPP(c_Power_Opower__class_Opower(_1063320), _1063322), _1063324)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1063320), _1063322), hAPP(c_Nat_OSuc, _1063324)))], (16215 ^ _779448) ^ [_1063451, _1063453, _1063455] : [class_Rings_Ocomm__semiring__1(_1063451), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1063451), _1063453), hAPP(c_Nat_OSuc, _1063455)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063451), _1063453), hAPP(hAPP(c_Power_Opower__class_Opower(_1063451), _1063453), _1063455)))], (16221 ^ _779448) ^ [_1063582, _1063584] : [class_Rings_Ocomm__semiring__1(_1063582), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1063582), _1063584), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1063582))], (16227 ^ _779448) ^ [_1063677, _1063679, _1063681, _1063683] : [class_Rings_Ocomm__semiring__1(_1063677), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063677), hAPP(hAPP(c_Power_Opower__class_Opower(_1063677), _1063679), _1063681)), hAPP(hAPP(c_Power_Opower__class_Opower(_1063677), _1063679), _1063683)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1063677), _1063679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063681), _1063683)))], (16233 ^ _779448) ^ [_1063832, _1063834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1063832)), -(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), _1063832), _1063834))))], (16239 ^ _779448) ^ [_1063929, _1063931, _1063933] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1063931), _1063933)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063929), _1063931)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1063929), _1063933)))], (16241 ^ _779448) ^ [_1063986, _1063988, _1063990] : [class_Rings_Oring__1(_1063986), hBOOL(hAPP(hAPP(c_member(_1063986), _1063988), c_Int_Oring__1__class_OInts(_1063986))), -(hBOOL(hAPP(hAPP(c_member(_1063986), hAPP(hAPP(c_Power_Opower__class_Opower(_1063986), _1063988), _1063990)), c_Int_Oring__1__class_OInts(_1063986))))], (16251 ^ _779448) ^ [_1064169, _1064171, _1064173] : [class_Rings_Osemiring__1(_1064169), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1064169, _1064171, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1064173) = _1064173)], (16257 ^ _779448) ^ [_1064256, _1064258, _1064260, _1064262] : [class_Rings_Osemiring__1(_1064256), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1064256, _1064258, hAPP(c_Nat_OSuc, _1064260), _1064262) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1064256, _1064258, _1064260, hAPP(_1064258, _1064262)))], (16263 ^ _779448) ^ [] : [-(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))], (16265 ^ _779448) ^ [_1064385] : [class_Rings_Osemiring__1(_1064385), -(hBOOL(hAPP(hAPP(c_member(_1064385), c_Groups_Ozero__class_Ozero(_1064385)), c_Nat_Osemiring__1__class_ONats(_1064385))))], (16271 ^ _779448) ^ [_1064480, _1064482, _1064484] : [class_Rings_Osemiring__1(_1064480), hBOOL(hAPP(hAPP(c_member(_1064480), _1064482), c_Nat_Osemiring__1__class_ONats(_1064480))), hBOOL(hAPP(hAPP(c_member(_1064480), _1064484), c_Nat_Osemiring__1__class_ONats(_1064480))), -(hBOOL(hAPP(hAPP(c_member(_1064480), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1064480), _1064482), _1064484)), c_Nat_Osemiring__1__class_ONats(_1064480))))], (16285 ^ _779448) ^ [_1064735, _1064737, _1064739] : [class_Rings_Osemiring__1(_1064735), hBOOL(hAPP(hAPP(c_member(_1064735), _1064737), c_Nat_Osemiring__1__class_ONats(_1064735))), hBOOL(hAPP(hAPP(c_member(_1064735), _1064739), c_Nat_Osemiring__1__class_ONats(_1064735))), -(hBOOL(hAPP(hAPP(c_member(_1064735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064735), _1064737), _1064739)), c_Nat_Osemiring__1__class_ONats(_1064735))))], (16299 ^ _779448) ^ [_1064990] : [class_Rings_Osemiring__1(_1064990), -(hBOOL(hAPP(hAPP(c_member(_1064990), c_Groups_Oone__class_Oone(_1064990)), c_Nat_Osemiring__1__class_ONats(_1064990))))], (16305 ^ _779448) ^ [_1065085, _1065087] : [class_Rings_Osemiring__1(_1065085), -(hBOOL(hAPP(hAPP(c_member(_1065085), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1065085), _1065087)), c_Nat_Osemiring__1__class_ONats(_1065085))))], (16311 ^ _779448) ^ [_1065188, _1065190] : [class_Groups_Omonoid__mult(_1065188), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065188), _1065190), 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(_1065188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065188), _1065190), _1065190)), _1065190))], (16317 ^ _779448) ^ [_1065320, _1065322] : [_1065320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065322), _1065320) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16323 ^ _779448) ^ [_1065403, _1065405] : [-(_1065403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065405), _1065403) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1065405), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1065405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1065403), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (16329 ^ _779448) ^ [_1065465, _1065467, _1065469, _1065471] : [class_Rings_Olinordered__semidom(_1065465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065465), _1065467), _1065469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065465), c_Groups_Ozero__class_Ozero(_1065465)), _1065467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065465), hAPP(hAPP(c_Power_Opower__class_Opower(_1065465), _1065467), _1065471)), hAPP(hAPP(c_Power_Opower__class_Opower(_1065465), _1065469), _1065471))))], (16347 ^ _779448) ^ [_1065794, _1065796, _1065798] : [class_Rings_Olinordered__semidom(_1065794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065794), c_Groups_Oone__class_Oone(_1065794)), _1065796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1065798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065794), c_Groups_Oone__class_Oone(_1065794)), hAPP(hAPP(c_Power_Opower__class_Opower(_1065794), _1065796), _1065798))))], (16361 ^ _779448) ^ [_1066035, _1066037, _1066039, _1066041] : [class_Rings_Olinordered__semidom(_1066035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066035), c_Groups_Oone__class_Oone(_1066035)), _1066037)), 16368 ^ _779448 : [(16369 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066035), hAPP(hAPP(c_Power_Opower__class_Opower(_1066035), _1066037), _1066039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1066035), _1066037), _1066041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066039), _1066041)))], (16375 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066039), _1066041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066035), hAPP(hAPP(c_Power_Opower__class_Opower(_1066035), _1066037), _1066039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1066035), _1066037), _1066041))))]]], (16381 ^ _779448) ^ [_1066410, _1066412, _1066414, _1066416] : [class_Rings_Olinordered__semidom(_1066410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066410), c_Groups_Oone__class_Oone(_1066410)), _1066412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066410), hAPP(hAPP(c_Power_Opower__class_Opower(_1066410), _1066412), _1066414)), hAPP(hAPP(c_Power_Opower__class_Opower(_1066410), _1066412), _1066416))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066414), _1066416)))], (16395 ^ _779448) ^ [_1066675, _1066677, _1066679, _1066681] : [class_Rings_Olinordered__semidom(_1066675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1066677), _1066679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066675), c_Groups_Ozero__class_Ozero(_1066675)), _1066681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066675), _1066681), c_Groups_Oone__class_Oone(_1066675))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066675), hAPP(hAPP(c_Power_Opower__class_Opower(_1066675), _1066681), _1066679)), hAPP(hAPP(c_Power_Opower__class_Opower(_1066675), _1066681), _1066677))))], (16413 ^ _779448) ^ [_1067014, _1067016, _1067018, _1067020] : [class_Rings_Olinordered__semidom(_1067014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067016), _1067018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067014), c_Groups_Ozero__class_Ozero(_1067014)), _1067020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067014), _1067020), c_Groups_Oone__class_Oone(_1067014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067014), hAPP(hAPP(c_Power_Opower__class_Opower(_1067014), _1067020), _1067018)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067014), _1067020), _1067016))))], (16431 ^ _779448) ^ [_1067353, _1067355, _1067357] : [class_Rings_Olinordered__semidom(_1067353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067353), c_Groups_Ozero__class_Ozero(_1067353)), _1067355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067353), _1067355), c_Groups_Oone__class_Oone(_1067353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067353), hAPP(hAPP(c_Power_Opower__class_Opower(_1067353), _1067355), hAPP(c_Nat_OSuc, _1067357))), c_Groups_Oone__class_Oone(_1067353))))], (16445 ^ _779448) ^ [_1067614, _1067616, _1067618] : [class_Rings_Oring__1__no__zero__divisors(_1067614), -(_1067616 = c_Groups_Ozero__class_Ozero(_1067614)), hAPP(hAPP(c_Power_Opower__class_Opower(_1067614), _1067616), _1067618) = c_Groups_Ozero__class_Ozero(_1067614)], (16455 ^ _779448) ^ [_1067773] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1067773) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16467 ^ _779448) ^ [_1067912, _1067914] : [16468 ^ _779448 : [(16469 ^ _779448) ^ [] : [_1067914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16471 ^ _779448) ^ [] : [_1067912 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1067912), _1067914) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16457 ^ _779448) ^ [_1067814, _1067816] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1067814), _1067816) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1067816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1067814 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16485 ^ _779448) ^ [_1068162, _1068164] : [16486 ^ _779448 : [(16487 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068162))], (16489 ^ _779448) ^ [] : [_1068164 = 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), _1068162), _1068164))))], (16475 ^ _779448) ^ [_1068056, _1068058] : [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), _1068056), _1068058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068056))), -(_1068058 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16493 ^ _779448) ^ [_1068299, _1068301, _1068303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1068299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1068299), _1068301)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1068299), _1068303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068301), _1068303)))], (16503 ^ _779448) ^ [_1068480, _1068482, _1068484] : [class_Groups_Omonoid__mult(_1068480), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068480), hAPP(hAPP(c_Power_Opower__class_Opower(_1068480), _1068482), _1068484)), _1068482) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068480), _1068482), hAPP(hAPP(c_Power_Opower__class_Opower(_1068480), _1068482), _1068484)))], (16509 ^ _779448) ^ [_1068621, _1068623, _1068625, _1068627] : [class_Groups_Ocomm__monoid__mult(_1068621), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1068621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068621), _1068623), _1068625)), _1068627) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068621), hAPP(hAPP(c_Power_Opower__class_Opower(_1068621), _1068623), _1068627)), hAPP(hAPP(c_Power_Opower__class_Opower(_1068621), _1068625), _1068627)))], (16515 ^ _779448) ^ [_1068780, _1068782] : [class_Groups_Omonoid__mult(_1068780), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1068780), c_Groups_Oone__class_Oone(_1068780)), _1068782) = c_Groups_Oone__class_Oone(_1068780))], (16521 ^ _779448) ^ [_1068879, _1068881, _1068883] : [class_Rings_Osemiring__1(_1068879), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1068879), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1068881), _1068883)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1068879), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1068879), _1068881)), _1068883))], (16527 ^ _779448) ^ [_1069004, _1069006, _1069008, _1069010] : [class_Groups_Omonoid__mult(_1069004), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1069004), _1069006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069008), _1069010)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1069004), hAPP(hAPP(c_Power_Opower__class_Opower(_1069004), _1069006), _1069008)), _1069010))], (16533 ^ _779448) ^ [_1069143, _1069145] : [class_Groups_Omonoid__mult(_1069143), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1069143), _1069145), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1069145)], (16539 ^ _779448) ^ [_1069234, _1069236, _1069238, _1069240] : [class_Rings_Olinordered__semidom(_1069234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069234), _1069236), _1069238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069234), c_Groups_Ozero__class_Ozero(_1069234)), _1069236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069234), hAPP(hAPP(c_Power_Opower__class_Opower(_1069234), _1069236), _1069240)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069234), _1069238), _1069240))))], (16553 ^ _779448) ^ [_1069503, _1069505, _1069507] : [class_Rings_Olinordered__semidom(_1069503), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069503), c_Groups_Ozero__class_Ozero(_1069503)), _1069505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069503), c_Groups_Ozero__class_Ozero(_1069503)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069503), _1069505), _1069507))))], (16563 ^ _779448) ^ [_1069686, _1069688, _1069690] : [class_Rings_Olinordered__semidom(_1069686), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069686), c_Groups_Ozero__class_Ozero(_1069686)), _1069688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069686), c_Groups_Ozero__class_Ozero(_1069686)), hAPP(hAPP(c_Power_Opower__class_Opower(_1069686), _1069688), _1069690))))], (16573 ^ _779448) ^ [_1069869, _1069871, _1069873] : [class_Power_Opower(_1069869), class_Rings_Omult__zero(_1069869), class_Rings_Ono__zero__divisors(_1069869), class_Rings_Ozero__neq__one(_1069869), 16588 ^ _779448 : [(16589 ^ _779448) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1069869), _1069871), _1069873) = c_Groups_Ozero__class_Ozero(_1069869), 16592 ^ _779448 : [(16593 ^ _779448) ^ [] : [-(_1069871 = c_Groups_Ozero__class_Ozero(_1069869))], (16595 ^ _779448) ^ [] : [_1069873 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (16597 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1069869), _1069871), _1069873) = c_Groups_Ozero__class_Ozero(_1069869)), _1069871 = c_Groups_Ozero__class_Ozero(_1069869), -(_1069873 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (16607 ^ _779448) ^ [_1070361, _1070363, _1070365] : [class_Rings_Olinordered__semidom(_1070361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070361), c_Groups_Oone__class_Oone(_1070361)), _1070363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070361), c_Groups_Oone__class_Oone(_1070361)), hAPP(hAPP(c_Power_Opower__class_Opower(_1070361), _1070363), _1070365))))], (16617 ^ _779448) ^ [_1070544, _1070546] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1070544), c_Groups_Ozero__class_Ozero(_1070544)), hAPP(c_Nat_OSuc, _1070546)) = c_Groups_Ozero__class_Ozero(_1070544)), class_Power_Opower(_1070544), class_Rings_Osemiring__0(_1070544)], (16627 ^ _779448) ^ [_1070699, _1070701, _1070703, _1070705] : [class_Rings_Olinordered__semidom(_1070699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1070699), c_Groups_Oone__class_Oone(_1070699)), _1070701)), 16634 ^ _779448 : [(16635 ^ _779448) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1070699), _1070701), _1070703) = hAPP(hAPP(c_Power_Opower__class_Opower(_1070699), _1070701), _1070705), -(_1070703 = _1070705)], (16641 ^ _779448) ^ [] : [_1070703 = _1070705, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1070699), _1070701), _1070703) = hAPP(hAPP(c_Power_Opower__class_Opower(_1070699), _1070701), _1070705))]]], (16647 ^ _779448) ^ [_1071038, _1071040, _1071042] : [class_Power_Opower(_1071038), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071038), _1071040), hAPP(c_Nat_OSuc, _1071042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071038), _1071040), hAPP(hAPP(c_Power_Opower__class_Opower(_1071038), _1071040), _1071042)))], (16653 ^ _779448) ^ [_1071169, _1071171, _1071173] : [class_Groups_Omonoid__mult(_1071169), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071169), _1071171), hAPP(c_Nat_OSuc, _1071173)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071169), hAPP(hAPP(c_Power_Opower__class_Opower(_1071169), _1071171), _1071173)), _1071171))], (16659 ^ _779448) ^ [_1071300, _1071302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1071300)), -(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), _1071300), _1071302))))], (16665 ^ _779448) ^ [_1071397, _1071399] : [class_Power_Opower(_1071397), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071397), _1071399), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1071397))], (16671 ^ _779448) ^ [_1071492, _1071494, _1071496, _1071498] : [class_Groups_Omonoid__mult(_1071492), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1071492), _1071494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1071496), _1071498)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071492), hAPP(hAPP(c_Power_Opower__class_Opower(_1071492), _1071494), _1071496)), hAPP(hAPP(c_Power_Opower__class_Opower(_1071492), _1071494), _1071498)))], (16677 ^ _779448) ^ [_1071647, _1071649, _1071651, _1071653] : [class_Rings_Olinordered__semidom(_1071647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071647), hAPP(hAPP(c_Power_Opower__class_Opower(_1071647), _1071649), _1071651)), hAPP(hAPP(c_Power_Opower__class_Opower(_1071647), _1071653), _1071651))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071647), c_Groups_Ozero__class_Ozero(_1071647)), _1071653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071647), _1071649), _1071653)))], (16691 ^ _779448) ^ [_1071916, _1071918, _1071920, _1071922] : [class_Rings_Olinordered__semidom(_1071916), hAPP(hAPP(c_Power_Opower__class_Opower(_1071916), _1071918), hAPP(c_Nat_OSuc, _1071920)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1071916), _1071922), hAPP(c_Nat_OSuc, _1071920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071916), c_Groups_Ozero__class_Ozero(_1071916)), _1071918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071916), c_Groups_Ozero__class_Ozero(_1071916)), _1071922)), -(_1071918 = _1071922)], (16709 ^ _779448) ^ [_1072243, _1072245, _1072247, _1072249] : [class_Rings_Olinordered__semidom(_1072243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072243), hAPP(hAPP(c_Power_Opower__class_Opower(_1072243), _1072245), hAPP(c_Nat_OSuc, _1072247))), hAPP(hAPP(c_Power_Opower__class_Opower(_1072243), _1072249), hAPP(c_Nat_OSuc, _1072247)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072243), c_Groups_Ozero__class_Ozero(_1072243)), _1072249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1072243), _1072245), _1072249)))], (16723 ^ _779448) ^ [_1072524, _1072526, _1072528] : [class_Rings_Olinordered__semidom(_1072524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072524), c_Groups_Oone__class_Oone(_1072524)), _1072526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072524), c_Groups_Oone__class_Oone(_1072524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072524), _1072526), hAPP(hAPP(c_Power_Opower__class_Opower(_1072524), _1072526), _1072528)))))], (16733 ^ _779448) ^ [_1072723, _1072725, _1072727] : [class_Rings_Olinordered__semidom(_1072723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072723), c_Groups_Oone__class_Oone(_1072723)), _1072725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072723), hAPP(hAPP(c_Power_Opower__class_Opower(_1072723), _1072725), _1072727)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1072723), _1072725), hAPP(hAPP(c_Power_Opower__class_Opower(_1072723), _1072725), _1072727)))))], (16743 ^ _779448) ^ [_1072934, _1072936] : [class_Power_Opower(_1072934), class_Rings_Osemiring__0(_1072934), 16750 ^ _779448 : [(16751 ^ _779448) ^ [] : [_1072936 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1072934), c_Groups_Ozero__class_Ozero(_1072934)), _1072936) = c_Groups_Oone__class_Oone(_1072934))], (16757 ^ _779448) ^ [] : [-(_1072936 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1072934), c_Groups_Ozero__class_Ozero(_1072934)), _1072936) = c_Groups_Ozero__class_Ozero(_1072934))]]], (16763 ^ _779448) ^ [_1073208, _1073210, _1073212] : [class_Rings_Olinordered__semidom(_1073208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073208), c_Groups_Oone__class_Oone(_1073208)), _1073210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073208), c_Groups_Oone__class_Oone(_1073208)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073208), _1073210), hAPP(c_Nat_OSuc, _1073212)))))], (16773 ^ _779448) ^ [_1073397, _1073399, _1073401, _1073403] : [class_Rings_Olinordered__semidom(_1073397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073397), c_Groups_Oone__class_Oone(_1073397)), _1073399)), 16780 ^ _779448 : [(16781 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073397), hAPP(hAPP(c_Power_Opower__class_Opower(_1073397), _1073399), _1073401)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073397), _1073399), _1073403))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073401), _1073403)))], (16787 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073401), _1073403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073397), hAPP(hAPP(c_Power_Opower__class_Opower(_1073397), _1073399), _1073401)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073397), _1073399), _1073403))))]]], (16793 ^ _779448) ^ [_1073772, _1073774, _1073776, _1073778] : [class_Rings_Olinordered__semidom(_1073772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073772), c_Groups_Oone__class_Oone(_1073772)), _1073774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1073772), hAPP(hAPP(c_Power_Opower__class_Opower(_1073772), _1073774), _1073776)), hAPP(hAPP(c_Power_Opower__class_Opower(_1073772), _1073774), _1073778))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073776), _1073778)))], (16807 ^ _779448) ^ [_1074037, _1074039, _1074041, _1074043] : [class_Rings_Olinordered__semidom(_1074037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074039), _1074041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074037), c_Groups_Oone__class_Oone(_1074037)), _1074043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074037), hAPP(hAPP(c_Power_Opower__class_Opower(_1074037), _1074043), _1074039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074037), _1074043), _1074041))))], (16821 ^ _779448) ^ [_1074302, _1074304, _1074306, _1074308] : [class_Rings_Olinordered__semidom(_1074302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074304), _1074306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074302), c_Groups_Oone__class_Oone(_1074302)), _1074308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074302), hAPP(hAPP(c_Power_Opower__class_Opower(_1074302), _1074308), _1074304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074302), _1074308), _1074306))))], (16835 ^ _779448) ^ [_1074567, _1074569, _1074571] : [class_Rings_Olinordered__semidom(_1074567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074567), c_Groups_Ozero__class_Ozero(_1074567)), _1074569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074567), _1074569), c_Groups_Oone__class_Oone(_1074567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074567), _1074569), hAPP(hAPP(c_Power_Opower__class_Opower(_1074567), _1074569), _1074571))), hAPP(hAPP(c_Power_Opower__class_Opower(_1074567), _1074569), _1074571))))], (16849 ^ _779448) ^ [_1074850, _1074852, _1074854, _1074856] : [class_Rings_Olinordered__semidom(_1074850), hAPP(hAPP(c_Power_Opower__class_Opower(_1074850), _1074852), _1074854) = hAPP(hAPP(c_Power_Opower__class_Opower(_1074850), _1074856), _1074854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074850), c_Groups_Ozero__class_Ozero(_1074850)), _1074852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074850), c_Groups_Ozero__class_Ozero(_1074850)), _1074856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074854)), -(_1074852 = _1074856)], (16871 ^ _779448) ^ [_1075234, _1075236] : [_1075234 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1075234, _1075236) = _1075236)], (16877 ^ _779448) ^ [_1075311, _1075313] : [-(_1075311 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1075311, _1075313) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1075311), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1075313)))], (16883 ^ _779448) ^ [_1075364] : [class_Power_Opower(_1075364), -(c_Power_Opower__class_Opower(_1075364) = c_Power_Opower_Opower(_1075364, c_Groups_Oone__class_Oone(_1075364), c_Groups_Otimes__class_Otimes(_1075364)))], (16889 ^ _779448) ^ [_1075457, _1075459, _1075461] : [class_Rings_Olinordered__idom(_1075457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075457), _1075459), c_Groups_Ozero__class_Ozero(_1075457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075457), hAPP(hAPP(c_Power_Opower__class_Opower(_1075457), _1075459), 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)))), _1075461)))), c_Groups_Ozero__class_Ozero(_1075457))))], (16899 ^ _779448) ^ [_1075652, _1075654, _1075656] : [class_Rings_Olinordered__idom(_1075652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075652), c_Groups_Ozero__class_Ozero(_1075652)), hAPP(hAPP(c_Power_Opower__class_Opower(_1075652), _1075654), 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)))), _1075656))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075652), c_Groups_Ozero__class_Ozero(_1075652)), _1075654)))], (16909 ^ _779448) ^ [_1075847, _1075849, _1075851] : [class_Int_Onumber__ring(_1075847), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075847), _1075849), _1075851)), 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(_1075847), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075847), hAPP(hAPP(c_Power_Opower__class_Opower(_1075847), _1075849), 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(_1075847), _1075851), 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(_1075847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075847), hAPP(c_Int_Onumber__class_Onumber__of(_1075847), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1075849)), _1075851)))], (16915 ^ _779448) ^ [] : [-(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))], (16917 ^ _779448) ^ [_1076080, _1076082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1076080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076082)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076082), _1076080)), _1076082) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076080), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (16927 ^ _779448) ^ [_1076280, _1076282] : [c_Int_OBit0(_1076280) = c_Int_OBit0(_1076282), -(_1076280 = _1076282)], (16933 ^ _779448) ^ [_1076361, _1076363] : [_1076361 = _1076363, -(c_Int_OBit0(_1076361) = c_Int_OBit0(_1076363))], (16939 ^ _779448) ^ [_1076448, _1076450] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1076448))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1076450))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076448)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1076450)))], (16941 ^ _779448) ^ [_1076501] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076501) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16943 ^ _779448) ^ [_1076542, _1076544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076542)), c_Int_OBit0(_1076544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076542), _1076544)))], (16949 ^ _779448) ^ [_1076643, _1076645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076643), _1076645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076643)), c_Int_OBit0(_1076645))))], (16955 ^ _779448) ^ [_1076765, _1076767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076765)), c_Int_OBit0(_1076767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076765), _1076767)))], (16961 ^ _779448) ^ [_1076866, _1076868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1076866), _1076868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1076866)), c_Int_OBit0(_1076868))))], (16967 ^ _779448) ^ [_1076988, _1076990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1076988)), c_Int_OBit0(_1076990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076988), _1076990)))], (16973 ^ _779448) ^ [_1077089, _1077091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077089), _1077091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1077089)), c_Int_OBit0(_1077091))))], (16979 ^ _779448) ^ [_1077211, _1077213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1077211)), c_Int_OBit0(_1077213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077211), _1077213)))], (16985 ^ _779448) ^ [_1077312, _1077314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077312), _1077314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1077312)), c_Int_OBit0(_1077314))))], (16991 ^ _779448) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (16993 ^ _779448) ^ [_1077449] : [c_Int_OPls = c_Int_OBit0(_1077449), -(c_Int_OPls = _1077449)], (16999 ^ _779448) ^ [_1077524] : [c_Int_OPls = _1077524, -(c_Int_OPls = c_Int_OBit0(_1077524))], (17005 ^ _779448) ^ [_1077617] : [c_Int_OBit0(_1077617) = c_Int_OPls, -(_1077617 = c_Int_OPls)], (17011 ^ _779448) ^ [_1077692] : [_1077692 = c_Int_OPls, -(c_Int_OBit0(_1077692) = c_Int_OPls)], (17017 ^ _779448) ^ [_1077785, _1077787] : [c_Int_OBit0(_1077785) = c_Int_OBit1(_1077787)], (17019 ^ _779448) ^ [_1077826, _1077828] : [c_Int_OBit1(_1077826) = c_Int_OBit0(_1077828)], (17021 ^ _779448) ^ [_1077855] : [-(c_Int_OBit0(_1077855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077855), _1077855))], (17023 ^ _779448) ^ [_1077886, _1077888] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1077886)), c_Int_OBit0(_1077888)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077886), _1077888)))], (17025 ^ _779448) ^ [_1077929, _1077931] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1077929)), _1077931) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077929), _1077931)))], (17027 ^ _779448) ^ [_1077970, _1077972] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1077970)), c_Int_OBit0(_1077972)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077970), _1077972)))], (17029 ^ _779448) ^ [_1078013, _1078015] : [class_Divides_Osemiring__div(_1078013), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1078013), c_Groups_Ozero__class_Ozero(_1078013)), _1078015) = c_Groups_Ozero__class_Ozero(_1078013))], (17035 ^ _779448) ^ [_1078112, _1078114] : [class_Divides_Osemiring__div(_1078112), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1078112), _1078114), c_Groups_Ozero__class_Ozero(_1078112)) = c_Groups_Ozero__class_Ozero(_1078112))], (17041 ^ _779448) ^ [_1078211, _1078213] : [class_Divides_Osemiring__div(_1078211), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1078211), _1078213), c_Groups_Oone__class_Oone(_1078211)) = _1078213)], (17047 ^ _779448) ^ [_1078306, _1078308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078308)), -(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), _1078306), _1078308))))], (17057 ^ _779448) ^ [_1078459, _1078461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078459)), 17060 ^ _779448 : [(17061 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1078461), _1078459)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078461), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17067 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078461), 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), _1078461), _1078459)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17073 ^ _779448) ^ [_1078718, _1078720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 17076 ^ _779448 : [(17077 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1078720), _1078718)), 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)), _1078720)))], (17083 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1078720), _1078718)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17089 ^ _779448) ^ [_1078974, _1078976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078974), 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)), _1078976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1078974), _1078976)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17099 ^ _779448) ^ [_1079135] : [-(_1079135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1079135), _1079135) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17105 ^ _779448) ^ [_1079187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1079187)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079187), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17111 ^ _779448) ^ [_1079282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079282), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1079282)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17117 ^ _779448) ^ [_1079395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1079395))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1079395)))], (17123 ^ _779448) ^ [_1079478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1079478)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1079478))))], (17129 ^ _779448) ^ [_1079579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1079579)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079579), c_Int_OPls)))], (17135 ^ _779448) ^ [_1079674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079674), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1079674)), c_Int_OPls)))], (17141 ^ _779448) ^ [_1079790, _1079792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1079790)), c_Int_OBit1(_1079792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079790), _1079792)))], (17147 ^ _779448) ^ [_1079891, _1079893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1079891), _1079893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1079891)), c_Int_OBit1(_1079893))))], (17153 ^ _779448) ^ [_1080013, _1080015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1080013)), c_Int_OBit1(_1080015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1080013), _1080015)))], (17159 ^ _779448) ^ [_1080114, _1080116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1080114), _1080116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1080114)), c_Int_OBit1(_1080116))))], (17165 ^ _779448) ^ [_1080233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1080233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1080233)))], (17171 ^ _779448) ^ [_1080316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1080316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1080316))))], (17177 ^ _779448) ^ [_1080417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1080417)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080417), c_Int_OPls)))], (17183 ^ _779448) ^ [_1080512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080512), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1080512)), c_Int_OPls)))], (17189 ^ _779448) ^ [_1080628, _1080630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1080628)), c_Int_OBit0(_1080630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080628), _1080630)))], (17195 ^ _779448) ^ [_1080729, _1080731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080729), _1080731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1080729)), c_Int_OBit0(_1080731))))], (17201 ^ _779448) ^ [_1080851, _1080853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1080851)), c_Int_OBit0(_1080853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080851), _1080853)))], (17207 ^ _779448) ^ [_1080952, _1080954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1080952), _1080954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1080952)), c_Int_OBit0(_1080954))))], (17213 ^ _779448) ^ [_1081059, _1081061] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1081059)), c_Int_OBit0(_1081061)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1081059), _1081061)))], (17215 ^ _779448) ^ [_1081102, _1081104] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1081102)), c_Int_OBit1(_1081104)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1081102), _1081104)))], (17217 ^ _779448) ^ [_1081145] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1081145)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1081145)))], (17219 ^ _779448) ^ [_1081178, _1081180] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1081178)), c_Int_OBit1(_1081180)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1081178), _1081180)))], (17221 ^ _779448) ^ [_1081221, _1081223] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1081221)), c_Int_OBit0(_1081223)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1081221), _1081223)))], (17223 ^ _779448) ^ [_1081276] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081276)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081276))))], (17229 ^ _779448) ^ [_1081371] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1081371))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1081371)))))], (17235 ^ _779448) ^ [_1081472, _1081474, _1081476, _1081478] : [class_Divides_Osemiring__div(_1081472), -(_1081474 = c_Groups_Ozero__class_Ozero(_1081472)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081472), _1081474), _1081476)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081472), _1081474), _1081478)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081472), _1081476), _1081478))], (17245 ^ _779448) ^ [_1081634, _1081636, _1081638, _1081640] : [class_Divides_Osemiring__div(_1081634), -(_1081636 = c_Groups_Ozero__class_Ozero(_1081634)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081634), _1081638), _1081636)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081634), _1081640), _1081636)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081634), _1081638), _1081640))], (17255 ^ _779448) ^ [_1081796, _1081798, _1081800] : [class_Divides_Osemiring__div(_1081796), -(_1081798 = c_Groups_Ozero__class_Ozero(_1081796)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081796), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081796), _1081798), _1081800)), _1081798) = _1081800)], (17265 ^ _779448) ^ [_1081924, _1081926, _1081928] : [class_Divides_Osemiring__div(_1081924), -(_1081926 = c_Groups_Ozero__class_Ozero(_1081924)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1081924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1081924), _1081928), _1081926)), _1081926) = _1081928)], (17275 ^ _779448) ^ [_1082052, _1082054, _1082056, _1082058] : [class_Divides_Osemiring__div(_1082052), 17278 ^ _779448 : [(17279 ^ _779448) ^ [] : [_1082054 = c_Groups_Ozero__class_Ozero(_1082052), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1082052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082052), _1082054), _1082056)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082052), _1082054), _1082058)) = c_Groups_Ozero__class_Ozero(_1082052))], (17285 ^ _779448) ^ [] : [-(_1082054 = c_Groups_Ozero__class_Ozero(_1082052)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1082052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082052), _1082054), _1082056)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082052), _1082054), _1082058)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1082052), _1082056), _1082058))]]], (17291 ^ _779448) ^ [_1082358] : [-(c_Int_Opred(c_Int_OBit1(_1082358)) = c_Int_OBit0(_1082358))], (17293 ^ _779448) ^ [_1082387] : [-(c_Int_Opred(c_Int_OBit0(_1082387)) = c_Int_OBit1(c_Int_Opred(_1082387)))], (17295 ^ _779448) ^ [_1082418, _1082420] : [class_Divides_Osemiring__div(_1082418), -(_1082420 = c_Groups_Ozero__class_Ozero(_1082418)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1082418), _1082420), _1082420) = c_Groups_Oone__class_Oone(_1082418))], (17305 ^ _779448) ^ [_1082532] : [-(c_Int_Osucc(c_Int_OBit1(_1082532)) = c_Int_OBit0(c_Int_Osucc(_1082532)))], (17307 ^ _779448) ^ [_1082563] : [-(c_Int_Osucc(c_Int_OBit0(_1082563)) = c_Int_OBit1(_1082563))], (17309 ^ _779448) ^ [_1082592] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1082592)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1082592)), 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))))], (17311 ^ _779448) ^ [_1082638, _1082640] : [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), _1082638))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1082640))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1082638))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082640)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082638)))], (17317 ^ _779448) ^ [_1082775, _1082777] : [-(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), _1082775)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1082777))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1082775))) = 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), _1082777)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1082775)))], (17323 ^ _779448) ^ [_1082852, _1082854] : [class_Int_Onumber__ring(_1082852), -(hAPP(c_Int_Onumber__class_Onumber__of(_1082852), c_Int_OBit0(_1082854)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082852), c_Groups_Ozero__class_Ozero(_1082852)), hAPP(c_Int_Onumber__class_Onumber__of(_1082852), _1082854))), hAPP(c_Int_Onumber__class_Onumber__of(_1082852), _1082854)))], (17329 ^ _779448) ^ [_1083012, _1083014] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1083012), _1083014) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1083014 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17338 ^ _779448 : [(17339 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083012)))], (17341 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083012), _1083014)))]], 17342 ^ _779448 : [(17343 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083012), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17345 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083014), _1083012)))]]], (17347 ^ _779448) ^ [_1083243, _1083245] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1083243), _1083245) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17348 ^ _779448 : [(17349 ^ _779448) ^ [] : [_1083245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (17351 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083243)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083243), _1083245))], (17357 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083243), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1083245), _1083243))]]], (17365 ^ _779448) ^ [_1083538, _1083540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083538)), 17368 ^ _779448 : [(17369 ^ _779448) ^ [] : [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), _1083540), _1083538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083540)))], (17375 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083540)), -(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), _1083540), _1083538))))]]], (17381 ^ _779448) ^ [_1083779, _1083781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1083779)), 17384 ^ _779448 : [(17385 ^ _779448) ^ [] : [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), _1083781), _1083779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083779), _1083781)))], (17391 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083779), _1083781)), -(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), _1083781), _1083779))))]]], (17397 ^ _779448) ^ [_1084029, _1084031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084029)), 17400 ^ _779448 : [(17401 ^ _779448) ^ [] : [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), _1084029), _1084031))), 17404 ^ _779448 : [(17405 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084031), _1084029)))], (17407 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084031)))]]], (17409 ^ _779448) ^ [] : [-(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), _1084029), _1084031)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084031), _1084029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084031))]]], (17419 ^ _779448) ^ [_1084357, _1084359, _1084361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084359), _1084361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1084357), _1084361)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1084357), _1084359))))], (17433 ^ _779448) ^ [_1084596, _1084598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084598), 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), _1084596), _1084598)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17443 ^ _779448) ^ [_1084761, _1084763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084761), _1084763)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1084761), _1084763) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17453 ^ _779448) ^ [_1084916, _1084918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084916), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 17456 ^ _779448 : [(17457 ^ _779448) ^ [] : [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), _1084918), _1084916))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084918), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17463 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084918), 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), _1084918), _1084916))))]]], (17469 ^ _779448) ^ [_1085172, _1085174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085172), 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)), _1085174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085172), _1085174)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17479 ^ _779448) ^ [_1085337, _1085339, _1085341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085337), 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)), _1085339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085339), _1085341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085337), _1085339)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085337), _1085341))))], (17493 ^ _779448) ^ [_1085582, _1085584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085582), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085584), _1085582)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085582), _1085584) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17503 ^ _779448) ^ [_1085743, _1085745, _1085747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085743), _1085745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1085747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085743), _1085747)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085745), _1085747))))], (17513 ^ _779448) ^ [_1085924, _1085926, _1085928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085924), _1085926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085928), 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), _1085926), _1085928)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1085924), _1085928))))], (17523 ^ _779448) ^ [_1086111, _1086113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086111)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1086113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1086111), _1086113)), _1086111)))], (17533 ^ _779448) ^ [_1086270, _1086272, _1086274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1086270)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1086272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1086274), _1086270)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1086272), _1086274)), _1086270))], (17539 ^ _779448) ^ [_1086416, _1086418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086416)), c_Int_OBit1(_1086418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086416), _1086418)))], (17545 ^ _779448) ^ [_1086517, _1086519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086517), _1086519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086517)), c_Int_OBit1(_1086519))))], (17551 ^ _779448) ^ [_1086639, _1086641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086639)), c_Int_OBit1(_1086641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086639), _1086641)))], (17557 ^ _779448) ^ [_1086740, _1086742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086740), _1086742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1086740)), c_Int_OBit1(_1086742))))], (17563 ^ _779448) ^ [_1086862, _1086864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1086862)), c_Int_OBit0(_1086864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086862), _1086864)))], (17569 ^ _779448) ^ [_1086963, _1086965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086963), _1086965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1086963)), c_Int_OBit0(_1086965))))], (17575 ^ _779448) ^ [_1087085, _1087087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087085)), c_Int_OBit0(_1087087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087085), _1087087)))], (17581 ^ _779448) ^ [_1087186, _1087188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087186), _1087188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1087186)), c_Int_OBit0(_1087188))))], (17587 ^ _779448) ^ [_1087293, _1087295] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1087293)), _1087295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1087293), _1087295))), _1087295))], (17589 ^ _779448) ^ [_1087340, _1087342, _1087344, _1087346] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1087340, _1087342, _1087344), _1087346), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1087342)], (17591 ^ _779448) ^ [_1087379, _1087381, _1087383, _1087385, _1087387] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1087379, _1087381, _1087383), _1087385), hAPP(c_Nat_OSuc, _1087387)) = hAPP(hAPP(_1087383, _1087385), hAPP(hAPP(c_Power_Opower_Opower(_1087379, _1087381, _1087383), _1087385), _1087387)))], (17593 ^ _779448) ^ [_1087439, _1087441] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1087439)), c_Int_OBit1(_1087441)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1087439)), _1087441)))], (17595 ^ _779448) ^ [_1087484, _1087486, _1087488, _1087490] : [class_Divides_Osemiring__div(_1087484), -(_1087486 = c_Groups_Ozero__class_Ozero(_1087484)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087484), _1087488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087484), _1087486), _1087490))), _1087486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087484), _1087490), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087484), _1087488), _1087486)))], (17605 ^ _779448) ^ [_1087662, _1087664, _1087666, _1087668] : [class_Divides_Osemiring__div(_1087662), -(_1087664 = c_Groups_Ozero__class_Ozero(_1087662)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087662), _1087666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087662), _1087668), _1087664))), _1087664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087662), _1087668), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087662), _1087666), _1087664)))], (17615 ^ _779448) ^ [_1087840, _1087842, _1087844] : [class_Divides_Osemiring__div(_1087840), -(_1087842 = c_Groups_Ozero__class_Ozero(_1087840)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087840), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087840), _1087844), _1087842)), _1087842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087840), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1087840), _1087844), _1087842)), c_Groups_Oone__class_Oone(_1087840)))], (17625 ^ _779448) ^ [_1088004, _1088006, _1088008] : [class_Divides_Osemiring__div(_1088004), -(_1088006 = c_Groups_Ozero__class_Ozero(_1088004)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1088004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088004), _1088006), _1088008)), _1088006) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088004), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1088004), _1088008), _1088006)), c_Groups_Oone__class_Oone(_1088004)))], (17635 ^ _779448) ^ [_1088168, _1088170] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1088168)), c_Int_OBit1(_1088170)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088168), c_Int_Osucc(_1088170))))], (17637 ^ _779448) ^ [_1088213, _1088215, _1088217] : [class_Int_Onumber__ring(_1088213), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1088213), _1088215), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1088217))) = hAPP(hAPP(c_HOL_OLet(_1088213, _1088213), hAPP(hAPP(c_Power_Opower__class_Opower(_1088213), _1088215), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088217))), hAPP(hAPP(c_COMBS(_1088213, _1088213, _1088213), c_Groups_Otimes__class_Otimes(_1088213)), c_COMBI(_1088213))))], (17643 ^ _779448) ^ [_1088384, _1088386] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1088384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1088386))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1088384), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088386))), 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))))], (17645 ^ _779448) ^ [_1088435, _1088437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1088435)), -(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)))), _1088437))), 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)))), _1088435)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1088437), _1088435))], (17651 ^ _779448) ^ [_1088558, _1088560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088558), 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)))), _1088560))), 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)))), _1088558)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088560), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1088558))], (17657 ^ _779448) ^ [_1088699, _1088701] : [class_Int_Onumber__ring(_1088699), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088699), c_Groups_Oone__class_Oone(_1088699)), c_Groups_Oone__class_Oone(_1088699))), hAPP(c_Int_Onumber__class_Onumber__of(_1088699), _1088701)) = hAPP(c_Int_Onumber__class_Onumber__of(_1088699), c_Int_OBit0(_1088701)))], (17663 ^ _779448) ^ [_1088838] : [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), _1088838))), 17666 ^ _779448 : [(17667 ^ _779448) ^ [] : [-(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(_1088838)))))], (17669 ^ _779448) ^ [] : [-(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(_1088838)))))]]], (17671 ^ _779448) ^ [_1088977, _1088979, _1088981] : [class_Int_Onumber__ring(_1088977), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1088977), hAPP(c_Int_Onumber__class_Onumber__of(_1088977), _1088979)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1088981))) = hAPP(hAPP(c_HOL_OLet(_1088977, _1088977), hAPP(hAPP(c_Power_Opower__class_Opower(_1088977), hAPP(c_Int_Onumber__class_Onumber__of(_1088977), _1088979)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088981))), hAPP(hAPP(c_COMBS(_1088977, _1088977, _1088977), c_Groups_Otimes__class_Otimes(_1088977)), c_COMBI(_1088977))))], (17677 ^ _779448) ^ [_1089168, _1089170] : [class_Int_Onumber__ring(_1089168), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089168), hAPP(c_Int_Onumber__class_Onumber__of(_1089168), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1089170) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089168), _1089170), _1089170))], (17683 ^ _779448) ^ [_1089285, _1089287] : [class_Int_Onumber__ring(_1089285), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089285), _1089287), hAPP(c_Int_Onumber__class_Onumber__of(_1089285), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089285), _1089287), _1089287))], (17689 ^ _779448) ^ [_1089402] : [class_Int_Onumber__ring(_1089402), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089402), c_Groups_Oone__class_Oone(_1089402)), c_Groups_Oone__class_Oone(_1089402)) = hAPP(c_Int_Onumber__class_Onumber__of(_1089402), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (17741 ^ _779448) ^ [_1090487, _1090489, _1090491] : [-(hBOOL(hAPP(_1090487, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1090489), _1090491)))), 17744 ^ _779448 : [(17745 ^ _779448) ^ [] : [-(_1090491 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17747 ^ _779448) ^ [] : [hBOOL(hAPP(_1090487, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 17750 ^ _779448 : [(17751 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1090491)))], (17755 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17753 ^ [_1090487, _1090489, _1090491])))], (17757 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 17753 ^ [_1090487, _1090489, _1090491]), _1090491)))], (17759 ^ _779448) ^ [] : [-(_1090489 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1090491), 17752 ^ [_1090487, _1090489, _1090491])), 17753 ^ [_1090487, _1090489, _1090491]))], (17761 ^ _779448) ^ [] : [hBOOL(hAPP(_1090487, 17752 ^ [_1090487, _1090489, _1090491]))]], 17762 ^ _779448 : [(17763 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090491), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17767 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1090491), 17765 ^ [_1090487, _1090489, _1090491])))], (17769 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 17765 ^ [_1090487, _1090489, _1090491]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17771 ^ _779448) ^ [] : [-(_1090489 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1090491), 17764 ^ [_1090487, _1090489, _1090491])), 17765 ^ [_1090487, _1090489, _1090491]))], (17773 ^ _779448) ^ [] : [hBOOL(hAPP(_1090487, 17764 ^ [_1090487, _1090489, _1090491]))]]], (17695 ^ _779448) ^ [_1089527, _1089529, _1089531] : [hBOOL(hAPP(_1089527, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1089529), _1089531))), 17698 ^ _779448 : [(17699 ^ _779448) ^ [] : [_1089531 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1089527, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17705 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089531)), 17708 ^ _779448 : [(17709 ^ _779448) ^ [_1089861] : [-(hBOOL(hAPP(_1089527, _1089861))), 17710 ^ _779448 : [(17711 ^ _779448) ^ [_1089932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1089932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089932), _1089531)), _1089529 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089531), _1089861)), _1089932)]]]]], (17723 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089531), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 17726 ^ _779448 : [(17727 ^ _779448) ^ [_1090191] : [-(hBOOL(hAPP(_1089527, _1090191))), 17728 ^ _779448 : [(17729 ^ _779448) ^ [_1090265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1089531), _1090265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1090265), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1089529 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089531), _1090191)), _1090265)]]]]]]], (17777 ^ _779448) ^ [_1091201, _1091203, _1091205, _1091207] : [_1091201 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1091203), _1091205)), _1091207), -(_1091203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1091201), _1091203) = _1091205), 17784 ^ _779448 : [(17785 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1091203)))], (17787 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1091207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091207), _1091203))]], 17792 ^ _779448 : [(17793 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1091203))], (17795 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091203), _1091207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1091207), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (17807 ^ _779448) ^ [_1091670, _1091672] : [class_Rings_Oring__1__no__zero__divisors(_1091670), 17810 ^ _779448 : [(17811 ^ _779448) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1091670), _1091672), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1091670), -(_1091672 = c_Groups_Ozero__class_Ozero(_1091670))], (17817 ^ _779448) ^ [] : [_1091672 = c_Groups_Ozero__class_Ozero(_1091670), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091670), _1091672), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1091670))]]], (17823 ^ _779448) ^ [_1091911] : [class_Rings_Osemiring__1(_1091911), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091911), c_Groups_Ozero__class_Ozero(_1091911)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1091911))], (17829 ^ _779448) ^ [] : [-(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))))], (17831 ^ _779448) ^ [] : [-(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))))], (17833 ^ _779448) ^ [_1092044, _1092046] : [class_Rings_Ocomm__semiring__1(_1092044), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092044), _1092046), _1092046) = hAPP(hAPP(c_Power_Opower__class_Opower(_1092044), _1092046), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17839 ^ _779448) ^ [_1092151, _1092153] : [class_Groups_Omonoid__mult(_1092151), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092151), _1092153), 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(_1092151), _1092153), _1092153))], (17845 ^ _779448) ^ [] : [-(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))))))], (17847 ^ _779448) ^ [_1092276] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092276), 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, _1092276)))], (17849 ^ _779448) ^ [_1092311] : [-(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)))), _1092311) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1092311)))], (17851 ^ _779448) ^ [_1092343] : [class_Rings_Osemiring__1(_1092343), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092343), c_Groups_Oone__class_Oone(_1092343)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1092343))], (17857 ^ _779448) ^ [_1092440] : [-(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)))), _1092440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1092440), _1092440))], (17859 ^ _779448) ^ [_1092472] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1092472), 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), _1092472), _1092472))], (17861 ^ _779448) ^ [_1092507, _1092509, _1092511] : [class_Groups_Omonoid__mult(_1092507), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1092507), _1092509), 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)))), _1092511)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1092507), hAPP(hAPP(c_Power_Opower__class_Opower(_1092507), _1092509), _1092511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17867 ^ _779448) ^ [] : [-(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)))))], (17869 ^ _779448) ^ [] : [-(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))))], (17871 ^ _779448) ^ [_1092674, _1092676, _1092678] : [class_Rings_Olinordered__semidom(_1092674), hAPP(hAPP(c_Power_Opower__class_Opower(_1092674), _1092676), 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(_1092674), _1092678), 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(_1092674), c_Groups_Ozero__class_Ozero(_1092674)), _1092676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092674), c_Groups_Ozero__class_Ozero(_1092674)), _1092678)), -(_1092676 = _1092678)], (17889 ^ _779448) ^ [_1092981, _1092983, _1092985] : [class_Rings_Olinordered__semidom(_1092981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092981), hAPP(hAPP(c_Power_Opower__class_Opower(_1092981), _1092983), 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(_1092981), _1092985), 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(_1092981), c_Groups_Ozero__class_Ozero(_1092981)), _1092985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1092981), _1092983), _1092985)))], (17903 ^ _779448) ^ [_1093244, _1093246] : [class_Rings_Olinordered__idom(_1093244), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093244), c_Groups_Ozero__class_Ozero(_1093244)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093244), _1093246), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (17909 ^ _779448) ^ [_1093353, _1093355] : [class_Rings_Olinordered__idom(_1093353), 17912 ^ _779448 : [(17913 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093353), c_Groups_Ozero__class_Ozero(_1093353)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093353), _1093355), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1093355 = c_Groups_Ozero__class_Ozero(_1093353)], (17919 ^ _779448) ^ [] : [-(_1093355 = c_Groups_Ozero__class_Ozero(_1093353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093353), c_Groups_Ozero__class_Ozero(_1093353)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093353), _1093355), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (17925 ^ _779448) ^ [_1093577, _1093579] : [class_Rings_Olinordered__idom(_1093577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093577), hAPP(hAPP(c_Power_Opower__class_Opower(_1093577), _1093579), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1093577)))], (17931 ^ _779448) ^ [_1093687, _1093689, _1093691] : [class_Rings_Olinordered__idom(_1093687), 17934 ^ _779448 : [(17935 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093687), hAPP(hAPP(c_Power_Opower__class_Opower(_1093687), _1093689), 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(_1093687), _1093691), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1093687), 17938 ^ _779448 : [(17939 ^ _779448) ^ [] : [-(_1093689 = c_Groups_Ozero__class_Ozero(_1093687))], (17941 ^ _779448) ^ [] : [-(_1093691 = c_Groups_Ozero__class_Ozero(_1093687))]]], (17943 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093687), hAPP(hAPP(c_Power_Opower__class_Opower(_1093687), _1093689), 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(_1093687), _1093691), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1093687)), _1093689 = c_Groups_Ozero__class_Ozero(_1093687), _1093691 = c_Groups_Ozero__class_Ozero(_1093687)]]], (17953 ^ _779448) ^ [_1094062, _1094064] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1094062), hAPP(c_Int_Onumber__class_Onumber__of(_1094062), _1094064)), 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(_1094062), hAPP(c_Int_Onumber__class_Onumber__of(_1094062), _1094064)), hAPP(c_Int_Onumber__class_Onumber__of(_1094062), _1094064))), class_Groups_Omonoid__mult(_1094062), class_Int_Onumber(_1094062)], (17963 ^ _779448) ^ [_1094249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1094249), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1094249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1094249 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17973 ^ _779448) ^ [_1094347, _1094349, _1094351] : [class_Rings_Ocomm__semiring__1(_1094347), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1094347), _1094349), 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)))), _1094351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094347), hAPP(hAPP(c_Power_Opower__class_Opower(_1094347), _1094349), _1094351)), hAPP(hAPP(c_Power_Opower__class_Opower(_1094347), _1094349), _1094351)))], (17979 ^ _779448) ^ [_1094494, _1094496, _1094498] : [class_Rings_Olinordered__semidom(_1094494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094494), hAPP(hAPP(c_Power_Opower__class_Opower(_1094494), _1094496), 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(_1094494), _1094498), 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(_1094494), c_Groups_Ozero__class_Ozero(_1094494)), _1094498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1094494), _1094496), _1094498)))], (17993 ^ _779448) ^ [_1094757, _1094759, _1094761] : [class_Rings_Olinordered__idom(_1094757), 17996 ^ _779448 : [(17997 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094757), hAPP(hAPP(c_Power_Opower__class_Opower(_1094757), _1094759), 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(_1094757), _1094761), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094757))), 18000 ^ _779448 : [(18001 ^ _779448) ^ [] : [-(_1094759 = c_Groups_Ozero__class_Ozero(_1094757))], (18003 ^ _779448) ^ [] : [-(_1094761 = c_Groups_Ozero__class_Ozero(_1094757))]]], (18005 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094757), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094757), hAPP(hAPP(c_Power_Opower__class_Opower(_1094757), _1094759), 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(_1094757), _1094761), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1094757)))), _1094759 = c_Groups_Ozero__class_Ozero(_1094757), _1094761 = c_Groups_Ozero__class_Ozero(_1094757)]]], (18015 ^ _779448) ^ [_1095153, _1095155, _1095157] : [class_Rings_Olinordered__idom(_1095153), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095153), c_Groups_Ozero__class_Ozero(_1095153)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095153), hAPP(hAPP(c_Power_Opower__class_Opower(_1095153), _1095155), 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(_1095153), _1095157), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (18021 ^ _779448) ^ [_1095296, _1095298, _1095300] : [class_Rings_Olinordered__idom(_1095296), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095296), hAPP(hAPP(c_Power_Opower__class_Opower(_1095296), _1095298), 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(_1095296), _1095300), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1095296)))], (18027 ^ _779448) ^ [_1095440, _1095442, _1095444] : [class_Rings_Olinordered__idom(_1095440), 18030 ^ _779448 : [(18041 ^ _779448) ^ [] : [18042 ^ _779448 : [(18043 ^ _779448) ^ [] : [-(_1095442 = c_Groups_Ozero__class_Ozero(_1095440))], (18045 ^ _779448) ^ [] : [-(_1095444 = c_Groups_Ozero__class_Ozero(_1095440))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095440), c_Groups_Ozero__class_Ozero(_1095440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095440), hAPP(hAPP(c_Power_Opower__class_Opower(_1095440), _1095442), 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(_1095440), _1095444), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (18031 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095440), c_Groups_Ozero__class_Ozero(_1095440)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095440), hAPP(hAPP(c_Power_Opower__class_Opower(_1095440), _1095442), 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(_1095440), _1095444), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1095442 = c_Groups_Ozero__class_Ozero(_1095440), _1095444 = c_Groups_Ozero__class_Ozero(_1095440)]]], (18049 ^ _779448) ^ [_1095815, _1095817, _1095819] : [class_Int_Onumber__ring(_1095815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1095815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095815), _1095817), _1095819)), 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(_1095815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095815), hAPP(hAPP(c_Power_Opower__class_Opower(_1095815), _1095817), 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(_1095815), _1095819), 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(_1095815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095815), hAPP(c_Int_Onumber__class_Onumber__of(_1095815), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1095817)), _1095819)))], (18055 ^ _779448) ^ [_1096030, _1096032, _1096034] : [class_Rings_Olinordered__idom(_1096030), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096030), c_Groups_Ozero__class_Ozero(_1096030)), hAPP(hAPP(c_Power_Opower__class_Opower(_1096030), _1096032), 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)))), _1096034)))))], (18061 ^ _779448) ^ [_1096147, _1096149, _1096151] : [class_Groups_Omonoid__mult(_1096147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096147), _1096149), 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)))), _1096151))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096147), _1096149), hAPP(hAPP(c_Power_Opower__class_Opower(_1096147), hAPP(hAPP(c_Power_Opower__class_Opower(_1096147), _1096149), _1096151)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (18067 ^ _779448) ^ [_1096300, _1096302, _1096304] : [class_Rings_Ocomm__semiring__1(_1096300), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096300), _1096302), 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)))), _1096304))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096300), _1096302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096300), hAPP(hAPP(c_Power_Opower__class_Opower(_1096300), _1096302), _1096304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1096300), _1096302), _1096304))))], (18073 ^ _779448) ^ [_1096469, _1096471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1096469), 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)))), _1096471)), 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)))), _1096469)) = 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), _1096471), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1096469))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18079 ^ _779448) ^ [_1096629, _1096631] : [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), _1096629))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1096631)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1096629))) = 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), _1096631), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096629)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18085 ^ _779448) ^ [_1096776, _1096778] : [-(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), _1096776)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1096778)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1096776))) = 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), _1096778)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096776)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18091 ^ _779448) ^ [_1096858, _1096860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096858)), -(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)))), _1096860)), 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)))), _1096858)) = 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, _1096860, _1096858))))], (18097 ^ _779448) ^ [_1096985, _1096987] : [class_Rings_Osemiring__1(_1096985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096987)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096985), 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)))), _1096987))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096985), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096985), hAPP(c_Int_Onat, _1096987))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1096985), hAPP(c_Int_Onat, _1096987))))], (18107 ^ _779448) ^ [_1097186] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1097186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1097186)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18109 ^ _779448) ^ [_1097221, _1097223] : [class_Int_Onumber__ring(_1097221), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1097221), hAPP(c_Int_Onumber__class_Onumber__of(_1097221), 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)))), _1097223))) = hAPP(c_Int_Onumber__class_Onumber__of(_1097221), c_Int_OMin))], (18115 ^ _779448) ^ [_1097344, _1097346] : [class_Int_Onumber__ring(_1097344), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1097344), hAPP(c_Int_Onumber__class_Onumber__of(_1097344), 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)))), _1097346)) = c_Groups_Oone__class_Oone(_1097344))], (18121 ^ _779448) ^ [_1097470, _1097472] : [c_Code__Numeral_OSuc__code__numeral(_1097470) = c_Code__Numeral_OSuc__code__numeral(_1097472), -(_1097470 = _1097472)], (18127 ^ _779448) ^ [_1097551, _1097553] : [_1097551 = _1097553, -(c_Code__Numeral_OSuc__code__numeral(_1097551) = c_Code__Numeral_OSuc__code__numeral(_1097553))], (18133 ^ _779448) ^ [_1097638, _1097640, _1097642] : [class_Divides_Osemiring__div(_1097638), -(c_Divides_Odiv__class_Omod(_1097638, c_Divides_Odiv__class_Omod(_1097638, _1097640, _1097642), _1097642) = c_Divides_Odiv__class_Omod(_1097638, _1097640, _1097642))], (18139 ^ _779448) ^ [_1097739] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1097739, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18141 ^ _779448) ^ [_1097766, _1097768] : [class_Divides_Osemiring__div(_1097766), -(c_Divides_Odiv__class_Omod(_1097766, c_Groups_Ozero__class_Ozero(_1097766), _1097768) = c_Groups_Ozero__class_Ozero(_1097766))], (18147 ^ _779448) ^ [_1097857, _1097859] : [class_Divides_Osemiring__div(_1097857), -(c_Divides_Odiv__class_Omod(_1097857, _1097859, c_Groups_Ozero__class_Ozero(_1097857)) = _1097859)], (18153 ^ _779448) ^ [_1097944, _1097946] : [class_Divides_Osemiring__div(_1097944), -(c_Divides_Odiv__class_Omod(_1097944, _1097946, _1097946) = c_Groups_Ozero__class_Ozero(_1097944))], (18159 ^ _779448) ^ [_1098031, _1098033, _1098035] : [class_Divides_Osemiring__div(_1098031), -(c_Divides_Odiv__class_Omod(_1098031, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098031), _1098033), _1098035), _1098035) = c_Divides_Odiv__class_Omod(_1098031, _1098033, _1098035))], (18165 ^ _779448) ^ [_1098140, _1098142, _1098144] : [class_Divides_Osemiring__div(_1098140), -(c_Divides_Odiv__class_Omod(_1098140, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098140), _1098142), _1098144), _1098142) = c_Divides_Odiv__class_Omod(_1098140, _1098144, _1098142))], (18171 ^ _779448) ^ [_1098249, _1098251, _1098253, _1098255] : [class_Divides_Osemiring__div(_1098249), -(c_Divides_Odiv__class_Omod(_1098249, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098249), _1098251), _1098253), _1098255) = c_Divides_Odiv__class_Omod(_1098249, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098249), _1098251), c_Divides_Odiv__class_Omod(_1098249, _1098253, _1098255)), _1098255))], (18177 ^ _779448) ^ [_1098384, _1098386, _1098388, _1098390] : [class_Divides_Osemiring__div(_1098384), -(c_Divides_Odiv__class_Omod(_1098384, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098384), _1098386), _1098388), _1098390) = c_Divides_Odiv__class_Omod(_1098384, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098384), c_Divides_Odiv__class_Omod(_1098384, _1098386, _1098390)), _1098388), _1098390))], (18183 ^ _779448) ^ [_1098519, _1098521, _1098523, _1098525] : [class_Divides_Osemiring__div(_1098519), -(c_Divides_Odiv__class_Omod(_1098519, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098519), _1098521), _1098523), _1098525) = c_Divides_Odiv__class_Omod(_1098519, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098519), c_Divides_Odiv__class_Omod(_1098519, _1098521, _1098525)), c_Divides_Odiv__class_Omod(_1098519, _1098523, _1098525)), _1098525))], (18189 ^ _779448) ^ [_1098662, _1098664, _1098666, _1098668] : [class_Divides_Osemiring__div(_1098662), -(c_Divides_Odiv__class_Omod(_1098662, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098662), _1098664), c_Divides_Odiv__class_Omod(_1098662, _1098666, _1098668)), _1098668) = c_Divides_Odiv__class_Omod(_1098662, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098662), _1098664), _1098666), _1098668))], (18195 ^ _779448) ^ [_1098797, _1098799, _1098801, _1098803] : [class_Divides_Osemiring__div(_1098797), -(c_Divides_Odiv__class_Omod(_1098797, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098797), c_Divides_Odiv__class_Omod(_1098797, _1098799, _1098801)), _1098803), _1098801) = c_Divides_Odiv__class_Omod(_1098797, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098797), _1098799), _1098803), _1098801))], (18201 ^ _779448) ^ [_1098932, _1098934, _1098936, _1098938, _1098940, _1098942] : [class_Divides_Osemiring__div(_1098932), c_Divides_Odiv__class_Omod(_1098932, _1098934, _1098936) = c_Divides_Odiv__class_Omod(_1098932, _1098938, _1098936), c_Divides_Odiv__class_Omod(_1098932, _1098940, _1098936) = c_Divides_Odiv__class_Omod(_1098932, _1098942, _1098936), -(c_Divides_Odiv__class_Omod(_1098932, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098932), _1098934), _1098940), _1098936) = c_Divides_Odiv__class_Omod(_1098932, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098932), _1098938), _1098942), _1098936))], (18215 ^ _779448) ^ [_1099215, _1099217, _1099219, _1099221] : [class_Divides_Osemiring__div(_1099215), -(c_Divides_Odiv__class_Omod(_1099215, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099215), _1099217), _1099219), _1099221) = c_Divides_Odiv__class_Omod(_1099215, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099215), _1099217), c_Divides_Odiv__class_Omod(_1099215, _1099219, _1099221)), _1099221))], (18221 ^ _779448) ^ [_1099350, _1099352, _1099354, _1099356] : [class_Divides_Osemiring__div(_1099350), -(c_Divides_Odiv__class_Omod(_1099350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099350), _1099352), _1099354), _1099356) = c_Divides_Odiv__class_Omod(_1099350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099350), c_Divides_Odiv__class_Omod(_1099350, _1099352, _1099356)), _1099354), _1099356))], (18227 ^ _779448) ^ [_1099485, _1099487, _1099489, _1099491] : [class_Divides_Osemiring__div(_1099485), -(c_Divides_Odiv__class_Omod(_1099485, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099485), _1099487), _1099489), _1099491) = c_Divides_Odiv__class_Omod(_1099485, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099485), c_Divides_Odiv__class_Omod(_1099485, _1099487, _1099491)), c_Divides_Odiv__class_Omod(_1099485, _1099489, _1099491)), _1099491))], (18233 ^ _779448) ^ [_1099628, _1099630, _1099632, _1099634] : [class_Divides_Osemiring__div(_1099628), -(c_Divides_Odiv__class_Omod(_1099628, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099628), _1099630), _1099632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099628), _1099630), _1099634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099628), _1099630), c_Divides_Odiv__class_Omod(_1099628, _1099632, _1099634)))], (18239 ^ _779448) ^ [_1099771, _1099773, _1099775, _1099777] : [class_Divides_Osemiring__div(_1099771), -(c_Divides_Odiv__class_Omod(_1099771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099771), _1099773), _1099775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099771), _1099777), _1099775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099771), c_Divides_Odiv__class_Omod(_1099771, _1099773, _1099777)), _1099775))], (18245 ^ _779448) ^ [_1099914, _1099916, _1099918, _1099920] : [class_Divides_Osemiring__div(_1099914), -(c_Divides_Odiv__class_Omod(_1099914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099914), c_Divides_Odiv__class_Omod(_1099914, _1099916, _1099918)), _1099920), _1099918) = c_Divides_Odiv__class_Omod(_1099914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099914), _1099916), _1099920), _1099918))], (18251 ^ _779448) ^ [_1100049, _1100051, _1100053, _1100055, _1100057, _1100059] : [class_Divides_Osemiring__div(_1100049), c_Divides_Odiv__class_Omod(_1100049, _1100051, _1100053) = c_Divides_Odiv__class_Omod(_1100049, _1100055, _1100053), c_Divides_Odiv__class_Omod(_1100049, _1100057, _1100053) = c_Divides_Odiv__class_Omod(_1100049, _1100059, _1100053), -(c_Divides_Odiv__class_Omod(_1100049, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100049), _1100051), _1100057), _1100053) = c_Divides_Odiv__class_Omod(_1100049, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100049), _1100055), _1100059), _1100053))], (18265 ^ _779448) ^ [_1100332, _1100334, _1100336, _1100338, _1100340, _1100342] : [class_Divides_Oring__div(_1100332), c_Divides_Odiv__class_Omod(_1100332, _1100334, _1100336) = c_Divides_Odiv__class_Omod(_1100332, _1100338, _1100336), c_Divides_Odiv__class_Omod(_1100332, _1100340, _1100336) = c_Divides_Odiv__class_Omod(_1100332, _1100342, _1100336), -(c_Divides_Odiv__class_Omod(_1100332, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100332), _1100334), _1100340), _1100336) = c_Divides_Odiv__class_Omod(_1100332, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100332), _1100338), _1100342), _1100336))], (18279 ^ _779448) ^ [_1100615, _1100617, _1100619, _1100621] : [class_Divides_Oring__div(_1100615), -(c_Divides_Odiv__class_Omod(_1100615, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100615), _1100617), _1100619), _1100621) = c_Divides_Odiv__class_Omod(_1100615, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100615), c_Divides_Odiv__class_Omod(_1100615, _1100617, _1100621)), c_Divides_Odiv__class_Omod(_1100615, _1100619, _1100621)), _1100621))], (18285 ^ _779448) ^ [_1100758, _1100760, _1100762, _1100764] : [class_Divides_Oring__div(_1100758), -(c_Divides_Odiv__class_Omod(_1100758, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100758), _1100760), _1100762), _1100764) = c_Divides_Odiv__class_Omod(_1100758, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100758), c_Divides_Odiv__class_Omod(_1100758, _1100760, _1100764)), _1100762), _1100764))], (18291 ^ _779448) ^ [_1100893, _1100895, _1100897, _1100899] : [class_Divides_Oring__div(_1100893), -(c_Divides_Odiv__class_Omod(_1100893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100893), _1100895), _1100897), _1100899) = c_Divides_Odiv__class_Omod(_1100893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100893), _1100895), c_Divides_Odiv__class_Omod(_1100893, _1100897, _1100899)), _1100899))], (18297 ^ _779448) ^ [_1101028, _1101030, _1101032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1101028), _1101030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1101028), _1101032)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1101030), _1101032))))], (18303 ^ _779448) ^ [_1101151, _1101153] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1101151), _1101153)), _1101151)))], (18305 ^ _779448) ^ [_1101187, _1101189, _1101191] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1101187), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1101189), _1101191)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1101187), _1101189)), _1101191))], (18307 ^ _779448) ^ [_1101238] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1101238) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18309 ^ _779448) ^ [_1101265] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101265, _1101265) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18311 ^ _779448) ^ [_1101292] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101292)) = _1101292)], (18313 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (18315 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (18317 ^ _779448) ^ [_1101363, _1101365, _1101367] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101363), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101365, _1101367)), _1101367) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101363), _1101365), _1101367))], (18319 ^ _779448) ^ [_1101414, _1101416, _1101418] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101414), _1101416), _1101418) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1101414), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101416, _1101418)), _1101418))], (18321 ^ _779448) ^ [] : [c_Int_OPls = c_Int_OMin], (18323 ^ _779448) ^ [] : [c_Int_OMin = c_Int_OPls], (18325 ^ _779448) ^ [_1101525] : [c_Int_OBit1(_1101525) = c_Int_OMin, -(_1101525 = c_Int_OMin)], (18331 ^ _779448) ^ [_1101600] : [_1101600 = c_Int_OMin, -(c_Int_OBit1(_1101600) = c_Int_OMin)], (18337 ^ _779448) ^ [_1101693] : [c_Int_OMin = c_Int_OBit1(_1101693), -(c_Int_OMin = _1101693)], (18343 ^ _779448) ^ [_1101768] : [c_Int_OMin = _1101768, -(c_Int_OMin = c_Int_OBit1(_1101768))], (18349 ^ _779448) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (18351 ^ _779448) ^ [_1101876] : [c_Int_OBit0(_1101876) = c_Int_OMin], (18353 ^ _779448) ^ [_1101910] : [c_Int_OMin = c_Int_OBit0(_1101910)], (18355 ^ _779448) ^ [_1101935, _1101937, _1101939] : [-(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, _1101935, _1101937)), _1101939), _1101937) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1101935), _1101939), _1101937))], (18357 ^ _779448) ^ [_1101986, _1101988, _1101990] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1101986), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1101988, _1101990)), _1101990) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1101986), _1101988), _1101990))], (18359 ^ _779448) ^ [_1102037, _1102039, _1102041] : [-(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, _1102037, _1102039)), _1102041), _1102039) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1102037), _1102041), _1102039))], (18361 ^ _779448) ^ [_1102088, _1102090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102088)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1102088), _1102090)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1102088)), hAPP(c_Int_Onat, _1102090)))], (18367 ^ _779448) ^ [_1102211, _1102213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1102213)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1102211)), hAPP(c_Int_Onat, _1102213)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1102211), _1102213)))], (18377 ^ _779448) ^ [_1102390, _1102392, _1102394] : [class_Divides_Osemiring__div(_1102390), -(c_Divides_Odiv__class_Omod(_1102390, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102390), _1102392), _1102394), _1102394) = c_Groups_Ozero__class_Ozero(_1102390))], (18383 ^ _779448) ^ [_1102495, _1102497, _1102499] : [class_Divides_Osemiring__div(_1102495), -(c_Divides_Odiv__class_Omod(_1102495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102495), _1102497), _1102499), _1102497) = c_Groups_Ozero__class_Ozero(_1102495))], (18389 ^ _779448) ^ [_1102600, _1102602, _1102604, _1102606] : [class_Divides_Osemiring__div(_1102600), -(c_Divides_Odiv__class_Omod(_1102600, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102600), _1102602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102600), _1102604), _1102606)), _1102606) = c_Divides_Odiv__class_Omod(_1102600, _1102602, _1102606))], (18395 ^ _779448) ^ [_1102727, _1102729, _1102731, _1102733] : [class_Divides_Osemiring__div(_1102727), -(c_Divides_Odiv__class_Omod(_1102727, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102727), _1102729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102727), _1102731), _1102733)), _1102731) = c_Divides_Odiv__class_Omod(_1102727, _1102729, _1102731))], (18401 ^ _779448) ^ [_1102854, _1102856] : [class_Divides_Osemiring__div(_1102854), -(c_Divides_Odiv__class_Omod(_1102854, _1102856, c_Groups_Oone__class_Oone(_1102854)) = c_Groups_Ozero__class_Ozero(_1102854))], (18407 ^ _779448) ^ [_1102945, _1102947, _1102949] : [class_Divides_Osemiring__div(_1102945), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1102945), c_Divides_Odiv__class_Omod(_1102945, _1102947, _1102949)), _1102949) = c_Groups_Ozero__class_Ozero(_1102945))], (18413 ^ _779448) ^ [_1103050] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1103050), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1103050)], (18415 ^ _779448) ^ [_1103079, _1103081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103079), _1103081)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1103079), _1103081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18421 ^ _779448) ^ [_1103190, _1103192, _1103194] : [_1103190 = 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), _1103190), _1103192)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103190), _1103194)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18427 ^ _779448) ^ [_1103299, _1103301, _1103303] : [-(_1103299 = 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), _1103299), _1103301)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103299), _1103303)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1103301), _1103303))], (18433 ^ _779448) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18435 ^ _779448) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18437 ^ _779448) ^ [_1103411] : [18438 ^ _779448 : [(18439 ^ _779448) ^ [_1103468] : [hBOOL(hAPP(_1103411, _1103468))]], 18441 ^ _779448 : [(18442 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18440 ^ [_1103411])))], (18444 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1103411, hAPP(c_Int_Onat, 18440 ^ [_1103411]))))]]], (18446 ^ _779448) ^ [_1103554] : [-(hBOOL(hAPP(_1103554, 18453 ^ [_1103554]))), 18447 ^ _779448 : [(18448 ^ _779448) ^ [_1103606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1103606)), hBOOL(hAPP(_1103554, hAPP(c_Int_Onat, _1103606)))]]], (18468 ^ _779448) ^ [_1103930] : [18470 ^ _779448 : [(18471 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18469 ^ [_1103930])))], (18473 ^ _779448) ^ [] : [hBOOL(hAPP(_1103930, hAPP(c_Int_Onat, 18469 ^ [_1103930])))]], 18474 ^ _779448 : [(18475 ^ _779448) ^ [_1104063] : [-(hBOOL(hAPP(_1103930, _1104063)))]]], (18457 ^ _779448) ^ [_1103745] : [hBOOL(hAPP(_1103745, 18458 ^ [_1103745])), 18461 ^ _779448 : [(18462 ^ _779448) ^ [_1103839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1103839)), -(hBOOL(hAPP(_1103745, hAPP(c_Int_Onat, _1103839))))]]], (18477 ^ _779448) ^ [_1104096, _1104098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104098)), 18484 ^ _779448 : [(18485 ^ _779448) ^ [] : [hAPP(c_Int_Onat, _1104096) = hAPP(c_Int_Onat, _1104098), -(_1104096 = _1104098)], (18491 ^ _779448) ^ [] : [_1104096 = _1104098, -(hAPP(c_Int_Onat, _1104096) = hAPP(c_Int_Onat, _1104098))]]], (18497 ^ _779448) ^ [_1104381, _1104383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104383)), 18504 ^ _779448 : [(18505 ^ _779448) ^ [] : [hAPP(c_Int_Onat, _1104381) = hAPP(c_Int_Onat, _1104383), -(_1104381 = _1104383)], (18511 ^ _779448) ^ [] : [_1104381 = _1104383, -(hAPP(c_Int_Onat, _1104381) = hAPP(c_Int_Onat, _1104383))]]], (18517 ^ _779448) ^ [_1104666, _1104668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1104666, _1104668)), _1104666)))], (18523 ^ _779448) ^ [_1104765, _1104767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104767)), -(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, _1104765, _1104767))))], (18533 ^ _779448) ^ [_1104914, _1104916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104914), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1104914), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1104916, _1104914))))], (18539 ^ _779448) ^ [_1105019, _1105021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1105019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1105021, _1105019)), _1105019)))], (18545 ^ _779448) ^ [_1105118, _1105120] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105118)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105120)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1105118), _1105120)))], (18547 ^ _779448) ^ [_1105164, _1105166] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1105164), _1105166)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105164)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105166)))], (18549 ^ _779448) ^ [_1105210] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105210) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1105210)))], (18551 ^ _779448) ^ [_1105242] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1105242)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105242))], (18553 ^ _779448) ^ [_1105289, _1105291] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1105289, _1105291) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1105289 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1105291), 18556 ^ [_1105289, _1105291]))], (18560 ^ _779448) ^ [_1105394, _1105396] : [18561 ^ _779448 : [(18562 ^ _779448) ^ [_1105443] : [_1105394 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1105396), _1105443)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1105394, _1105396) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18566 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18568 ^ _779448) ^ [_1105522] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1105522), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18570 ^ _779448) ^ [_1105548] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1105548, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1105548)], (18572 ^ _779448) ^ [_1105577, _1105579] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1105577, _1105579)), _1105579) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18574 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18576 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (18578 ^ _779448) ^ [_1105666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1105666)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105666), c_Int_OMin)))], (18584 ^ _779448) ^ [_1105761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105761), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1105761)), c_Int_OMin)))], (18590 ^ _779448) ^ [_1105874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1105874))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1105874)))], (18596 ^ _779448) ^ [_1105957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1105957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1105957))))], (18602 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (18604 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (18606 ^ _779448) ^ [_1106100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106100)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106100), c_Int_OMin)))], (18612 ^ _779448) ^ [_1106195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106195), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1106195)), c_Int_OMin)))], (18618 ^ _779448) ^ [_1106308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1106308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106308)))], (18624 ^ _779448) ^ [_1106391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1106391))))], (18630 ^ _779448) ^ [_1106492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1106492)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106492), c_Int_OMin)))], (18636 ^ _779448) ^ [_1106587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106587), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1106587)), c_Int_OMin)))], (18642 ^ _779448) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18644 ^ _779448) ^ [_1106718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1106718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106718)))], (18650 ^ _779448) ^ [_1106801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1106801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1106801))))], (18656 ^ _779448) ^ [] : [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)], (18658 ^ _779448) ^ [_1106914] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1106914)), -(hAPP(c_Int_Onat, _1106914) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18664 ^ _779448) ^ [_1106999, _1107001, _1107003] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1106999), _1107001)), _1107003) = 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), _1106999), _1107003)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1107001), _1107003))), 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, _1106999, _1107003)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1107001, _1107003))), _1107003)))], (18666 ^ _779448) ^ [_1107078] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1107078))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1107078)) = _1107078)], (18672 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (18674 ^ _779448) ^ [_1107138] : [-(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)), _1107138)) = _1107138)], (18676 ^ _779448) ^ [_1107176] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1107176)], (18678 ^ _779448) ^ [_1107210] : [c_Code__Numeral_OSuc__code__numeral(_1107210) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (18680 ^ _779448) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (18682 ^ _779448) ^ [_1107253] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1107253) = c_Int_Opred(_1107253))], (18684 ^ _779448) ^ [_1107281] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1107281), c_Int_OMin) = c_Int_Opred(_1107281))], (18686 ^ _779448) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (18688 ^ _779448) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (18690 ^ _779448) ^ [_1107357, _1107359] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1107357))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107357)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107359)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18696 ^ _779448) ^ [_1107462, _1107464] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1107462)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107462)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1107464)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1107462)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1107464))))], (18702 ^ _779448) ^ [_1107532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1107532)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1107532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1107532), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18708 ^ _779448) ^ [_1107631] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1107631), c_Int_OMin) = c_Int_Osucc(_1107631))], (18710 ^ _779448) ^ [_1107662] : [-(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), _1107662)) = 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), _1107662))))], (18712 ^ _779448) ^ [_1107700, _1107702, _1107704, _1107706] : [class_Divides_Osemiring__div(_1107700), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107700), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1107700), _1107702), _1107704)), _1107704)), c_Divides_Odiv__class_Omod(_1107700, _1107702, _1107704))), _1107706) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107700), _1107702), _1107706))], (18718 ^ _779448) ^ [_1107867, _1107869, _1107871, _1107873] : [class_Divides_Osemiring__div(_1107867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107867), _1107869), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1107867), _1107871), _1107869))), c_Divides_Odiv__class_Omod(_1107867, _1107871, _1107869))), _1107873) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107867), _1107871), _1107873))], (18724 ^ _779448) ^ [_1108034, _1108036, _1108038] : [class_Divides_Osemiring__div(_1108034), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108034), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1108034), _1108036), _1108038)), _1108038)), c_Divides_Odiv__class_Omod(_1108034, _1108036, _1108038)) = _1108036)], (18730 ^ _779448) ^ [_1108167, _1108169, _1108171] : [class_Divides_Osemiring__div(_1108167), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108167), _1108169), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1108167), _1108171), _1108169))), c_Divides_Odiv__class_Omod(_1108167, _1108171, _1108169)) = _1108171)], (18736 ^ _779448) ^ [_1108300, _1108302, _1108304] : [class_Divides_Osemiring__div(_1108300), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108300), c_Divides_Odiv__class_Omod(_1108300, _1108302, _1108304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108300), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1108300), _1108302), _1108304)), _1108304)) = _1108302)], (18742 ^ _779448) ^ [] : [-(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))))], (18744 ^ _779448) ^ [_1108451, _1108453, _1108455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108451), _1108453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1108455), _1108453)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1108455), _1108451))))], (18754 ^ _779448) ^ [_1108632, _1108634, _1108636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108632)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108632), _1108634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108632), _1108636)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1108634), _1108636))], (18760 ^ _779448) ^ [_1108763, _1108765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108763)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108765), _1108763)), _1108763) = _1108765)], (18766 ^ _779448) ^ [_1108868, _1108870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108868)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108868), _1108870)), _1108868) = _1108870)], (18772 ^ _779448) ^ [_1108973, _1108975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1108973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1108975), _1108973)), _1108975)))], (18782 ^ _779448) ^ [_1109132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109132), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1109132) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18788 ^ _779448) ^ [_1109235] : [hAPP(c_Int_Onat, _1109235) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109235), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18794 ^ _779448) ^ [_1109322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109322), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1109322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18800 ^ _779448) ^ [_1109430, _1109432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109430)), hAPP(c_Int_Onat, _1109432))), 18803 ^ _779448 : [(18804 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109432)))], (18806 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109430), _1109432)))]]], (18808 ^ _779448) ^ [_1109565, _1109567] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109565)), hAPP(c_Int_Onat, _1109567)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109565), _1109567))], (18818 ^ _779448) ^ [_1109732, _1109734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109732)), 18821 ^ _779448 : [(18822 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109734)), hAPP(c_Int_Onat, _1109732))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109734), _1109732)))], (18828 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109734), _1109732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109734)), hAPP(c_Int_Onat, _1109732))))]]], (18834 ^ _779448) ^ [_1109991, _1109993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109993)), 18841 ^ _779448 : [(18842 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1109991)), hAPP(c_Int_Onat, _1109993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109991), _1109993)))], (18848 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109991), _1109993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1109991)), hAPP(c_Int_Onat, _1109993))))]]], (18854 ^ _779448) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18856 ^ _779448) ^ [_1110324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110324)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1110324)) = _1110324)], (18862 ^ _779448) ^ [_1110430, _1110432] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110430) = _1110432, 18865 ^ _779448 : [(18866 ^ _779448) ^ [] : [-(_1110430 = hAPP(c_Int_Onat, _1110432))], (18868 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110432)))]]], (18870 ^ _779448) ^ [_1110545, _1110547] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110545) = _1110547), _1110545 = hAPP(c_Int_Onat, _1110547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110547))], (18880 ^ _779448) ^ [_1110698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110698)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1110698)) = _1110698)], (18886 ^ _779448) ^ [_1110783] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110783))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1110783)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18892 ^ _779448) ^ [_1110842, _1110844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110842), hAPP(c_Int_Onat, _1110844))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110842)), _1110844)))], (18898 ^ _779448) ^ [_1110947, _1110949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110947)), _1110949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110947), hAPP(c_Int_Onat, _1110949))))], (18904 ^ _779448) ^ [_1111058, _1111060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111058), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111060), _1111058)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1111058, _1111060) = _1111058)], (18914 ^ _779448) ^ [_1111215, _1111217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111215), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 18917 ^ _779448 : [(18918 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1111217, _1111215)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18920 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111215), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1111217, _1111215))))]]], (18922 ^ _779448) ^ [_1111364, _1111366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111364), 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, _1111366, _1111364)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18928 ^ _779448) ^ [_1111469, _1111471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111469)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1111469), _1111471)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1111469, _1111471) = _1111469)], (18938 ^ _779448) ^ [_1111620, _1111622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111620)), 18941 ^ _779448 : [(18942 ^ _779448) ^ [] : [-(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, _1111622, _1111620))))], (18944 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1111622, _1111620)), _1111620)))]]], (18946 ^ _779448) ^ [_1111757, _1111759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111757)), -(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, _1111759, _1111757))))], (18952 ^ _779448) ^ [_1111862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1111862)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111862), c_Int_OMin)))], (18958 ^ _779448) ^ [_1111957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111957), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1111957)), c_Int_OMin)))], (18964 ^ _779448) ^ [_1112070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1112070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1112070)))], (18970 ^ _779448) ^ [_1112153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1112153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1112153))))], (18976 ^ _779448) ^ [_1112242, _1112244, _1112246] : [-(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), _1112242), _1112244)), _1112244)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112242, _1112244))), _1112246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112242), _1112246))], (18978 ^ _779448) ^ [_1112303, _1112305, _1112307] : [-(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), _1112303), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1112305), _1112303))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112305, _1112303))), _1112307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1112305), _1112307))], (18980 ^ _779448) ^ [_1112364, _1112366, _1112368] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112364), _1112366)), _1112368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112364), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1112366), _1112368))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112364), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112366, _1112368))), _1112368)))], (18982 ^ _779448) ^ [_1112437, _1112439] : [-(_1112437 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112439), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1112437), _1112439))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112437, _1112439)))], (18984 ^ _779448) ^ [_1112484] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1112484)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1112484)))], (18986 ^ _779448) ^ [_1112532, _1112534] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112532), _1112534) = c_Groups_Oone__class_Oone(tc_Int_Oint), 18991 ^ _779448 : [(18992 ^ _779448) ^ [] : [-(_1112532 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18994 ^ _779448) ^ [] : [-(_1112534 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 18995 ^ _779448 : [(18996 ^ _779448) ^ [] : [-(_1112532 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (18998 ^ _779448) ^ [] : [-(_1112534 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (19000 ^ _779448) ^ [_1112716, _1112718] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112716), _1112718) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 19001 ^ _779448 : [(19002 ^ _779448) ^ [] : [_1112716 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1112718 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (19008 ^ _779448) ^ [] : [_1112716 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1112718 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (19016 ^ _779448) ^ [_1112942, _1112944] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112942), _1112944) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1112942 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1112942 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (19026 ^ _779448) ^ [_1113044] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1113044)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1113044)))], (19028 ^ _779448) ^ [_1113077] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1113077)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1113077)))], (19030 ^ _779448) ^ [_1113110, _1113112] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1113110, _1113112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1113110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1113110), _1113112)), _1113112)))], (19032 ^ _779448) ^ [_1113157, _1113159] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1113157), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1113159), _1113157)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1113159), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1113159, _1113157)))], (19034 ^ _779448) ^ [_1113204, _1113206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1113204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113206), _1113204))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1113206), _1113204) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1113206), _1113204)), _1113204)))], (19044 ^ _779448) ^ [_1113352, _1113354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1113352)), 19047 ^ _779448 : [(19048 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113354), _1113352)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1113354), _1113352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19054 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113354), _1113352))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1113354), _1113352) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1113354), _1113352)), _1113352)))]]], (19084 ^ _779448) ^ [_1114061, _1114063, _1114065] : [-(hBOOL(hAPP(_1114061, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1114063), _1114065)))), 19087 ^ _779448 : [(19088 ^ _779448) ^ [] : [-(_1114065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19090 ^ _779448) ^ [] : [hBOOL(hAPP(_1114061, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 19091 ^ _779448 : [(19092 ^ _779448) ^ [] : [_1114065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19096 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19094 ^ [_1114061, _1114063, _1114065]), _1114065)))], (19098 ^ _779448) ^ [] : [-(_1114063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1114065), 19093 ^ [_1114061, _1114063, _1114065])), 19094 ^ [_1114061, _1114063, _1114065]))], (19100 ^ _779448) ^ [] : [hBOOL(hAPP(_1114061, 19093 ^ [_1114061, _1114063, _1114065]))]]], (19060 ^ _779448) ^ [_1113624, _1113626, _1113628] : [hBOOL(hAPP(_1113624, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1113626), _1113628))), 19063 ^ _779448 : [(19064 ^ _779448) ^ [] : [_1113628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1113624, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19070 ^ _779448) ^ [] : [-(_1113628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19073 ^ _779448 : [(19074 ^ _779448) ^ [_1113876, _1113878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113876), _1113628)), _1113626 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1113628), _1113878)), _1113876), -(hBOOL(hAPP(_1113624, _1113878)))]]]]], (19104 ^ _779448) ^ [_1114495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1114495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114495)))], (19110 ^ _779448) ^ [_1114580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1114580))))], (19116 ^ _779448) ^ [_1114671, _1114673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114673)), 19123 ^ _779448 : [(19124 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1114671)), hAPP(c_Int_Onat, _1114673))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114671), _1114673)))], (19130 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114671), _1114673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1114671)), hAPP(c_Int_Onat, _1114673))))]]], (19136 ^ _779448) ^ [_1114986, _1114988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114986)), 19139 ^ _779448 : [(19140 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1114986)), hAPP(c_Int_Onat, _1114988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114986), _1114988)))], (19146 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114986), _1114988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1114986)), hAPP(c_Int_Onat, _1114988))))]]], (19168 ^ _779448) ^ [_1115452, _1115454] : [-(_1115452 = hAPP(c_Int_Onat, _1115454)), 19171 ^ _779448 : [(19172 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115454)))], (19174 ^ _779448) ^ [] : [_1115454 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1115452)]], 19175 ^ _779448 : [(19176 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115454))], (19178 ^ _779448) ^ [] : [_1115452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19152 ^ _779448) ^ [_1115260, _1115262] : [_1115260 = hAPP(c_Int_Onat, _1115262), 19155 ^ _779448 : [(19156 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115262)), -(_1115262 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1115260))], (19162 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115262))), -(_1115260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19198 ^ _779448) ^ [_1115883, _1115885] : [-(hAPP(c_Int_Onat, _1115883) = _1115885), 19201 ^ _779448 : [(19202 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115883)))], (19204 ^ _779448) ^ [] : [_1115883 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1115885)]], 19205 ^ _779448 : [(19206 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115883))], (19208 ^ _779448) ^ [] : [_1115885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (19182 ^ _779448) ^ [_1115691, _1115693] : [hAPP(c_Int_Onat, _1115691) = _1115693, 19185 ^ _779448 : [(19186 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115691)), -(_1115691 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1115693))], (19192 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115691))), -(_1115693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19212 ^ _779448) ^ [_1116107, _1116109] : [19213 ^ _779448 : [(19214 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116107))], (19216 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116109))]], 19217 ^ _779448 : [(19218 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1116107)), hAPP(c_Int_Onat, _1116109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116107), _1116109)))], (19224 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116107), _1116109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1116107)), hAPP(c_Int_Onat, _1116109))))]]], (19246 ^ _779448) ^ [_1116686, _1116688] : [-(hBOOL(hAPP(_1116686, hAPP(c_Int_Onat, _1116688)))), 19250 ^ _779448 : [(19251 ^ _779448) ^ [] : [-(_1116688 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19249 ^ [_1116686, _1116688]))], (19253 ^ _779448) ^ [] : [hBOOL(hAPP(_1116686, 19249 ^ [_1116686, _1116688]))]], 19254 ^ _779448 : [(19255 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116688), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19257 ^ _779448) ^ [] : [hBOOL(hAPP(_1116686, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19230 ^ _779448) ^ [_1116423, _1116425] : [hBOOL(hAPP(_1116423, hAPP(c_Int_Onat, _1116425))), 19233 ^ _779448 : [(19234 ^ _779448) ^ [_1116523] : [_1116425 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1116523), -(hBOOL(hAPP(_1116423, _1116523)))], (19240 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116425), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1116423, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (19261 ^ _779448) ^ [_1116949, _1116951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116951)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1116949)), hAPP(c_Int_Onat, _1116951)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1116949), _1116951)))], (19271 ^ _779448) ^ [_1117128, _1117130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117130)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117128), _1117130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1117128)), hAPP(c_Int_Onat, _1117130)))], (19281 ^ _779448) ^ [_1117322, _1117324] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1117322) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117324), 19284 ^ _779448 : [(19285 ^ _779448) ^ [] : [-(_1117322 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117324)))], (19287 ^ _779448) ^ [] : [-(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), _1117324))))]]], (19289 ^ _779448) ^ [_1117455, _1117457] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1117455) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117457)), _1117455 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1117457)), 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), _1117457)))], (19299 ^ _779448) ^ [_1117620, _1117622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117622)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1117620)), hAPP(c_Int_Onat, _1117622)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117620), _1117622)))], (19309 ^ _779448) ^ [_1117799, _1117801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117799)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117799), _1117801)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1117799)), hAPP(c_Int_Onat, _1117801)))], (19315 ^ _779448) ^ [_1117922, _1117924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117922), _1117924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117922, _1117924) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1117922), _1117924))], (19325 ^ _779448) ^ [_1118097, _1118099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118097), _1118099)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1118099), _1118097)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1118099)), hAPP(c_Int_Onat, _1118097)))], (19335 ^ _779448) ^ [] : [-(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)))))], (19337 ^ _779448) ^ [_1118300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118300)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1118300) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (19343 ^ _779448) ^ [_1118385, _1118387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118385)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1118385)), _1118387) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1118385), _1118387)))], (19349 ^ _779448) ^ [_1118502, _1118504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118502)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1118502), _1118504)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1118502)), _1118504))], (19355 ^ _779448) ^ [_1118619, _1118621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118621)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1118619)), hAPP(c_Int_Onat, _1118621)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1118619, _1118621)))], (19365 ^ _779448) ^ [_1118792] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1118792)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1118792)], (19367 ^ _779448) ^ [_1118832, _1118834] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1118832)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1118834)), hAPP(c_Int_Onat, _1118832)) = hAPP(c_Int_Onat, _1118834))], (19373 ^ _779448) ^ [_1118937, _1118939] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1118937))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1118939)), hAPP(c_Int_Onat, _1118937)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1118939), _1118937)), 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)))], (19379 ^ _779448) ^ [_1119001, _1119003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119001), _1119003)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1119003), _1119001) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119003), _1119001)), _1119001)))], (19389 ^ _779448) ^ [_1119186, _1119188, _1119190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1119186)), 19392 ^ _779448 : [(19403 ^ _779448) ^ [] : [_1119188 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1119190), _1119186), 19406 ^ _779448 : [(19407 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119186), _1119188)), _1119190)))], (19409 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119186), hAPP(c_Nat_OSuc, _1119188)))))]]], (19393 ^ _779448) ^ [] : [-(_1119188 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1119190), _1119186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119186), _1119188)), _1119190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119186), hAPP(c_Nat_OSuc, _1119188))))]]], (19411 ^ _779448) ^ [_1119588, _1119590, _1119592] : [hBOOL(hAPP(_1119588, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1119590), _1119592))), 19416 ^ _779448 : [(19417 ^ _779448) ^ [] : [-(_1119592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19419 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1119588, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 19421 ^ _779448 : [(19422 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119592), 19420 ^ [_1119588, _1119590, _1119592])), _1119590)))], (19424 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119592), hAPP(c_Nat_OSuc, 19420 ^ [_1119588, _1119590, _1119592])))))], (19426 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1119588, 19420 ^ [_1119588, _1119590, _1119592])))]]], (19428 ^ _779448) ^ [_1119892, _1119894, _1119896] : [-(hBOOL(hAPP(_1119892, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1119894), _1119896)))), 19429 ^ _779448 : [(19430 ^ _779448) ^ [] : [_1119896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1119892, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19436 ^ _779448) ^ [_1120060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119896), _1120060)), _1119894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119896), hAPP(c_Nat_OSuc, _1120060)))), hBOOL(hAPP(_1119892, _1120060))]]], (19448 ^ _779448) ^ [_1120290, _1120292] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1120290), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1120292)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1120290), 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)))), _1120292)))], (19450 ^ _779448) ^ [_1120339, _1120341] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1120339)))), _1120341) = 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)))), _1120339)), _1120341))], (19452 ^ _779448) ^ [_1120388, _1120390] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1120388)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1120390)) = 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)))), _1120388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1120390)))], (19454 ^ _779448) ^ [_1120443] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1120443))), 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), _1120443), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (19456 ^ _779448) ^ [_1120487] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120487), _1120487)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1120487)], (19458 ^ _779448) ^ [_1120534] : [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, _1120534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1120534)))], (19464 ^ _779448) ^ [_1120619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1120619)), -(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, _1120619))))], (19470 ^ _779448) ^ [_1120710, _1120712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120710)), 19473 ^ _779448 : [(19474 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1120710)), _1120712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120710), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1120712))))], (19480 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120710), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1120712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1120710)), _1120712)))]]], (19486 ^ _779448) ^ [_1120969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120969)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1120969)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1120969)))], (19492 ^ _779448) ^ [] : [-(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)))))], (19494 ^ _779448) ^ [_1121090, _1121092, _1121094, _1121096] : [_1121090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121092), _1121094)), _1121096), -(_1121092 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121090, _1121092) = _1121096), 19501 ^ _779448 : [(19502 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121092)))], (19504 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121096), _1121092))]], 19509 ^ _779448 : [(19510 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121092))], (19512 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121092), _1121096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121096), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (19524 ^ _779448) ^ [_1121555, _1121557, _1121559, _1121561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121557), _1121559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121559), 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), _1121557), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121561, _1121555))), _1121559)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19538 ^ _779448) ^ [_1121814, _1121816, _1121818, _1121820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121816), _1121818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1121818), 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), _1121816), _1121814)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121816), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121820, _1121814))), _1121818))))], (19552 ^ _779448) ^ [_1122085, _1122087, _1122089, _1122091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122087), _1122089)), -(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), _1122089), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122091, _1122085))), _1122087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122089), _1122085))))], (19566 ^ _779448) ^ [_1122350, _1122352, _1122354, _1122356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122352), _1122354)), -(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), _1122354), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122356, _1122350))), _1122352))))], (19626 ^ _779448) ^ [_1123492, _1123494, _1123496] : [-(hBOOL(hAPP(_1123492, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1123494, _1123496)))), 19629 ^ _779448 : [(19630 ^ _779448) ^ [] : [-(_1123496 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19632 ^ _779448) ^ [] : [hBOOL(hAPP(_1123492, _1123494))]], 19635 ^ _779448 : [(19636 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123496)))], (19640 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19638 ^ [_1123492, _1123494, _1123496])))], (19642 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19638 ^ [_1123492, _1123494, _1123496]), _1123496)))], (19644 ^ _779448) ^ [] : [-(_1123494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123496), 19637 ^ [_1123492, _1123494, _1123496])), 19638 ^ [_1123492, _1123494, _1123496]))], (19646 ^ _779448) ^ [] : [hBOOL(hAPP(_1123492, 19638 ^ [_1123492, _1123494, _1123496]))]], 19647 ^ _779448 : [(19648 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19652 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123496), 19650 ^ [_1123492, _1123494, _1123496])))], (19654 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 19650 ^ [_1123492, _1123494, _1123496]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19656 ^ _779448) ^ [] : [-(_1123494 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1123496), 19649 ^ [_1123492, _1123494, _1123496])), 19650 ^ [_1123492, _1123494, _1123496]))], (19658 ^ _779448) ^ [] : [hBOOL(hAPP(_1123492, 19650 ^ [_1123492, _1123494, _1123496]))]]], (19580 ^ _779448) ^ [_1122615, _1122617, _1122619] : [hBOOL(hAPP(_1122615, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122617, _1122619))), 19583 ^ _779448 : [(19584 ^ _779448) ^ [] : [_1122619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1122615, _1122617)))], (19590 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122619)), 19593 ^ _779448 : [(19594 ^ _779448) ^ [_1122945, _1122947] : [-(hBOOL(hAPP(_1122615, _1122945))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122945), _1122619)), _1122617 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122619), _1122947)), _1122945)]]], (19608 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122619), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19611 ^ _779448 : [(19612 ^ _779448) ^ [_1123237, _1123239] : [-(hBOOL(hAPP(_1122615, _1123237))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122619), _1123237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1123237), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1122617 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122619), _1123239)), _1123237)]]]]], (19662 ^ _779448) ^ [_1124204, _1124206] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124204)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1124206))) = 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), _1124204), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1124206))))], (19664 ^ _779448) ^ [_1124256, _1124258, _1124260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124256)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1124258, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124260), _1124256)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1124260), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1124258), _1124260), _1124256))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1124258, _1124260)))], (19670 ^ _779448) ^ [_1124426, _1124428] : [hAPP(c_Nat_OSuc, _1124426) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1124428), -(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(_1124428))), 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)), _1124426))))))], (19676 ^ _779448) ^ [_1124549, _1124551] : [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(_1124551))), 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)), _1124549))))), -(hAPP(c_Nat_OSuc, _1124549) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1124551))], (19682 ^ _779448) ^ [_1124693, _1124695] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1124693) = hAPP(c_Nat_OSuc, _1124695), -(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(_1124693))), 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)), _1124695))))))], (19688 ^ _779448) ^ [_1124816, _1124818] : [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(_1124816))), 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)), _1124818))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1124816) = hAPP(c_Nat_OSuc, _1124818))], (19694 ^ _779448) ^ [_1124945, _1124947, _1124949, _1124951] : [-(c_Nat_Onat_Onat__case(_1124945, _1124947, _1124949, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1124951)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1124945), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1124951))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1124945, _1124945), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1124945, tc_fun(_1124945, _1124945)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1124945, tc_fun(_1124945, _1124945)), tc_Int_Oint), c_If(_1124945)), c_Nat__Numeral_Oneg)), _1124947)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1124945, tc_Int_Oint), _1124949), c_Int_Onat))))], (19696 ^ _779448) ^ [] : [-(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))))], (19698 ^ _779448) ^ [_1125065, _1125067, _1125069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125065), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19701 ^ _779448 : [(19720 ^ _779448) ^ [] : [19723 ^ _779448 : [(19724 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125065), 19722 ^ [_1125065, _1125067, _1125069])))], (19726 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 19722 ^ [_1125065, _1125067, _1125069]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19728 ^ _779448) ^ [] : [-(_1125069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125065), 19721 ^ [_1125065, _1125067, _1125069])), 19722 ^ [_1125065, _1125067, _1125069]))], (19730 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1125067, 19721 ^ [_1125065, _1125067, _1125069]), 19722 ^ [_1125065, _1125067, _1125069]))]], -(hBOOL(hAPP(hAPP(_1125067, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125069), _1125065)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125069, _1125065))))], (19702 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1125067, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125069), _1125065)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125069, _1125065))), 19705 ^ _779448 : [(19706 ^ _779448) ^ [_1125275, _1125277] : [-(hBOOL(hAPP(hAPP(_1125067, _1125277), _1125275))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125065), _1125275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125275), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1125069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125065), _1125277)), _1125275)]]]]], (19734 ^ _779448) ^ [_1125798, _1125800, _1125802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125798)), 19737 ^ _779448 : [(19756 ^ _779448) ^ [] : [19759 ^ _779448 : [(19760 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19758 ^ [_1125798, _1125800, _1125802])))], (19762 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19758 ^ [_1125798, _1125800, _1125802]), _1125798)))], (19764 ^ _779448) ^ [] : [-(_1125802 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125798), 19757 ^ [_1125798, _1125800, _1125802])), 19758 ^ [_1125798, _1125800, _1125802]))], (19766 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1125800, 19757 ^ [_1125798, _1125800, _1125802]), 19758 ^ [_1125798, _1125800, _1125802]))]], -(hBOOL(hAPP(hAPP(_1125800, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125802), _1125798)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125802, _1125798))))], (19738 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1125800, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125802), _1125798)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1125802, _1125798))), 19741 ^ _779448 : [(19742 ^ _779448) ^ [_1125999, _1126001] : [-(hBOOL(hAPP(hAPP(_1125800, _1126001), _1125999))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1125999), _1125798)), _1125802 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1125798), _1126001)), _1125999)]]]]], (19770 ^ _779448) ^ [_1126513, _1126515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126513)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1126513), _1126515)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126513), _1126515) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (19780 ^ _779448) ^ [_1126689, _1126691] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126689))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126689)), _1126691) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1126691))], (19786 ^ _779448) ^ [_1126794, _1126796] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126794)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126794)), _1126796) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126794)), _1126796)))], (19792 ^ _779448) ^ [_1126867, _1126869] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126867))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126867)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126869)) = 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), _1126869)))], (19798 ^ _779448) ^ [_1126984, _1126986] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126984)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126984)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126986)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1126984)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1126986))))], (19804 ^ _779448) ^ [_1127069, _1127071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127071))), -(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(_1127071))), 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), _1127069)), c_Int_Onat))))))], (19810 ^ _779448) ^ [_1127214, _1127216] : [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(_1127216))), 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), _1127214)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127214)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127216))))], (19816 ^ _779448) ^ [_1127380, _1127382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127380)), hAPP(c_Nat_OSuc, _1127382))), -(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(_1127380))), 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)), _1127382)))))], (19822 ^ _779448) ^ [_1127507, _1127509] : [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(_1127507))), 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)), _1127509)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127507)), hAPP(c_Nat_OSuc, _1127509))))], (19828 ^ _779448) ^ [_1127655, _1127657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127655)), hAPP(c_Nat_OSuc, _1127657))), -(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(_1127655))), 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)), _1127657)))))], (19834 ^ _779448) ^ [_1127782, _1127784] : [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(_1127782))), 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)), _1127784)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127782)), hAPP(c_Nat_OSuc, _1127784))))], (19840 ^ _779448) ^ [_1127930, _1127932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127930)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1127932))), -(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(_1127932))), 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), _1127930)), c_Int_Onat))))))], (19846 ^ _779448) ^ [_1128075, _1128077] : [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(_1128077))), 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), _1128075)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1128075)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128077))))], (19852 ^ _779448) ^ [_1128226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1128226)), -(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), _1128226), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (19858 ^ _779448) ^ [_1128321, _1128323, _1128325, _1128327, _1128329] : [-(c_Nat_Onat_Onat__case(_1128321, _1128323, _1128325, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128327)), _1128329)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1128321), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1128327))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1128321, _1128321), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1128321, tc_fun(_1128321, _1128321)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1128321, tc_fun(_1128321, _1128321)), tc_Int_Oint), c_If(_1128321)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1128321, _1128323, _1128325, _1128329))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1128321, tc_Int_Oint), _1128325), 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)), _1128329)))))], (19860 ^ _779448) ^ [_1128439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128439)), -(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), _1128439), 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)))))))], (19866 ^ _779448) ^ [_1128546, _1128548] : [-(c_Int_Onat__aux(_1128546, _1128548) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1128546)), _1128548))], (19868 ^ _779448) ^ [_1128583] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1128583)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1128583)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19870 ^ _779448) ^ [_1128620, _1128622, _1128624, _1128626, _1128628] : [-(hAPP(c_Nat_Onat_Onat__rec(_1128620, _1128622, _1128624), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128626)), _1128628)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1128620), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1128626))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1128620, _1128620), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1128620, tc_fun(_1128620, _1128620)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1128620, tc_fun(_1128620, _1128620)), tc_Int_Oint), c_If(_1128620)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1128620, _1128622, _1128624), _1128628))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1128620, _1128620), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1128620, _1128620), tc_Int_Oint), _1128624), 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)), _1128628))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1128620, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1128620, _1128622, _1128624)), 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)), _1128628))))))], (19872 ^ _779448) ^ [_1128772, _1128774, _1128776, _1128778] : [-(hAPP(c_Nat_Onat_Onat__rec(_1128772, _1128774, _1128776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128778)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1128772), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1128778))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1128772, _1128772), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1128772, tc_fun(_1128772, _1128772)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1128772, tc_fun(_1128772, _1128772)), tc_Int_Oint), c_If(_1128772)), c_Nat__Numeral_Oneg)), _1128774)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1128772, _1128772), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1128772, _1128772), tc_Int_Oint), _1128776), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1128772, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1128772, _1128774, _1128776)), c_Int_Onat)))))], (19874 ^ _779448) ^ [] : [-(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))))], (19876 ^ _779448) ^ [_1128930, _1128932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128930), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128932)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128930)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1128932))], (19882 ^ _779448) ^ [_1129041, _1129043] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129041), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1129043)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1129041)) = 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), _1129043), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1129041)))), 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)))], (19888 ^ _779448) ^ [_1129120] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1129120))), -(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), _1129120)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19894 ^ _779448) ^ [_1129213] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1129213)))), -(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), _1129213)) = 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), _1129213))))], (19900 ^ _779448) ^ [_1129271, _1129273] : [class_Groups_Oordered__ab__group__add(_1129271), -(c_Fun_Oinj__on(_1129271, _1129271, c_Groups_Ouminus__class_Ouminus(_1129271), _1129273))], (19906 ^ _779448) ^ [_1129354, _1129356] : [-(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), _1129354))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129356))))], (19908 ^ _779448) ^ [_1129393, _1129395] : [-(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, _1129393)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1129395))))], (19910 ^ _779448) ^ [_1129435, _1129437] : [class_Groups_Ogroup__add(_1129435), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1129435), hAPP(c_Groups_Ouminus__class_Ouminus(_1129435), _1129437)) = _1129437)], (19916 ^ _779448) ^ [_1129530, _1129532, _1129534] : [class_Groups_Ogroup__add(_1129530), 19919 ^ _779448 : [(19920 ^ _779448) ^ [] : [_1129532 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129530), _1129534), -(_1129534 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129530), _1129532))], (19926 ^ _779448) ^ [] : [_1129534 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129530), _1129532), -(_1129532 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129530), _1129534))]]], (19932 ^ _779448) ^ [_1129771, _1129773, _1129775] : [class_Groups_Ogroup__add(_1129771), 19935 ^ _779448 : [(19936 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1129771), _1129773) = _1129775, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1129771), _1129775) = _1129773)], (19942 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1129771), _1129775) = _1129773, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1129771), _1129773) = _1129775)]]], (19948 ^ _779448) ^ [_1130012, _1130014, _1130016] : [class_Groups_Ogroup__add(_1130012), 19951 ^ _779448 : [(19952 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1130012), _1130014) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130012), _1130016), -(_1130014 = _1130016)], (19958 ^ _779448) ^ [] : [_1130014 = _1130016, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130012), _1130014) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130012), _1130016))]]], (19964 ^ _779448) ^ [_1130253, _1130255, _1130257, _1130259] : [class_Groups_Ouminus(_1130253), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1130255, _1130253)), _1130257), _1130259) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130253), hAPP(_1130257, _1130259)))], (19970 ^ _779448) ^ [_1130370, _1130372] : [class_Lattices_Oboolean__algebra(_1130370), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130370), hAPP(c_Groups_Ouminus__class_Ouminus(_1130370), _1130372)) = _1130372)], (19976 ^ _779448) ^ [_1130465, _1130467, _1130469, _1130471] : [class_Groups_Ouminus(_1130465), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1130467, _1130465)), _1130469), _1130471) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130465), hAPP(_1130469, _1130471)))], (19982 ^ _779448) ^ [_1130582, _1130584, _1130586] : [class_Lattices_Oboolean__algebra(_1130582), 19985 ^ _779448 : [(19986 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1130582), _1130584) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130582), _1130586), -(_1130584 = _1130586)], (19992 ^ _779448) ^ [] : [_1130584 = _1130586, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130582), _1130584) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130582), _1130586))]]], (19998 ^ _779448) ^ [_1130823] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1130823)) = _1130823)], (20000 ^ _779448) ^ [_1130852, _1130854] : [class_Int_Onumber__ring(_1130852), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130852), hAPP(c_Int_Onumber__class_Onumber__of(_1130852), _1130854)) = hAPP(c_Int_Onumber__class_Onumber__of(_1130852), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1130854)))], (20006 ^ _779448) ^ [_1130963, _1130965] : [class_Int_Onumber__ring(_1130963), -(hAPP(c_Int_Onumber__class_Onumber__of(_1130963), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1130965)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1130963), hAPP(c_Int_Onumber__class_Onumber__of(_1130963), _1130965)))], (20012 ^ _779448) ^ [_1131074, _1131076, _1131078] : [class_Int_Onumber__ring(_1131074), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131074), hAPP(c_Groups_Ouminus__class_Ouminus(_1131074), hAPP(c_Int_Onumber__class_Onumber__of(_1131074), _1131076))), _1131078) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131074), hAPP(c_Int_Onumber__class_Onumber__of(_1131074), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1131076))), _1131078))], (20018 ^ _779448) ^ [_1131219, _1131221, _1131223] : [class_Lattices_Oboolean__algebra(_1131219), 20021 ^ _779448 : [(20022 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131219), hAPP(c_Groups_Ouminus__class_Ouminus(_1131219), _1131221)), hAPP(c_Groups_Ouminus__class_Ouminus(_1131219), _1131223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131219), _1131223), _1131221)))], (20028 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131219), _1131223), _1131221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131219), hAPP(c_Groups_Ouminus__class_Ouminus(_1131219), _1131221)), hAPP(c_Groups_Ouminus__class_Ouminus(_1131219), _1131223))))]]], (20034 ^ _779448) ^ [_1131502, _1131504, _1131506] : [class_Lattices_Oboolean__algebra(_1131502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131502), _1131504), _1131506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131502), hAPP(c_Groups_Ouminus__class_Ouminus(_1131502), _1131506)), hAPP(c_Groups_Ouminus__class_Ouminus(_1131502), _1131504))))], (20044 ^ _779448) ^ [_1131681, _1131683, _1131685] : [class_Groups_Oordered__ab__group__add(_1131681), 20047 ^ _779448 : [(20048 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131681), _1131683), hAPP(c_Groups_Ouminus__class_Ouminus(_1131681), _1131685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131681), _1131685), hAPP(c_Groups_Ouminus__class_Ouminus(_1131681), _1131683))))], (20054 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131681), _1131685), hAPP(c_Groups_Ouminus__class_Ouminus(_1131681), _1131683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131681), _1131683), hAPP(c_Groups_Ouminus__class_Ouminus(_1131681), _1131685))))]]], (20060 ^ _779448) ^ [_1131964, _1131966, _1131968] : [class_Groups_Oordered__ab__group__add(_1131964), 20063 ^ _779448 : [(20064 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131964), hAPP(c_Groups_Ouminus__class_Ouminus(_1131964), _1131966)), _1131968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131964), hAPP(c_Groups_Ouminus__class_Ouminus(_1131964), _1131968)), _1131966)))], (20070 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131964), hAPP(c_Groups_Ouminus__class_Ouminus(_1131964), _1131968)), _1131966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131964), hAPP(c_Groups_Ouminus__class_Ouminus(_1131964), _1131966)), _1131968)))]]], (20076 ^ _779448) ^ [_1132247, _1132249, _1132251] : [class_Groups_Oordered__ab__group__add(_1132247), 20079 ^ _779448 : [(20080 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132247), hAPP(c_Groups_Ouminus__class_Ouminus(_1132247), _1132249)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132247), _1132251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132247), _1132251), _1132249)))], (20086 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132247), _1132251), _1132249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132247), hAPP(c_Groups_Ouminus__class_Ouminus(_1132247), _1132249)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132247), _1132251))))]]], (20092 ^ _779448) ^ [_1132530, _1132532, _1132534] : [class_Groups_Oordered__ab__group__add(_1132530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132530), _1132532), _1132534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132530), hAPP(c_Groups_Ouminus__class_Ouminus(_1132530), _1132534)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132530), _1132532))))], (20102 ^ _779448) ^ [_1132709] : [class_Groups_Ogroup__add(_1132709), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132709), c_Groups_Ozero__class_Ozero(_1132709)) = c_Groups_Ozero__class_Ozero(_1132709))], (20108 ^ _779448) ^ [_1132800, _1132802] : [class_Groups_Ogroup__add(_1132800), 20111 ^ _779448 : [(20112 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_1132800) = hAPP(c_Groups_Ouminus__class_Ouminus(_1132800), _1132802), -(c_Groups_Ozero__class_Ozero(_1132800) = _1132802)], (20118 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_1132800) = _1132802, -(c_Groups_Ozero__class_Ozero(_1132800) = hAPP(c_Groups_Ouminus__class_Ouminus(_1132800), _1132802))]]], (20124 ^ _779448) ^ [_1133032, _1133034] : [class_Groups_Olinordered__ab__group__add(_1133032), 20127 ^ _779448 : [(20128 ^ _779448) ^ [] : [_1133034 = hAPP(c_Groups_Ouminus__class_Ouminus(_1133032), _1133034), -(_1133034 = c_Groups_Ozero__class_Ozero(_1133032))], (20134 ^ _779448) ^ [] : [_1133034 = c_Groups_Ozero__class_Ozero(_1133032), -(_1133034 = hAPP(c_Groups_Ouminus__class_Ouminus(_1133032), _1133034))]]], (20140 ^ _779448) ^ [_1133258, _1133260] : [class_Groups_Ogroup__add(_1133258), 20143 ^ _779448 : [(20144 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1133258), _1133260) = c_Groups_Ozero__class_Ozero(_1133258), -(_1133260 = c_Groups_Ozero__class_Ozero(_1133258))], (20150 ^ _779448) ^ [] : [_1133260 = c_Groups_Ozero__class_Ozero(_1133258), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133258), _1133260) = c_Groups_Ozero__class_Ozero(_1133258))]]], (20156 ^ _779448) ^ [_1133490, _1133492] : [class_Groups_Olinordered__ab__group__add(_1133490), 20159 ^ _779448 : [(20160 ^ _779448) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1133490), _1133492) = _1133492, -(_1133492 = c_Groups_Ozero__class_Ozero(_1133490))], (20166 ^ _779448) ^ [] : [_1133492 = c_Groups_Ozero__class_Ozero(_1133490), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133490), _1133492) = _1133492)]]], (20172 ^ _779448) ^ [_1133716, _1133718, _1133720] : [class_Groups_Oordered__ab__group__add(_1133716), 20175 ^ _779448 : [(20176 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133716), _1133718), hAPP(c_Groups_Ouminus__class_Ouminus(_1133716), _1133720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133716), _1133720), hAPP(c_Groups_Ouminus__class_Ouminus(_1133716), _1133718))))], (20182 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133716), _1133720), hAPP(c_Groups_Ouminus__class_Ouminus(_1133716), _1133718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133716), _1133718), hAPP(c_Groups_Ouminus__class_Ouminus(_1133716), _1133720))))]]], (20188 ^ _779448) ^ [_1133999, _1134001, _1134003] : [class_Groups_Oordered__ab__group__add(_1133999), 20191 ^ _779448 : [(20192 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133999), hAPP(c_Groups_Ouminus__class_Ouminus(_1133999), _1134001)), _1134003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133999), hAPP(c_Groups_Ouminus__class_Ouminus(_1133999), _1134003)), _1134001)))], (20198 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133999), hAPP(c_Groups_Ouminus__class_Ouminus(_1133999), _1134003)), _1134001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1133999), hAPP(c_Groups_Ouminus__class_Ouminus(_1133999), _1134001)), _1134003)))]]], (20204 ^ _779448) ^ [_1134282, _1134284, _1134286] : [class_Groups_Oordered__ab__group__add(_1134282), 20207 ^ _779448 : [(20208 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134282), hAPP(c_Groups_Ouminus__class_Ouminus(_1134282), _1134284)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134282), _1134286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134282), _1134286), _1134284)))], (20214 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134282), _1134286), _1134284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1134282), hAPP(c_Groups_Ouminus__class_Ouminus(_1134282), _1134284)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134282), _1134286))))]]], (20220 ^ _779448) ^ [_1134565, _1134567, _1134569] : [class_Groups_Oab__group__add(_1134565), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1134565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134565), _1134567), _1134569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134565), hAPP(c_Groups_Ouminus__class_Ouminus(_1134565), _1134567)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134565), _1134569)))], (20226 ^ _779448) ^ [_1134704, _1134706, _1134708] : [class_Groups_Ogroup__add(_1134704), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1134704), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134704), _1134706), _1134708)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134704), hAPP(c_Groups_Ouminus__class_Ouminus(_1134704), _1134708)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134704), _1134706)))], (20232 ^ _779448) ^ [_1134843, _1134845, _1134847] : [class_Groups_Ogroup__add(_1134843), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134843), _1134845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134843), hAPP(c_Groups_Ouminus__class_Ouminus(_1134843), _1134845)), _1134847)) = _1134847)], (20238 ^ _779448) ^ [_1134962, _1134964, _1134966] : [class_Groups_Ogroup__add(_1134962), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134962), hAPP(c_Groups_Ouminus__class_Ouminus(_1134962), _1134964)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134962), _1134964), _1134966)) = _1134966)], (20244 ^ _779448) ^ [_1135081, _1135083, _1135085] : [class_Rings_Oidom(_1135081), 20247 ^ _779448 : [(20258 ^ _779448) ^ [] : [20259 ^ _779448 : [(20260 ^ _779448) ^ [] : [_1135083 = _1135085], (20262 ^ _779448) ^ [] : [_1135083 = hAPP(c_Groups_Ouminus__class_Ouminus(_1135081), _1135085)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135081), _1135083), _1135083) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135081), _1135085), _1135085))], (20248 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135081), _1135083), _1135083) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135081), _1135085), _1135085), -(_1135083 = _1135085), -(_1135083 = hAPP(c_Groups_Ouminus__class_Ouminus(_1135081), _1135085))]]], (20266 ^ _779448) ^ [_1135400, _1135402, _1135404] : [class_Rings_Oring(_1135400), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135400), hAPP(c_Groups_Ouminus__class_Ouminus(_1135400), _1135402)), hAPP(c_Groups_Ouminus__class_Ouminus(_1135400), _1135404)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135400), _1135402), _1135404))], (20272 ^ _779448) ^ [_1135529, _1135531, _1135533] : [class_Rings_Oring(_1135529), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135529), hAPP(c_Groups_Ouminus__class_Ouminus(_1135529), _1135531)), _1135533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135529), _1135531), hAPP(c_Groups_Ouminus__class_Ouminus(_1135529), _1135533)))], (20278 ^ _779448) ^ [_1135658, _1135660, _1135662] : [class_Rings_Oring(_1135658), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1135658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135658), _1135660), _1135662)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135658), hAPP(c_Groups_Ouminus__class_Ouminus(_1135658), _1135660)), _1135662))], (20284 ^ _779448) ^ [_1135787, _1135789, _1135791] : [class_Rings_Oring(_1135787), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1135787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135787), _1135789), _1135791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135787), _1135789), hAPP(c_Groups_Ouminus__class_Ouminus(_1135787), _1135791)))], (20290 ^ _779448) ^ [_1135916, _1135918, _1135920] : [class_Groups_Oab__group__add(_1135916), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1135916), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1135916), _1135918), _1135920)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1135916), _1135920), _1135918))], (20296 ^ _779448) ^ [_1136035, _1136037] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1136035), _1136037) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136035, _1136037)), _1136037))], (20298 ^ _779448) ^ [_1136078, _1136080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136078), _1136080)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136078, _1136080) = _1136078)], (20304 ^ _779448) ^ [_1136173, _1136175, _1136177] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1136173), _1136175)), _1136177) = 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), _1136173), _1136177)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1136175), _1136177))), 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, _1136173, _1136177)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136175, _1136177))), _1136177)))], (20306 ^ _779448) ^ [_1136256, _1136258, _1136260] : [class_Divides_Oring__div(_1136256), -(c_Divides_Odiv__class_Omod(_1136256, hAPP(c_Groups_Ouminus__class_Ouminus(_1136256), _1136258), _1136260) = c_Divides_Odiv__class_Omod(_1136256, hAPP(c_Groups_Ouminus__class_Ouminus(_1136256), c_Divides_Odiv__class_Omod(_1136256, _1136258, _1136260)), _1136260))], (20312 ^ _779448) ^ [_1136377, _1136379, _1136381, _1136383] : [class_Divides_Oring__div(_1136377), c_Divides_Odiv__class_Omod(_1136377, _1136379, _1136381) = c_Divides_Odiv__class_Omod(_1136377, _1136383, _1136381), -(c_Divides_Odiv__class_Omod(_1136377, hAPP(c_Groups_Ouminus__class_Ouminus(_1136377), _1136379), _1136381) = c_Divides_Odiv__class_Omod(_1136377, hAPP(c_Groups_Ouminus__class_Ouminus(_1136377), _1136383), _1136381))], (20322 ^ _779448) ^ [_1136564, _1136566] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136564, _1136566)), _1136564)))], (20324 ^ _779448) ^ [] : [-(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))], (20326 ^ _779448) ^ [_1136616, _1136618, _1136620] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136616), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136618, _1136620)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136616), _1136618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136616), _1136620)))], (20328 ^ _779448) ^ [_1136669, _1136671, _1136673] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1136669, _1136671)), _1136673) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136669), _1136673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1136671), _1136673)))], (20330 ^ _779448) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (20332 ^ _779448) ^ [_1136740, _1136742] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1136740), _1136742)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136740)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136742)))], (20334 ^ _779448) ^ [_1136786] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1136786)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136786)))], (20336 ^ _779448) ^ [_1136821] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1136821)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136821)))], (20338 ^ _779448) ^ [_1136854, _1136856] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136854)), _1136856) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136854), _1136856)))], (20340 ^ _779448) ^ [_1136897, _1136899] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1136897, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136899)) = 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), _1136897), _1136899)))], (20342 ^ _779448) ^ [_1136939, _1136941] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136939), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136941)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1136939, _1136941)))], (20344 ^ _779448) ^ [_1136981, _1136983] : [-(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, _1136981, _1136983)), _1136983) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1136981), _1136983))], (20346 ^ _779448) ^ [_1137024, _1137026] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1137024), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1137026)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1137024)), _1137026))], (20348 ^ _779448) ^ [_1137067, _1137069] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1137067)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1137069)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1137067), _1137069))], (20350 ^ _779448) ^ [_1137110, _1137112] : [class_Groups_Oordered__ab__group__add(_1137110), 20353 ^ _779448 : [(20354 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137110), c_Groups_Ozero__class_Ozero(_1137110)), hAPP(c_Groups_Ouminus__class_Ouminus(_1137110), _1137112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137110), _1137112), c_Groups_Ozero__class_Ozero(_1137110))))], (20360 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137110), _1137112), c_Groups_Ozero__class_Ozero(_1137110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137110), c_Groups_Ozero__class_Ozero(_1137110)), hAPP(c_Groups_Ouminus__class_Ouminus(_1137110), _1137112))))]]], (20366 ^ _779448) ^ [_1137384, _1137386] : [class_Groups_Olinordered__ab__group__add(_1137384), 20369 ^ _779448 : [(20370 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137384), _1137386), hAPP(c_Groups_Ouminus__class_Ouminus(_1137384), _1137386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137384), _1137386), c_Groups_Ozero__class_Ozero(_1137384))))], (20376 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137384), _1137386), c_Groups_Ozero__class_Ozero(_1137384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137384), _1137386), hAPP(c_Groups_Ouminus__class_Ouminus(_1137384), _1137386))))]]], (20382 ^ _779448) ^ [_1137652, _1137654] : [class_Groups_Oordered__ab__group__add(_1137652), 20385 ^ _779448 : [(20386 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137652), hAPP(c_Groups_Ouminus__class_Ouminus(_1137652), _1137654)), c_Groups_Ozero__class_Ozero(_1137652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137652), c_Groups_Ozero__class_Ozero(_1137652)), _1137654)))], (20392 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137652), c_Groups_Ozero__class_Ozero(_1137652)), _1137654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137652), hAPP(c_Groups_Ouminus__class_Ouminus(_1137652), _1137654)), c_Groups_Ozero__class_Ozero(_1137652))))]]], (20398 ^ _779448) ^ [_1137926, _1137928] : [class_Groups_Olinordered__ab__group__add(_1137926), 20401 ^ _779448 : [(20402 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137926), hAPP(c_Groups_Ouminus__class_Ouminus(_1137926), _1137928)), _1137928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137926), c_Groups_Ozero__class_Ozero(_1137926)), _1137928)))], (20408 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137926), c_Groups_Ozero__class_Ozero(_1137926)), _1137928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137926), hAPP(c_Groups_Ouminus__class_Ouminus(_1137926), _1137928)), _1137928)))]]], (20414 ^ _779448) ^ [_1138194, _1138196] : [class_Rings_Olinordered__idom(_1138194), 20417 ^ _779448 : [(20418 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138194), _1138196), hAPP(c_Groups_Ouminus__class_Ouminus(_1138194), _1138196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138194), _1138196), c_Groups_Ozero__class_Ozero(_1138194))))], (20424 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138194), _1138196), c_Groups_Ozero__class_Ozero(_1138194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138194), _1138196), hAPP(c_Groups_Ouminus__class_Ouminus(_1138194), _1138196))))]]], (20430 ^ _779448) ^ [_1138462, _1138464] : [class_Groups_Oordered__ab__group__add(_1138462), 20433 ^ _779448 : [(20434 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138462), c_Groups_Ozero__class_Ozero(_1138462)), hAPP(c_Groups_Ouminus__class_Ouminus(_1138462), _1138464))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138462), _1138464), c_Groups_Ozero__class_Ozero(_1138462))))], (20440 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138462), _1138464), c_Groups_Ozero__class_Ozero(_1138462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138462), c_Groups_Ozero__class_Ozero(_1138462)), hAPP(c_Groups_Ouminus__class_Ouminus(_1138462), _1138464))))]]], (20446 ^ _779448) ^ [_1138736, _1138738] : [class_Groups_Oordered__ab__group__add(_1138736), 20449 ^ _779448 : [(20450 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138736), hAPP(c_Groups_Ouminus__class_Ouminus(_1138736), _1138738)), c_Groups_Ozero__class_Ozero(_1138736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138736), c_Groups_Ozero__class_Ozero(_1138736)), _1138738)))], (20456 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138736), c_Groups_Ozero__class_Ozero(_1138736)), _1138738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138736), hAPP(c_Groups_Ouminus__class_Ouminus(_1138736), _1138738)), c_Groups_Ozero__class_Ozero(_1138736))))]]], (20462 ^ _779448) ^ [_1139010, _1139012] : [class_Groups_Olinordered__ab__group__add(_1139010), 20465 ^ _779448 : [(20466 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139010), hAPP(c_Groups_Ouminus__class_Ouminus(_1139010), _1139012)), _1139012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139010), c_Groups_Ozero__class_Ozero(_1139010)), _1139012)))], (20472 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139010), c_Groups_Ozero__class_Ozero(_1139010)), _1139012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139010), hAPP(c_Groups_Ouminus__class_Ouminus(_1139010), _1139012)), _1139012)))]]], (20478 ^ _779448) ^ [_1139278, _1139280] : [class_Groups_Ogroup__add(_1139278), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139278), _1139280), hAPP(c_Groups_Ouminus__class_Ouminus(_1139278), _1139280)) = c_Groups_Ozero__class_Ozero(_1139278))], (20484 ^ _779448) ^ [_1139383, _1139385, _1139387] : [class_Groups_Ogroup__add(_1139383), 20487 ^ _779448 : [(20488 ^ _779448) ^ [] : [_1139385 = hAPP(c_Groups_Ouminus__class_Ouminus(_1139383), _1139387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139383), _1139385), _1139387) = c_Groups_Ozero__class_Ozero(_1139383))], (20494 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139383), _1139385), _1139387) = c_Groups_Ozero__class_Ozero(_1139383), -(_1139385 = hAPP(c_Groups_Ouminus__class_Ouminus(_1139383), _1139387))]]], (20500 ^ _779448) ^ [_1139639, _1139641] : [class_Groups_Ogroup__add(_1139639), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139639), hAPP(c_Groups_Ouminus__class_Ouminus(_1139639), _1139641)), _1139641) = c_Groups_Ozero__class_Ozero(_1139639))], (20506 ^ _779448) ^ [_1139744, _1139746] : [class_Groups_Oab__group__add(_1139744), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139744), hAPP(c_Groups_Ouminus__class_Ouminus(_1139744), _1139746)), _1139746) = c_Groups_Ozero__class_Ozero(_1139744))], (20512 ^ _779448) ^ [_1139849, _1139851, _1139853] : [class_Groups_Ogroup__add(_1139849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139849), _1139851), _1139853) = c_Groups_Ozero__class_Ozero(_1139849), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1139849), _1139851) = _1139853)], (20522 ^ _779448) ^ [_1140010, _1140012] : [class_Groups_Ogroup__add(_1140010), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1140010), c_Groups_Ozero__class_Ozero(_1140010)), _1140012) = hAPP(c_Groups_Ouminus__class_Ouminus(_1140010), _1140012))], (20528 ^ _779448) ^ [_1140115, _1140117, _1140119] : [class_Rings_Ocomm__ring__1(_1140115), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1140115), _1140117), _1140119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140115), _1140117), hAPP(c_Groups_Ouminus__class_Ouminus(_1140115), _1140119)))], (20534 ^ _779448) ^ [_1140234, _1140236, _1140238] : [class_Groups_Ogroup__add(_1140234), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1140234), _1140236), hAPP(c_Groups_Ouminus__class_Ouminus(_1140234), _1140238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140234), _1140236), _1140238))], (20540 ^ _779448) ^ [_1140353, _1140355, _1140357] : [class_Groups_Oab__group__add(_1140353), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1140353), _1140355), _1140357) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140353), _1140355), hAPP(c_Groups_Ouminus__class_Ouminus(_1140353), _1140357)))], (20546 ^ _779448) ^ [_1140472, _1140474, _1140476] : [class_Groups_Ogroup__add(_1140472), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1140472), _1140474), _1140476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140472), _1140474), hAPP(c_Groups_Ouminus__class_Ouminus(_1140472), _1140476)))], (20552 ^ _779448) ^ [_1140591, _1140593] : [class_Rings_Ocomm__ring__1(_1140591), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1140591), _1140593) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140591), hAPP(c_Groups_Ouminus__class_Ouminus(_1140591), c_Groups_Oone__class_Oone(_1140591))), _1140593))], (20558 ^ _779448) ^ [_1140706, _1140708] : [class_Rings_Oring__1__no__zero__divisors(_1140706), 20561 ^ _779448 : [(20572 ^ _779448) ^ [] : [20573 ^ _779448 : [(20574 ^ _779448) ^ [] : [_1140708 = c_Groups_Oone__class_Oone(_1140706)], (20576 ^ _779448) ^ [] : [_1140708 = hAPP(c_Groups_Ouminus__class_Ouminus(_1140706), c_Groups_Oone__class_Oone(_1140706))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140706), _1140708), _1140708) = c_Groups_Oone__class_Oone(_1140706))], (20562 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140706), _1140708), _1140708) = c_Groups_Oone__class_Oone(_1140706), -(_1140708 = c_Groups_Oone__class_Oone(_1140706)), -(_1140708 = hAPP(c_Groups_Ouminus__class_Ouminus(_1140706), c_Groups_Oone__class_Oone(_1140706)))]]], (20580 ^ _779448) ^ [_1141022, _1141024] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141022, _1141024)) = _1141024, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1141022), _1141024) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20586 ^ _779448) ^ [_1141121, _1141123] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141121, _1141123)) = _1141123), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1141121), _1141123) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141121, _1141123)))], (20592 ^ _779448) ^ [_1141180] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141180, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20594 ^ _779448) ^ [_1141207, _1141209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141209, _1141207)), _1141207)))], (20600 ^ _779448) ^ [_1141321, _1141323] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141321, _1141323) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1141321 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141323), 20603 ^ [_1141321, _1141323]))], (20607 ^ _779448) ^ [_1141426, _1141428] : [20608 ^ _779448 : [(20609 ^ _779448) ^ [_1141475] : [_1141426 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141428), _1141475)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141426, _1141428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20613 ^ _779448) ^ [_1141547, _1141549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1141547), _1141549)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141547, _1141549) = _1141547)], (20619 ^ _779448) ^ [_1141636, _1141638] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1141636), _1141638))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141636, _1141638) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141636), _1141638), _1141638))], (20625 ^ _779448) ^ [_1141689, _1141691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1141689), _1141691))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141689, _1141691) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141689), _1141691), _1141691))], (20631 ^ _779448) ^ [_1141744, _1141746, _1141748] : [-(hAPP(c_Nat_Onat_Onat__rec(_1141744, _1141746, _1141748), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1141746)], (20633 ^ _779448) ^ [_1141778, _1141780, _1141782] : [-(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), _1141778), _1141780)), _1141782), _1141780) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141782, _1141780))], (20635 ^ _779448) ^ [_1141825, _1141827, _1141829] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141825), _1141827)), _1141829) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141825), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1141827), _1141829))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141825), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141827, _1141829))), _1141829)))], (20637 ^ _779448) ^ [_1141898, _1141900, _1141902] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141898, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141900), _1141902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1141900), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1141898), _1141900), _1141902))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141898, _1141900)))], (20639 ^ _779448) ^ [_1141961, _1141963, _1141965, _1141967] : [-(hAPP(c_Nat_Onat_Onat__rec(_1141961, _1141963, _1141965), hAPP(c_Nat_OSuc, _1141967)) = hAPP(hAPP(_1141965, _1141967), hAPP(c_Nat_Onat_Onat__rec(_1141961, _1141963, _1141965), _1141967)))], (20641 ^ _779448) ^ [_1142013, _1142015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1142013), _1142015)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142015, _1142013) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142015), _1142013), _1142013))], (20647 ^ _779448) ^ [_1142128, _1142130] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142128, _1142130) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142128), _1142130)), _1142130)))], (20649 ^ _779448) ^ [_1142175, _1142177] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142175), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142177), _1142175)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142177), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142177, _1142175)))], (20651 ^ _779448) ^ [_1142222, _1142224] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142222), _1142224)), _1142224) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1142222), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142222, _1142224)))], (20653 ^ _779448) ^ [_1142269] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142269)), _1142269) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20655 ^ _779448) ^ [_1142316, _1142318] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142318), 20658 ^ _779448 : [(20659 ^ _779448) ^ [] : [-(_1142316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20661 ^ _779448) ^ [] : [-(_1142318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20663 ^ _779448) ^ [_1142433, _1142435] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142433)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142435)), _1142433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1142435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20673 ^ _779448) ^ [_1142582, _1142584] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142582, _1142584)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142582), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142584)))], (20675 ^ _779448) ^ [_1142624, _1142626] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142624), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142626)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142624, _1142626)))], (20677 ^ _779448) ^ [_1142678, _1142680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142678)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1142680))))], (20679 ^ _779448) ^ [_1142716, _1142718] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142716), _1142718) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1142716, _1142718) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20685 ^ _779448) ^ [_1142806, _1142808] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1142806, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142808)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1142806, _1142808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20691 ^ _779448) ^ [_1142897, _1142899] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142897), _1142899) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142897), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142899)))], (20693 ^ _779448) ^ [_1142937, _1142939] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142937), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142939)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1142937), _1142939))], (20695 ^ _779448) ^ [_1142977, _1142979] : [class_Rings_Oring__1(_1142977), hBOOL(hAPP(hAPP(c_member(_1142977), _1142979), c_Int_Oring__1__class_OInts(_1142977))), -(hBOOL(hAPP(hAPP(c_member(_1142977), hAPP(c_Groups_Ouminus__class_Ouminus(_1142977), _1142979)), c_Int_Oring__1__class_OInts(_1142977))))], (20705 ^ _779448) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20707 ^ _779448) ^ [_1143168] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1143168) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143168))], (20709 ^ _779448) ^ [_1143197] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1143197)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143197))))], (20711 ^ _779448) ^ [_1143232, _1143234, _1143236] : [class_Rings_Oring__1(_1143232), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1143232), hAPP(c_Groups_Ouminus__class_Ouminus(_1143232), _1143234)), _1143236) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143232), hAPP(hAPP(c_Power_Opower__class_Opower(_1143232), hAPP(c_Groups_Ouminus__class_Ouminus(_1143232), c_Groups_Oone__class_Oone(_1143232))), _1143236)), hAPP(hAPP(c_Power_Opower__class_Opower(_1143232), _1143234), _1143236)))], (20717 ^ _779448) ^ [_1143397, _1143399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1143397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143399, _1143397)), _1143397)))], (20723 ^ _779448) ^ [_1143496, _1143498, _1143500] : [-(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), _1143496), _1143498)), _1143500)), _1143498) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1143500), _1143498))], (20725 ^ _779448) ^ [_1143549, _1143551] : [class_Int_Onumber__ring(_1143549), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143549), _1143551), hAPP(c_Int_Onumber__class_Onumber__of(_1143549), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143549), _1143551))], (20731 ^ _779448) ^ [_1143660, _1143662] : [class_Int_Onumber__ring(_1143660), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143660), hAPP(c_Int_Onumber__class_Onumber__of(_1143660), c_Int_OMin)), _1143662) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143660), _1143662))], (20737 ^ _779448) ^ [_1143771] : [class_Int_Onumber__ring(_1143771), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1143771), c_Groups_Oone__class_Oone(_1143771)) = hAPP(c_Int_Onumber__class_Onumber__of(_1143771), c_Int_OMin))], (20743 ^ _779448) ^ [_1143868] : [class_Int_Onumber__ring(_1143868), -(hAPP(c_Int_Onumber__class_Onumber__of(_1143868), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143868), c_Groups_Oone__class_Oone(_1143868)))], (20749 ^ _779448) ^ [_1143965, _1143967, _1143969] : [class_Int_Onumber__ring(_1143965), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1143965), hAPP(c_Int_Onumber__class_Onumber__of(_1143965), _1143967)), hAPP(c_Int_Onumber__class_Onumber__of(_1143965), _1143969)) = hAPP(c_Int_Onumber__class_Onumber__of(_1143965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1143967), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1143969))))], (20755 ^ _779448) ^ [_1144121, _1144123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144121)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144123)))), 20758 ^ _779448 : [(20759 ^ _779448) ^ [] : [-(_1144121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20761 ^ _779448) ^ [] : [-(_1144123 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20763 ^ _779448) ^ [_1144248, _1144250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144248)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144250))))), _1144248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1144250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20773 ^ _779448) ^ [_1144407] : [-(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), _1144407))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20775 ^ _779448) ^ [_1144441] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144441))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20777 ^ _779448) ^ [_1144473, _1144475] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144473)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1144475)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1144473), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144475))))], (20779 ^ _779448) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (20781 ^ _779448) ^ [_1144549, _1144551] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144549, _1144551) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144549, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144551)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20787 ^ _779448) ^ [_1144642, _1144644] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144642, _1144644) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144642, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144644)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144642, _1144644)), _1144644))], (20793 ^ _779448) ^ [_1144710, _1144712] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144710, _1144712) = 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), _1144710), _1144712) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20799 ^ _779448) ^ [_1144803, _1144805] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144803, _1144805) = 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), _1144803), _1144805) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1144805), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1144803, _1144805)))], (20805 ^ _779448) ^ [_1144862] : [-(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, _1144862))))))], (20807 ^ _779448) ^ [_1144896] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1144896), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1144896))], (20809 ^ _779448) ^ [_1144928, _1144930, _1144932, _1144934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144930), _1144932)), -(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), _1144932), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144934, _1144928))), _1144930)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144932), _1144928))))], (20843 ^ _779448) ^ [_1145584, _1145586, _1145588] : [-(hBOOL(hAPP(_1145584, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1145586, _1145588)))), 20846 ^ _779448 : [(20847 ^ _779448) ^ [] : [-(_1145588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20849 ^ _779448) ^ [] : [hBOOL(hAPP(_1145584, _1145586))]], 20850 ^ _779448 : [(20851 ^ _779448) ^ [] : [_1145588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20855 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20853 ^ [_1145584, _1145586, _1145588]), _1145588)))], (20857 ^ _779448) ^ [] : [-(_1145586 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145588), 20852 ^ [_1145584, _1145586, _1145588])), 20853 ^ [_1145584, _1145586, _1145588]))], (20859 ^ _779448) ^ [] : [hBOOL(hAPP(_1145584, 20853 ^ [_1145584, _1145586, _1145588]))]]], (20819 ^ _779448) ^ [_1145151, _1145153, _1145155] : [hBOOL(hAPP(_1145151, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1145153, _1145155))), 20822 ^ _779448 : [(20823 ^ _779448) ^ [] : [_1145155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1145151, _1145153)))], (20829 ^ _779448) ^ [] : [-(_1145155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20832 ^ _779448 : [(20833 ^ _779448) ^ [_1145399, _1145401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145399), _1145155)), _1145153 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145155), _1145401)), _1145399), -(hBOOL(hAPP(_1145151, _1145399)))]]]]], (20863 ^ _779448) ^ [_1145993, _1145995, _1145997, _1145999] : [class_Int_Onumber__ring(_1145993), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145993), hAPP(c_Int_Onumber__class_Onumber__of(_1145993), _1145995)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145993), _1145997), hAPP(c_Int_Onumber__class_Onumber__of(_1145993), _1145999))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1145993), hAPP(c_Int_Onumber__class_Onumber__of(_1145993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1145995), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145999)))), _1145997))], (20869 ^ _779448) ^ [_1146168, _1146170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1146168)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146168), _1146170)), _1146168) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20875 ^ _779448) ^ [_1146275, _1146277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146277)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1146275), hAPP(c_Int_Onat, _1146277)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1146275, _1146277)))], (20885 ^ _779448) ^ [_1146446, _1146448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1146448)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1146446, _1146448)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1146446), hAPP(c_Int_Onat, _1146448)))], (20895 ^ _779448) ^ [_1146617, _1146619] : [class_Int_Onumber__ring(_1146617), -(hAPP(c_Int_Onumber__class_Onumber__of(_1146617), c_Int_Opred(_1146619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146617), hAPP(c_Groups_Ouminus__class_Ouminus(_1146617), c_Groups_Oone__class_Oone(_1146617))), hAPP(c_Int_Onumber__class_Onumber__of(_1146617), _1146619)))], (20901 ^ _779448) ^ [_1146755] : [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, _1146755)))))], (20903 ^ _779448) ^ [_1146789] : [-(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, _1146789)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20905 ^ _779448) ^ [_1146826, _1146828] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1146826))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146828)) = 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)))), _1146826), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1146828)))], (20907 ^ _779448) ^ [_1146877, _1146879] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1146877))), _1146879) = 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)))), _1146877), _1146879))], (20909 ^ _779448) ^ [_1146922, _1146924] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1146922, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1146924)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1146922, 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)))), _1146924)))], (20911 ^ _779448) ^ [_1146967] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1146967)), 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, _1146967, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20913 ^ _779448) ^ [_1147004, _1147006] : [class_Rings_Oring__1(_1147004), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1147004), hAPP(c_Groups_Ouminus__class_Ouminus(_1147004), _1147006)), 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(_1147004), _1147006), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20919 ^ _779448) ^ [_1147121, _1147123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147121), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1147121), _1147123)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1147121))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1147123))))], (20925 ^ _779448) ^ [_1147261, _1147263] : [-(_1147261 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20928 ^ _779448 : [(20929 ^ _779448) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1147263, _1147261) = 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), _1147263)), _1147261) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1147263), _1147261)))], (20935 ^ _779448) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1147263, _1147261) = 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), _1147263)), _1147261) = 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), _1147263), _1147261))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20941 ^ _779448) ^ [_1147534, _1147536] : [-(_1147534 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20944 ^ _779448 : [(20945 ^ _779448) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1147536, _1147534) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1147536), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1147534)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1147536), _1147534)))], (20951 ^ _779448) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1147536, _1147534) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1147536), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1147534)) = 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), _1147536), _1147534))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20957 ^ _779448) ^ [_1147808, _1147810] : [class_Rings_Oring__1__no__zero__divisors(_1147808), 20960 ^ _779448 : [(20971 ^ _779448) ^ [] : [20972 ^ _779448 : [(20973 ^ _779448) ^ [] : [_1147810 = c_Groups_Oone__class_Oone(_1147808)], (20975 ^ _779448) ^ [] : [_1147810 = hAPP(c_Groups_Ouminus__class_Ouminus(_1147808), c_Groups_Oone__class_Oone(_1147808))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1147808), _1147810), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1147808))], (20961 ^ _779448) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1147808), _1147810), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1147808), -(_1147810 = c_Groups_Oone__class_Oone(_1147808)), -(_1147810 = hAPP(c_Groups_Ouminus__class_Ouminus(_1147808), c_Groups_Oone__class_Oone(_1147808)))]]], (20979 ^ _779448) ^ [_1148115, _1148117, _1148119] : [class_Rings_Oring__1(_1148115), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1148115), hAPP(c_Groups_Ouminus__class_Ouminus(_1148115), _1148117)), 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)))), _1148119)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1148115), _1148117), 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)))), _1148119)))], (20985 ^ _779448) ^ [_1148246, _1148248] : [class_Int_Onumber__ring(_1148246), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148246), c_Groups_Oone__class_Oone(_1148246)), hAPP(c_Int_Onumber__class_Onumber__of(_1148246), _1148248)) = hAPP(c_Int_Onumber__class_Onumber__of(_1148246), 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), _1148248))))], (20991 ^ _779448) ^ [_1148373, _1148375] : [class_Int_Onumber__ring(_1148373), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148373), hAPP(c_Int_Onumber__class_Onumber__of(_1148373), _1148375)), c_Groups_Oone__class_Oone(_1148373)) = hAPP(c_Int_Onumber__class_Onumber__of(_1148373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1148375), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (20997 ^ _779448) ^ [_1148509, _1148511] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148509))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148509), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148511)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21003 ^ _779448) ^ [_1148611, _1148613] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148611)))), 21006 ^ _779448 : [(21007 ^ _779448) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148613))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148611), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148613)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148611))], (21013 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148613)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148611), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1148613)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148611), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1148613))))]]], (21019 ^ _779448) ^ [] : [-(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))], (21021 ^ _779448) ^ [_1148914] : [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, _1148914, 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, _1148914, 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))], (21027 ^ _779448) ^ [_1149005] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1149005, 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, _1149005, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21033 ^ _779448) ^ [_1149102, _1149104] : [class_Rings_Oring__1(_1149102), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1149102), hAPP(c_Groups_Ouminus__class_Ouminus(_1149102), c_Groups_Oone__class_Oone(_1149102))), 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)))), _1149104)) = c_Groups_Oone__class_Oone(_1149102))], (21039 ^ _779448) ^ [_1149217, _1149219] : [class_Rings_Oring__1(_1149217), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1149217), hAPP(c_Groups_Ouminus__class_Ouminus(_1149217), c_Groups_Oone__class_Oone(_1149217))), 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)))), _1149219))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1149217), c_Groups_Oone__class_Oone(_1149217)))], (21045 ^ _779448) ^ [_1149354] : [_1149354 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1149354) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21051 ^ _779448) ^ [_1149430] : [-(_1149430 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 21054 ^ _779448 : [(21055 ^ _779448) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1149430, 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, _1149430) = 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), _1149430), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21061 ^ _779448) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1149430, 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, _1149430) = 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), _1149430), 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)))]]], (21067 ^ _779448) ^ [_1149690, _1149692] : [class_Int_Onumber__ring(_1149690), 21070 ^ _779448 : [(21071 ^ _779448) ^ [] : [c_Groups_Oone__class_Oone(_1149690) = hAPP(c_Int_Onumber__class_Onumber__of(_1149690), _1149692), -(c_Int_Oiszero(_1149690, hAPP(c_Int_Onumber__class_Onumber__of(_1149690), 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), _1149692)))))], (21077 ^ _779448) ^ [] : [c_Int_Oiszero(_1149690, hAPP(c_Int_Onumber__class_Onumber__of(_1149690), 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), _1149692)))), -(c_Groups_Oone__class_Oone(_1149690) = hAPP(c_Int_Onumber__class_Onumber__of(_1149690), _1149692))]]], (21083 ^ _779448) ^ [_1149949, _1149951] : [class_Int_Onumber__ring(_1149949), 21086 ^ _779448 : [(21087 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149949), _1149951) = c_Groups_Oone__class_Oone(_1149949), -(c_Int_Oiszero(_1149949, hAPP(c_Int_Onumber__class_Onumber__of(_1149949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149951), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (21093 ^ _779448) ^ [] : [c_Int_Oiszero(_1149949, hAPP(c_Int_Onumber__class_Onumber__of(_1149949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149951), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1149949), _1149951) = c_Groups_Oone__class_Oone(_1149949))]]], (21099 ^ _779448) ^ [_1150217, _1150219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150217)), -(c_SMT_Oz3div(_1150219, _1150217) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150219), _1150217))], (21105 ^ _779448) ^ [_1150310, _1150312] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150310))), -(c_SMT_Oz3div(_1150312, _1150310) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150312), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1150310))))], (21111 ^ _779448) ^ [_1150374, _1150376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150374)), -(c_SMT_Oz3mod(_1150376, _1150374) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1150376, _1150374))], (21117 ^ _779448) ^ [_1150463, _1150465] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150463))), -(c_SMT_Oz3mod(_1150465, _1150463) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1150465, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1150463)))], (21123 ^ _779448) ^ [_1150513, _1150515] : [class_Int_Onumber__ring(_1150513), 21126 ^ _779448 : [(21127 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150513), _1150515) = c_Groups_Ozero__class_Ozero(_1150513), -(c_Int_Oiszero(_1150513, hAPP(c_Int_Onumber__class_Onumber__of(_1150513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (21133 ^ _779448) ^ [] : [c_Int_Oiszero(_1150513, hAPP(c_Int_Onumber__class_Onumber__of(_1150513), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1150513), _1150515) = c_Groups_Ozero__class_Ozero(_1150513))]]], (21139 ^ _779448) ^ [_1150768, _1150770, _1150772] : [-(hBOOL(hAPP(hAPP(c_member(_1150768), _1150770), _1150772))), -(hBOOL(hAPP(hAPP(c_member(_1150768), _1150770), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1150768, tc_HOL_Obool)), _1150772))))], (21145 ^ _779448) ^ [_1150828, _1150830, _1150832] : [hBOOL(hAPP(hAPP(c_member(_1150828), _1150830), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1150828, tc_HOL_Obool)), _1150832))), hBOOL(hAPP(hAPP(c_member(_1150828), _1150830), _1150832))], (21151 ^ _779448) ^ [_1150952, _1150954, _1150956] : [hBOOL(hAPP(hAPP(c_member(_1150952), _1150954), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1150952, tc_HOL_Obool)), _1150956))), hBOOL(hAPP(hAPP(c_member(_1150952), _1150954), _1150956))], (21157 ^ _779448) ^ [_1151094, _1151096, _1151098] : [hBOOL(hAPP(hAPP(c_member(_1151094), _1151096), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151094, tc_HOL_Obool)), _1151098))), hBOOL(hAPP(hAPP(c_member(_1151094), _1151096), _1151098))], (21163 ^ _779448) ^ [_1151212, _1151214, _1151216] : [-(hBOOL(hAPP(hAPP(c_member(_1151212), _1151214), _1151216))), -(hBOOL(hAPP(hAPP(c_member(_1151212), _1151214), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151212, tc_HOL_Obool)), _1151216))))], (21169 ^ _779448) ^ [_1151274, _1151276, _1151278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151274, tc_HOL_Obool)), _1151276), _1151278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151274, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151274, tc_HOL_Obool)), _1151278)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151274, tc_HOL_Obool)), _1151276))))], (21175 ^ _779448) ^ [_1151443, _1151445, _1151447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151443, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151443, tc_HOL_Obool)), _1151445)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151443, tc_HOL_Obool)), _1151447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151443, tc_HOL_Obool)), _1151447), _1151445)))], (21181 ^ _779448) ^ [_1151590, _1151592, _1151594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151590, tc_HOL_Obool)), _1151594), _1151592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1151590, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151590, tc_HOL_Obool)), _1151592)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1151590, tc_HOL_Obool)), _1151594))))], (21187 ^ _779448) ^ [_1151743] : [class_Rings_Osemiring__1(_1151743), -(c_Int_Oiszero(_1151743, c_Groups_Ozero__class_Ozero(_1151743)))], (21193 ^ _779448) ^ [_1151820, _1151822] : [class_Rings_Osemiring__1(_1151820), 21196 ^ _779448 : [(21197 ^ _779448) ^ [] : [c_Int_Oiszero(_1151820, _1151822), -(_1151822 = c_Groups_Ozero__class_Ozero(_1151820))], (21203 ^ _779448) ^ [] : [_1151822 = c_Groups_Ozero__class_Ozero(_1151820), -(c_Int_Oiszero(_1151820, _1151822))]]], (21209 ^ _779448) ^ [_1152031] : [class_Rings_Osemiring__1(_1152031), c_Int_Oiszero(_1152031, c_Groups_Oone__class_Oone(_1152031))], (21215 ^ _779448) ^ [_1152124, _1152126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1152124, tc_HOL_Obool)), _1152126), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1152124, tc_HOL_Obool)), _1152126))), -(_1152126 = c_Orderings_Obot__class_Obot(tc_fun(_1152124, tc_HOL_Obool)))], (21221 ^ _779448) ^ [_1152243, _1152245] : [_1152245 = c_Orderings_Obot__class_Obot(tc_fun(_1152243, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1152243, tc_HOL_Obool)), _1152245), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1152243, tc_HOL_Obool)), _1152245))))], (21227 ^ _779448) ^ [_1152368] : [class_Int_Onumber__ring(_1152368), -(c_Int_Oiszero(_1152368, hAPP(c_Int_Onumber__class_Onumber__of(_1152368), c_Int_OPls)))], (21233 ^ _779448) ^ [_1152451, _1152453] : [c_Int_Oiszero(_1152451, hAPP(c_Int_Onumber__class_Onumber__of(_1152451), c_Int_OBit1(_1152453))), class_Int_Onumber__ring(_1152451), class_Int_Oring__char__0(_1152451)], (21243 ^ _779448) ^ [_1152591, _1152593] : [class_Int_Onumber__ring(_1152591), class_Int_Oring__char__0(_1152591), 21250 ^ _779448 : [(21251 ^ _779448) ^ [] : [c_Int_Oiszero(_1152591, hAPP(c_Int_Onumber__class_Onumber__of(_1152591), c_Int_OBit0(_1152593))), -(c_Int_Oiszero(_1152591, hAPP(c_Int_Onumber__class_Onumber__of(_1152591), _1152593)))], (21257 ^ _779448) ^ [] : [c_Int_Oiszero(_1152591, hAPP(c_Int_Onumber__class_Onumber__of(_1152591), _1152593)), -(c_Int_Oiszero(_1152591, hAPP(c_Int_Onumber__class_Onumber__of(_1152591), c_Int_OBit0(_1152593))))]]], (21263 ^ _779448) ^ [_1152884] : [class_Int_Onumber__ring(_1152884), c_Int_Oiszero(_1152884, hAPP(c_Int_Onumber__class_Onumber__of(_1152884), c_Int_OMin))], (21269 ^ _779448) ^ [_1152968] : [class_Int_Onumber__ring(_1152968), c_Int_Oiszero(_1152968, hAPP(c_Int_Onumber__class_Onumber__of(_1152968), c_Int_OBit1(c_Int_OPls)))], (21275 ^ _779448) ^ [_1153052, _1153054, _1153056] : [class_Int_Onumber__ring(_1153052), 21278 ^ _779448 : [(21279 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1153052), _1153054) = hAPP(c_Int_Onumber__class_Onumber__of(_1153052), _1153056), -(c_Int_Oiszero(_1153052, hAPP(c_Int_Onumber__class_Onumber__of(_1153052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153054), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1153056)))))], (21285 ^ _779448) ^ [] : [c_Int_Oiszero(_1153052, hAPP(c_Int_Onumber__class_Onumber__of(_1153052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153054), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1153056)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153052), _1153054) = hAPP(c_Int_Onumber__class_Onumber__of(_1153052), _1153056))]]], (21291 ^ _779448) ^ [_1153335, _1153337] : [class_Int_Onumber__ring(_1153335), 21294 ^ _779448 : [(21295 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_1153335) = hAPP(c_Int_Onumber__class_Onumber__of(_1153335), _1153337), -(c_Int_Oiszero(_1153335, hAPP(c_Int_Onumber__class_Onumber__of(_1153335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1153337)))))], (21301 ^ _779448) ^ [] : [c_Int_Oiszero(_1153335, hAPP(c_Int_Onumber__class_Onumber__of(_1153335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1153337)))), -(c_Groups_Ozero__class_Ozero(_1153335) = hAPP(c_Int_Onumber__class_Onumber__of(_1153335), _1153337))]]], (21307 ^ _779448) ^ [_1153594, _1153596] : [c_Nat__Transfer_Onat__set(_1153594), c_Nat__Transfer_Onat__set(_1153596), 21314 ^ _779448 : [(21315 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1153594), _1153596)), -(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), _1153594)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153596))))], (21321 ^ _779448) ^ [] : [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), _1153594)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1153594), _1153596)))]]], (21327 ^ _779448) ^ [_1153897, _1153899] : [c_Nat__Transfer_Onat__set(_1153897), c_Nat__Transfer_Onat__set(_1153899), 21334 ^ _779448 : [(21335 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1153897), _1153899)), -(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), _1153897)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153899))))], (21341 ^ _779448) ^ [] : [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), _1153897)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1153897), _1153899)))]]], (21347 ^ _779448) ^ [_1154200, _1154202] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1154200)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154202)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1154202))), 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), _1154200)), c_Int_Onat)))))], (21349 ^ _779448) ^ [_1154263, _1154265] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1154263)), hAPP(c_Nat_OSuc, _1154265)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1154263))), 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)), _1154265)))))], (21351 ^ _779448) ^ [_1154320, _1154322] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1154320, _1154322)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1154322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154320), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21353 ^ _779448) ^ [_1154367, _1154369] : [class_Rings_Oring__1(_1154367), 21356 ^ _779448 : [(21357 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154369), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154367), _1154369) = hAPP(c_Groups_Ouminus__class_Ouminus(_1154367), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154367), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154369)))))], (21363 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154369), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154367), _1154369) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154367), hAPP(c_Int_Onat, _1154369)))]]], (21369 ^ _779448) ^ [_1154629, _1154631] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1154629, _1154631))))], (21371 ^ _779448) ^ [_1154660, _1154662] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154660, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154660, tc_HOL_Obool)), _1154662)) = _1154662)], (21373 ^ _779448) ^ [_1154719, _1154721, _1154723] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154719, tc_HOL_Obool)), _1154721) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154719, tc_HOL_Obool)), _1154723), -(_1154721 = _1154723)], (21379 ^ _779448) ^ [_1154826, _1154828, _1154830] : [_1154828 = _1154830, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154826, tc_HOL_Obool)), _1154828) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1154826, tc_HOL_Obool)), _1154830))], (21385 ^ _779448) ^ [_1154939, _1154941] : [class_Orderings_Olinorder(_1154939), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1154939), _1154941), _1154941) = _1154941)], (21391 ^ _779448) ^ [_1155030, _1155032, _1155034] : [class_Orderings_Olinorder(_1155030), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155030), _1155032), _1155034) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155030), _1155034), _1155032))], (21397 ^ _779448) ^ [_1155139, _1155141, _1155143] : [class_Orderings_Olinorder(_1155139), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155139), _1155141), _1155143) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155139), _1155143), _1155141))], (21403 ^ _779448) ^ [_1155248, _1155250, _1155252] : [class_Orderings_Olinorder(_1155248), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155248), _1155250), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155248), _1155250), _1155252)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155248), _1155250), _1155252))], (21409 ^ _779448) ^ [_1155373, _1155375, _1155377] : [class_Orderings_Olinorder(_1155373), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155373), _1155375), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155373), _1155375), _1155377)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155373), _1155375), _1155377))], (21415 ^ _779448) ^ [_1155498, _1155500, _1155502, _1155504] : [class_Orderings_Olinorder(_1155498), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155498), _1155500), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155498), _1155502), _1155504)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155498), _1155502), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155498), _1155500), _1155504)))], (21421 ^ _779448) ^ [_1155641, _1155643, _1155645, _1155647] : [class_Orderings_Olinorder(_1155641), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155641), _1155643), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155641), _1155645), _1155647)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155641), _1155645), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155641), _1155643), _1155647)))], (21427 ^ _779448) ^ [_1155784, _1155786, _1155788, _1155790] : [class_Orderings_Olinorder(_1155784), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155784), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155784), _1155786), _1155788)), _1155790) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155784), _1155786), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155784), _1155788), _1155790)))], (21433 ^ _779448) ^ [_1155927, _1155929, _1155931, _1155933] : [class_Orderings_Olinorder(_1155927), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155927), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155927), _1155929), _1155931)), _1155933) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155927), _1155929), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1155927), _1155931), _1155933)))], (21439 ^ _779448) ^ [_1156070, _1156072, _1156074] : [class_Int_Oring__char__0(_1156070), 21442 ^ _779448 : [(21443 ^ _779448) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1156070), _1156072) = hAPP(c_Int_Oring__1__class_Oof__int(_1156070), _1156074), -(_1156072 = _1156074)], (21449 ^ _779448) ^ [] : [_1156072 = _1156074, -(hAPP(c_Int_Oring__1__class_Oof__int(_1156070), _1156072) = hAPP(c_Int_Oring__1__class_Oof__int(_1156070), _1156074))]]], (21455 ^ _779448) ^ [_1156311, _1156313, _1156315] : [class_Orderings_Olinorder(_1156311), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156311), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156311), _1156313), _1156315)), _1156313)))], (21461 ^ _779448) ^ [_1156418, _1156420, _1156422] : [class_Orderings_Olinorder(_1156418), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156418), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156418), _1156420), _1156422)), _1156422)))], (21467 ^ _779448) ^ [_1156525, _1156527, _1156529] : [class_Orderings_Olinorder(_1156525), 21470 ^ _779448 : [(21471 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156525), _1156527), _1156529)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156525), _1156527), _1156529) = _1156527)], (21477 ^ _779448) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156525), _1156527), _1156529) = _1156527, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156525), _1156527), _1156529)))]]], (21483 ^ _779448) ^ [_1156781, _1156783, _1156785, _1156787] : [class_Orderings_Olinorder(_1156781), 21486 ^ _779448 : [(21487 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156781), _1156785), _1156787))), 21490 ^ _779448 : [(21491 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), _1156785)))], (21493 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), _1156787)))]]], (21495 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1156781), _1156785), _1156787)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), _1156785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156781), _1156783), _1156787))]]], (21505 ^ _779448) ^ [_1157161, _1157163, _1157165, _1157167] : [class_Orderings_Olinorder(_1157161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157161), _1157163), _1157165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157161), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157161), _1157163), _1157167)), _1157165)))], (21515 ^ _779448) ^ [_1157340, _1157342, _1157344, _1157346] : [class_Orderings_Olinorder(_1157340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157340), _1157342), _1157344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157340), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157340), _1157346), _1157342)), _1157344)))], (21525 ^ _779448) ^ [_1157519, _1157521, _1157523] : [class_Orderings_Olinorder(_1157519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157519), _1157521), _1157523)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157519), _1157521), _1157523) = _1157521)], (21535 ^ _779448) ^ [_1157680, _1157682, _1157684] : [class_Orderings_Olinorder(_1157680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157680), _1157682), _1157684)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157680), _1157684), _1157682) = _1157682)], (21545 ^ _779448) ^ [_1157841, _1157843, _1157845, _1157847] : [class_Orderings_Olinorder(_1157841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157841), _1157843), _1157845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157841), _1157843), _1157847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157841), _1157843), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157841), _1157845), _1157847))))], (21559 ^ _779448) ^ [_1158090, _1158092, _1158094, _1158096] : [class_Orderings_Olinorder(_1158090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158090), _1158092), _1158094)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158090), _1158092), _1158096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158090), _1158092), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158090), _1158094), _1158096))))], (21573 ^ _779448) ^ [_1158339, _1158341, _1158343, _1158345, _1158347] : [class_Orderings_Olinorder(_1158339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158339), _1158341), _1158343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158339), _1158345), _1158347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158339), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158339), _1158341), _1158345)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158339), _1158343), _1158347))))], (21587 ^ _779448) ^ [_1158610, _1158612, _1158614, _1158616] : [class_Orderings_Olinorder(_1158610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158610), _1158612), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158610), _1158614), _1158616))), 21594 ^ _779448 : [(21595 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158610), _1158612), _1158614)))], (21597 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158610), _1158612), _1158616)))]]], (21599 ^ _779448) ^ [_1158833, _1158835, _1158837, _1158839] : [class_Orderings_Olinorder(_1158833), 21602 ^ _779448 : [(21613 ^ _779448) ^ [] : [21614 ^ _779448 : [(21615 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), _1158835), _1158839))], (21617 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), _1158837), _1158839))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158833), _1158835), _1158837)), _1158839)))], (21603 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158833), _1158835), _1158837)), _1158839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), _1158835), _1158839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158833), _1158837), _1158839)))]]], (21621 ^ _779448) ^ [_1159182, _1159184, _1159186, _1159188] : [class_Orderings_Olinorder(_1159182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159182), _1159184), _1159186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159182), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159182), _1159188), _1159184)), _1159186)))], (21631 ^ _779448) ^ [_1159361, _1159363, _1159365, _1159367] : [class_Orderings_Olinorder(_1159361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159361), _1159363), _1159365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159361), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159361), _1159363), _1159367)), _1159365)))], (21641 ^ _779448) ^ [_1159540, _1159542, _1159544, _1159546] : [class_Orderings_Olinorder(_1159540), 21644 ^ _779448 : [(21645 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159540), _1159544), _1159546))), 21648 ^ _779448 : [(21649 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), _1159544)))], (21651 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), _1159546)))]]], (21653 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159540), _1159544), _1159546)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), _1159544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159540), _1159542), _1159546))]]], (21663 ^ _779448) ^ [_1159920, _1159922, _1159924, _1159926] : [class_Orderings_Olinorder(_1159920), 21666 ^ _779448 : [(21677 ^ _779448) ^ [] : [21678 ^ _779448 : [(21679 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), _1159922), _1159926))], (21681 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), _1159924), _1159926))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159920), _1159922), _1159924)), _1159926)))], (21667 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1159920), _1159922), _1159924)), _1159926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), _1159922), _1159926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159920), _1159924), _1159926)))]]], (21685 ^ _779448) ^ [_1160269, _1160271, _1160273, _1160275] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1160269), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160269), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160269), _1160271), _1160273)), _1160275) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160269), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160269), _1160271), _1160275)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1160269), _1160273), _1160275)))], (21691 ^ _779448) ^ [_1160428, _1160430, _1160432, _1160434] : [class_Groups_Oordered__ab__group__add(_1160428), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160428), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160428), _1160430), _1160432)), _1160434) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160428), _1160430), _1160434)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160428), _1160432), _1160434)))], (21697 ^ _779448) ^ [_1160587] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160587) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21699 ^ _779448) ^ [_1160613] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1160613), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21701 ^ _779448) ^ [_1160642, _1160644] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1160642)), hAPP(c_Nat_OSuc, _1160644)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1160642), _1160644)))], (21703 ^ _779448) ^ [_1160688, _1160690, _1160692] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160688), _1160690)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160692), _1160690)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1160688), _1160692)), _1160690))], (21705 ^ _779448) ^ [_1160745, _1160747] : [class_Int_Onumber__ring(_1160745), -(hAPP(c_Int_Onumber__class_Onumber__of(_1160745), _1160747) = hAPP(c_Int_Oring__1__class_Oof__int(_1160745), _1160747))], (21711 ^ _779448) ^ [_1160840] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1160840) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1160840))], (21713 ^ _779448) ^ [_1160869] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160869)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1160869))], (21715 ^ _779448) ^ [_1160901] : [class_Orderings_Olinorder(_1160901), -(c_Finite__Set_Ofun__left__comm__idem(_1160901, _1160901, c_Orderings_Oord__class_Omin(_1160901)))], (21721 ^ _779448) ^ [_1160980, _1160982, _1160984] : [class_Int_Onumber(_1160980), class_Orderings_Oord(_1160980), 21728 ^ _779448 : [(21729 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160980), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160982)), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160984))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160980), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160982)), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160984)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160982))], (21735 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160980), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160982)), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160984)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160980), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160982)), hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160984)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160980), _1160984))]]], (21741 ^ _779448) ^ [_1161372, _1161374] : [class_Int_Oring__char__0(_1161372), 21744 ^ _779448 : [(21745 ^ _779448) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1161372), _1161374) = c_Groups_Ozero__class_Ozero(_1161372), -(_1161374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21751 ^ _779448) ^ [] : [_1161374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1161372), _1161374) = c_Groups_Ozero__class_Ozero(_1161372))]]], (21757 ^ _779448) ^ [_1161598, _1161600] : [class_Int_Oring__char__0(_1161598), 21760 ^ _779448 : [(21761 ^ _779448) ^ [] : [c_Groups_Ozero__class_Ozero(_1161598) = hAPP(c_Int_Oring__1__class_Oof__int(_1161598), _1161600), -(_1161600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21767 ^ _779448) ^ [] : [_1161600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1161598) = hAPP(c_Int_Oring__1__class_Oof__int(_1161598), _1161600))]]], (21773 ^ _779448) ^ [_1161824] : [class_Rings_Oring__1(_1161824), -(hAPP(c_Int_Oring__1__class_Oof__int(_1161824), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1161824))], (21779 ^ _779448) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (21781 ^ _779448) ^ [_1161929, _1161931, _1161933] : [class_Rings_Olinordered__idom(_1161929), 21784 ^ _779448 : [(21785 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161929), hAPP(c_Int_Oring__1__class_Oof__int(_1161929), _1161931)), hAPP(c_Int_Oring__1__class_Oof__int(_1161929), _1161933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1161931), _1161933)))], (21791 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1161931), _1161933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161929), hAPP(c_Int_Oring__1__class_Oof__int(_1161929), _1161931)), hAPP(c_Int_Oring__1__class_Oof__int(_1161929), _1161933))))]]], (21797 ^ _779448) ^ [_1162206, _1162208, _1162210] : [class_Rings_Olinordered__idom(_1162206), 21800 ^ _779448 : [(21801 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162206), hAPP(c_Int_Oring__1__class_Oof__int(_1162206), _1162208)), hAPP(c_Int_Oring__1__class_Oof__int(_1162206), _1162210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162208), _1162210)))], (21807 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162208), _1162210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162206), hAPP(c_Int_Oring__1__class_Oof__int(_1162206), _1162208)), hAPP(c_Int_Oring__1__class_Oof__int(_1162206), _1162210))))]]], (21813 ^ _779448) ^ [_1162483, _1162485, _1162487] : [class_Rings_Oring__1(_1162483), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1162485), _1162487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162483), hAPP(c_Int_Oring__1__class_Oof__int(_1162483), _1162485)), hAPP(c_Int_Oring__1__class_Oof__int(_1162483), _1162487)))], (21819 ^ _779448) ^ [_1162618, _1162620] : [class_Int_Onumber__ring(_1162618), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162618), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162620)) = hAPP(c_Int_Onumber__class_Onumber__of(_1162618), _1162620))], (21825 ^ _779448) ^ [_1162719, _1162721, _1162723] : [class_Rings_Oring__1(_1162719), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1162721), _1162723)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162719), hAPP(c_Int_Oring__1__class_Oof__int(_1162719), _1162721)), hAPP(c_Int_Oring__1__class_Oof__int(_1162719), _1162723)))], (21831 ^ _779448) ^ [_1162854] : [class_Rings_Oring__1(_1162854), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162854), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1162854))], (21837 ^ _779448) ^ [_1162941, _1162943, _1162945] : [class_Rings_Oring__1(_1162941), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1162943), _1162945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1162941), hAPP(c_Int_Oring__1__class_Oof__int(_1162941), _1162943)), hAPP(c_Int_Oring__1__class_Oof__int(_1162941), _1162945)))], (21843 ^ _779448) ^ [_1163076, _1163078] : [class_Rings_Oring__1(_1163076), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163076), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1163078)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1163076), _1163078))], (21849 ^ _779448) ^ [_1163177, _1163179] : [class_Rings_Oring__1(_1163177), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163177), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1163179)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1163177), hAPP(c_Int_Oring__1__class_Oof__int(_1163177), _1163179)))], (21855 ^ _779448) ^ [_1163288, _1163290] : [class_Rings_Oring__1(_1163288), -(hBOOL(hAPP(hAPP(c_member(_1163288), hAPP(c_Int_Oring__1__class_Oof__int(_1163288), _1163290)), c_Int_Oring__1__class_OInts(_1163288))))], (21861 ^ _779448) ^ [_1163391, _1163393, _1163395] : [class_Rings_Oring__1(_1163391), -(hAPP(c_Int_Oring__1__class_Oof__int(_1163391), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1163393), _1163395)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1163391), hAPP(c_Int_Oring__1__class_Oof__int(_1163391), _1163393)), _1163395))], (21877 ^ _779448) ^ [_1163685] : [21879 ^ _779448 : [(21880 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21878 ^ [_1163685]), _1163685)))], (21882 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21878 ^ [_1163685]))]], -(c_Nat__Transfer_Onat__set(_1163685))], (21867 ^ _779448) ^ [_1163528] : [c_Nat__Transfer_Onat__set(_1163528), 21870 ^ _779448 : [(21871 ^ _779448) ^ [_1163594] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1163594), _1163528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1163594)))]]], (21886 ^ _779448) ^ [_1163833, _1163835, _1163837] : [class_Orderings_Oorder(_1163833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163833), _1163835), _1163837)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1163833, _1163837, _1163835) = c_Orderings_Obot__class_Obot(tc_fun(_1163833, tc_HOL_Obool)))], (21896 ^ _779448) ^ [_1163996, _1163998, _1164000] : [class_Groups_Oordered__ab__group__add(_1163996), -(hAPP(c_Set_Oimage(_1163996, _1163996, c_Groups_Ouminus__class_Ouminus(_1163996)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1163996, _1163998, _1164000)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1163996, hAPP(c_Groups_Ouminus__class_Ouminus(_1163996), _1164000), hAPP(c_Groups_Ouminus__class_Ouminus(_1163996), _1163998)))], (21902 ^ _779448) ^ [_1164127] : [-(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)), _1164127)))], (21904 ^ _779448) ^ [_1164152, _1164154] : [c_Nat__Transfer_Onat__set(_1164152), c_Nat__Transfer_Onat__set(_1164154), 21911 ^ _779448 : [(21912 ^ _779448) ^ [] : [_1164152 = _1164154, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1164152) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1164154))], (21918 ^ _779448) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1164152) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1164154), -(_1164152 = _1164154)]]], (21924 ^ _779448) ^ [_1164425] : [class_Int_Onumber__ring(_1164425), -(hAPP(c_Int_Oring__1__class_Oof__int(_1164425), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1164425), c_Int_OMin))], (21930 ^ _779448) ^ [_1164518, _1164520] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1164518)), _1164520) = 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), _1164518)), _1164520))], (21932 ^ _779448) ^ [_1164563, _1164565] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1164563), hAPP(c_Nat_OSuc, _1164565)) = 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)), _1164565)), _1164563))], (21934 ^ _779448) ^ [_1164608, _1164610] : [c_Nat__Transfer_Onat__set(_1164608), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1164610), _1164608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164610)))], (21944 ^ _779448) ^ [_1164749, _1164751] : [class_Rings_Olinordered__idom(_1164749), 21947 ^ _779448 : [(21948 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164749), c_Groups_Ozero__class_Ozero(_1164749)), hAPP(c_Int_Oring__1__class_Oof__int(_1164749), _1164751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164751)))], (21954 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164749), c_Groups_Ozero__class_Ozero(_1164749)), hAPP(c_Int_Oring__1__class_Oof__int(_1164749), _1164751))))]]], (21960 ^ _779448) ^ [_1165002, _1165004] : [class_Rings_Olinordered__idom(_1165002), 21963 ^ _779448 : [(21964 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165002), hAPP(c_Int_Oring__1__class_Oof__int(_1165002), _1165004)), c_Groups_Ozero__class_Ozero(_1165002))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1165004), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21970 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1165004), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165002), hAPP(c_Int_Oring__1__class_Oof__int(_1165002), _1165004)), c_Groups_Ozero__class_Ozero(_1165002))))]]], (21976 ^ _779448) ^ [_1165264, _1165266] : [class_Rings_Olinordered__idom(_1165264), 21979 ^ _779448 : [(21980 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165264), hAPP(c_Int_Oring__1__class_Oof__int(_1165264), _1165266)), c_Groups_Ozero__class_Ozero(_1165264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165266), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21986 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1165266), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165264), hAPP(c_Int_Oring__1__class_Oof__int(_1165264), _1165266)), c_Groups_Ozero__class_Ozero(_1165264))))]]], (21992 ^ _779448) ^ [_1165526, _1165528] : [class_Rings_Olinordered__idom(_1165526), 21995 ^ _779448 : [(21996 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165526), c_Groups_Ozero__class_Ozero(_1165526)), hAPP(c_Int_Oring__1__class_Oof__int(_1165526), _1165528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165528)))], (22002 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165526), c_Groups_Ozero__class_Ozero(_1165526)), hAPP(c_Int_Oring__1__class_Oof__int(_1165526), _1165528))))]]], (22008 ^ _779448) ^ [_1165779, _1165781] : [class_Rings_Oring__1(_1165779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1165781)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165779), hAPP(c_Int_Onat, _1165781)) = hAPP(c_Int_Oring__1__class_Oof__int(_1165779), _1165781))], (22018 ^ _779448) ^ [_1165936] : [c_Nat__Transfer_Onat__set(_1165936), -(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), _1165936)) = _1165936)], (22024 ^ _779448) ^ [_1166021] : [c_Nat__Transfer_Onat__set(_1166021), 22027 ^ _779448 : [(22028 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1166021)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1166021))))], (22034 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1166021))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1166021)))]]], (22040 ^ _779448) ^ [_1166241] : [c_Nat__Transfer_Onat__set(_1166241), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1166241) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1166241)))], (22046 ^ _779448) ^ [_1166332, _1166334, _1166336] : [class_Orderings_Olinorder(_1166332), -(_1166334 = c_Orderings_Obot__class_Obot(tc_fun(_1166332, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1166332, tc_HOL_Obool)), _1166334), _1166336)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166332), _1166336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166332), hAPP(c_Finite__Set_Ofold1(_1166332, c_Orderings_Oord__class_Omin(_1166332)), _1166336)), hAPP(c_Finite__Set_Ofold1(_1166332, c_Orderings_Oord__class_Omin(_1166332)), _1166334))))], (22064 ^ _779448) ^ [_1166658, _1166660, _1166662] : [class_Orderings_Olinorder(_1166658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166658), _1166660)), -(_1166660 = c_Orderings_Obot__class_Obot(tc_fun(_1166658, tc_HOL_Obool))), 22075 ^ _779448 : [(22076 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166658), hAPP(c_Finite__Set_Ofold1(_1166658, c_Orderings_Oord__class_Omin(_1166658)), _1166660)), _1166662)), 22080 ^ _779448 : [(22081 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166658), 22079 ^ [_1166658, _1166660, _1166662]), _1166660)))], (22083 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166658), 22079 ^ [_1166658, _1166660, _1166662]), _1166662)))]]], (22085 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166658), hAPP(c_Finite__Set_Ofold1(_1166658, c_Orderings_Oord__class_Omin(_1166658)), _1166660)), _1166662))), 22086 ^ _779448 : [(22087 ^ _779448) ^ [_1167047] : [hBOOL(hAPP(hAPP(c_member(_1166658), _1167047), _1166660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166658), _1167047), _1166662))]]]]], (22095 ^ _779448) ^ [_1167208, _1167210, _1167212] : [class_Orderings_Olinorder(_1167208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167208), _1167210)), -(_1167210 = c_Orderings_Obot__class_Obot(tc_fun(_1167208, tc_HOL_Obool))), 22106 ^ _779448 : [(22117 ^ _779448) ^ [] : [22119 ^ _779448 : [(22120 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1167208), 22118 ^ [_1167208, _1167210, _1167212]), _1167210)))], (22122 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167208), _1167212), 22118 ^ [_1167208, _1167210, _1167212]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167208), _1167212), hAPP(c_Finite__Set_Ofold1(_1167208, c_Orderings_Oord__class_Omin(_1167208)), _1167210))))], (22107 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167208), _1167212), hAPP(c_Finite__Set_Ofold1(_1167208, c_Orderings_Oord__class_Omin(_1167208)), _1167210))), 22110 ^ _779448 : [(22111 ^ _779448) ^ [_1167501] : [hBOOL(hAPP(hAPP(c_member(_1167208), _1167501), _1167210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167208), _1167212), _1167501)))]]]]], (22126 ^ _779448) ^ [_1167786, _1167788, _1167790] : [class_Orderings_Olinorder(_1167786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167786), _1167788)), -(_1167788 = c_Orderings_Obot__class_Obot(tc_fun(_1167786, tc_HOL_Obool))), 22137 ^ _779448 : [(22148 ^ _779448) ^ [] : [22150 ^ _779448 : [(22151 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1167786), 22149 ^ [_1167786, _1167788, _1167790]), _1167788)))], (22153 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167786), _1167790), 22149 ^ [_1167786, _1167788, _1167790]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167786), _1167790), hAPP(c_Finite__Set_Ofold1(_1167786, c_Orderings_Oord__class_Omin(_1167786)), _1167788))))], (22138 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167786), _1167790), hAPP(c_Finite__Set_Ofold1(_1167786, c_Orderings_Oord__class_Omin(_1167786)), _1167788))), 22141 ^ _779448 : [(22142 ^ _779448) ^ [_1168079] : [hBOOL(hAPP(hAPP(c_member(_1167786), _1168079), _1167788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167786), _1167790), _1168079)))]]]]], (22157 ^ _779448) ^ [_1168364, _1168366, _1168368] : [class_Orderings_Olinorder(_1168364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168364), _1168366)), -(_1168366 = c_Orderings_Obot__class_Obot(tc_fun(_1168364, tc_HOL_Obool))), 22168 ^ _779448 : [(22169 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168364), hAPP(c_Finite__Set_Ofold1(_1168364, c_Orderings_Oord__class_Omin(_1168364)), _1168366)), _1168368)), 22173 ^ _779448 : [(22174 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168364), 22172 ^ [_1168364, _1168366, _1168368]), _1168366)))], (22176 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168364), 22172 ^ [_1168364, _1168366, _1168368]), _1168368)))]]], (22178 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168364), hAPP(c_Finite__Set_Ofold1(_1168364, c_Orderings_Oord__class_Omin(_1168364)), _1168366)), _1168368))), 22179 ^ _779448 : [(22180 ^ _779448) ^ [_1168753] : [hBOOL(hAPP(hAPP(c_member(_1168364), _1168753), _1168366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168364), _1168753), _1168368))]]]]], (22188 ^ _779448) ^ [_1168914, _1168916, _1168918] : [class_Orderings_Olinorder(_1168914), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168914), _1168916)), hBOOL(hAPP(hAPP(c_member(_1168914), _1168918), _1168916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168914), hAPP(c_Finite__Set_Ofold1(_1168914, c_Orderings_Oord__class_Omin(_1168914)), _1168916)), _1168918)))], (22202 ^ _779448) ^ [_1169151, _1169153] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1169151, _1169153))))], (22204 ^ _779448) ^ [_1169182, _1169184] : [class_Orderings_Olinorder(_1169182), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169182), _1169184), _1169184) = _1169184)], (22210 ^ _779448) ^ [_1169273, _1169275] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1169273, _1169275)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1169275), hAPP(c_Nat_OSuc, _1169273)))], (22212 ^ _779448) ^ [_1169314, _1169316, _1169318, _1169320] : [class_Orderings_Olinorder(_1169314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169314), _1169316)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1169314, _1169314, c_Orderings_Oord__class_Omin(_1169314)), _1169318), hAPP(hAPP(c_Set_Oinsert(_1169314), _1169320), _1169316)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169314), _1169320), hAPP(hAPP(c_Finite__Set_Ofold(_1169314, _1169314, c_Orderings_Oord__class_Omin(_1169314)), _1169318), _1169316)))], (22222 ^ _779448) ^ [_1169537, _1169539, _1169541, _1169543] : [class_Orderings_Olinorder(_1169537), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169537), _1169539)), hBOOL(hAPP(hAPP(c_member(_1169537), _1169541), _1169539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169537), hAPP(hAPP(c_Finite__Set_Ofold(_1169537, _1169537, c_Orderings_Oord__class_Omin(_1169537)), _1169543), _1169539)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169537), _1169541), _1169543))))], (22236 ^ _779448) ^ [_1169804, _1169806, _1169808, _1169810] : [c_Big__Operators_Osemilattice__big(_1169804, _1169806, _1169808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169804), _1169810)), -(hAPP(_1169808, _1169810) = hAPP(c_Finite__Set_Ofold1(_1169804, _1169806), _1169810))], (22246 ^ _779448) ^ [_1169969] : [class_Orderings_Olinorder(_1169969), -(c_Orderings_Oord_Omax(_1169969, hAPP(c_COMBC(_1169969, _1169969, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1169969))) = c_Orderings_Oord__class_Omin(_1169969))], (22252 ^ _779448) ^ [_1170070, _1170072] : [class_Rings_Oring__1(_1170070), 22255 ^ _779448 : [(22256 ^ _779448) ^ [] : [_1170072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1170070), _1170072) = c_Groups_Ozero__class_Ozero(_1170070))], (22262 ^ _779448) ^ [] : [-(_1170072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22265 ^ _779448 : [(22266 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170072), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1170070), _1170072) = hAPP(c_Groups_Ouminus__class_Ouminus(_1170070), hAPP(c_Int_Oring__1__class_Oof__int(_1170070), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170072))))], (22272 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170072), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1170070), _1170072) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1170070), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1170070, _1170070)), tc_fun(tc_Int_Oint, _1170070)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1170070, _1170070), _1170070), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1170070, _1170070)), tc_fun(tc_Int_Oint, _1170070)), tc_Int_Oint), c_COMBB(tc_fun(_1170070, _1170070), _1170070, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1170070, tc_fun(tc_fun(_1170070, _1170070), _1170070), tc_Int_Oint), c_HOL_OLet(_1170070, _1170070)), c_Int_Oring__1__class_Oof__int(_1170070)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1170070, _1170070), tc_fun(_1170070, _1170070)), hAPP(hAPP(c_COMBB(tc_fun(_1170070, tc_fun(_1170070, _1170070)), tc_fun(tc_fun(_1170070, _1170070), tc_fun(_1170070, _1170070)), tc_Int_Oint), c_COMBS(_1170070, _1170070, _1170070)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1170070, _1170070), tc_fun(_1170070, tc_fun(_1170070, _1170070))), hAPP(hAPP(c_COMBB(tc_fun(_1170070, tc_fun(_1170070, _1170070)), tc_fun(tc_fun(_1170070, _1170070), tc_fun(_1170070, tc_fun(_1170070, _1170070))), tc_Int_Oint), c_COMBB(_1170070, tc_fun(_1170070, _1170070), _1170070)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1170070, tc_fun(_1170070, _1170070)), tc_Int_Oint), c_If(_1170070)), 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(_1170070, _1170070, _1170070), c_Groups_Oplus__class_Oplus(_1170070)), c_COMBI(_1170070))))), hAPP(hAPP(c_COMBC(_1170070, _1170070, _1170070), hAPP(hAPP(c_COMBB(_1170070, tc_fun(_1170070, _1170070), _1170070), c_Groups_Oplus__class_Oplus(_1170070)), hAPP(hAPP(c_COMBS(_1170070, _1170070, _1170070), c_Groups_Oplus__class_Oplus(_1170070)), c_COMBI(_1170070)))), c_Groups_Oone__class_Oone(_1170070))))), c_Divides_Odivmod__int(_1170072, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (22278 ^ _779448) ^ [_1170983, _1170985, _1170987, _1170989, _1170991, _1170993, _1170995] : [c_Big__Operators_Ocomm__monoid__big(_1170983, _1170985, _1170987, _1170989, _1170991), 22281 ^ _779448 : [(22282 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1170985), _1170993)), -(hAPP(hAPP(_1170991, _1170995), _1170993) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1170983, _1170985, _1170987), _1170995), _1170989), _1170993))], (22288 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1170985), _1170993))), -(hAPP(hAPP(_1170991, _1170995), _1170993) = _1170989)]]], (22294 ^ _779448) ^ [_1171251] : [class_Orderings_Oord(_1171251), -(c_Orderings_Oord__class_Omin(_1171251) = c_Orderings_Oord_Omin(_1171251, c_Orderings_Oord__class_Oless__eq(_1171251)))], (22300 ^ _779448) ^ [_1171338, _1171340, _1171342, _1171344, _1171346, _1171348, _1171350] : [c_Big__Operators_Ocomm__monoid__big(_1171338, _1171340, _1171342, _1171344, _1171346), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171340), _1171348))), -(hAPP(hAPP(_1171346, _1171350), _1171348) = _1171344)], (22310 ^ _779448) ^ [_1171466, _1171468] : [c_Nat__Transfer_Ois__nat(_1171466), c_Nat__Transfer_Onat__set(_1171468), 22317 ^ _779448 : [(22318 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1171466), _1171468)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1171466)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1171468))))], (22324 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1171466)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1171468))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1171466), _1171468)))]]], (22330 ^ _779448) ^ [_1171769, _1171771] : [-(c_Divides_Odivmod__int__rel(_1171769, _1171771) = 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, _1171769))), 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), _1171771)))))), 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)), _1171771))), 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)), _1171771))))), 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)), _1171771)))), 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), _1171771))), 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))))))))], (22332 ^ _779448) ^ [_1171884, _1171886, _1171888] : [class_Orderings_Olinorder(_1171884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171884), _1171886)), hBOOL(hAPP(hAPP(c_member(_1171884), _1171888), _1171886)), 22343 ^ _779448 : [(22344 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171884, tc_HOL_Obool)), _1171886), hAPP(hAPP(c_Set_Oinsert(_1171884), _1171888), c_Orderings_Obot__class_Obot(tc_fun(_1171884, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1171884, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1171884, _1171886) = _1171888)], (22350 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171884, tc_HOL_Obool)), _1171886), hAPP(hAPP(c_Set_Oinsert(_1171884), _1171888), c_Orderings_Obot__class_Obot(tc_fun(_1171884, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1171884, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1171884, _1171886) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171884), _1171888), c_Big__Operators_Olinorder__class_OMin(_1171884, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171884, tc_HOL_Obool)), _1171886), hAPP(hAPP(c_Set_Oinsert(_1171884), _1171888), c_Orderings_Obot__class_Obot(tc_fun(_1171884, tc_HOL_Obool)))))))]]], (22356 ^ _779448) ^ [] : [-(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)))))], (22358 ^ _779448) ^ [_1172408, _1172410, _1172412] : [class_Orderings_Olinorder(_1172408), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172408), _1172410)), hBOOL(hAPP(hAPP(c_member(_1172408), _1172412), _1172410)), 22369 ^ _779448 : [(22370 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172408, tc_HOL_Obool)), _1172410), hAPP(hAPP(c_Set_Oinsert(_1172408), _1172412), c_Orderings_Obot__class_Obot(tc_fun(_1172408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1172408, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1172408, c_Orderings_Oord__class_Omin(_1172408), _1172410) = _1172412)], (22376 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172408, tc_HOL_Obool)), _1172410), hAPP(hAPP(c_Set_Oinsert(_1172408), _1172412), c_Orderings_Obot__class_Obot(tc_fun(_1172408, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1172408, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1172408, c_Orderings_Oord__class_Omin(_1172408), _1172410) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1172408), _1172412), c_Big__Operators_Olattice_OInf__fin(_1172408, c_Orderings_Oord__class_Omin(_1172408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172408, tc_HOL_Obool)), _1172410), hAPP(hAPP(c_Set_Oinsert(_1172408), _1172412), c_Orderings_Obot__class_Obot(tc_fun(_1172408, tc_HOL_Obool)))))))]]], (22382 ^ _779448) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (22384 ^ _779448) ^ [_1172950, _1172952] : [c_Nat__Transfer_Ois__nat(_1172950), c_Nat__Transfer_Ois__nat(_1172952), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1172950), _1172952)))], (22394 ^ _779448) ^ [_1173085] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173085)))], (22396 ^ _779448) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22398 ^ _779448) ^ [_1173128, _1173130] : [c_Nat__Transfer_Ois__nat(_1173128), c_Nat__Transfer_Ois__nat(_1173130), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173128), _1173130)))], (22408 ^ _779448) ^ [_1173263, _1173265] : [c_Nat__Transfer_Ois__nat(_1173263), c_Nat__Transfer_Ois__nat(_1173265), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1173263, _1173265)))], (22418 ^ _779448) ^ [_1173394, _1173396] : [c_Nat__Transfer_Ois__nat(_1173394), c_Nat__Transfer_Ois__nat(_1173396), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1173394), _1173396)))], (22428 ^ _779448) ^ [_1173529, _1173531] : [c_Nat__Transfer_Ois__nat(_1173529), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1173529), _1173531)))], (22434 ^ _779448) ^ [_1173614, _1173616] : [c_Nat__Transfer_Ois__nat(_1173614), c_Nat__Transfer_Ois__nat(_1173616), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1173614, _1173616)))], (22444 ^ _779448) ^ [_1173743, _1173745] : [class_Orderings_Olinorder(_1173743), -(c_Big__Operators_Olinorder__class_OMin(_1173743, hAPP(hAPP(c_Set_Oinsert(_1173743), _1173745), c_Orderings_Obot__class_Obot(tc_fun(_1173743, tc_HOL_Obool)))) = _1173745)], (22450 ^ _779448) ^ [_1173862] : [c_Nat__Transfer_Ois__nat(_1173862), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173862)))], (22456 ^ _779448) ^ [_1173935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173935)), -(c_Nat__Transfer_Ois__nat(_1173935))], (22462 ^ _779448) ^ [_1174010, _1174012] : [-(_1174010 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1174012, _1174010), c_Divides_Odivmod__int(_1174012, _1174010))))], (22468 ^ _779448) ^ [_1174054, _1174056, _1174058] : [class_Orderings_Olinorder(_1174054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174054), _1174056)), hBOOL(hAPP(hAPP(c_member(_1174054), _1174058), _1174056)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1174054), _1174058), c_Big__Operators_Olattice_OInf__fin(_1174054, c_Orderings_Oord__class_Omin(_1174054), _1174056)) = c_Big__Operators_Olattice_OInf__fin(_1174054, c_Orderings_Oord__class_Omin(_1174054), _1174056))], (22482 ^ _779448) ^ [_1174301, _1174303, _1174305] : [class_Orderings_Olinorder(_1174301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174301), _1174303)), hBOOL(hAPP(hAPP(c_member(_1174301), _1174305), _1174303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174301), c_Big__Operators_Olinorder__class_OMin(_1174301, _1174303)), _1174305)))], (22496 ^ _779448) ^ [_1174528, _1174530] : [class_Orderings_Olinorder(_1174528), -(c_Big__Operators_Olattice_OInf__fin(_1174528, c_Orderings_Oord__class_Omin(_1174528), hAPP(hAPP(c_Set_Oinsert(_1174528), _1174530), c_Orderings_Obot__class_Obot(tc_fun(_1174528, tc_HOL_Obool)))) = _1174530)], (22502 ^ _779448) ^ [_1174641, _1174643] : [c_Nat__Transfer_Onat__set(_1174641), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1174643), _1174641)), -(c_Nat__Transfer_Ois__nat(_1174643))], (22512 ^ _779448) ^ [_1174776, _1174778] : [class_Orderings_Olinorder(_1174776), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174776), _1174778)), -(_1174778 = c_Orderings_Obot__class_Obot(tc_fun(_1174776, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1174776), c_Big__Operators_Olinorder__class_OMin(_1174776, _1174778)), _1174778)))], (22526 ^ _779448) ^ [_1174956, _1174958, _1174960] : [class_Orderings_Olinorder(_1174956), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174956), _1174958)), hBOOL(hAPP(hAPP(c_member(_1174956), _1174960), _1174958)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1174956), _1174960), c_Big__Operators_Olinorder__class_OMin(_1174956, _1174958)) = c_Big__Operators_Olinorder__class_OMin(_1174956, _1174958))], (22540 ^ _779448) ^ [_1175191, _1175193] : [class_Orderings_Olinorder(_1175191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175191), _1175193)), -(c_Big__Operators_Olattice_OInf__fin(_1175191, c_Orderings_Oord__class_Omin(_1175191), _1175193) = hAPP(c_Finite__Set_Ofold1(_1175191, c_Orderings_Oord__class_Omin(_1175191)), _1175193))], (22550 ^ _779448) ^ [_1175354, _1175356] : [class_Orderings_Olinorder(_1175354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175354), _1175356)), -(c_Big__Operators_Olinorder__class_OMin(_1175354, _1175356) = hAPP(c_Finite__Set_Ofold1(_1175354, c_Orderings_Oord__class_Omin(_1175354)), _1175356))], (22560 ^ _779448) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (22562 ^ _779448) ^ [_1175529, _1175531, _1175533] : [class_Orderings_Olinorder(_1175529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175529), _1175531)), -(_1175531 = c_Orderings_Obot__class_Obot(tc_fun(_1175529, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1175529, c_Orderings_Oord__class_Omin(_1175529), hAPP(hAPP(c_Set_Oinsert(_1175529), _1175533), _1175531)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1175529), _1175533), c_Big__Operators_Olattice_OInf__fin(_1175529, c_Orderings_Oord__class_Omin(_1175529), _1175531)))], (22576 ^ _779448) ^ [_1175749, _1175751, _1175753] : [class_Orderings_Olinorder(_1175749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175749), _1175751)), -(_1175753 = c_Orderings_Obot__class_Obot(tc_fun(_1175749, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1175749, tc_HOL_Obool)), _1175753), _1175751)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1175749), c_Big__Operators_Olattice_OInf__fin(_1175749, c_Orderings_Oord__class_Omin(_1175749), _1175753)), c_Big__Operators_Olattice_OInf__fin(_1175749, c_Orderings_Oord__class_Omin(_1175749), _1175751)) = c_Big__Operators_Olattice_OInf__fin(_1175749, c_Orderings_Oord__class_Omin(_1175749), _1175751))], (22594 ^ _779448) ^ [_1176081, _1176083, _1176085] : [class_Orderings_Olinorder(_1176081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176081, tc_HOL_Obool)), _1176083), _1176085)), -(_1176083 = c_Orderings_Obot__class_Obot(tc_fun(_1176081, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1176081), _1176085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176081), c_Big__Operators_Olinorder__class_OMin(_1176081, _1176085)), c_Big__Operators_Olinorder__class_OMin(_1176081, _1176083))))], (22612 ^ _779448) ^ [_1176387, _1176389, _1176391] : [class_Orderings_Olinorder(_1176387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1176387), _1176389)), -(c_Big__Operators_Olattice_OInf__fin(_1176387, c_Orderings_Oord__class_Omin(_1176387), hAPP(hAPP(c_Set_Oinsert(_1176387), _1176391), _1176389)) = hAPP(hAPP(c_Finite__Set_Ofold(_1176387, _1176387, c_Orderings_Oord__class_Omin(_1176387)), _1176391), _1176389))], (22622 ^ _779448) ^ [_1176578, _1176580, _1176582] : [class_Orderings_Olinorder(_1176578), hBOOL(hAPP(c_Finite__Set_Ofinite(_1176578), _1176580)), -(_1176580 = c_Orderings_Obot__class_Obot(tc_fun(_1176578, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1176578, hAPP(hAPP(c_Set_Oinsert(_1176578), _1176582), _1176580)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176578), _1176582), c_Big__Operators_Olinorder__class_OMin(_1176578, _1176580)))], (22636 ^ _779448) ^ [_1176786, _1176788, _1176790] : [class_Orderings_Olinorder(_1176786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1176786), _1176788)), -(_1176790 = c_Orderings_Obot__class_Obot(tc_fun(_1176786, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176786, tc_HOL_Obool)), _1176790), _1176788)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1176786), c_Big__Operators_Olinorder__class_OMin(_1176786, _1176790)), c_Big__Operators_Olinorder__class_OMin(_1176786, _1176788)) = c_Big__Operators_Olinorder__class_OMin(_1176786, _1176788))], (22654 ^ _779448) ^ [_1177100, _1177102, _1177104] : [class_Orderings_Olinorder(_1177100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177100), _1177102)), -(c_Big__Operators_Olinorder__class_OMin(_1177100, hAPP(hAPP(c_Set_Oinsert(_1177100), _1177104), _1177102)) = hAPP(hAPP(c_Finite__Set_Ofold(_1177100, _1177100, c_Orderings_Oord__class_Omin(_1177100)), _1177104), _1177102))], (22664 ^ _779448) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22666 ^ _779448) ^ [_1177303, _1177305, _1177307] : [class_Orderings_Olinorder(_1177303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177303), _1177305)), -(hBOOL(hAPP(hAPP(c_member(_1177303), _1177307), _1177305))), -(_1177305 = c_Orderings_Obot__class_Obot(tc_fun(_1177303, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1177303, c_Orderings_Oord__class_Omin(_1177303), hAPP(hAPP(c_Set_Oinsert(_1177303), _1177307), _1177305)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1177303), _1177307), c_Big__Operators_Olattice_OInf__fin(_1177303, c_Orderings_Oord__class_Omin(_1177303), _1177305)))], (22684 ^ _779448) ^ [_1177552, _1177554, _1177556] : [class_Orderings_Olinorder(_1177552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177552), _1177554)), 22691 ^ _779448 : [(22692 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1177552, tc_HOL_Obool)), _1177554), hAPP(hAPP(c_Set_Oinsert(_1177552), _1177556), c_Orderings_Obot__class_Obot(tc_fun(_1177552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1177552, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1177552, c_Orderings_Oord__class_Omin(_1177552), hAPP(hAPP(c_Set_Oinsert(_1177552), _1177556), _1177554)) = _1177556)], (22698 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1177552, tc_HOL_Obool)), _1177554), hAPP(hAPP(c_Set_Oinsert(_1177552), _1177556), c_Orderings_Obot__class_Obot(tc_fun(_1177552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1177552, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1177552, c_Orderings_Oord__class_Omin(_1177552), hAPP(hAPP(c_Set_Oinsert(_1177552), _1177556), _1177554)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1177552), _1177556), c_Big__Operators_Olattice_OInf__fin(_1177552, c_Orderings_Oord__class_Omin(_1177552), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1177552, tc_HOL_Obool)), _1177554), hAPP(hAPP(c_Set_Oinsert(_1177552), _1177556), c_Orderings_Obot__class_Obot(tc_fun(_1177552, tc_HOL_Obool)))))))]]], (22704 ^ _779448) ^ [_1178040, _1178042, _1178044] : [class_Orderings_Olinorder(_1178040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178040), _1178042)), -(hBOOL(hAPP(hAPP(c_member(_1178040), _1178044), _1178042))), -(c_Big__Operators_Olattice_OInf__fin(_1178040, c_Orderings_Oord__class_Omin(_1178040), hAPP(hAPP(c_Set_Oinsert(_1178040), _1178044), _1178042)) = hAPP(hAPP(c_Finite__Set_Ofold(_1178040, _1178040, c_Orderings_Oord__class_Omin(_1178040)), _1178044), _1178042))], (22718 ^ _779448) ^ [_1178260, _1178262, _1178264] : [class_Orderings_Olinorder(_1178260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178260), _1178262)), -(hBOOL(hAPP(hAPP(c_member(_1178260), _1178264), _1178262))), -(_1178262 = c_Orderings_Obot__class_Obot(tc_fun(_1178260, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1178260, hAPP(hAPP(c_Set_Oinsert(_1178260), _1178264), _1178262)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178260), _1178264), c_Big__Operators_Olinorder__class_OMin(_1178260, _1178262)))], (22736 ^ _779448) ^ [_1178497, _1178499, _1178501] : [class_Orderings_Olinorder(_1178497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178497), _1178499)), 22743 ^ _779448 : [(22744 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178497, tc_HOL_Obool)), _1178499), hAPP(hAPP(c_Set_Oinsert(_1178497), _1178501), c_Orderings_Obot__class_Obot(tc_fun(_1178497, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1178497, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1178497, hAPP(hAPP(c_Set_Oinsert(_1178497), _1178501), _1178499)) = _1178501)], (22750 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178497, tc_HOL_Obool)), _1178499), hAPP(hAPP(c_Set_Oinsert(_1178497), _1178501), c_Orderings_Obot__class_Obot(tc_fun(_1178497, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1178497, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1178497, hAPP(hAPP(c_Set_Oinsert(_1178497), _1178501), _1178499)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1178497), _1178501), c_Big__Operators_Olinorder__class_OMin(_1178497, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1178497, tc_HOL_Obool)), _1178499), hAPP(hAPP(c_Set_Oinsert(_1178497), _1178501), c_Orderings_Obot__class_Obot(tc_fun(_1178497, tc_HOL_Obool)))))))]]], (22756 ^ _779448) ^ [_1178967, _1178969, _1178971] : [class_Orderings_Olinorder(_1178967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178967), _1178969)), -(hBOOL(hAPP(hAPP(c_member(_1178967), _1178971), _1178969))), -(c_Big__Operators_Olinorder__class_OMin(_1178967, hAPP(hAPP(c_Set_Oinsert(_1178967), _1178971), _1178969)) = hAPP(hAPP(c_Finite__Set_Ofold(_1178967, _1178967, c_Orderings_Oord__class_Omin(_1178967)), _1178971), _1178969))], (22770 ^ _779448) ^ [_1179181, _1179183] : [class_Orderings_Olinorder(_1179181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179181), _1179183)), -(_1179183 = c_Orderings_Obot__class_Obot(tc_fun(_1179181, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1179181), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179181), 22783 ^ [_1179181, _1179183]), 22784 ^ [_1179181, _1179183])), hAPP(hAPP(c_Set_Oinsert(_1179181), 22783 ^ [_1179181, _1179183]), hAPP(hAPP(c_Set_Oinsert(_1179181), 22784 ^ [_1179181, _1179183]), c_Orderings_Obot__class_Obot(tc_fun(_1179181, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1179181), c_Big__Operators_Olattice_OInf__fin(_1179181, c_Orderings_Oord__class_Omin(_1179181), _1179183)), _1179183)))], (22790 ^ _779448) ^ [_1179631, _1179633] : [class_Orderings_Olinorder(_1179631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179631), _1179633)), -(_1179633 = c_Orderings_Obot__class_Obot(tc_fun(_1179631, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1179631), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1179631), 22803 ^ [_1179631, _1179633]), 22804 ^ [_1179631, _1179633])), hAPP(hAPP(c_Set_Oinsert(_1179631), 22803 ^ [_1179631, _1179633]), hAPP(hAPP(c_Set_Oinsert(_1179631), 22804 ^ [_1179631, _1179633]), c_Orderings_Obot__class_Obot(tc_fun(_1179631, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1179631), c_Big__Operators_Olinorder__class_OMin(_1179631, _1179633)), _1179633)))], (22810 ^ _779448) ^ [_1180075, _1180077, _1180079, _1180081, _1180083] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1180075, _1180077), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1180079), _1180081))), -(_1180077 = 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)), _1180083)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1180075, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180077), _1180083)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180079), _1180083)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180077), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1180079, _1180083))), _1180081)))))], (22824 ^ _779448) ^ [_1180381, _1180383, _1180385, _1180387, _1180389, _1180391] : [class_Groups_Ocomm__monoid__mult(_1180381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180383), _1180385)), 22831 ^ _779448 : [(22832 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1180383), _1180387), _1180385)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1180383, _1180381), hAPP(hAPP(c_COMBC(_1180383, _1180381, _1180381), hAPP(hAPP(c_COMBS(_1180383, _1180381, tc_fun(_1180381, _1180381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1180381, tc_fun(_1180381, _1180381)), _1180383), c_If(_1180381)), hAPP(hAPP(c_COMBC(_1180383, _1180383, tc_HOL_Obool), c_fequal), _1180387))), _1180389)), _1180391)), _1180385) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180381), hAPP(_1180389, _1180387)), hAPP(hAPP(c_Power_Opower__class_Opower(_1180381), _1180391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1180383), _1180385)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22838 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180383), _1180387), _1180385))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1180383, _1180381), hAPP(hAPP(c_COMBC(_1180383, _1180381, _1180381), hAPP(hAPP(c_COMBS(_1180383, _1180381, tc_fun(_1180381, _1180381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1180381, tc_fun(_1180381, _1180381)), _1180383), c_If(_1180381)), hAPP(hAPP(c_COMBC(_1180383, _1180383, tc_HOL_Obool), c_fequal), _1180387))), _1180389)), _1180391)), _1180385) = hAPP(hAPP(c_Power_Opower__class_Opower(_1180381), _1180391), hAPP(c_Finite__Set_Ocard(_1180383), _1180385)))]]], (22844 ^ _779448) ^ [_1180993, _1180995, _1180997] : [-(hAPP(c_Divides_Oadjust(_1180993), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1180995), _1180997)) = 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), _1180997), _1180993)), 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)))), _1180995)), 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)))), _1180995)), _1180997))))], (22846 ^ _779448) ^ [_1181073, _1181075, _1181077, _1181079] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1181073), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1181075, tc_Int_Oint), _1181077), _1181079)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1181075, _1181073), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1181073, _1181075), c_Int_Oring__1__class_Oof__int(_1181073)), _1181077)), _1181079)), class_Groups_Ocomm__monoid__mult(_1181073), class_Rings_Oring__1(_1181073)], (22856 ^ _779448) ^ [_1181276, _1181278, _1181280] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1181276, tc_Nat_Onat), _1181278), _1181280) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1181276, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1181276), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1181278)), _1181280)))], (22858 ^ _779448) ^ [_1181355, _1181357, _1181359, _1181361] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1181355, tc_fun(_1181357, tc_HOL_Obool))), _1181359), _1181361)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1181355, _1181357)), hAPP(hAPP(c_Product__Type_OPair(_1181355, _1181357), _1181359), _1181361)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1181355, _1181357), tc_HOL_Obool)))))], (22864 ^ _779448) ^ [_1181512, _1181514, _1181516, _1181518] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1181512, _1181514)), hAPP(hAPP(c_Product__Type_OPair(_1181512, _1181514), _1181516), _1181518)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1181512, _1181514), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1181512, tc_fun(_1181514, tc_HOL_Obool))), _1181516), _1181518)))], (22870 ^ _779448) ^ [_1181696, _1181698, _1181700, _1181702] : [hAPP(hAPP(c_COMBC(_1181696, tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_fun(_1181698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1181698, tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_fun(_1181698, tc_HOL_Obool)), _1181696), c_COMBC(_1181698, tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1181698, tc_prod(_1181696, _1181698)), tc_fun(_1181698, tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), _1181696), hAPP(c_COMBB(tc_prod(_1181696, _1181698), tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool), _1181698), c_member(tc_prod(_1181696, _1181698)))), c_Product__Type_OPair(_1181696, _1181698)))), _1181700) = hAPP(hAPP(c_COMBC(_1181696, tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_fun(_1181698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1181698, tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_fun(_1181698, tc_HOL_Obool)), _1181696), c_COMBC(_1181698, tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1181698, tc_prod(_1181696, _1181698)), tc_fun(_1181698, tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool)), _1181696), hAPP(c_COMBB(tc_prod(_1181696, _1181698), tc_fun(tc_fun(tc_prod(_1181696, _1181698), tc_HOL_Obool), tc_HOL_Obool), _1181698), c_member(tc_prod(_1181696, _1181698)))), c_Product__Type_OPair(_1181696, _1181698)))), _1181702), -(_1181700 = _1181702)], (22876 ^ _779448) ^ [_1182245, _1182247, _1182249, _1182251] : [_1182249 = _1182251, -(hAPP(hAPP(c_COMBC(_1182245, tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_fun(_1182247, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182247, tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_fun(_1182247, tc_HOL_Obool)), _1182245), c_COMBC(_1182247, tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182247, tc_prod(_1182245, _1182247)), tc_fun(_1182247, tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), _1182245), hAPP(c_COMBB(tc_prod(_1182245, _1182247), tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool), _1182247), c_member(tc_prod(_1182245, _1182247)))), c_Product__Type_OPair(_1182245, _1182247)))), _1182249) = hAPP(hAPP(c_COMBC(_1182245, tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_fun(_1182247, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182247, tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_fun(_1182247, tc_HOL_Obool)), _1182245), c_COMBC(_1182247, tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182247, tc_prod(_1182245, _1182247)), tc_fun(_1182247, tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool)), _1182245), hAPP(c_COMBB(tc_prod(_1182245, _1182247), tc_fun(tc_fun(tc_prod(_1182245, _1182247), tc_HOL_Obool), tc_HOL_Obool), _1182247), c_member(tc_prod(_1182245, _1182247)))), c_Product__Type_OPair(_1182245, _1182247)))), _1182251))], (22882 ^ _779448) ^ [_1182821, _1182823, _1182825, _1182827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1182821, tc_fun(_1182823, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1182821, tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_fun(_1182823, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182823, tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_fun(_1182823, tc_HOL_Obool)), _1182821), c_COMBC(_1182823, tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182823, tc_prod(_1182821, _1182823)), tc_fun(_1182823, tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), _1182821), hAPP(c_COMBB(tc_prod(_1182821, _1182823), tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool), _1182823), c_member(tc_prod(_1182821, _1182823)))), c_Product__Type_OPair(_1182821, _1182823)))), _1182825)), hAPP(hAPP(c_COMBC(_1182821, tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_fun(_1182823, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182823, tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_fun(_1182823, tc_HOL_Obool)), _1182821), c_COMBC(_1182823, tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1182823, tc_prod(_1182821, _1182823)), tc_fun(_1182823, tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool)), _1182821), hAPP(c_COMBB(tc_prod(_1182821, _1182823), tc_fun(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool), tc_HOL_Obool), _1182823), c_member(tc_prod(_1182821, _1182823)))), c_Product__Type_OPair(_1182821, _1182823)))), _1182827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1182821, _1182823), tc_HOL_Obool)), _1182825), _1182827)))], (22888 ^ _779448) ^ [_1183422, _1183424, _1183426, _1183428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool)), _1183426), _1183428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1183422, tc_fun(_1183424, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1183422, tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_fun(_1183424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183424, tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_fun(_1183424, tc_HOL_Obool)), _1183422), c_COMBC(_1183424, tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183424, tc_prod(_1183422, _1183424)), tc_fun(_1183424, tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), _1183422), hAPP(c_COMBB(tc_prod(_1183422, _1183424), tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool), _1183424), c_member(tc_prod(_1183422, _1183424)))), c_Product__Type_OPair(_1183422, _1183424)))), _1183426)), hAPP(hAPP(c_COMBC(_1183422, tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_fun(_1183424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183424, tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_fun(_1183424, tc_HOL_Obool)), _1183422), c_COMBC(_1183424, tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1183424, tc_prod(_1183422, _1183424)), tc_fun(_1183424, tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool)), _1183422), hAPP(c_COMBB(tc_prod(_1183422, _1183424), tc_fun(tc_fun(tc_prod(_1183422, _1183424), tc_HOL_Obool), tc_HOL_Obool), _1183424), c_member(tc_prod(_1183422, _1183424)))), c_Product__Type_OPair(_1183422, _1183424)))), _1183428))))], (22894 ^ _779448) ^ [_1184029, _1184031, _1184033, _1184035] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1184029), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184031, tc_Nat_Onat), _1184033), _1184035)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184031, _1184029), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1184029, _1184031), c_Nat_Osemiring__1__class_Oof__nat(_1184029)), _1184033)), _1184035)), class_Groups_Ocomm__monoid__mult(_1184029), class_Rings_Osemiring__1(_1184029)], (22904 ^ _779448) ^ [_1184232, _1184234, _1184236] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184232, tc_Nat_Onat), _1184234), _1184236)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184232, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1184232), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184234)), _1184236))], (22906 ^ _779448) ^ [_1184290, _1184292, _1184294, _1184296, _1184298] : [class_Groups_Ocomm__monoid__mult(_1184290), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184292, _1184290), hAPP(hAPP(c_COMBS(_1184292, _1184290, _1184290), hAPP(hAPP(c_COMBB(_1184290, tc_fun(_1184290, _1184290), _1184292), c_Groups_Otimes__class_Otimes(_1184290)), _1184294)), _1184296)), _1184298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184290), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184292, _1184290), _1184294), _1184298)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184292, _1184290), _1184296), _1184298)))], (22912 ^ _779448) ^ [_1184491, _1184493, _1184495] : [class_Groups_Ocomm__monoid__mult(_1184491), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184493, _1184491), hAPP(c_COMBK(_1184491, _1184493), c_Groups_Oone__class_Oone(_1184491))), _1184495) = c_Groups_Oone__class_Oone(_1184491))], (22918 ^ _779448) ^ [_1184606, _1184608, _1184610] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1184606), _1184608), _1184610) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1184606), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1184606, tc_Int_Oint), _1184608), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184610))), class_Groups_Ocomm__monoid__add(_1184606), class_Groups_Ocomm__monoid__mult(_1184606)], (22928 ^ _779448) ^ [_1184797, _1184799, _1184801, _1184803] : [class_Rings_Ocomm__semiring__1(_1184797), class_Rings_Ono__zero__divisors(_1184797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1184799), _1184801)), 22939 ^ _779448 : [(22940 ^ _779448) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184799, _1184797), _1184803), _1184801) = c_Groups_Ozero__class_Ozero(_1184797), 22944 ^ _779448 : [(22945 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1184799), 22943 ^ [_1184797, _1184799, _1184801, _1184803]), _1184801)))], (22947 ^ _779448) ^ [] : [-(hAPP(_1184803, 22943 ^ [_1184797, _1184799, _1184801, _1184803]) = c_Groups_Ozero__class_Ozero(_1184797))]]], (22949 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1184799, _1184797), _1184803), _1184801) = c_Groups_Ozero__class_Ozero(_1184797)), 22950 ^ _779448 : [(22951 ^ _779448) ^ [_1185175] : [hBOOL(hAPP(hAPP(c_member(_1184799), _1185175), _1184801)), hAPP(_1184803, _1185175) = c_Groups_Ozero__class_Ozero(_1184797)]]]]], (22959 ^ _779448) ^ [_1185330, _1185332, _1185334, _1185336] : [class_Rings_Ocomm__semiring__1(_1185330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1185332), _1185334)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185332, _1185330), _1185336), _1185334) = c_Groups_Ozero__class_Ozero(_1185330)), 22968 ^ _779448 : [(22969 ^ _779448) ^ [_1185511] : [hBOOL(hAPP(hAPP(c_member(_1185332), _1185511), _1185334)), hAPP(_1185336, _1185511) = c_Groups_Ozero__class_Ozero(_1185330)]]], (22977 ^ _779448) ^ [_1185660, _1185662, _1185664] : [class_Groups_Ocomm__monoid__mult(_1185660), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185662, _1185660), _1185664), c_Orderings_Obot__class_Obot(tc_fun(_1185662, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1185660))], (22983 ^ _779448) ^ [_1185769, _1185771, _1185773] : [class_Groups_Ocomm__monoid__mult(_1185769), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185771, _1185769), _1185773), c_Orderings_Obot__class_Obot(tc_fun(_1185771, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1185769))], (22989 ^ _779448) ^ [_1185878, _1185880, _1185882, _1185884] : [class_Groups_Ocomm__monoid__mult(_1185878), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1185880), _1185882))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1185880, _1185878), _1185884), _1185882) = c_Groups_Oone__class_Oone(_1185878))], (22999 ^ _779448) ^ [_1186002, _1186004, _1186006, _1186008] : [class_Groups_Ocomm__monoid__mult(_1186002), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1186004), _1186006))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186004, _1186002), _1186008), _1186006) = c_Groups_Oone__class_Oone(_1186002))], (23009 ^ _779448) ^ [_1186126, _1186128, _1186130] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1186126), _1186128)), 23012 ^ _779448 : [(23023 ^ _779448) ^ [] : [23025 ^ _779448 : [(23026 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1186126), 23024 ^ [_1186126, _1186128, _1186130]), _1186128)))], (23028 ^ _779448) ^ [] : [hAPP(_1186130, 23024 ^ [_1186126, _1186128, _1186130]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186126, tc_Nat_Onat), _1186130), _1186128) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (23013 ^ _779448) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186126, tc_Nat_Onat), _1186130), _1186128) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 23016 ^ _779448 : [(23017 ^ _779448) ^ [_1186288] : [hBOOL(hAPP(hAPP(c_member(_1186126), _1186288), _1186128)), -(hAPP(_1186130, _1186288) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (23032 ^ _779448) ^ [_1186546, _1186548, _1186550] : [class_Groups_Ocomm__monoid__add(_1186546), class_Groups_Ocomm__monoid__mult(_1186546), c_Nat__Transfer_Onat__set(_1186548), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1186546), _1186550), _1186548) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1186546), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1186546, tc_Nat_Onat), _1186550), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1186548)))], (23046 ^ _779448) ^ [_1186791, _1186793, _1186795, _1186797, _1186799] : [class_Groups_Ocomm__monoid__mult(_1186791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1186793), _1186795)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186793, _1186791), hAPP(hAPP(c_COMBS(_1186793, _1186791, _1186791), hAPP(hAPP(c_COMBB(_1186791, tc_fun(_1186791, _1186791), _1186793), c_Groups_Otimes__class_Otimes(_1186791)), _1186797)), _1186799)), _1186795) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186791), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186793, _1186791), _1186797), _1186795)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1186793, _1186791), _1186799), _1186795)))], (23056 ^ _779448) ^ [_1187058, _1187060, _1187062, _1187064, _1187066, _1187068] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187058, _1187060), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187062), _1187064))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187058, _1187060), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187066), _1187068))), -(_1187060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187064 = _1187068)], (23070 ^ _779448) ^ [_1187262, _1187264, _1187266, _1187268, _1187270, _1187272] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187262, _1187264), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187266), _1187268))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187262, _1187264), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187270), _1187272))), -(_1187264 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187266 = _1187270)], (23084 ^ _779448) ^ [_1187466, _1187468, _1187470] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1187466, _1187466), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1187468), _1187470))), -(_1187466 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1187470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23094 ^ _779448) ^ [_1187578] : [-(_1187578 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1187578), 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)))))], (23100 ^ _779448) ^ [_1187617, _1187619, _1187621] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1187617), _1187619)), 23103 ^ _779448 : [(23114 ^ _779448) ^ [] : [23116 ^ _779448 : [(23117 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187617), 23115 ^ [_1187617, _1187619, _1187621]), _1187619)))], (23119 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1187621, 23115 ^ [_1187617, _1187619, _1187621])))]], -(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(_1187617, tc_Nat_Onat), _1187621), _1187619))))], (23104 ^ _779448) ^ [] : [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(_1187617, tc_Nat_Onat), _1187621), _1187619))), 23107 ^ _779448 : [(23108 ^ _779448) ^ [_1187785] : [hBOOL(hAPP(hAPP(c_member(_1187617), _1187785), _1187619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1187621, _1187785))))]]]]], (23123 ^ _779448) ^ [_1188053, _1188055, _1188057, _1188059, _1188061, _1188063, _1188065, _1188067] : [class_Groups_Ocomm__monoid__mult(_1188053), c_Fun_Oinj__on(_1188055, _1188057, _1188059, _1188061), _1188063 = hAPP(c_Set_Oimage(_1188055, _1188057, _1188059), _1188061), _1188065 = hAPP(c_Fun_Ocomp(_1188057, _1188053, _1188055, _1188067), _1188059), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188057, _1188053), _1188067), _1188063) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188055, _1188053), _1188065), _1188061))], (23141 ^ _779448) ^ [_1188402, _1188404, _1188406, _1188408, _1188410, _1188412] : [class_Groups_Ocomm__monoid__mult(_1188402), c_Fun_Oinj__on(_1188404, _1188406, _1188408, _1188410), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188406, _1188402), _1188412), hAPP(c_Set_Oimage(_1188404, _1188406, _1188408), _1188410)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188404, _1188402), hAPP(c_Fun_Ocomp(_1188406, _1188402, _1188404, _1188412), _1188408)), _1188410))], (23151 ^ _779448) ^ [_1188615, _1188617, _1188619, _1188621, _1188623] : [class_Groups_Ocomm__monoid__mult(_1188615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1188617), _1188619)), 23158 ^ _779448 : [(23159 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1188617), _1188621), _1188619)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188617, _1188615), hAPP(hAPP(c_COMBC(_1188617, _1188615, _1188615), hAPP(hAPP(c_COMBS(_1188617, _1188615, tc_fun(_1188615, _1188615)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188615, tc_fun(_1188615, _1188615)), _1188617), c_If(_1188615)), hAPP(c_fequal, _1188621))), _1188623)), c_Groups_Oone__class_Oone(_1188615))), _1188619) = hAPP(_1188623, _1188621))], (23165 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1188617), _1188621), _1188619))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1188617, _1188615), hAPP(hAPP(c_COMBC(_1188617, _1188615, _1188615), hAPP(hAPP(c_COMBS(_1188617, _1188615, tc_fun(_1188615, _1188615)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188615, tc_fun(_1188615, _1188615)), _1188617), c_If(_1188615)), hAPP(c_fequal, _1188621))), _1188623)), c_Groups_Oone__class_Oone(_1188615))), _1188619) = c_Groups_Oone__class_Oone(_1188615))]]], (23171 ^ _779448) ^ [_1189125, _1189127, _1189129, _1189131, _1189133] : [class_Groups_Ocomm__monoid__mult(_1189125), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189127), _1189129)), 23178 ^ _779448 : [(23179 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1189127), _1189131), _1189129)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1189127, _1189125), hAPP(hAPP(c_COMBC(_1189127, _1189125, _1189125), hAPP(hAPP(c_COMBS(_1189127, _1189125, tc_fun(_1189125, _1189125)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189125, tc_fun(_1189125, _1189125)), _1189127), c_If(_1189125)), hAPP(hAPP(c_COMBC(_1189127, _1189127, tc_HOL_Obool), c_fequal), _1189131))), _1189133)), c_Groups_Oone__class_Oone(_1189125))), _1189129) = hAPP(_1189133, _1189131))], (23185 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189127), _1189131), _1189129))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1189127, _1189125), hAPP(hAPP(c_COMBC(_1189127, _1189125, _1189125), hAPP(hAPP(c_COMBS(_1189127, _1189125, tc_fun(_1189125, _1189125)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189125, tc_fun(_1189125, _1189125)), _1189127), c_If(_1189125)), hAPP(hAPP(c_COMBC(_1189127, _1189127, tc_HOL_Obool), c_fequal), _1189131))), _1189133)), c_Groups_Oone__class_Oone(_1189125))), _1189129) = c_Groups_Oone__class_Oone(_1189125))]]], (23191 ^ _779448) ^ [_1189663, _1189665, _1189667, _1189669] : [class_Groups_Ocomm__monoid__mult(_1189663), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189665), _1189667)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1189665, _1189663), hAPP(c_COMBK(_1189663, _1189665), _1189669)), _1189667) = hAPP(hAPP(c_Power_Opower__class_Opower(_1189663), _1189669), hAPP(c_Finite__Set_Ocard(_1189665), _1189667)))], (23201 ^ _779448) ^ [_1189862, _1189864, _1189866] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189862, _1189862), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189864), _1189866))), -(_1189862 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1189864 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23211 ^ _779448) ^ [_1189978, _1189980, _1189982, _1189984] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1189978, _1189980), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1189982), _1189984))), -(_1189980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1189978, _1189980) = _1189984)], (23221 ^ _779448) ^ [_1190104, _1190106, _1190108, _1190110] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1190104, _1190106), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1190108), _1190110))), -(_1190106 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190104), _1190106) = _1190108)], (23231 ^ _779448) ^ [_1190234, _1190236, _1190238, _1190240, _1190242] : [class_Groups_Ocomm__monoid__mult(_1190234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1190236), _1190238)), -(hBOOL(hAPP(hAPP(c_member(_1190236), _1190240), _1190238))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190236, _1190234), _1190242), hAPP(hAPP(c_Set_Oinsert(_1190236), _1190240), _1190238)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190234), hAPP(_1190242, _1190240)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190236, _1190234), _1190242), _1190238)))], (23245 ^ _779448) ^ [_1190484, _1190486, _1190488, _1190490, _1190492] : [class_Groups_Ocomm__monoid__mult(_1190484), hBOOL(hAPP(c_Finite__Set_Ofinite(_1190486), _1190488)), -(hBOOL(hAPP(hAPP(c_member(_1190486), _1190490), _1190488))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190486, _1190484), _1190492), hAPP(hAPP(c_Set_Oinsert(_1190486), _1190490), _1190488)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190484), hAPP(_1190492, _1190490)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190486, _1190484), _1190492), _1190488)))], (23259 ^ _779448) ^ [_1190734, _1190736, _1190738, _1190740, _1190742] : [class_Groups_Ocomm__monoid__mult(_1190734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1190736), _1190738)), c_Fun_Oinj__on(_1190736, _1190736, _1190740, _1190738), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190736, _1190734), _1190742), hAPP(c_Set_Oimage(_1190736, _1190736, _1190740), _1190738)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1190736, _1190734), hAPP(c_Fun_Ocomp(_1190736, _1190734, _1190736, _1190742), _1190740)), _1190738))], (23273 ^ _779448) ^ [_1191009, _1191011, _1191013, _1191015] : [class_Groups_Ocomm__monoid__mult(_1191009), 23276 ^ _779448 : [(23277 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1191011), _1191013)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191011, _1191009), _1191015), _1191013) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1191009, _1191011, c_Groups_Otimes__class_Otimes(_1191009)), _1191015), c_Groups_Oone__class_Oone(_1191009)), _1191013))], (23283 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1191011), _1191013))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191011, _1191009), _1191015), _1191013) = c_Groups_Oone__class_Oone(_1191009))]]], (23289 ^ _779448) ^ [_1191281, _1191283, _1191285, _1191287] : [class_Groups_Ocomm__monoid__mult(_1191281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191283), _1191285)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191283, _1191281), _1191287), _1191285) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1191281, _1191283, c_Groups_Otimes__class_Otimes(_1191281)), _1191287), c_Groups_Oone__class_Oone(_1191281)), _1191285))], (23299 ^ _779448) ^ [_1191476, _1191478] : [-(c_Divides_Odivmod__int(_1191476, _1191478) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1191476), _1191478)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191476, _1191478)))], (23301 ^ _779448) ^ [_1191520, _1191522, _1191524, _1191526, _1191528] : [class_Groups_Ocomm__monoid__mult(_1191520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191522), _1191524)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191522, _1191520), _1191526), hAPP(hAPP(c_Set_Oinsert(_1191522), _1191528), _1191524)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191520), hAPP(_1191526, _1191528)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191522, _1191520), _1191526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1191522, tc_HOL_Obool)), _1191524), hAPP(hAPP(c_Set_Oinsert(_1191522), _1191528), c_Orderings_Obot__class_Obot(tc_fun(_1191522, tc_HOL_Obool)))))))], (23311 ^ _779448) ^ [_1191785, _1191787] : [-(_1191785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1191787, _1191785), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1191787), _1191785)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191787, _1191785)))))], (23317 ^ _779448) ^ [_1191842, _1191844, _1191846, _1191848, _1191850] : [class_Groups_Ocomm__monoid__mult(_1191842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191844), _1191846)), hBOOL(hAPP(hAPP(c_member(_1191844), _1191848), _1191846)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191844, _1191842), _1191850), _1191846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191842), hAPP(_1191850, _1191848)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191844, _1191842), _1191850), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1191844, tc_HOL_Obool)), _1191846), hAPP(hAPP(c_Set_Oinsert(_1191844), _1191848), c_Orderings_Obot__class_Obot(tc_fun(_1191844, tc_HOL_Obool)))))))], (23331 ^ _779448) ^ [_1192167, _1192169, _1192171, _1192173, _1192175, _1192177, _1192179] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192167, _1192169), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192171), _1192173))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192175, _1192169), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192177), _1192179))), -(_1192169 = 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), _1192167), _1192175), _1192169), 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), _1192171), _1192177)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192173), _1192179)), _1192169))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1192173), _1192179), _1192169)))))], (23345 ^ _779448) ^ [_1192477, _1192479, _1192481, _1192483] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192477, _1192479), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192481), _1192483))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192477), _1192479), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1192483), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192481)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1192481)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1192483), 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), _1192479), _1192483))))))], (23351 ^ _779448) ^ [_1192704, _1192706, _1192708, _1192710] : [_1192704 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192706), _1192708)), _1192710), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1192704, _1192706), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1192708), _1192710)))), 23358 ^ _779448 : [(23359 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192706)))], (23361 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192710), _1192706))]], 23366 ^ _779448 : [(23367 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192706))], (23369 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192706), _1192710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192710), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23377 ^ _779448) ^ [_1193166, _1193168, _1193170, _1193172, _1193174] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1193166, _1193168), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1193170), _1193172))), -(_1193168 = 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), _1193174), _1193166), _1193168), 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), _1193174), _1193170)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193174), _1193172)), _1193168))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193174), _1193172), _1193168)))))], (23387 ^ _779448) ^ [_1193388] : [-(c_Divides_Oadjust(_1193388) = 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)), _1193388))))), 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)), _1193388))))), 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))))))))], (23389 ^ _779448) ^ [_1193449, _1193451, _1193453, _1193455, _1193457, _1193459, _1193461] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1193449, _1193451)), hAPP(hAPP(c_Product__Type_OPair(_1193449, _1193451), _1193453), _1193455)), _1193457)), -(hBOOL(hAPP(hAPP(c_member(_1193459), hAPP(hAPP(_1193461, _1193453), _1193455)), hAPP(c_Set_Oimage(tc_prod(_1193449, _1193451), _1193459, hAPP(c_Product__Type_Oprod_Oprod__case(_1193449, _1193451, _1193459), _1193461)), _1193457))))], (23395 ^ _779448) ^ [_1193643, _1193645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193643), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1193645, _1193643) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193645), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1193643)))], (23401 ^ _779448) ^ [_1193749, _1193751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193749), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23404 ^ _779448 : [(23405 ^ _779448) ^ [] : [23406 ^ _779448 : [(23407 ^ _779448) ^ [] : [_1193751 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23409 ^ _779448) ^ [] : [_1193749 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1193751, _1193749) = 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)))], (23413 ^ _779448) ^ [] : [-(c_Nitpick_Onorm__frac(_1193751, _1193749) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1193751), _1193749)), 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), _1193751))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1193749)))), -(_1193751 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1193749 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (23423 ^ _779448) ^ [_1194047] : [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), _1194047))), 23426 ^ _779448 : [(23427 ^ _779448) ^ [] : [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), _1194047)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194047)) = 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), _1194047))))], (23433 ^ _779448) ^ [] : [-(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), _1194047))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194047)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194047)), 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), _1194047)))))]]], (23439 ^ _779448) ^ [_1194337, _1194339, _1194341, _1194343, _1194345] : [hBOOL(hAPP(hAPP(_1194337, _1194339), _1194341)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194343, _1194345, tc_HOL_Obool), _1194337), hAPP(hAPP(c_Product__Type_OPair(_1194343, _1194345), _1194339), _1194341))))], (23445 ^ _779448) ^ [_1194466, _1194468, _1194470, _1194472, _1194474] : [hBOOL(hAPP(hAPP(_1194466, _1194468), _1194470)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194472, _1194474, tc_HOL_Obool), _1194466), hAPP(hAPP(c_Product__Type_OPair(_1194472, _1194474), _1194468), _1194470))))], (23451 ^ _779448) ^ [_1194595, _1194597, _1194599, _1194601, _1194603, _1194605, _1194607] : [hBOOL(hAPP(hAPP(c_member(_1194595), _1194597), hAPP(hAPP(_1194599, _1194601), _1194603))), -(hBOOL(hAPP(hAPP(c_member(_1194595), _1194597), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194605, _1194607, tc_fun(_1194595, tc_HOL_Obool)), _1194599), hAPP(hAPP(c_Product__Type_OPair(_1194605, _1194607), _1194601), _1194603)))))], (23457 ^ _779448) ^ [_1194784, _1194786, _1194788, _1194790] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1194784, tc_fun(_1194786, tc_HOL_Obool))), _1194788), _1194790))], (23459 ^ _779448) ^ [_1194826, _1194828, _1194830] : [-(c_Fun_Oinj__on(tc_prod(_1194826, _1194828), tc_prod(_1194828, _1194826), hAPP(c_Product__Type_Oprod_Oprod__case(_1194826, _1194828, tc_prod(_1194828, _1194826)), hAPP(c_COMBC(_1194828, _1194826, tc_prod(_1194828, _1194826)), c_Product__Type_OPair(_1194828, _1194826))), _1194830))], (23461 ^ _779448) ^ [_1194884, _1194886, _1194888, _1194890, _1194892, _1194894, _1194896] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1194884, _1194886, tc_fun(_1194888, tc_HOL_Obool)), _1194890), hAPP(hAPP(c_Product__Type_OPair(_1194884, _1194886), _1194892), _1194894)), _1194896)), -(hBOOL(hAPP(hAPP(hAPP(_1194890, _1194892), _1194894), _1194896)))], (23467 ^ _779448) ^ [_1195035, _1195037, _1195039] : [_1195035 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1195037, _1195037), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1195037, _1195037), tc_HOL_Obool)), _1195035), _1195039)))], (23473 ^ _779448) ^ [_1195156, _1195158, _1195160, _1195162, _1195164, _1195166] : [hBOOL(hAPP(hAPP(_1195156, _1195158), _1195160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195162, tc_fun(_1195164, tc_HOL_Obool))), _1195156), _1195166)), -(hBOOL(hAPP(hAPP(_1195166, _1195158), _1195160)))], (23483 ^ _779448) ^ [_1195347, _1195349, _1195351, _1195353, _1195355, _1195357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195347, tc_fun(_1195349, tc_HOL_Obool))), _1195351), _1195353)), hBOOL(hAPP(hAPP(_1195351, _1195355), _1195357)), -(hBOOL(hAPP(hAPP(_1195353, _1195355), _1195357)))], (23493 ^ _779448) ^ [_1195556, _1195558, _1195560] : [hBOOL(hAPP(_1195556, 23494 ^ [_1195556, _1195558, _1195560])), 23497 ^ _779448 : [(23498 ^ _779448) ^ [_1195667, _1195669] : [-(hBOOL(hAPP(_1195556, hAPP(hAPP(c_Product__Type_OPair(_1195558, _1195560), _1195669), _1195667))))]]], (23500 ^ _779448) ^ [_1195703, _1195705, _1195707] : [hBOOL(hAPP(_1195703, hAPP(hAPP(c_Product__Type_OPair(_1195705, _1195707), 23501 ^ [_1195703, _1195705, _1195707]), 23502 ^ [_1195703, _1195705, _1195707]))), 23505 ^ _779448 : [(23506 ^ _779448) ^ [_1195850] : [-(hBOOL(hAPP(_1195703, _1195850)))]]], (23508 ^ _779448) ^ [_1195908, _1195910, _1195912, _1195914, _1195916, _1195918] : [hAPP(hAPP(c_Product__Type_OPair(_1195908, _1195910), _1195912), _1195914) = hAPP(hAPP(c_Product__Type_OPair(_1195908, _1195910), _1195916), _1195918), 23511 ^ _779448 : [(23512 ^ _779448) ^ [] : [-(_1195912 = _1195916)], (23514 ^ _779448) ^ [] : [-(_1195914 = _1195918)]]], (23516 ^ _779448) ^ [_1196051, _1196053, _1196055, _1196057, _1196059, _1196061] : [-(hAPP(hAPP(c_Product__Type_OPair(_1196051, _1196053), _1196055), _1196057) = hAPP(hAPP(c_Product__Type_OPair(_1196051, _1196053), _1196059), _1196061)), _1196055 = _1196059, _1196057 = _1196061], (23526 ^ _779448) ^ [_1196234, _1196236, _1196238, _1196240, _1196242, _1196244] : [hAPP(hAPP(c_Product__Type_OPair(_1196234, _1196236), _1196238), _1196240) = hAPP(hAPP(c_Product__Type_OPair(_1196234, _1196236), _1196242), _1196244), 23529 ^ _779448 : [(23530 ^ _779448) ^ [] : [-(_1196238 = _1196242)], (23532 ^ _779448) ^ [] : [-(_1196240 = _1196244)]]], (23534 ^ _779448) ^ [_1196385, _1196387, _1196389, _1196391, _1196393, _1196395] : [_1196385 = _1196387, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196389, _1196391, _1196393), _1196395), _1196385) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196389, _1196391, _1196393), _1196395), _1196387))], (23540 ^ _779448) ^ [_1196510, _1196512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196510), 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)), _1196512)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1196510, _1196512), c_Divides_OnegDivAlg(_1196510, _1196512))))], (23550 ^ _779448) ^ [_1196669, _1196671, _1196673, _1196675, _1196677, _1196679, _1196681, _1196683] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196669, _1196671, _1196673), _1196675), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196677, _1196679, tc_prod(_1196669, _1196671)), _1196681), _1196683)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196677, _1196679, _1196673), hAPP(hAPP(c_COMBB(tc_fun(_1196679, tc_prod(_1196669, _1196671)), tc_fun(_1196679, _1196673), _1196677), hAPP(c_COMBB(tc_prod(_1196669, _1196671), _1196673, _1196679), hAPP(c_Product__Type_Oprod_Oprod__case(_1196669, _1196671, _1196673), _1196675))), _1196681)), _1196683))], (23552 ^ _779448) ^ [_1196775, _1196777, _1196779, _1196781, _1196783, _1196785] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196775, _1196777, _1196779), _1196781), hAPP(hAPP(c_Product__Type_OPair(_1196775, _1196777), _1196783), _1196785)) = hAPP(hAPP(_1196781, _1196783), _1196785))], (23554 ^ _779448) ^ [_1196833, _1196835, _1196837, _1196839, _1196841, _1196843] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196833, _1196835, _1196837), _1196839), hAPP(hAPP(c_Product__Type_OPair(_1196833, _1196835), _1196841), _1196843)) = hAPP(hAPP(_1196839, _1196841), _1196843))], (23556 ^ _779448) ^ [_1196891, _1196893, _1196895, _1196897, _1196899] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1196891, _1196893, tc_HOL_Obool), _1196895), hAPP(hAPP(c_Product__Type_OPair(_1196891, _1196893), _1196897), _1196899))), -(hBOOL(hAPP(hAPP(_1196895, _1196897), _1196899)))], (23562 ^ _779448) ^ [_1197020, _1197022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197020), 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)), _1197022)), -(c_Divides_OnegDivAlg(_1197020, _1197022) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1197020), _1197022)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1197020, _1197022)))], (23572 ^ _779448) ^ [_1197201] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1197201) = 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), _1197201), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23574 ^ _779448) ^ [_1197236, _1197238, _1197240, _1197242] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1197236, _1197238, _1197240), hAPP(hAPP(c_COMBB(tc_fun(_1197238, tc_prod(_1197236, _1197238)), tc_fun(_1197238, _1197240), _1197236), hAPP(c_COMBB(tc_prod(_1197236, _1197238), _1197240, _1197238), _1197242)), c_Product__Type_OPair(_1197236, _1197238))) = _1197242)], (23576 ^ _779448) ^ [_1197304, _1197306, _1197308, _1197310] : [-(c_HOL_OThe(tc_prod(_1197304, _1197306), hAPP(c_Product__Type_Oprod_Oprod__case(_1197304, _1197306, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1197304, tc_fun(_1197306, tc_HOL_Obool), tc_fun(_1197306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1197306, tc_HOL_Obool), tc_fun(_1197306, tc_HOL_Obool)), _1197304), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1197306)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1197304), c_fconj), hAPP(c_fequal, _1197308)))), hAPP(c_fequal, _1197310)))) = hAPP(hAPP(c_Product__Type_OPair(_1197304, _1197306), _1197308), _1197310))], (23578 ^ _779448) ^ [_1197410, _1197412, _1197414] : [-(c_HOL_OThe(tc_prod(_1197410, _1197412), _1197414) = c_HOL_OThe(tc_prod(_1197410, _1197412), hAPP(c_Product__Type_Oprod_Oprod__case(_1197410, _1197412, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1197412, tc_prod(_1197410, _1197412)), tc_fun(_1197412, tc_HOL_Obool), _1197410), hAPP(c_COMBB(tc_prod(_1197410, _1197412), tc_HOL_Obool, _1197412), _1197414)), c_Product__Type_OPair(_1197410, _1197412)))))], (23580 ^ _779448) ^ [_1197497, _1197499] : [23581 ^ _779448 : [(23582 ^ _779448) ^ [] : [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), _1197497), _1197499)))], (23584 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197499), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1197497, _1197499) = 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), _1197497), _1197499)))], (23588 ^ _779448) ^ [_1197656, _1197658] : [-(c_Divides_OnegDivAlg(_1197656, _1197658) = hAPP(c_Divides_Oadjust(_1197658), c_Divides_OnegDivAlg(_1197656, 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)))), _1197658)))), -(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), _1197656), _1197658)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197658), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23598 ^ _779448) ^ [_1197728, _1197730] : [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), _1197728))), 23601 ^ _779448 : [(23602 ^ _779448) ^ [] : [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), _1197730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197730), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728)) = 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), _1197730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728))))], (23608 ^ _779448) ^ [] : [-(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), _1197730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197730), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197728)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197730), 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), _1197728)))))]]], (23614 ^ _779448) ^ [_1198076, _1198078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1198076)), 23617 ^ _779448 : [(23618 ^ _779448) ^ [] : [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), _1198078), _1198076))), -(c_Divides_OnegDivAlg(_1198078, _1198076) = 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), _1198078), _1198076)))], (23624 ^ _779448) ^ [] : [-(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), _1198078), _1198076)))), -(c_Divides_OnegDivAlg(_1198078, _1198076) = hAPP(c_Divides_Oadjust(_1198076), c_Divides_OnegDivAlg(_1198078, 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)))), _1198076))))]]], (23630 ^ _779448) ^ [_1198364, _1198366, _1198368, _1198370, _1198372] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1198364, _1198366, _1198368), _1198370), _1198372)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1198364, _1198366)), hAPP(hAPP(c_Product__Type_OPair(_1198364, _1198366), _1198370), _1198372)), _1198368)))], (23636 ^ _779448) ^ [_1198499, _1198501, _1198503, _1198505, _1198507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1198499, _1198501)), hAPP(hAPP(c_Product__Type_OPair(_1198499, _1198501), _1198505), _1198507)), _1198503)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1198499, _1198501, _1198503), _1198505), _1198507)))], (23642 ^ _779448) ^ [_1198640, _1198642] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1198640, _1198642) = 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), _1198640), _1198642)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1198640, _1198642)))], (23644 ^ _779448) ^ [_1198699, _1198701] : [c_Nitpick_Orefl_H(_1198699, _1198701), 23647 ^ _779448 : [(23648 ^ _779448) ^ [_1198777] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1198699, _1198699)), hAPP(hAPP(c_Product__Type_OPair(_1198699, _1198699), _1198777), _1198777)), _1198701)))]]], (23650 ^ _779448) ^ [_1198819, _1198821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1198819, _1198819)), hAPP(hAPP(c_Product__Type_OPair(_1198819, _1198819), 23651 ^ [_1198819, _1198821]), 23651 ^ [_1198819, _1198821])), _1198821)), -(c_Nitpick_Orefl_H(_1198819, _1198821))], (23657 ^ _779448) ^ [_1198986] : [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), _1198986))), 23660 ^ _779448 : [(23661 ^ _779448) ^ [] : [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), _1198986))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198986)) = 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)))], (23667 ^ _779448) ^ [] : [-(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), _1198986)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198986)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1198986)), 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), _1198986)))))]]], (23673 ^ _779448) ^ [_1199255, _1199257] : [23674 ^ _779448 : [(23675 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199255), _1199257))], (23677 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199257), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1199255, _1199257) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199255))], (23681 ^ _779448) ^ [_1199396, _1199398] : [-(c_Divides_OposDivAlg(_1199396, _1199398) = hAPP(c_Divides_Oadjust(_1199398), c_Divides_OposDivAlg(_1199396, 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)))), _1199398)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199396), _1199398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199398), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23691 ^ _779448) ^ [_1199465] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1199465) = 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)))], (23693 ^ _779448) ^ [_1199491, _1199493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199493)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1199491, _1199493), c_Divides_OposDivAlg(_1199491, _1199493))))], (23703 ^ _779448) ^ [_1199644, _1199646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199646)), -(c_Divides_OposDivAlg(_1199644, _1199646) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1199644), _1199646)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1199644, _1199646)))], (23713 ^ _779448) ^ [_1199819, _1199821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199819)), 23716 ^ _779448 : [(23717 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199821), _1199819)), -(c_Divides_OposDivAlg(_1199821, _1199819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199821))], (23723 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199821), _1199819))), -(c_Divides_OposDivAlg(_1199821, _1199819) = hAPP(c_Divides_Oadjust(_1199819), c_Divides_OposDivAlg(_1199821, 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)))), _1199819))))]]], (23729 ^ _779448) ^ [_1200059, _1200061] : [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), _1200059))), 23732 ^ _779448 : [(23733 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200061)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200059))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200059)) = 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), _1200061)))], (23739 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200061)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200059)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200061), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200059)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200059)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1200061), 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), _1200059)))))]]], (23771 ^ _779448) ^ [_1200756, _1200758] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200756))), 23774 ^ _779448 : [(23775 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200758)), -(c_Divides_Odivmod__int(_1200756, _1200758) = c_Divides_OnegDivAlg(_1200756, _1200758))], (23781 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200758))), -(c_Divides_Odivmod__int(_1200756, _1200758) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200756), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200758))))]]], (23745 ^ _779448) ^ [_1200386, _1200388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200386)), 23748 ^ _779448 : [(23749 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200388)), -(c_Divides_Odivmod__int(_1200386, _1200388) = c_Divides_OposDivAlg(_1200386, _1200388))], (23755 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200388))), 23758 ^ _779448 : [(23759 ^ _779448) ^ [] : [_1200386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1200386, _1200388) = 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)))], (23765 ^ _779448) ^ [] : [-(_1200386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1200386, _1200388) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200386), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1200388))))]]]]], (23787 ^ _779448) ^ [_1200984, _1200986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1200984), _1200986)), -(c_Divides_Odivmod__nat(_1200986, _1200984) = 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), _1200986), _1200984)), _1200984))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200986), _1200984), _1200984)))], (23797 ^ _779448) ^ [_1201195, _1201197] : [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), _1201195), _1201197))), 23800 ^ _779448 : [(23801 ^ _779448) ^ [] : [23802 ^ _779448 : [(23803 ^ _779448) ^ [] : [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), _1201195), _1201197)))], (23805 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201197), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1201195, _1201197) = 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), _1201195), _1201197)))], (23809 ^ _779448) ^ [] : [-(c_Divides_OnegDivAlg(_1201195, _1201197) = hAPP(c_Divides_Oadjust(_1201197), c_Divides_OnegDivAlg(_1201195, 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)))), _1201197)))), -(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), _1201195), _1201197)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201197), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23819 ^ _779448) ^ [_1201542, _1201544, _1201546] : [23821 ^ _779448 : [(23822 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201542), 23820 ^ [_1201542, _1201544, _1201546]), _1201544)))], (23824 ^ _779448) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1201546, 23820 ^ [_1201542, _1201544, _1201546]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1201542, tc_Int_Oint), _1201546), _1201544) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1201542, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1201542), c_Int_Onat), _1201546)), _1201544)))], (23828 ^ _779448) ^ [_1201772, _1201774] : [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), _1201772), _1201774))), 23831 ^ _779448 : [(23832 ^ _779448) ^ [] : [23833 ^ _779448 : [(23834 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201772), _1201774))], (23836 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201774), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1201772, _1201774) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201772))], (23840 ^ _779448) ^ [] : [-(c_Divides_OposDivAlg(_1201772, _1201774) = hAPP(c_Divides_Oadjust(_1201774), c_Divides_OposDivAlg(_1201772, 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)))), _1201774)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201772), _1201774))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201774), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23850 ^ _779448) ^ [_1202095, _1202097, _1202099, _1202101] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1202095, _1202097), _1202099)), hBOOL(hAPP(hAPP(_1202097, _1202101), _1202099)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1202095, _1202097), _1202101)))], (23870 ^ _779448) ^ [_1202466, _1202468, _1202470] : [23872 ^ _779448 : [(23873 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1202468, 23871 ^ [_1202466, _1202468, _1202470]), _1202470)))], (23875 ^ _779448) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1202466, _1202468), 23871 ^ [_1202466, _1202468, _1202470]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1202466, _1202468), _1202470)))], (23860 ^ _779448) ^ [_1202280, _1202282, _1202284] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1202280, _1202282), _1202284)), 23863 ^ _779448 : [(23864 ^ _779448) ^ [_1202365] : [hBOOL(hAPP(hAPP(_1202282, _1202365), _1202284)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1202280, _1202282), _1202365)))]]], (23889 ^ _779448) ^ [_1202856, _1202858, _1202860] : [23891 ^ _779448 : [(23892 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1202858, 23890 ^ [_1202856, _1202858, _1202860]), _1202860)))], (23894 ^ _779448) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1202856, _1202858), 23890 ^ [_1202856, _1202858, _1202860]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1202856, _1202858), _1202860)))], (23879 ^ _779448) ^ [_1202670, _1202672, _1202674] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1202670, _1202672), _1202674)), 23882 ^ _779448 : [(23883 ^ _779448) ^ [_1202755] : [hBOOL(hAPP(hAPP(_1202672, _1202755), _1202674)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1202670, _1202672), _1202755)))]]], (23898 ^ _779448) ^ [_1203042] : [-(c_Divides_Odivmod__nat(_1203042, 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)), _1203042))], (23900 ^ _779448) ^ [_1203071, _1203073, _1203075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203071, tc_fun(_1203071, tc_HOL_Obool))), _1203073), _1203075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1203071, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1203071, _1203075)), c_Wellfounded_Oaccp(_1203071, _1203073))))], (23906 ^ _779448) ^ [_1203208, _1203210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203208), _1203210)), -(c_Divides_Odivmod__nat(_1203208, _1203210) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203208))], (23912 ^ _779448) ^ [_1203307, _1203309] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1203307), _1203309)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1203307), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1203309)))], (23914 ^ _779448) ^ [_1203350, _1203352] : [-(c_Divides_Odivmod__nat(_1203350, _1203352) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1203350), _1203352)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1203350, _1203352)))], (23916 ^ _779448) ^ [_1203394, _1203396, _1203398] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1203394), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1203396)), _1203398)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1203394, _1203396), hAPP(c_Divides_OnegateSnd, _1203398))))], (23922 ^ _779448) ^ [_1203520, _1203522] : [23923 ^ _779448 : [(23924 ^ _779448) ^ [] : [_1203520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23926 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203522), _1203520))]], -(c_Divides_Odivmod__nat(_1203522, _1203520) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203522))], (23930 ^ _779448) ^ [_1203651, _1203653] : [-(c_Divides_Odivmod__nat(_1203653, _1203651) = 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), _1203653), _1203651), _1203651))), -(_1203651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203653), _1203651)))], (23940 ^ _779448) ^ [_1203716, _1203718] : [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), _1203716), _1203718))), 23943 ^ _779448 : [(23944 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1203716, _1203718) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1203716), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1203718)))], (23950 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203718), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23953 ^ _779448 : [(23954 ^ _779448) ^ [] : [23955 ^ _779448 : [(23956 ^ _779448) ^ [] : [_1203716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23958 ^ _779448) ^ [] : [_1203718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1203716, _1203718) = 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)))], (23962 ^ _779448) ^ [] : [-(c_Nitpick_Onorm__frac(_1203716, _1203718) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1203716), _1203718)), 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), _1203716))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1203718)))), -(_1203716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1203718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (23972 ^ _779448) ^ [_1204208, _1204210, _1204212] : [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), _1204208), _1204210))), -(hBOOL(hAPP(hAPP(_1204212, _1204208), _1204210))), 23979 ^ _779448 : [(23980 ^ _779448) ^ [] : [-(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), 23977 ^ [_1204208, _1204210, _1204212]), 23978 ^ [_1204208, _1204210, _1204212]))))], (23992 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1204212, 23977 ^ [_1204208, _1204210, _1204212]), 23978 ^ [_1204208, _1204210, _1204212]))], (23982 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1204212, 23977 ^ [_1204208, _1204210, _1204212]), 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)))), 23978 ^ [_1204208, _1204210, _1204212])))), -(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), 23977 ^ [_1204208, _1204210, _1204212]), 23978 ^ [_1204208, _1204210, _1204212])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23978 ^ [_1204208, _1204210, _1204212]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23996 ^ _779448) ^ [_1204703, _1204705, _1204707] : [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), _1204703), _1204705))), -(hBOOL(hAPP(hAPP(_1204707, _1204703), _1204705))), 24003 ^ _779448 : [(24004 ^ _779448) ^ [] : [-(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), 24001 ^ [_1204703, _1204705, _1204707]), 24002 ^ [_1204703, _1204705, _1204707]))))], (24016 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1204707, 24001 ^ [_1204703, _1204705, _1204707]), 24002 ^ [_1204703, _1204705, _1204707]))], (24006 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1204707, 24001 ^ [_1204703, _1204705, _1204707]), 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)))), 24002 ^ [_1204703, _1204705, _1204707])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24001 ^ [_1204703, _1204705, _1204707]), 24002 ^ [_1204703, _1204705, _1204707]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24002 ^ [_1204703, _1204705, _1204707]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (24020 ^ _779448) ^ [_1205189, _1205191, _1205193, _1205195, _1205197] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205189, _1205191), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1205193), _1205195))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205191)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205197), _1205189), _1205191), 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), _1205197), _1205193)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205197), _1205195)), _1205191))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205197), _1205195), _1205191)))))], (24030 ^ _779448) ^ [_1205458, _1205460, _1205462, _1205464, _1205466] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205458, _1205460), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1205462), _1205464))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205466)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205460), _1205466)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1205462), _1205466)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205460), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1205462, _1205466))), _1205464)))))], (24044 ^ _779448) ^ [_1205765, _1205767, _1205769, _1205771] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205765, _1205767), _1205769)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205765, _1205767), _1205771)), -(_1205769 = _1205771)], (24054 ^ _779448) ^ [_1205922, _1205924] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205922, _1205924), c_Divides_Odivmod__nat(_1205922, _1205924))))], (24056 ^ _779448) ^ [_1205955, _1205957, _1205959] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1205955, _1205957), _1205959)), -(c_Divides_Odivmod__nat(_1205955, _1205957) = _1205959)], (24062 ^ _779448) ^ [_1206050, _1206052] : [-(c_Divides_Odivmod__nat(_1206050, _1206052) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1206050, _1206052)))], (24064 ^ _779448) ^ [_1206084, _1206086, _1206088, _1206090] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206084, _1206086), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1206088), _1206090))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206084, _1206086) = _1206090)], (24070 ^ _779448) ^ [_1206195, _1206197, _1206199, _1206201] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206195, _1206197), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1206199), _1206201))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206195), _1206197) = _1206199)], (24076 ^ _779448) ^ [_1206310, _1206312] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206310, _1206312), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1206310), _1206312)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1206310, _1206312)))))], (24078 ^ _779448) ^ [_1206356, _1206358, _1206360, _1206362, _1206364, _1206366, _1206368] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206356, _1206358), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1206360), _1206362))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1206364, _1206358), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1206366), _1206368))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206358)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206356), _1206364), _1206358), 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), _1206360), _1206366)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206362), _1206368)), _1206358))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206362), _1206368), _1206358)))))], (24092 ^ _779448) ^ [_1206717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206717)), 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), _1206717)) = 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), _1206717))))))], (24098 ^ _779448) ^ [_1206873, _1206875, _1206877, _1206879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1206873, _1206873)), hAPP(hAPP(c_Product__Type_OPair(_1206873, _1206873), _1206875), _1206877)), hAPP(c_Wellfounded_Omeasure(_1206873), _1206879))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1206879, _1206875)), hAPP(_1206879, _1206877))))], (24104 ^ _779448) ^ [_1207020, _1207022, _1207024, _1207026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1207026, _1207022)), hAPP(_1207026, _1207024))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1207020, _1207020)), hAPP(hAPP(c_Product__Type_OPair(_1207020, _1207020), _1207022), _1207024)), hAPP(c_Wellfounded_Omeasure(_1207020), _1207026))))], (24110 ^ _779448) ^ [_1207173, _1207175, _1207177] : [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), _1207173), _1207175))), -(hBOOL(hAPP(hAPP(_1207177, _1207173), _1207175))), 24117 ^ _779448 : [(24118 ^ _779448) ^ [] : [-(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), 24115 ^ [_1207173, _1207175, _1207177]), 24116 ^ [_1207173, _1207175, _1207177]))))], (24126 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1207177, 24115 ^ [_1207173, _1207175, _1207177]), 24116 ^ [_1207173, _1207175, _1207177]))], (24120 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24116 ^ [_1207173, _1207175, _1207177]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1207177, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24115 ^ [_1207173, _1207175, _1207177])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24116 ^ [_1207173, _1207175, _1207177]))))]]], (24130 ^ _779448) ^ [_1207646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1207646)), 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), _1207646)) = 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), _1207646))))))], (24136 ^ _779448) ^ [_1207779, _1207781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1207779), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1207781), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207779, _1207781) = 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), _1207779), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207781)))))], (24146 ^ _779448) ^ [_1207966, _1207968, _1207970, _1207972, _1207974, _1207976, _1207978] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1207966, _1207968, _1207970), hAPP(c_Fun_Ocomp(_1207972, tc_fun(_1207968, _1207970), _1207966, _1207974), _1207976)), _1207978) = hAPP(hAPP(_1207974, hAPP(_1207976, hAPP(c_Product__Type_Ofst(_1207966, _1207968), _1207978))), hAPP(c_Product__Type_Osnd(_1207966, _1207968), _1207978)))], (24148 ^ _779448) ^ [_1208043, _1208045, _1208047, _1208049, _1208051] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1208043, _1208045, _1208047), _1208049), _1208051) = hAPP(hAPP(_1208049, hAPP(c_Product__Type_Ofst(_1208043, _1208045), _1208051)), hAPP(c_Product__Type_Osnd(_1208043, _1208045), _1208051)))], (24150 ^ _779448) ^ [_1208102, _1208104, _1208106, _1208108, _1208110] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1208102, _1208104, _1208106), _1208108), _1208110) = hAPP(hAPP(_1208108, hAPP(c_Product__Type_Ofst(_1208102, _1208104), _1208110)), hAPP(c_Product__Type_Osnd(_1208102, _1208104), _1208110)))], (24152 ^ _779448) ^ [_1208161, _1208163, _1208165, _1208167, _1208169, _1208171] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1208161, _1208163), _1208163, _1208165), hAPP(hAPP(c_COMBB(_1208167, tc_fun(_1208163, _1208165), tc_prod(_1208161, _1208163)), _1208169), hAPP(hAPP(c_COMBB(_1208161, _1208167, tc_prod(_1208161, _1208163)), _1208171), c_Product__Type_Ofst(_1208161, _1208163)))), c_Product__Type_Osnd(_1208161, _1208163)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1208161, _1208163, _1208165), hAPP(hAPP(c_COMBB(_1208167, tc_fun(_1208163, _1208165), _1208161), _1208169), _1208171)))], (24154 ^ _779448) ^ [_1208262, _1208264, _1208266, _1208268, _1208270] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1208262, _1208264, _1208266), _1208268), _1208270) = hAPP(hAPP(_1208268, hAPP(c_Product__Type_Ofst(_1208262, _1208264), _1208270)), hAPP(c_Product__Type_Osnd(_1208262, _1208264), _1208270)))], (24156 ^ _779448) ^ [_1208321, _1208323, _1208325, _1208327] : [hAPP(c_Product__Type_Ofst(_1208321, _1208323), _1208325) = hAPP(c_Product__Type_Ofst(_1208321, _1208323), _1208327), hAPP(c_Product__Type_Osnd(_1208321, _1208323), _1208325) = hAPP(c_Product__Type_Osnd(_1208321, _1208323), _1208327), -(_1208325 = _1208327)], (24166 ^ _779448) ^ [_1208527, _1208529, _1208531, _1208533] : [_1208527 = _1208529, 24169 ^ _779448 : [(24170 ^ _779448) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1208531, _1208533), _1208527) = hAPP(c_Product__Type_Ofst(_1208531, _1208533), _1208529))], (24172 ^ _779448) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1208531, _1208533), _1208527) = hAPP(c_Product__Type_Osnd(_1208531, _1208533), _1208529))]]], (24174 ^ _779448) ^ [_1208678, _1208680, _1208682, _1208684] : [-(_1208678 = _1208680), hAPP(c_Product__Type_Ofst(_1208682, _1208684), _1208678) = hAPP(c_Product__Type_Ofst(_1208682, _1208684), _1208680), hAPP(c_Product__Type_Osnd(_1208682, _1208684), _1208678) = hAPP(c_Product__Type_Osnd(_1208682, _1208684), _1208680)], (24184 ^ _779448) ^ [_1208865, _1208867, _1208869] : [-(_1208865 = hAPP(hAPP(c_Product__Type_OPair(_1208867, _1208869), hAPP(c_Product__Type_Ofst(_1208867, _1208869), _1208865)), hAPP(c_Product__Type_Osnd(_1208867, _1208869), _1208865)))], (24186 ^ _779448) ^ [_1208913, _1208915, _1208917] : [-(hAPP(hAPP(c_Product__Type_OPair(_1208913, _1208915), hAPP(c_Product__Type_Ofst(_1208913, _1208915), _1208917)), hAPP(c_Product__Type_Osnd(_1208913, _1208915), _1208917)) = _1208917)], (24188 ^ _779448) ^ [_1208961, _1208963, _1208965, _1208967, _1208969] : [hAPP(c_Product__Type_Ofst(_1208961, _1208963), hAPP(hAPP(c_Product__Type_OPair(_1208961, _1208963), _1208965), _1208967)) = _1208969, -(_1208965 = _1208969)], (24194 ^ _779448) ^ [_1209074, _1209076, _1209078, _1209080] : [-(hAPP(c_Product__Type_Ofst(_1209074, _1209076), hAPP(hAPP(c_Product__Type_OPair(_1209074, _1209076), _1209078), _1209080)) = _1209078)], (24196 ^ _779448) ^ [_1209118, _1209120, _1209122, _1209124, _1209126] : [hAPP(c_Product__Type_Osnd(_1209118, _1209120), hAPP(hAPP(c_Product__Type_OPair(_1209118, _1209120), _1209122), _1209124)) = _1209126, -(_1209124 = _1209126)], (24202 ^ _779448) ^ [_1209231, _1209233, _1209235, _1209237] : [-(hAPP(c_Product__Type_Osnd(_1209231, _1209233), hAPP(hAPP(c_Product__Type_OPair(_1209231, _1209233), _1209235), _1209237)) = _1209237)], (24204 ^ _779448) ^ [_1209275, _1209277, _1209279] : [-(c_HOL_OThe(tc_prod(_1209275, _1209277), hAPP(c_Product__Type_Oprod_Oprod__case(_1209275, _1209277, tc_HOL_Obool), _1209279)) = c_HOL_OThe(tc_prod(_1209275, _1209277), hAPP(hAPP(c_COMBS(tc_prod(_1209275, _1209277), _1209277, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1209275, tc_fun(_1209277, tc_HOL_Obool), tc_prod(_1209275, _1209277)), _1209279), c_Product__Type_Ofst(_1209275, _1209277))), c_Product__Type_Osnd(_1209275, _1209277))))], (24206 ^ _779448) ^ [_1209356, _1209358, _1209360] : [-(hAPP(c_Product__Type_Ofst(_1209356, _1209358), _1209360) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1209356, _1209358, _1209356), c_COMBK(_1209356, _1209358)), _1209360))], (24208 ^ _779448) ^ [_1209402, _1209404, _1209406] : [-(hAPP(c_Product__Type_Osnd(_1209402, _1209404), _1209406) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1209402, _1209404, _1209404), hAPP(c_COMBK(tc_fun(_1209404, _1209404), _1209402), c_COMBI(_1209404))), _1209406))], (24210 ^ _779448) ^ [_1209456, _1209458] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209456), _1209458) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1209456, _1209458)))], (24212 ^ _779448) ^ [_1209493, _1209495] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1209493, _1209495) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1209493, _1209495)))], (24214 ^ _779448) ^ [_1209528, _1209530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209528), 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)), _1209530)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209528), _1209530) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1209528, _1209530)))], (24224 ^ _779448) ^ [_1209695, _1209697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209695), 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)), _1209697)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1209695, _1209697) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1209695, _1209697)))], (24234 ^ _779448) ^ [_1209858, _1209860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209860)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1209858), _1209860) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1209858, _1209860)))], (24244 ^ _779448) ^ [_1210019, _1210021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210021)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1210019, _1210021) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1210019, _1210021)))], (24254 ^ _779448) ^ [_1210176] : [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), _1210176))), -(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), _1210176)) = 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), _1210176))))], (24260 ^ _779448) ^ [_1210291] : [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), _1210291))), -(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), _1210291)) = 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), _1210291))))], (24266 ^ _779448) ^ [_1210408, _1210410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210410), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210408), _1210410) = 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), _1210408), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1210410)))))], (24276 ^ _779448) ^ [_1210593, _1210595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210595), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1210593, _1210595) = 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), _1210593), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1210595)))))], (24286 ^ _779448) ^ [_1210774, _1210776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1210774), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210776), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210774), _1210776) = 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), _1210774), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1210776)))))], (24296 ^ _779448) ^ [_1210965, _1210967, _1210969, _1210971, _1210973] : [-(c_Product__Type_Oprod_Oprod__size(_1210965, _1210967, _1210969, _1210971, _1210973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1210969, hAPP(c_Product__Type_Ofst(_1210965, _1210967), _1210973))), hAPP(_1210971, hAPP(c_Product__Type_Osnd(_1210965, _1210967), _1210973)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24298 ^ _779448) ^ [_1211032, _1211034, _1211036, _1211038, _1211040, _1211042] : [hBOOL(hAPP(_1211032, _1211034)), hBOOL(hAPP(_1211036, _1211038)), 24305 ^ _779448 : [(24306 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1211032, hAPP(c_Product__Type_Ofst(_1211040, _1211042), hAPP(hAPP(c_Product__Type_OPair(_1211040, _1211042), _1211034), _1211038)))))], (24308 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1211036, hAPP(c_Product__Type_Osnd(_1211040, _1211042), hAPP(hAPP(c_Product__Type_OPair(_1211040, _1211042), _1211034), _1211038)))))]]], (24310 ^ _779448) ^ [_1211279, _1211281, _1211283, _1211285, _1211287] : [hBOOL(hAPP(hAPP(_1211279, _1211281), _1211283)), -(hBOOL(hAPP(hAPP(_1211279, hAPP(c_Product__Type_Osnd(_1211285, _1211287), hAPP(hAPP(c_Product__Type_OPair(_1211285, _1211287), _1211283), _1211281))), hAPP(c_Product__Type_Ofst(_1211285, _1211287), hAPP(hAPP(c_Product__Type_OPair(_1211285, _1211287), _1211283), _1211281)))))], (24316 ^ _779448) ^ [_1211442, _1211444, _1211446, _1211448, _1211450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1211442, _1211444)), hAPP(_1211442, _1211446))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1211448, _1211448)), hAPP(hAPP(c_Product__Type_OPair(_1211448, _1211448), _1211444), _1211446)), _1211450)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1211448, _1211448)), hAPP(hAPP(c_Product__Type_OPair(_1211448, _1211448), _1211444), _1211446)), c_Wellfounded_Omlex__prod(_1211448, _1211442, _1211450))))], (24326 ^ _779448) ^ [_1211689, _1211691, _1211693, _1211695, _1211697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1211689, _1211691)), hAPP(_1211689, _1211693))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1211695, _1211695)), hAPP(hAPP(c_Product__Type_OPair(_1211695, _1211695), _1211691), _1211693)), c_Wellfounded_Omlex__prod(_1211695, _1211689, _1211697))))], (24332 ^ _779448) ^ [_1211840, _1211842] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1211840), _1211842) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1211840, _1211842)))], (24334 ^ _779448) ^ [_1211877, _1211879] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1211877, _1211879) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1211877, _1211879)))], (24368 ^ _779448) ^ [_1212466, _1212468, _1212470] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1212466, _1212468), _1212470))), _1212466 = 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), _1212470)), _1212468)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1212470)), 24375 ^ _779448 : [(24376 ^ _779448) ^ [] : [-(_1212468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24378 ^ _779448) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1212470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 24379 ^ _779448 : [(24380 ^ _779448) ^ [] : [_1212468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24382 ^ _779448) ^ [] : [24383 ^ _779448 : [(24384 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212468)))], (24386 ^ _779448) ^ [] : [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), _1212470))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1212470)), _1212468))]], 24391 ^ _779448 : [(24392 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1212468))], (24394 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1212468), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1212470))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1212470)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (24336 ^ _779448) ^ [_1211930, _1211932, _1211934] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1211930, _1211932), _1211934)), 24339 ^ _779448 : [(24340 ^ _779448) ^ [] : [-(_1211930 = 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), _1211934)), _1211932)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1211934)))], (24342 ^ _779448) ^ [] : [_1211932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1211934) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24348 ^ _779448) ^ [] : [-(_1211932 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24351 ^ _779448 : [(24352 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211932)), 24355 ^ _779448 : [(24356 ^ _779448) ^ [] : [-(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), _1211934))))], (24358 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1211934)), _1211932)))]]], (24360 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211932))), 24363 ^ _779448 : [(24364 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211932), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1211934))))], (24366 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1211934)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (24402 ^ _779448) ^ [_1213075, _1213077, _1213079, _1213081, _1213083, _1213085] : [-(c_Product__Type_Oprod_Oprod__rec(_1213075, _1213077, _1213079, _1213081, hAPP(hAPP(c_Product__Type_OPair(_1213075, _1213077), _1213083), _1213085)) = hAPP(hAPP(_1213081, _1213083), _1213085))], (24404 ^ _779448) ^ [_1213162, _1213164, _1213166, _1213168, _1213170, _1213172, _1213174, _1213176] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1213162, _1213164), tc_prod(_1213162, _1213164))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1213162, _1213164), tc_prod(_1213162, _1213164)), hAPP(hAPP(c_Product__Type_OPair(_1213162, _1213164), _1213166), _1213168)), hAPP(hAPP(c_Product__Type_OPair(_1213162, _1213164), _1213170), _1213172))), c_Wellfounded_Olex__prod(_1213162, _1213164, _1213174, _1213176))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1213162, _1213162)), hAPP(hAPP(c_Product__Type_OPair(_1213162, _1213162), _1213166), _1213170)), _1213174))), 24411 ^ _779448 : [(24412 ^ _779448) ^ [] : [-(_1213166 = _1213170)], (24414 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1213164, _1213164)), hAPP(hAPP(c_Product__Type_OPair(_1213164, _1213164), _1213168), _1213172)), _1213176)))]]], (24416 ^ _779448) ^ [_1213487, _1213489, _1213491, _1213493, _1213495, _1213497, _1213499, _1213501] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1213487, _1213489), tc_prod(_1213487, _1213489))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1213487, _1213489), tc_prod(_1213487, _1213489)), hAPP(hAPP(c_Product__Type_OPair(_1213487, _1213489), _1213491), _1213493)), hAPP(hAPP(c_Product__Type_OPair(_1213487, _1213489), _1213495), _1213497))), c_Wellfounded_Olex__prod(_1213487, _1213489, _1213499, _1213501)))), 24417 ^ _779448 : [(24418 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1213487, _1213487)), hAPP(hAPP(c_Product__Type_OPair(_1213487, _1213487), _1213491), _1213495)), _1213499))], (24420 ^ _779448) ^ [] : [_1213491 = _1213495, hBOOL(hAPP(hAPP(c_member(tc_prod(_1213489, _1213489)), hAPP(hAPP(c_Product__Type_OPair(_1213489, _1213489), _1213493), _1213497)), _1213501))]]], (24428 ^ _779448) ^ [_1213880, _1213882, _1213884] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1213880, tc_HOL_Obool), tc_fun(_1213880, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1213880, tc_HOL_Obool), tc_fun(_1213880, tc_HOL_Obool)), _1213882), _1213884)), c_Wellfounded_Ofinite__psubset(_1213880))), 24431 ^ _779448 : [(24432 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1213880, tc_HOL_Obool)), _1213882), _1213884)))], (24434 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1213880), _1213884)))]]], (24436 ^ _779448) ^ [_1214075, _1214077, _1214079] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1214075, tc_HOL_Obool), tc_fun(_1214075, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1214075, tc_HOL_Obool), tc_fun(_1214075, tc_HOL_Obool)), _1214077), _1214079)), c_Wellfounded_Ofinite__psubset(_1214075)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1214075, tc_HOL_Obool)), _1214077), _1214079)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214075), _1214079))], (24446 ^ _779448) ^ [_1214304, _1214306, _1214308, _1214310, _1214312] : [class_Fields_Ofield(_1214304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214306), _1214308)), -(hAPP(_1214310, _1214312) = c_Groups_Ozero__class_Ozero(_1214304)), 24457 ^ _779448 : [(24458 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1214306), _1214312), _1214308)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1214306, _1214304), _1214310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1214306, tc_HOL_Obool)), _1214308), hAPP(hAPP(c_Set_Oinsert(_1214306), _1214312), c_Orderings_Obot__class_Obot(tc_fun(_1214306, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214304), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1214306, _1214304), _1214310), _1214308)), hAPP(_1214310, _1214312)))], (24464 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1214306), _1214312), _1214308))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1214306, _1214304), _1214310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1214306, tc_HOL_Obool)), _1214308), hAPP(hAPP(c_Set_Oinsert(_1214306), _1214312), c_Orderings_Obot__class_Obot(tc_fun(_1214306, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1214306, _1214304), _1214310), _1214308))]]], (24470 ^ _779448) ^ [_1214845, _1214847] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1214847)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1214847))), 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, _1214845))), 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), _1214845)), c_Int_Onat)))))], (24472 ^ _779448) ^ [_1214917, _1214919, _1214921] : [class_Orderings_Olinorder(_1214917), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1214917), _1214919), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1214917), _1214919), _1214921)) = _1214919)], (24478 ^ _779448) ^ [_1215026, _1215028, _1215030] : [class_Orderings_Olinorder(_1215026), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215026), _1215028), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215026), _1215028), _1215030)) = _1215028)], (24484 ^ _779448) ^ [_1215135, _1215137, _1215139, _1215141] : [class_Orderings_Olinorder(_1215135), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215135), _1215137), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215135), _1215139), _1215141)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215135), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215135), _1215137), _1215139)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215135), _1215137), _1215141)))], (24490 ^ _779448) ^ [_1215294, _1215296, _1215298, _1215300] : [class_Orderings_Olinorder(_1215294), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215294), _1215296), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215294), _1215298), _1215300)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215294), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215294), _1215296), _1215298)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215294), _1215296), _1215300)))], (24496 ^ _779448) ^ [_1215453, _1215455, _1215457, _1215459] : [class_Orderings_Olinorder(_1215453), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215453), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215453), _1215455), _1215457)), _1215459) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215453), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215453), _1215455), _1215459)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215453), _1215457), _1215459)))], (24502 ^ _779448) ^ [_1215612, _1215614, _1215616, _1215618] : [class_Orderings_Olinorder(_1215612), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215612), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215612), _1215614), _1215616)), _1215618) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215612), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215612), _1215614), _1215618)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1215612), _1215616), _1215618)))], (24508 ^ _779448) ^ [_1215771, _1215773, _1215775, _1215777] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1215771), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215771), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215771), _1215773), _1215775)), _1215777) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1215771), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215771), _1215773), _1215777)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215771), _1215775), _1215777)))], (24514 ^ _779448) ^ [_1215930, _1215932, _1215934, _1215936] : [class_Rings_Odivision__ring(_1215930), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215930), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1215930), _1215932), _1215934)), _1215936) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1215930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215930), _1215932), _1215936)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215930), _1215934), _1215936)))], (24520 ^ _779448) ^ [_1216089, _1216091] : [class_Rings_Odivision__ring(_1216089), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216089), _1216091), c_Groups_Oone__class_Oone(_1216089)) = _1216091)], (24526 ^ _779448) ^ [_1216184, _1216186, _1216188, _1216190] : [class_Groups_Oordered__ab__group__add(_1216184), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216184), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216184), _1216186), _1216188)), _1216190) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216184), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216184), _1216186), _1216190)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216184), _1216188), _1216190)))], (24532 ^ _779448) ^ [_1216343, _1216345, _1216347, _1216349] : [class_Orderings_Olinorder(_1216343), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216343), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216343), _1216345), _1216347)), _1216349) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216343), _1216345), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216343), _1216347), _1216349)))], (24538 ^ _779448) ^ [_1216486, _1216488, _1216490, _1216492] : [class_Orderings_Olinorder(_1216486), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216486), _1216488), _1216490)), _1216492) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216486), _1216488), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216486), _1216490), _1216492)))], (24544 ^ _779448) ^ [_1216629, _1216631, _1216633, _1216635] : [class_Orderings_Olinorder(_1216629), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216629), _1216631), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216629), _1216633), _1216635)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216629), _1216633), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216629), _1216631), _1216635)))], (24550 ^ _779448) ^ [_1216772, _1216774, _1216776, _1216778] : [class_Orderings_Olinorder(_1216772), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216772), _1216774), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216772), _1216776), _1216778)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216772), _1216776), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216772), _1216774), _1216778)))], (24556 ^ _779448) ^ [_1216915, _1216917, _1216919] : [class_Orderings_Olinorder(_1216915), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216915), _1216917), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216915), _1216917), _1216919)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1216915), _1216917), _1216919))], (24562 ^ _779448) ^ [_1217040, _1217042, _1217044] : [class_Orderings_Olinorder(_1217040), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217040), _1217042), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217040), _1217042), _1217044)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217040), _1217042), _1217044))], (24568 ^ _779448) ^ [_1217165, _1217167, _1217169] : [class_Orderings_Olinorder(_1217165), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217165), _1217167), _1217169) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217165), _1217169), _1217167))], (24574 ^ _779448) ^ [_1217274, _1217276, _1217278] : [class_Orderings_Olinorder(_1217274), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217274), _1217276), _1217278) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217274), _1217278), _1217276))], (24580 ^ _779448) ^ [_1217383, _1217385] : [class_Orderings_Olinorder(_1217383), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217383), _1217385), _1217385) = _1217385)], (24586 ^ _779448) ^ [_1217474, _1217476, _1217478, _1217480] : [class_Rings_Odivision__ring(_1217474), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217474), _1217476), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217474), _1217478), _1217480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217474), _1217476), _1217478)), _1217480))], (24592 ^ _779448) ^ [_1217617, _1217619, _1217621, _1217623] : [class_Rings_Odivision__ring(_1217617), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217617), _1217619), _1217621)), _1217623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217617), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217617), _1217619), _1217623)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217617), _1217621), _1217623)))], (24598 ^ _779448) ^ [_1217776, _1217778, _1217780, _1217782] : [class_Orderings_Olinorder(_1217776), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217776), _1217778), _1217780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217776), _1217778), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217776), _1217782), _1217780))))], (24608 ^ _779448) ^ [_1217955, _1217957, _1217959, _1217961] : [class_Orderings_Olinorder(_1217955), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217955), _1217957), _1217959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217955), _1217957), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1217955), _1217959), _1217961))))], (24618 ^ _779448) ^ [_1218134, _1218136, _1218138, _1218140] : [class_Orderings_Olinorder(_1218134), 24621 ^ _779448 : [(24632 ^ _779448) ^ [] : [24633 ^ _779448 : [(24634 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), _1218138))], (24636 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), _1218140))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218134), _1218138), _1218140))))], (24622 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218134), _1218138), _1218140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), _1218138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218134), _1218136), _1218140)))]]], (24640 ^ _779448) ^ [_1218483, _1218485, _1218487, _1218489] : [class_Orderings_Olinorder(_1218483), 24643 ^ _779448 : [(24644 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218483), _1218485), _1218487)), _1218489)), 24647 ^ _779448 : [(24648 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), _1218485), _1218489)))], (24650 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), _1218487), _1218489)))]]], (24652 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1218483), _1218485), _1218487)), _1218489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), _1218485), _1218489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218483), _1218487), _1218489))]]], (24662 ^ _779448) ^ [_1218863, _1218865] : [class_Rings_Odivision__ring__inverse__zero(_1218863), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218863), _1218865), c_Groups_Ozero__class_Ozero(_1218863)) = c_Groups_Ozero__class_Ozero(_1218863))], (24668 ^ _779448) ^ [_1218962, _1218964] : [class_Rings_Odivision__ring(_1218962), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218962), c_Groups_Ozero__class_Ozero(_1218962)), _1218964) = c_Groups_Ozero__class_Ozero(_1218962))], (24674 ^ _779448) ^ [_1219061, _1219063] : [class_Orderings_Olinorder(_1219061), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219061), _1219063), _1219063) = _1219063)], (24680 ^ _779448) ^ [_1219152, _1219154, _1219156, _1219158] : [class_Fields_Ofield__inverse__zero(_1219152), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219152), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219152), _1219154), _1219156)), _1219158) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219152), hAPP(hAPP(c_Power_Opower__class_Opower(_1219152), _1219154), _1219158)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219152), _1219156), _1219158)))], (24686 ^ _779448) ^ [_1219311, _1219313] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1219311)), hAPP(c_Nat_OSuc, _1219313)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1219311), _1219313)))], (24688 ^ _779448) ^ [_1219357] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1219357) = _1219357)], (24690 ^ _779448) ^ [_1219383] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1219383), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1219383)], (24692 ^ _779448) ^ [_1219412, _1219414, _1219416] : [class_Rings_Odivision__ring(_1219412), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1219412), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219412), _1219414), _1219416)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219412), hAPP(c_Groups_Ouminus__class_Ouminus(_1219412), _1219414)), _1219416))], (24698 ^ _779448) ^ [_1219541, _1219543, _1219545, _1219547] : [class_Orderings_Olinorder(_1219541), 24701 ^ _779448 : [(24712 ^ _779448) ^ [] : [24713 ^ _779448 : [(24714 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), _1219545))], (24716 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), _1219547))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219541), _1219545), _1219547))))], (24702 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219541), _1219545), _1219547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), _1219545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219541), _1219543), _1219547)))]]], (24720 ^ _779448) ^ [_1219890, _1219892, _1219894, _1219896] : [class_Orderings_Olinorder(_1219890), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219890), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1219890), _1219892), _1219894)), _1219896)), 24727 ^ _779448 : [(24728 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219890), _1219892), _1219896)))], (24730 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219890), _1219894), _1219896)))]]], (24732 ^ _779448) ^ [_1220113, _1220115, _1220117, _1220119, _1220121] : [class_Orderings_Olinorder(_1220113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220113), _1220115), _1220117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220113), _1220119), _1220121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220113), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220113), _1220115), _1220119)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220113), _1220117), _1220121))))], (24746 ^ _779448) ^ [_1220384, _1220386, _1220388, _1220390] : [class_Orderings_Olinorder(_1220384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220384), _1220386), _1220388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220384), _1220390), _1220388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220384), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220384), _1220386), _1220390)), _1220388)))], (24760 ^ _779448) ^ [_1220633, _1220635, _1220637, _1220639] : [class_Orderings_Olinorder(_1220633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220633), _1220635), _1220637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220633), _1220639), _1220637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220633), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220633), _1220635), _1220639)), _1220637)))], (24774 ^ _779448) ^ [_1220882, _1220884, _1220886] : [class_Orderings_Olinorder(_1220882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220882), _1220884), _1220886)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1220882), _1220886), _1220884) = _1220886)], (24784 ^ _779448) ^ [_1221043, _1221045, _1221047] : [class_Orderings_Olinorder(_1221043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221043), _1221045), _1221047)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221043), _1221045), _1221047) = _1221047)], (24794 ^ _779448) ^ [_1221204, _1221206, _1221208, _1221210] : [class_Orderings_Olinorder(_1221204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221204), _1221206), _1221208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221204), _1221206), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221204), _1221210), _1221208))))], (24804 ^ _779448) ^ [_1221383, _1221385, _1221387, _1221389] : [class_Orderings_Olinorder(_1221383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221383), _1221385), _1221387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221383), _1221385), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221383), _1221387), _1221389))))], (24814 ^ _779448) ^ [_1221562, _1221564, _1221566, _1221568] : [class_Orderings_Olinorder(_1221562), 24817 ^ _779448 : [(24818 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221562), _1221564), _1221566)), _1221568)), 24821 ^ _779448 : [(24822 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), _1221564), _1221568)))], (24824 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), _1221566), _1221568)))]]], (24826 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221562), _1221564), _1221566)), _1221568))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), _1221564), _1221568)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221562), _1221566), _1221568))]]], (24836 ^ _779448) ^ [_1221942, _1221944, _1221946] : [class_Orderings_Olinorder(_1221942), 24839 ^ _779448 : [(24840 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221942), _1221944), _1221946)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221942), _1221944), _1221946) = _1221946)], (24846 ^ _779448) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1221942), _1221944), _1221946) = _1221946, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221942), _1221944), _1221946)))]]], (24852 ^ _779448) ^ [_1222198, _1222200, _1222202] : [class_Orderings_Olinorder(_1222198), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222198), _1222200), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222198), _1222202), _1222200))))], (24858 ^ _779448) ^ [_1222305, _1222307, _1222309] : [class_Orderings_Olinorder(_1222305), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222305), _1222307), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222305), _1222307), _1222309))))], (24864 ^ _779448) ^ [_1222412] : [class_Orderings_Olinorder(_1222412), -(c_Finite__Set_Ofun__left__comm__idem(_1222412, _1222412, c_Orderings_Oord__class_Omax(_1222412)))], (24870 ^ _779448) ^ [_1222491, _1222493, _1222495, _1222497] : [class_Rings_Odivision__ring(_1222491), -(_1222493 = c_Groups_Ozero__class_Ozero(_1222491)), 24877 ^ _779448 : [(24878 ^ _779448) ^ [] : [_1222495 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222491), _1222497), _1222493), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222491), _1222495), _1222493) = _1222497)], (24884 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222491), _1222495), _1222493) = _1222497, -(_1222495 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222491), _1222497), _1222493))]]], (24890 ^ _779448) ^ [_1222819, _1222821, _1222823, _1222825] : [class_Rings_Odivision__ring(_1222819), -(_1222821 = c_Groups_Ozero__class_Ozero(_1222819)), 24897 ^ _779448 : [(24898 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222819), _1222823), _1222821) = _1222825, -(_1222823 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222819), _1222825), _1222821))], (24904 ^ _779448) ^ [] : [_1222823 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222819), _1222825), _1222821), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222819), _1222823), _1222821) = _1222825)]]], (24910 ^ _779448) ^ [_1223147, _1223149, _1223151, _1223153] : [class_Rings_Odivision__ring(_1223147), -(_1223149 = c_Groups_Ozero__class_Ozero(_1223147)), _1223151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223147), _1223153), _1223149), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223147), _1223151), _1223149) = _1223153)], (24924 ^ _779448) ^ [_1223377, _1223379, _1223381, _1223383] : [class_Rings_Odivision__ring(_1223377), -(_1223379 = c_Groups_Ozero__class_Ozero(_1223377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223377), _1223381), _1223379) = _1223383, -(_1223381 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223377), _1223383), _1223379))], (24938 ^ _779448) ^ [_1223607, _1223609] : [class_Rings_Odivision__ring__inverse__zero(_1223607), 24941 ^ _779448 : [(24942 ^ _779448) ^ [] : [_1223609 = c_Groups_Ozero__class_Ozero(_1223607), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223607), _1223609), _1223609) = c_Groups_Ozero__class_Ozero(_1223607))], (24948 ^ _779448) ^ [] : [-(_1223609 = c_Groups_Ozero__class_Ozero(_1223607)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223607), _1223609), _1223609) = c_Groups_Oone__class_Oone(_1223607))]]], (24954 ^ _779448) ^ [_1223829, _1223831] : [class_Rings_Odivision__ring(_1223829), -(_1223831 = c_Groups_Ozero__class_Ozero(_1223829)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223829), _1223831), _1223831) = c_Groups_Oone__class_Oone(_1223829))], (24964 ^ _779448) ^ [_1223943, _1223945, _1223947] : [class_Rings_Odivision__ring(_1223943), -(_1223945 = c_Groups_Ozero__class_Ozero(_1223943)), 24971 ^ _779448 : [(24972 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223943), _1223947), _1223945) = c_Groups_Oone__class_Oone(_1223943), -(_1223947 = _1223945)], (24978 ^ _779448) ^ [] : [_1223947 = _1223945, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1223943), _1223947), _1223945) = c_Groups_Oone__class_Oone(_1223943))]]], (24984 ^ _779448) ^ [_1224245, _1224247, _1224249] : [class_Int_Onumber(_1224245), class_Orderings_Oord(_1224245), 24991 ^ _779448 : [(24992 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224245), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224247)), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224249))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224245), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224247)), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224249)) = hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224249))], (24998 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224245), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224247)), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224249)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1224245), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224247)), hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224249)) = hAPP(c_Int_Onumber__class_Onumber__of(_1224245), _1224247))]]], (25004 ^ _779448) ^ [_1224637, _1224639, _1224641] : [class_Rings_Odivision__ring(_1224637), -(_1224639 = c_Groups_Ozero__class_Ozero(_1224637)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1224637), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224637), _1224641), _1224639)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224637), _1224641), hAPP(c_Groups_Ouminus__class_Ouminus(_1224637), _1224639)))], (25014 ^ _779448) ^ [_1224785, _1224787, _1224789] : [class_Rings_Odivision__ring(_1224785), -(_1224787 = c_Groups_Ozero__class_Ozero(_1224785)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224785), hAPP(c_Groups_Ouminus__class_Ouminus(_1224785), _1224789)), hAPP(c_Groups_Ouminus__class_Ouminus(_1224785), _1224787)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224785), _1224789), _1224787))], (25024 ^ _779448) ^ [_1224933, _1224935, _1224937, _1224939] : [class_Fields_Ofield(_1224933), -(_1224935 = c_Groups_Ozero__class_Ozero(_1224933)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1224933), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224933), _1224937), _1224935)), _1224939) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1224933), hAPP(hAPP(c_Power_Opower__class_Opower(_1224933), _1224937), _1224939)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224933), _1224935), _1224939)))], (25034 ^ _779448) ^ [_1225111, _1225113, _1225115, _1225117] : [class_Orderings_Olinorder(_1225111), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225111), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225111), _1225113), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225111), _1225115), _1225117))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225111), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225111), _1225113), _1225115)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225111), _1225113), _1225117)))))], (25040 ^ _779448) ^ [_1225284, _1225286, _1225288, _1225290] : [class_Orderings_Olinorder(_1225284), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225284), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225284), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225284), _1225286), _1225288)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225284), _1225286), _1225290))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225284), _1225286), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225284), _1225288), _1225290)))))], (25046 ^ _779448) ^ [_1225457, _1225459, _1225461] : [class_Fields_Ofield__inverse__zero(_1225457), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1225457), c_Groups_Oone__class_Oone(_1225457)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225457), _1225459), _1225461)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1225457), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1225457), c_Groups_Oone__class_Oone(_1225457)), _1225459)), _1225461))], (25052 ^ _779448) ^ [_1225606, _1225608, _1225610] : [class_Groups_Olinordered__ab__group__add(_1225606), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1225606), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225606), _1225608), _1225610)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225606), hAPP(c_Groups_Ouminus__class_Ouminus(_1225606), _1225608)), hAPP(c_Groups_Ouminus__class_Ouminus(_1225606), _1225610)))], (25058 ^ _779448) ^ [_1225745, _1225747, _1225749] : [class_Groups_Olinordered__ab__group__add(_1225745), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1225745), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1225745), _1225747), _1225749)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1225745), hAPP(c_Groups_Ouminus__class_Ouminus(_1225745), _1225747)), hAPP(c_Groups_Ouminus__class_Ouminus(_1225745), _1225749)))], (25064 ^ _779448) ^ [_1225884, _1225886] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1225884), _1225886)), _1225886) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1225884), _1225886))], (25066 ^ _779448) ^ [_1225927, _1225929, _1225931, _1225933, _1225935] : [class_Fields_Ofield__inverse__zero(_1225927), hBOOL(hAPP(c_Finite__Set_Ofinite(_1225929), _1225931)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225929, _1225927), hAPP(hAPP(c_COMBS(_1225929, _1225927, _1225927), hAPP(hAPP(c_COMBB(_1225927, tc_fun(_1225927, _1225927), _1225929), c_Rings_Oinverse__class_Odivide(_1225927)), _1225933)), _1225935)), _1225931) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1225927), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225929, _1225927), _1225933), _1225931)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225929, _1225927), _1225935), _1225931)))], (25076 ^ _779448) ^ [_1226194, _1226196, _1226198, _1226200] : [class_Fields_Ofield__inverse__zero(_1226194), class_Int_Onumber(_1226194), 25083 ^ _779448 : [(25100 ^ _779448) ^ [] : [-(_1226196 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1226194), _1226198), hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200))), 25103 ^ _779448 : [(25104 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200) = c_Groups_Ozero__class_Ozero(_1226194)], (25106 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226194), _1226196), hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200)) = _1226198]], 25107 ^ _779448 : [(25108 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200) = c_Groups_Ozero__class_Ozero(_1226194))], (25110 ^ _779448) ^ [] : [_1226196 = c_Groups_Ozero__class_Ozero(_1226194)]]], (25084 ^ _779448) ^ [] : [_1226196 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1226194), _1226198), hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200)), 25087 ^ _779448 : [(25088 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200) = c_Groups_Ozero__class_Ozero(_1226194)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226194), _1226196), hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200)) = _1226198)], (25094 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1226194), _1226200) = c_Groups_Ozero__class_Ozero(_1226194), -(_1226196 = c_Groups_Ozero__class_Ozero(_1226194))]]]]], (25114 ^ _779448) ^ [_1226804, _1226806, _1226808, _1226810] : [class_Fields_Ofield__inverse__zero(_1226804), class_Int_Onumber(_1226804), 25121 ^ _779448 : [(25138 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1226804), _1226808), _1226810)), 25141 ^ _779448 : [(25142 ^ _779448) ^ [] : [_1226810 = c_Groups_Ozero__class_Ozero(_1226804)], (25144 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226804), hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806)), _1226810) = _1226808]], 25145 ^ _779448 : [(25146 ^ _779448) ^ [] : [-(_1226810 = c_Groups_Ozero__class_Ozero(_1226804))], (25148 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806) = c_Groups_Ozero__class_Ozero(_1226804)]]], (25122 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1226804), _1226808), _1226810), 25125 ^ _779448 : [(25126 ^ _779448) ^ [] : [-(_1226810 = c_Groups_Ozero__class_Ozero(_1226804)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226804), hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806)), _1226810) = _1226808)], (25132 ^ _779448) ^ [] : [_1226810 = c_Groups_Ozero__class_Ozero(_1226804), -(hAPP(c_Int_Onumber__class_Onumber__of(_1226804), _1226806) = c_Groups_Ozero__class_Ozero(_1226804))]]]]], (25152 ^ _779448) ^ [_1227399, _1227401, _1227403, _1227405] : [class_Fields_Ofield__inverse__zero(_1227399), class_Int_Onumber(_1227399), 25159 ^ _779448 : [(25176 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1227399), _1227401), _1227403) = hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405)), 25179 ^ _779448 : [(25180 ^ _779448) ^ [] : [_1227403 = c_Groups_Ozero__class_Ozero(_1227399)], (25182 ^ _779448) ^ [] : [_1227401 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227399), hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405)), _1227403)]], 25183 ^ _779448 : [(25184 ^ _779448) ^ [] : [-(_1227403 = c_Groups_Ozero__class_Ozero(_1227399))], (25186 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405) = c_Groups_Ozero__class_Ozero(_1227399)]]], (25160 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1227399), _1227401), _1227403) = hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405), 25163 ^ _779448 : [(25164 ^ _779448) ^ [] : [-(_1227403 = c_Groups_Ozero__class_Ozero(_1227399)), -(_1227401 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227399), hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405)), _1227403))], (25170 ^ _779448) ^ [] : [_1227403 = c_Groups_Ozero__class_Ozero(_1227399), -(hAPP(c_Int_Onumber__class_Onumber__of(_1227399), _1227405) = c_Groups_Ozero__class_Ozero(_1227399))]]]]], (25190 ^ _779448) ^ [_1227994, _1227996, _1227998, _1228000] : [class_Fields_Ofield__inverse__zero(_1227994), class_Int_Onumber(_1227994), 25197 ^ _779448 : [(25214 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1227994), _1227996), hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998)) = _1228000), 25217 ^ _779448 : [(25218 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998) = c_Groups_Ozero__class_Ozero(_1227994)], (25220 ^ _779448) ^ [] : [_1227996 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227994), _1228000), hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998))]], 25221 ^ _779448 : [(25222 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998) = c_Groups_Ozero__class_Ozero(_1227994))], (25224 ^ _779448) ^ [] : [_1228000 = c_Groups_Ozero__class_Ozero(_1227994)]]], (25198 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1227994), _1227996), hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998)) = _1228000, 25201 ^ _779448 : [(25202 ^ _779448) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998) = c_Groups_Ozero__class_Ozero(_1227994)), -(_1227996 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227994), _1228000), hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998)))], (25208 ^ _779448) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1227994), _1227998) = c_Groups_Ozero__class_Ozero(_1227994), -(_1228000 = c_Groups_Ozero__class_Ozero(_1227994))]]]]], (25228 ^ _779448) ^ [_1228604, _1228606] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1228604), _1228606), hAPP(c_Int_Onumber__class_Onumber__of(_1228604), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1228604)), class_Fields_Ofield__inverse__zero(_1228604), class_Int_Onumber__ring(_1228604)], (25238 ^ _779448) ^ [_1228759, _1228761] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1228759)), _1228761) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1228759), 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), _1228759)), _1228761))], (25240 ^ _779448) ^ [_1228807, _1228809] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1228807), hAPP(c_Nat_OSuc, _1228809)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1228809), 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)), _1228809)), _1228807))], (25242 ^ _779448) ^ [_1228855, _1228857] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1228855), _1228857), hAPP(c_Int_Onumber__class_Onumber__of(_1228855), c_Int_OBit1(c_Int_OPls))) = _1228857), class_Fields_Ofield(_1228855), class_Int_Onumber__ring(_1228855)], (25252 ^ _779448) ^ [_1229006, _1229008] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1229006), _1229008), hAPP(c_Int_Onumber__class_Onumber__of(_1229006), c_Int_OBit1(c_Int_OPls))) = _1229008), class_Fields_Ofield(_1229006), class_Int_Onumber__ring(_1229006)], (25262 ^ _779448) ^ [_1229157, _1229159] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1229157), _1229159), hAPP(c_Int_Onumber__class_Onumber__of(_1229157), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1229157), _1229159)), class_Fields_Ofield__inverse__zero(_1229157), class_Int_Onumber__ring(_1229157)], (25272 ^ _779448) ^ [_1229318] : [class_Orderings_Oord(_1229318), -(c_Orderings_Oord__class_Omax(_1229318) = c_Orderings_Oord_Omax(_1229318, c_Orderings_Oord__class_Oless__eq(_1229318)))], (25278 ^ _779448) ^ [_1229405, _1229407, _1229409, _1229411] : [class_Orderings_Olinorder(_1229405), hBOOL(hAPP(c_Finite__Set_Ofinite(_1229405), _1229407)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1229405, _1229405, c_Orderings_Oord__class_Omax(_1229405)), _1229409), hAPP(hAPP(c_Set_Oinsert(_1229405), _1229411), _1229407)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1229405), _1229411), hAPP(hAPP(c_Finite__Set_Ofold(_1229405, _1229405, c_Orderings_Oord__class_Omax(_1229405)), _1229409), _1229407)))], (25288 ^ _779448) ^ [_1229628] : [class_Orderings_Olinorder(_1229628), -(c_Orderings_Oord_Omin(_1229628, hAPP(c_COMBC(_1229628, _1229628, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1229628))) = c_Orderings_Oord__class_Omax(_1229628))], (25294 ^ _779448) ^ [_1229729, _1229731, _1229733, _1229735] : [class_Fields_Olinordered__field__inverse__zero(_1229729), class_Int_Onumber(_1229729), 25301 ^ _779448 : [(25328 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229731), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1229729), _1229733), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))))), 25331 ^ _779448 : [(25332 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), c_Groups_Ozero__class_Ozero(_1229729)), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))))], (25334 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229729), _1229731), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))), _1229733))]], 25335 ^ _779448 : [(25336 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), c_Groups_Ozero__class_Ozero(_1229729)), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)))], (25338 ^ _779448) ^ [] : [25339 ^ _779448 : [(25340 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)), c_Groups_Ozero__class_Ozero(_1229729))))], (25342 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229729), _1229731), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))))]], 25343 ^ _779448 : [(25344 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)), c_Groups_Ozero__class_Ozero(_1229729)))], (25346 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229731), c_Groups_Ozero__class_Ozero(_1229729)))]]]]], (25302 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229731), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1229729), _1229733), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)))), 25305 ^ _779448 : [(25306 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), c_Groups_Ozero__class_Ozero(_1229729)), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229729), _1229731), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735))), _1229733)))], (25312 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), c_Groups_Ozero__class_Ozero(_1229729)), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)))), 25315 ^ _779448 : [(25316 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)), c_Groups_Ozero__class_Ozero(_1229729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229729), _1229731), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)))))], (25322 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), hAPP(c_Int_Onumber__class_Onumber__of(_1229729), _1229735)), c_Groups_Ozero__class_Ozero(_1229729)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229729), _1229731), c_Groups_Ozero__class_Ozero(_1229729))))]]]]]]], (25350 ^ _779448) ^ [_1230843, _1230845, _1230847, _1230849] : [class_Fields_Olinordered__field__inverse__zero(_1230843), class_Int_Onumber(_1230843), 25357 ^ _779448 : [(25384 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1230843), _1230847), _1230849)))), 25387 ^ _779448 : [(25388 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), c_Groups_Ozero__class_Ozero(_1230843)), _1230849)))], (25390 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), _1230849)), _1230847))]], 25391 ^ _779448 : [(25392 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), c_Groups_Ozero__class_Ozero(_1230843)), _1230849))], (25394 ^ _779448) ^ [] : [25395 ^ _779448 : [(25396 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230849), c_Groups_Ozero__class_Ozero(_1230843))))], (25398 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), _1230849)))]], 25399 ^ _779448 : [(25400 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230849), c_Groups_Ozero__class_Ozero(_1230843)))], (25402 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), c_Groups_Ozero__class_Ozero(_1230843)))]]]]], (25358 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1230843), _1230847), _1230849))), 25361 ^ _779448 : [(25362 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), c_Groups_Ozero__class_Ozero(_1230843)), _1230849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), _1230849)), _1230847)))], (25368 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), c_Groups_Ozero__class_Ozero(_1230843)), _1230849))), 25371 ^ _779448 : [(25372 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230849), c_Groups_Ozero__class_Ozero(_1230843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), _1230849))))], (25378 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), _1230849), c_Groups_Ozero__class_Ozero(_1230843)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230843), hAPP(c_Int_Onumber__class_Onumber__of(_1230843), _1230845)), c_Groups_Ozero__class_Ozero(_1230843))))]]]]]]], (25406 ^ _779448) ^ [_1231912, _1231914, _1231916, _1231918] : [class_Fields_Olinordered__field__inverse__zero(_1231912), class_Int_Onumber(_1231912), 25413 ^ _779448 : [(25440 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231912), _1231914), _1231916)), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)))), 25443 ^ _779448 : [(25444 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), _1231916)))], (25446 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231912), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)), _1231916)))]], 25447 ^ _779448 : [(25448 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), _1231916))], (25450 ^ _779448) ^ [] : [25451 ^ _779448 : [(25452 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231916), c_Groups_Ozero__class_Ozero(_1231912))))], (25454 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231912), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)), _1231916)), _1231914))]], 25455 ^ _779448 : [(25456 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231916), c_Groups_Ozero__class_Ozero(_1231912)))], (25458 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)))]]]]], (25414 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231912), _1231914), _1231916)), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918))), 25417 ^ _779448 : [(25418 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), _1231916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231912), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)), _1231916))))], (25424 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), _1231916))), 25427 ^ _779448 : [(25428 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231916), c_Groups_Ozero__class_Ozero(_1231912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231912), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918)), _1231916)), _1231914)))], (25434 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), _1231916), c_Groups_Ozero__class_Ozero(_1231912)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231912), c_Groups_Ozero__class_Ozero(_1231912)), hAPP(c_Int_Onumber__class_Onumber__of(_1231912), _1231918))))]]]]]]], (25462 ^ _779448) ^ [_1232981, _1232983, _1232985, _1232987] : [class_Fields_Olinordered__field__inverse__zero(_1232981), class_Int_Onumber(_1232981), 25469 ^ _779448 : [(25496 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232981), _1232983), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))), _1232987))), 25499 ^ _779448 : [(25500 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))))], (25502 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), _1232983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232981), _1232987), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))))]], 25503 ^ _779448 : [(25504 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)))], (25506 ^ _779448) ^ [] : [25507 ^ _779448 : [(25508 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)), c_Groups_Ozero__class_Ozero(_1232981))))], (25510 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232981), _1232987), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))), _1232983))]], 25511 ^ _779448 : [(25512 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)), c_Groups_Ozero__class_Ozero(_1232981)))], (25514 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), _1232987))]]]]], (25470 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232981), _1232983), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))), _1232987)), 25473 ^ _779448 : [(25474 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), _1232983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232981), _1232987), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)))))], (25480 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)))), 25483 ^ _779448 : [(25484 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)), c_Groups_Ozero__class_Ozero(_1232981))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232981), _1232987), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985))), _1232983)))], (25490 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), hAPP(c_Int_Onumber__class_Onumber__of(_1232981), _1232985)), c_Groups_Ozero__class_Ozero(_1232981)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232981), c_Groups_Ozero__class_Ozero(_1232981)), _1232987)))]]]]]]], (25518 ^ _779448) ^ [_1234095, _1234097, _1234099, _1234101] : [class_Fields_Ofield(_1234095), -(_1234097 = c_Groups_Ozero__class_Ozero(_1234095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1234099), _1234101)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1234095), _1234097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1234101), _1234099)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234095), hAPP(hAPP(c_Power_Opower__class_Opower(_1234095), _1234097), _1234101)), hAPP(hAPP(c_Power_Opower__class_Opower(_1234095), _1234097), _1234099)))], (25532 ^ _779448) ^ [_1234379, _1234381, _1234383, _1234385] : [class_Orderings_Olinorder(_1234379), hBOOL(hAPP(c_Finite__Set_Ofinite(_1234379), _1234381)), hBOOL(hAPP(hAPP(c_member(_1234379), _1234383), _1234381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1234379), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234379), _1234383), _1234385)), hAPP(hAPP(c_Finite__Set_Ofold(_1234379, _1234379, c_Orderings_Oord__class_Omax(_1234379)), _1234385), _1234381))))], (25546 ^ _779448) ^ [_1234646, _1234648] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234646), hAPP(c_Int_Onumber__class_Onumber__of(_1234646), c_Int_OMin)), _1234648) = hAPP(c_Groups_Ouminus__class_Ouminus(_1234646), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1234646), c_Groups_Oone__class_Oone(_1234646)), _1234648))), class_Fields_Ofield__inverse__zero(_1234646), class_Int_Onumber__ring(_1234646)], (25556 ^ _779448) ^ [_1234827, _1234829, _1234831] : [class_Orderings_Olinorder(_1234827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1234827), _1234829)), hBOOL(hAPP(hAPP(c_member(_1234827), _1234831), _1234829)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1234827), _1234831), c_Big__Operators_Olattice_OInf__fin(_1234827, c_Orderings_Oord__class_Omin(_1234827), _1234829)) = _1234831)], (25570 ^ _779448) ^ [_1235062, _1235064, _1235066, _1235068] : [class_Fields_Olinordered__field__inverse__zero(_1235062), class_Int_Onumber(_1235062), 25577 ^ _779448 : [(25604 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235062), _1235064), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))), _1235068))), 25607 ^ _779448 : [(25608 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))))], (25610 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), _1235064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235062), _1235068), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))))]], 25611 ^ _779448 : [(25612 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)))], (25614 ^ _779448) ^ [] : [25615 ^ _779448 : [(25616 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)), c_Groups_Ozero__class_Ozero(_1235062))))], (25618 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235062), _1235068), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))), _1235064))]], 25619 ^ _779448 : [(25620 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)), c_Groups_Ozero__class_Ozero(_1235062)))], (25622 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), _1235068))]]]]], (25578 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1235062), _1235064), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))), _1235068)), 25581 ^ _779448 : [(25582 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), _1235064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235062), _1235068), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)))))], (25588 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)))), 25591 ^ _779448 : [(25592 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)), c_Groups_Ozero__class_Ozero(_1235062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235062), _1235068), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066))), _1235064)))], (25598 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235062), hAPP(c_Int_Onumber__class_Onumber__of(_1235062), _1235066)), c_Groups_Ozero__class_Ozero(_1235062)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235062), c_Groups_Ozero__class_Ozero(_1235062)), _1235068)))]]]]]]], (25626 ^ _779448) ^ [_1236176, _1236178, _1236180, _1236182] : [class_Fields_Olinordered__field__inverse__zero(_1236176), class_Int_Onumber(_1236176), 25633 ^ _779448 : [(25660 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236176), _1236178), _1236180)), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)))), 25663 ^ _779448 : [(25664 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), _1236180)))], (25666 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), _1236178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236176), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)), _1236180)))]], 25667 ^ _779448 : [(25668 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), _1236180))], (25670 ^ _779448) ^ [] : [25671 ^ _779448 : [(25672 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), _1236180), c_Groups_Ozero__class_Ozero(_1236176))))], (25674 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236176), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)), _1236180)), _1236178))]], 25675 ^ _779448 : [(25676 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), _1236180), c_Groups_Ozero__class_Ozero(_1236176)))], (25678 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)))]]]]], (25634 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1236176), _1236178), _1236180)), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182))), 25637 ^ _779448 : [(25638 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), _1236180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), _1236178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236176), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)), _1236180))))], (25644 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), _1236180))), 25647 ^ _779448 : [(25648 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), _1236180), c_Groups_Ozero__class_Ozero(_1236176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236176), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182)), _1236180)), _1236178)))], (25654 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1236176), _1236180), c_Groups_Ozero__class_Ozero(_1236176)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236176), c_Groups_Ozero__class_Ozero(_1236176)), hAPP(c_Int_Onumber__class_Onumber__of(_1236176), _1236182))))]]]]]]], (25682 ^ _779448) ^ [_1237245, _1237247, _1237249, _1237251] : [class_Fields_Olinordered__field__inverse__zero(_1237245), class_Int_Onumber(_1237245), 25689 ^ _779448 : [(25716 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237245), _1237249), _1237251)))), 25719 ^ _779448 : [(25720 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), c_Groups_Ozero__class_Ozero(_1237245)), _1237251)))], (25722 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), _1237251)), _1237249))]], 25723 ^ _779448 : [(25724 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), c_Groups_Ozero__class_Ozero(_1237245)), _1237251))], (25726 ^ _779448) ^ [] : [25727 ^ _779448 : [(25728 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), _1237251), c_Groups_Ozero__class_Ozero(_1237245))))], (25730 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), _1237249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), _1237251)))]], 25731 ^ _779448 : [(25732 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), _1237251), c_Groups_Ozero__class_Ozero(_1237245)))], (25734 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), c_Groups_Ozero__class_Ozero(_1237245)))]]]]], (25690 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1237245), _1237249), _1237251))), 25693 ^ _779448 : [(25694 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), c_Groups_Ozero__class_Ozero(_1237245)), _1237251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), _1237251)), _1237249)))], (25700 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), c_Groups_Ozero__class_Ozero(_1237245)), _1237251))), 25703 ^ _779448 : [(25704 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), _1237251), c_Groups_Ozero__class_Ozero(_1237245))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), _1237249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), _1237251))))], (25710 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237245), _1237251), c_Groups_Ozero__class_Ozero(_1237245)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237245), hAPP(c_Int_Onumber__class_Onumber__of(_1237245), _1237247)), c_Groups_Ozero__class_Ozero(_1237245))))]]]]]]], (25738 ^ _779448) ^ [_1238314, _1238316, _1238318, _1238320] : [class_Fields_Olinordered__field__inverse__zero(_1238314), class_Int_Onumber(_1238314), 25745 ^ _779448 : [(25772 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238314), _1238318), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))))), 25775 ^ _779448 : [(25776 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), c_Groups_Ozero__class_Ozero(_1238314)), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))))], (25778 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238314), _1238316), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))), _1238318))]], 25779 ^ _779448 : [(25780 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), c_Groups_Ozero__class_Ozero(_1238314)), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)))], (25782 ^ _779448) ^ [] : [25783 ^ _779448 : [(25784 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)), c_Groups_Ozero__class_Ozero(_1238314))))], (25786 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238314), _1238316), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))))]], 25787 ^ _779448 : [(25788 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)), c_Groups_Ozero__class_Ozero(_1238314)))], (25790 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238316), c_Groups_Ozero__class_Ozero(_1238314)))]]]]], (25746 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238316), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1238314), _1238318), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)))), 25749 ^ _779448 : [(25750 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), c_Groups_Ozero__class_Ozero(_1238314)), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238314), _1238316), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320))), _1238318)))], (25756 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), c_Groups_Ozero__class_Ozero(_1238314)), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)))), 25759 ^ _779448 : [(25760 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)), c_Groups_Ozero__class_Ozero(_1238314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1238314), _1238316), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)))))], (25766 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238314), hAPP(c_Int_Onumber__class_Onumber__of(_1238314), _1238320)), c_Groups_Ozero__class_Ozero(_1238314)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1238314), _1238316), c_Groups_Ozero__class_Ozero(_1238314))))]]]]]]], (25794 ^ _779448) ^ [_1239428, _1239430] : [class_Fields_Olinordered__field__inverse__zero(_1239428), class_Int_Onumber__ring(_1239428), 25801 ^ _779448 : [(25802 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239428), c_Groups_Ozero__class_Ozero(_1239428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239428), _1239430), hAPP(c_Int_Onumber__class_Onumber__of(_1239428), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239428), c_Groups_Ozero__class_Ozero(_1239428)), _1239430)))], (25808 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239428), c_Groups_Ozero__class_Ozero(_1239428)), _1239430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239428), c_Groups_Ozero__class_Ozero(_1239428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239428), _1239430), hAPP(c_Int_Onumber__class_Onumber__of(_1239428), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (25814 ^ _779448) ^ [_1239778, _1239780] : [class_Fields_Olinordered__field__inverse__zero(_1239778), class_Int_Onumber__ring(_1239778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239778), c_Groups_Ozero__class_Ozero(_1239778)), _1239780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239778), c_Groups_Ozero__class_Ozero(_1239778)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1239778), _1239780), hAPP(c_Int_Onumber__class_Onumber__of(_1239778), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25828 ^ _779448) ^ [_1240019, _1240021] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1240019)), hAPP(c_Nat_OSuc, _1240021)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1240019))), 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, _1240021))), 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)), _1240021)))))], (25830 ^ _779448) ^ [_1240085, _1240087, _1240089, _1240091] : [class_Fields_Olinordered__field__inverse__zero(_1240085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240085), _1240087), _1240089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240085), _1240091), c_Groups_Ozero__class_Ozero(_1240085))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240085), c_Groups_Ozero__class_Ozero(_1240085)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240085), _1240087), _1240089))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240085), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240085), _1240091), _1240087)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240085), _1240091), _1240089))))], (25848 ^ _779448) ^ [_1240444, _1240446, _1240448, _1240450] : [class_Fields_Olinordered__field(_1240444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240444), _1240446), _1240448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240444), c_Groups_Ozero__class_Ozero(_1240444)), _1240450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240444), c_Groups_Ozero__class_Ozero(_1240444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240444), _1240448), _1240446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240444), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240444), _1240450), _1240448)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240444), _1240450), _1240446))))], (25866 ^ _779448) ^ [_1240803, _1240805, _1240807, _1240809] : [class_Fields_Olinordered__field(_1240803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240803), _1240805), c_Groups_Ozero__class_Ozero(_1240803))), 25873 ^ _779448 : [(25874 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240803), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240803), _1240807), _1240805)), _1240809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240803), _1240809), _1240805)), _1240807)))], (25880 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1240803), _1240809), _1240805)), _1240807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240803), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1240803), _1240807), _1240805)), _1240809)))]]], (25886 ^ _779448) ^ [_1241184, _1241186, _1241188, _1241190] : [class_Fields_Olinordered__field(_1241184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241184), _1241186), c_Groups_Ozero__class_Ozero(_1241184))), 25893 ^ _779448 : [(25894 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241184), _1241188), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241184), _1241190), _1241186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241184), _1241190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241184), _1241188), _1241186))))], (25900 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241184), _1241190), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241184), _1241188), _1241186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241184), _1241188), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241184), _1241190), _1241186))))]]], (25906 ^ _779448) ^ [_1241565, _1241567, _1241569, _1241571] : [class_Fields_Olinordered__field(_1241565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241565), c_Groups_Ozero__class_Ozero(_1241565)), _1241567)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241565), _1241569), _1241567)), _1241571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241565), _1241569), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241565), _1241571), _1241567))))], (25920 ^ _779448) ^ [_1241834, _1241836, _1241838, _1241840, _1241842] : [class_Fields_Ofield__inverse__zero(_1241834), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241834), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241834), _1241836), _1241838)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241834), _1241840), _1241842)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1241834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241834), _1241836), _1241840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1241834), _1241838), _1241842)))], (25926 ^ _779448) ^ [_1242011, _1242013, _1242015] : [class_Fields_Ofield__inverse__zero(_1242011), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1242011), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242011), _1242013), _1242015)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242011), _1242013), hAPP(c_Groups_Ouminus__class_Ouminus(_1242011), _1242015)))], (25932 ^ _779448) ^ [_1242140, _1242142, _1242144] : [class_Fields_Ofield__inverse__zero(_1242140), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242140), hAPP(c_Groups_Ouminus__class_Ouminus(_1242140), _1242142)), hAPP(c_Groups_Ouminus__class_Ouminus(_1242140), _1242144)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242140), _1242142), _1242144))], (25938 ^ _779448) ^ [_1242269, _1242271, _1242273] : [class_Fields_Olinordered__field__inverse__zero(_1242269), 25941 ^ _779448 : [(25942 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242269), _1242271), _1242273))), 25947 ^ _779448 : [(25948 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), _1242271)))], (25950 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), _1242273)))]], 25951 ^ _779448 : [(25952 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), _1242271), c_Groups_Ozero__class_Ozero(_1242269))))], (25954 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), _1242273), c_Groups_Ozero__class_Ozero(_1242269))))]]], (25956 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242269), _1242271), _1242273)))), 25957 ^ _779448 : [(25958 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), _1242271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), c_Groups_Ozero__class_Ozero(_1242269)), _1242273))], (25964 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), _1242271), c_Groups_Ozero__class_Ozero(_1242269))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242269), _1242273), c_Groups_Ozero__class_Ozero(_1242269)))]]]]], (25972 ^ _779448) ^ [_1242859, _1242861, _1242863] : [class_Fields_Olinordered__field__inverse__zero(_1242859), 25975 ^ _779448 : [(25976 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242859), _1242861), _1242863)), c_Groups_Ozero__class_Ozero(_1242859))), 25981 ^ _779448 : [(25982 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), c_Groups_Ozero__class_Ozero(_1242859)), _1242861)))], (25984 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), _1242863), c_Groups_Ozero__class_Ozero(_1242859))))]], 25985 ^ _779448 : [(25986 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), _1242861), c_Groups_Ozero__class_Ozero(_1242859))))], (25988 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), c_Groups_Ozero__class_Ozero(_1242859)), _1242863)))]]], (25990 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1242859), _1242861), _1242863)), c_Groups_Ozero__class_Ozero(_1242859)))), 25991 ^ _779448 : [(25992 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), c_Groups_Ozero__class_Ozero(_1242859)), _1242861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), _1242863), c_Groups_Ozero__class_Ozero(_1242859)))], (25998 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), _1242861), c_Groups_Ozero__class_Ozero(_1242859))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242859), c_Groups_Ozero__class_Ozero(_1242859)), _1242863))]]]]], (26006 ^ _779448) ^ [_1243449, _1243451, _1243453, _1243455] : [class_Fields_Olinordered__field__inverse__zero(_1243449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243449), _1243451), _1243453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243449), c_Groups_Ozero__class_Ozero(_1243449)), _1243455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243449), _1243451), _1243455)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243449), _1243453), _1243455))))], (26020 ^ _779448) ^ [_1243718, _1243720, _1243722, _1243724] : [class_Fields_Olinordered__field__inverse__zero(_1243718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243718), _1243720), _1243722)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243718), _1243724), c_Groups_Ozero__class_Ozero(_1243718))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243718), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243718), _1243722), _1243724)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243718), _1243720), _1243724))))], (26034 ^ _779448) ^ [_1243987, _1243989, _1243991, _1243993] : [class_Fields_Olinordered__field(_1243987), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243987), _1243989), _1243991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243987), _1243993), c_Groups_Ozero__class_Ozero(_1243987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243987), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243987), _1243991), _1243993)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1243987), _1243989), _1243993))))], (26048 ^ _779448) ^ [_1244256, _1244258, _1244260, _1244262] : [class_Fields_Olinordered__field(_1244256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244256), _1244258), _1244260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244256), c_Groups_Ozero__class_Ozero(_1244256)), _1244262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244256), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244256), _1244258), _1244262)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244256), _1244260), _1244262))))], (26062 ^ _779448) ^ [_1244525, _1244527, _1244529] : [class_Fields_Olinordered__field(_1244525), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244525), _1244527), c_Groups_Ozero__class_Ozero(_1244525))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244525), _1244529), c_Groups_Ozero__class_Ozero(_1244525))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244525), c_Groups_Ozero__class_Ozero(_1244525)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244525), _1244527), _1244529))))], (26076 ^ _779448) ^ [_1244780, _1244782, _1244784] : [class_Fields_Olinordered__field(_1244780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244780), _1244782), c_Groups_Ozero__class_Ozero(_1244780))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244780), c_Groups_Ozero__class_Ozero(_1244780)), _1244784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244780), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1244780), _1244782), _1244784)), c_Groups_Ozero__class_Ozero(_1244780))))], (26090 ^ _779448) ^ [_1245035, _1245037, _1245039] : [class_Fields_Olinordered__field(_1245035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245035), c_Groups_Ozero__class_Ozero(_1245035)), _1245037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245035), _1245039), c_Groups_Ozero__class_Ozero(_1245035))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245035), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245035), _1245037), _1245039)), c_Groups_Ozero__class_Ozero(_1245035))))], (26104 ^ _779448) ^ [_1245290, _1245292, _1245294] : [class_Fields_Olinordered__field(_1245290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245290), c_Groups_Ozero__class_Ozero(_1245290)), _1245292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245290), c_Groups_Ozero__class_Ozero(_1245290)), _1245294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245290), c_Groups_Ozero__class_Ozero(_1245290)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245290), _1245292), _1245294))))], (26118 ^ _779448) ^ [_1245545, _1245547, _1245549] : [class_Fields_Olinordered__field__inverse__zero(_1245545), 26121 ^ _779448 : [(26122 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245545), _1245547), _1245549)), c_Groups_Ozero__class_Ozero(_1245545))), 26127 ^ _779448 : [(26128 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), c_Groups_Ozero__class_Ozero(_1245545)), _1245547)))], (26130 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), _1245549), c_Groups_Ozero__class_Ozero(_1245545))))]], 26131 ^ _779448 : [(26132 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), _1245547), c_Groups_Ozero__class_Ozero(_1245545))))], (26134 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), c_Groups_Ozero__class_Ozero(_1245545)), _1245549)))]]], (26136 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1245545), _1245547), _1245549)), c_Groups_Ozero__class_Ozero(_1245545)))), 26137 ^ _779448 : [(26138 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), c_Groups_Ozero__class_Ozero(_1245545)), _1245547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), _1245549), c_Groups_Ozero__class_Ozero(_1245545)))], (26144 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), _1245547), c_Groups_Ozero__class_Ozero(_1245545))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1245545), c_Groups_Ozero__class_Ozero(_1245545)), _1245549))]]]]], (26152 ^ _779448) ^ [_1246135, _1246137, _1246139] : [class_Fields_Olinordered__field__inverse__zero(_1246135), 26155 ^ _779448 : [(26156 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246135), _1246137), _1246139))), 26161 ^ _779448 : [(26162 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), _1246137)))], (26164 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), _1246139)))]], 26165 ^ _779448 : [(26166 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), _1246137), c_Groups_Ozero__class_Ozero(_1246135))))], (26168 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), _1246139), c_Groups_Ozero__class_Ozero(_1246135))))]]], (26170 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246135), _1246137), _1246139)))), 26171 ^ _779448 : [(26172 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), _1246137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), c_Groups_Ozero__class_Ozero(_1246135)), _1246139))], (26178 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), _1246137), c_Groups_Ozero__class_Ozero(_1246135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246135), _1246139), c_Groups_Ozero__class_Ozero(_1246135)))]]]]], (26186 ^ _779448) ^ [_1246725, _1246727, _1246729, _1246731, _1246733] : [class_Fields_Ofield(_1246725), -(_1246727 = c_Groups_Ozero__class_Ozero(_1246725)), -(_1246729 = c_Groups_Ozero__class_Ozero(_1246725)), 26197 ^ _779448 : [(26198 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246725), _1246731), _1246727) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246725), _1246733), _1246729), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246725), _1246731), _1246729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246725), _1246733), _1246727))], (26204 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246725), _1246731), _1246729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246725), _1246733), _1246727), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246725), _1246731), _1246727) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1246725), _1246733), _1246729))]]], (26210 ^ _779448) ^ [_1247174, _1247176, _1247178, _1247180] : [class_Fields_Ofield__inverse__zero(_1247174), -(_1247176 = c_Groups_Ozero__class_Ozero(_1247174)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247174), _1247176), _1247178)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247174), _1247176), _1247180)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247174), _1247178), _1247180))], (26220 ^ _779448) ^ [_1247336, _1247338, _1247340, _1247342] : [class_Fields_Ofield__inverse__zero(_1247336), -(_1247338 = c_Groups_Ozero__class_Ozero(_1247336)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247336), _1247340), _1247338)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247336), _1247342), _1247338)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247336), _1247340), _1247342))], (26230 ^ _779448) ^ [_1247498, _1247500, _1247502, _1247504] : [class_Fields_Ofield__inverse__zero(_1247498), 26233 ^ _779448 : [(26250 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247498), _1247500), _1247502) = _1247504), 26253 ^ _779448 : [(26254 ^ _779448) ^ [] : [_1247502 = c_Groups_Ozero__class_Ozero(_1247498)], (26256 ^ _779448) ^ [] : [_1247500 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247498), _1247504), _1247502)]], 26257 ^ _779448 : [(26258 ^ _779448) ^ [] : [-(_1247502 = c_Groups_Ozero__class_Ozero(_1247498))], (26260 ^ _779448) ^ [] : [_1247504 = c_Groups_Ozero__class_Ozero(_1247498)]]], (26234 ^ _779448) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247498), _1247500), _1247502) = _1247504, 26237 ^ _779448 : [(26238 ^ _779448) ^ [] : [-(_1247502 = c_Groups_Ozero__class_Ozero(_1247498)), -(_1247500 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247498), _1247504), _1247502))], (26244 ^ _779448) ^ [] : [_1247502 = c_Groups_Ozero__class_Ozero(_1247498), -(_1247504 = c_Groups_Ozero__class_Ozero(_1247498))]]]]], (26264 ^ _779448) ^ [_1247992, _1247994, _1247996, _1247998] : [class_Fields_Ofield__inverse__zero(_1247992), 26267 ^ _779448 : [(26284 ^ _779448) ^ [] : [-(_1247994 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247992), _1247996), _1247998)), 26287 ^ _779448 : [(26288 ^ _779448) ^ [] : [_1247998 = c_Groups_Ozero__class_Ozero(_1247992)], (26290 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247992), _1247994), _1247998) = _1247996]], 26291 ^ _779448 : [(26292 ^ _779448) ^ [] : [-(_1247998 = c_Groups_Ozero__class_Ozero(_1247992))], (26294 ^ _779448) ^ [] : [_1247994 = c_Groups_Ozero__class_Ozero(_1247992)]]], (26268 ^ _779448) ^ [] : [_1247994 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1247992), _1247996), _1247998), 26271 ^ _779448 : [(26272 ^ _779448) ^ [] : [-(_1247998 = c_Groups_Ozero__class_Ozero(_1247992)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247992), _1247994), _1247998) = _1247996)], (26278 ^ _779448) ^ [] : [_1247998 = c_Groups_Ozero__class_Ozero(_1247992), -(_1247994 = c_Groups_Ozero__class_Ozero(_1247992))]]]]], (26298 ^ _779448) ^ [_1248486, _1248488, _1248490] : [class_Fields_Olinordered__field(_1248486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248486), c_Groups_Ozero__class_Ozero(_1248486)), _1248488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248486), c_Groups_Ozero__class_Ozero(_1248486)), _1248490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248486), c_Groups_Ozero__class_Ozero(_1248486)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248486), _1248488), _1248490))))], (26312 ^ _779448) ^ [_1248741, _1248743, _1248745] : [class_Fields_Olinordered__field(_1248741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248741), c_Groups_Ozero__class_Ozero(_1248741)), _1248743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248741), _1248745), c_Groups_Ozero__class_Ozero(_1248741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248741), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248741), _1248743), _1248745)), c_Groups_Ozero__class_Ozero(_1248741))))], (26326 ^ _779448) ^ [_1248996, _1248998, _1249000, _1249002, _1249004] : [class_Fields_Olinordered__field(_1248996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248996), c_Groups_Ozero__class_Ozero(_1248996)), _1248998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248996), _1248998), _1249000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248996), c_Groups_Ozero__class_Ozero(_1248996)), _1249002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248996), _1249002), _1249004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1248996), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248996), _1248998), _1249004)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248996), _1249000), _1249002))))], (26348 ^ _779448) ^ [_1249419, _1249421, _1249423, _1249425, _1249427] : [class_Fields_Olinordered__field(_1249419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249419), c_Groups_Ozero__class_Ozero(_1249419)), _1249421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249419), _1249421), _1249423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249419), c_Groups_Ozero__class_Ozero(_1249419)), _1249425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249419), _1249425), _1249427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249419), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249419), _1249421), _1249427)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249419), _1249423), _1249425))))], (26370 ^ _779448) ^ [_1249842, _1249844, _1249846, _1249848, _1249850] : [class_Fields_Olinordered__field(_1249842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249842), c_Groups_Ozero__class_Ozero(_1249842)), _1249844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249842), _1249844), _1249846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1249842), c_Groups_Ozero__class_Ozero(_1249842)), _1249848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249842), _1249848), _1249850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249842), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249842), _1249844), _1249850)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249842), _1249846), _1249848))))], (26392 ^ _779448) ^ [_1250265, _1250267, _1250269] : [class_Fields_Olinordered__field(_1250265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250265), _1250267), c_Groups_Ozero__class_Ozero(_1250265))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250265), c_Groups_Ozero__class_Ozero(_1250265)), _1250269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250265), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250265), _1250267), _1250269)), c_Groups_Ozero__class_Ozero(_1250265))))], (26406 ^ _779448) ^ [_1250520, _1250522, _1250524] : [class_Fields_Olinordered__field(_1250520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250520), _1250522), c_Groups_Ozero__class_Ozero(_1250520))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250520), _1250524), c_Groups_Ozero__class_Ozero(_1250520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250520), c_Groups_Ozero__class_Ozero(_1250520)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250520), _1250522), _1250524))))], (26420 ^ _779448) ^ [_1250775, _1250777, _1250779, _1250781] : [class_Fields_Olinordered__field(_1250775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250775), _1250777), _1250779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250775), _1250781), c_Groups_Ozero__class_Ozero(_1250775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250775), c_Groups_Ozero__class_Ozero(_1250775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250775), _1250777), _1250779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250775), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250775), _1250781), _1250777)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250775), _1250781), _1250779))))], (26438 ^ _779448) ^ [_1251134, _1251136, _1251138, _1251140] : [class_Fields_Olinordered__field(_1251134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251134), _1251136), _1251138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251134), c_Groups_Ozero__class_Ozero(_1251134)), _1251140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251134), c_Groups_Ozero__class_Ozero(_1251134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251134), _1251138), _1251136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251134), _1251140), _1251138)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251134), _1251140), _1251136))))], (26456 ^ _779448) ^ [_1251493, _1251495, _1251497, _1251499] : [class_Fields_Olinordered__field(_1251493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251493), _1251495), c_Groups_Ozero__class_Ozero(_1251493))), 26463 ^ _779448 : [(26464 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251493), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251493), _1251497), _1251495)), _1251499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251493), _1251499), _1251495)), _1251497)))], (26470 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251493), _1251499), _1251495)), _1251497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251493), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251493), _1251497), _1251495)), _1251499)))]]], (26476 ^ _779448) ^ [_1251874, _1251876, _1251878, _1251880] : [class_Fields_Olinordered__field(_1251874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251874), _1251876), c_Groups_Ozero__class_Ozero(_1251874))), 26483 ^ _779448 : [(26484 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251874), _1251878), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251874), _1251880), _1251876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251874), _1251880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251874), _1251878), _1251876))))], (26490 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251874), _1251880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251874), _1251878), _1251876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251874), _1251878), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251874), _1251880), _1251876))))]]], (26496 ^ _779448) ^ [_1252255, _1252257, _1252259, _1252261] : [class_Fields_Olinordered__field(_1252255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252255), c_Groups_Ozero__class_Ozero(_1252255)), _1252257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252255), _1252259), _1252257)), _1252261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252255), _1252259), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252255), _1252261), _1252257))))], (26510 ^ _779448) ^ [_1252524, _1252526, _1252528, _1252530] : [class_Fields_Olinordered__field(_1252524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252524), c_Groups_Ozero__class_Ozero(_1252524)), _1252526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252524), _1252528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252524), _1252530), _1252526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252524), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252524), _1252528), _1252526)), _1252530)))], (26524 ^ _779448) ^ [_1252793, _1252795, _1252797, _1252799] : [class_Fields_Olinordered__field(_1252793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252793), c_Groups_Ozero__class_Ozero(_1252793)), _1252795)), 26531 ^ _779448 : [(26532 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252793), _1252797), _1252795)), _1252799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252793), _1252797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252793), _1252799), _1252795))))], (26538 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252793), _1252797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1252793), _1252799), _1252795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252793), _1252797), _1252795)), _1252799)))]]], (26544 ^ _779448) ^ [_1253174, _1253176, _1253178, _1253180] : [class_Fields_Olinordered__field(_1253174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253174), c_Groups_Ozero__class_Ozero(_1253174)), _1253176)), 26551 ^ _779448 : [(26552 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253174), _1253178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253174), _1253180), _1253176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253174), _1253178), _1253176)), _1253180)))], (26558 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253174), _1253178), _1253176)), _1253180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253174), _1253178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253174), _1253180), _1253176))))]]], (26564 ^ _779448) ^ [_1253555, _1253557, _1253559, _1253561] : [class_Fields_Olinordered__field__inverse__zero(_1253555), 26567 ^ _779448 : [(26594 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253555), _1253557), _1253559)), _1253561))), 26597 ^ _779448 : [(26598 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253559)))], (26600 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253555), _1253561), _1253559)))]], 26601 ^ _779448 : [(26602 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253559))], (26604 ^ _779448) ^ [] : [26605 ^ _779448 : [(26606 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253559), c_Groups_Ozero__class_Ozero(_1253555))))], (26608 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253555), _1253561), _1253559)), _1253557))]], 26609 ^ _779448 : [(26610 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253559), c_Groups_Ozero__class_Ozero(_1253555)))], (26612 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253561))]]]]], (26568 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253555), _1253557), _1253559)), _1253561)), 26571 ^ _779448 : [(26572 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253555), _1253561), _1253559))))], (26578 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253559))), 26581 ^ _779448 : [(26582 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253559), c_Groups_Ozero__class_Ozero(_1253555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253555), _1253561), _1253559)), _1253557)))], (26588 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), _1253559), c_Groups_Ozero__class_Ozero(_1253555)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253555), c_Groups_Ozero__class_Ozero(_1253555)), _1253561)))]]]]]]], (26616 ^ _779448) ^ [_1254508, _1254510, _1254512, _1254514] : [class_Fields_Olinordered__field__inverse__zero(_1254508), 26619 ^ _779448 : [(26646 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254510), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254508), _1254512), _1254514)))), 26649 ^ _779448 : [(26650 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), c_Groups_Ozero__class_Ozero(_1254508)), _1254514)))], (26652 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254508), _1254510), _1254514)), _1254512))]], 26653 ^ _779448 : [(26654 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), c_Groups_Ozero__class_Ozero(_1254508)), _1254514))], (26656 ^ _779448) ^ [] : [26657 ^ _779448 : [(26658 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254514), c_Groups_Ozero__class_Ozero(_1254508))))], (26660 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254508), _1254510), _1254514)))]], 26661 ^ _779448 : [(26662 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254514), c_Groups_Ozero__class_Ozero(_1254508)))], (26664 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254510), c_Groups_Ozero__class_Ozero(_1254508)))]]]]], (26620 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254510), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254508), _1254512), _1254514))), 26623 ^ _779448 : [(26624 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), c_Groups_Ozero__class_Ozero(_1254508)), _1254514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254508), _1254510), _1254514)), _1254512)))], (26630 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), c_Groups_Ozero__class_Ozero(_1254508)), _1254514))), 26633 ^ _779448 : [(26634 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254514), c_Groups_Ozero__class_Ozero(_1254508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254508), _1254510), _1254514))))], (26640 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254514), c_Groups_Ozero__class_Ozero(_1254508)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254508), _1254510), c_Groups_Ozero__class_Ozero(_1254508))))]]]]]]], (26668 ^ _779448) ^ [_1255461, _1255463, _1255465, _1255467] : [class_Fields_Ofield__inverse__zero(_1255461), -(_1255463 = c_Groups_Ozero__class_Ozero(_1255461)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255461), _1255465), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255461), _1255467), _1255463)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255461), _1255467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255461), _1255465), _1255463))), _1255463))], (26678 ^ _779448) ^ [_1255639, _1255641, _1255643, _1255645] : [class_Fields_Ofield(_1255639), -(_1255641 = c_Groups_Ozero__class_Ozero(_1255639)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255639), _1255643), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255639), _1255645), _1255641)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255639), _1255641), _1255643)), _1255645)), _1255641))], (26688 ^ _779448) ^ [_1255817, _1255819, _1255821, _1255823] : [class_Fields_Ofield__inverse__zero(_1255817), -(_1255819 = c_Groups_Ozero__class_Ozero(_1255817)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255817), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255817), _1255821), _1255819)), _1255823) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255817), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255817), _1255821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255817), _1255823), _1255819))), _1255819))], (26698 ^ _779448) ^ [_1255995, _1255997, _1255999, _1256001] : [class_Fields_Ofield(_1255995), -(_1255997 = c_Groups_Ozero__class_Ozero(_1255995)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255995), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255995), _1255999), _1255997)), _1256001) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1255995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255995), _1255999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1255995), _1255997), _1256001))), _1255997))], (26708 ^ _779448) ^ [_1256173, _1256175, _1256177, _1256179, _1256181] : [class_Fields_Ofield(_1256173), -(_1256175 = c_Groups_Ozero__class_Ozero(_1256173)), -(_1256177 = c_Groups_Ozero__class_Ozero(_1256173)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256173), _1256179), _1256175)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256173), _1256181), _1256177)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1256173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256173), _1256179), _1256177)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256173), _1256181), _1256175))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256173), _1256175), _1256177)))], (26722 ^ _779448) ^ [_1256420, _1256422, _1256424, _1256426, _1256428] : [class_Fields_Ofield(_1256420), -(_1256422 = c_Groups_Ozero__class_Ozero(_1256420)), -(_1256424 = c_Groups_Ozero__class_Ozero(_1256420)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256420), _1256426), _1256422)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256420), _1256428), _1256424)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256420), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256420), _1256426), _1256424)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256420), _1256428), _1256422))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256420), _1256422), _1256424)))], (26736 ^ _779448) ^ [_1256667, _1256669, _1256671, _1256673] : [class_Fields_Ofield(_1256667), -(_1256669 = c_Groups_Ozero__class_Ozero(_1256667)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256667), _1256671), _1256669)), _1256673) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256667), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256667), _1256671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256667), _1256669), _1256673))), _1256669))], (26746 ^ _779448) ^ [_1256845, _1256847, _1256849, _1256851] : [class_Fields_Ofield(_1256845), -(_1256847 = c_Groups_Ozero__class_Ozero(_1256845)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256845), _1256849), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256845), _1256851), _1256847)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1256845), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1256845), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1256845), _1256847), _1256849)), _1256851)), _1256847))], (26756 ^ _779448) ^ [_1257023, _1257025, _1257027] : [class_Fields_Olinordered__field(_1257023), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257023), _1257025), _1257027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257023), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257023), _1257025), _1257027)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257023), c_Groups_Oone__class_Oone(_1257023)), c_Groups_Oone__class_Oone(_1257023)))), _1257027)))], (26766 ^ _779448) ^ [_1257238, _1257240, _1257242] : [class_Fields_Olinordered__field(_1257238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257238), _1257240), _1257242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257238), _1257240), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257238), _1257240), _1257242)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1257238), c_Groups_Oone__class_Oone(_1257238)), c_Groups_Oone__class_Oone(_1257238))))))], (26776 ^ _779448) ^ [_1257453, _1257455, _1257457, _1257459] : [class_Fields_Olinordered__field__inverse__zero(_1257453), 26779 ^ _779448 : [(26806 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257453), _1257457), _1257459)))), 26809 ^ _779448 : [(26810 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), c_Groups_Ozero__class_Ozero(_1257453)), _1257459)))], (26812 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257453), _1257455), _1257459)), _1257457))]], 26813 ^ _779448 : [(26814 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), c_Groups_Ozero__class_Ozero(_1257453)), _1257459))], (26816 ^ _779448) ^ [] : [26817 ^ _779448 : [(26818 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), _1257459), c_Groups_Ozero__class_Ozero(_1257453))))], (26820 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257453), _1257455), _1257459)))]], 26821 ^ _779448 : [(26822 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), _1257459), c_Groups_Ozero__class_Ozero(_1257453)))], (26824 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257455), c_Groups_Ozero__class_Ozero(_1257453)))]]]]], (26780 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257453), _1257457), _1257459))), 26783 ^ _779448 : [(26784 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), c_Groups_Ozero__class_Ozero(_1257453)), _1257459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257453), _1257455), _1257459)), _1257457)))], (26790 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), c_Groups_Ozero__class_Ozero(_1257453)), _1257459))), 26793 ^ _779448 : [(26794 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), _1257459), c_Groups_Ozero__class_Ozero(_1257453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1257453), _1257455), _1257459))))], (26800 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257453), _1257459), c_Groups_Ozero__class_Ozero(_1257453)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257453), _1257455), c_Groups_Ozero__class_Ozero(_1257453))))]]]]]]], (26828 ^ _779448) ^ [_1258406, _1258408, _1258410, _1258412] : [class_Fields_Olinordered__field__inverse__zero(_1258406), 26831 ^ _779448 : [(26858 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1258406), _1258408), _1258410)), _1258412))), 26861 ^ _779448 : [(26862 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258410)))], (26864 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), _1258408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258406), _1258412), _1258410)))]], 26865 ^ _779448 : [(26866 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258410))], (26868 ^ _779448) ^ [] : [26869 ^ _779448 : [(26870 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), _1258410), c_Groups_Ozero__class_Ozero(_1258406))))], (26872 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258406), _1258412), _1258410)), _1258408))]], 26873 ^ _779448 : [(26874 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), _1258410), c_Groups_Ozero__class_Ozero(_1258406)))], (26876 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258412))]]]]], (26832 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1258406), _1258408), _1258410)), _1258412)), 26835 ^ _779448 : [(26836 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), _1258408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258406), _1258412), _1258410))))], (26842 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258410))), 26845 ^ _779448 : [(26846 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), _1258410), c_Groups_Ozero__class_Ozero(_1258406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1258406), _1258412), _1258410)), _1258408)))], (26852 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1258406), _1258410), c_Groups_Ozero__class_Ozero(_1258406)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1258406), c_Groups_Ozero__class_Ozero(_1258406)), _1258412)))]]]]]]], (26880 ^ _779448) ^ [_1259359, _1259361, _1259363, _1259365] : [class_Fields_Olinordered__field(_1259359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259359), c_Groups_Ozero__class_Ozero(_1259359)), _1259361)), 26887 ^ _779448 : [(26888 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259359), _1259363), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259359), _1259365), _1259361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259359), _1259363), _1259361)), _1259365)))], (26894 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259359), _1259363), _1259361)), _1259365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259359), _1259363), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259359), _1259365), _1259361))))]]], (26900 ^ _779448) ^ [_1259740, _1259742, _1259744, _1259746] : [class_Fields_Olinordered__field(_1259740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259740), c_Groups_Ozero__class_Ozero(_1259740)), _1259742)), 26907 ^ _779448 : [(26908 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259740), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259740), _1259744), _1259742)), _1259746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259740), _1259744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259740), _1259746), _1259742))))], (26914 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259740), _1259744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1259740), _1259746), _1259742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259740), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1259740), _1259744), _1259742)), _1259746)))]]], (26920 ^ _779448) ^ [_1260121, _1260123, _1260125, _1260127] : [class_Fields_Olinordered__field(_1260121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260121), c_Groups_Ozero__class_Ozero(_1260121)), _1260123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260121), _1260125), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1260121), _1260127), _1260123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1260121), _1260125), _1260123)), _1260127)))], (26934 ^ _779448) ^ [_1260390, _1260392, _1260394, _1260396, _1260398, _1260400, _1260402] : [hBOOL(hAPP(_1260390, _1260392)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1260394, _1260394)), hAPP(hAPP(c_Product__Type_OPair(_1260394, _1260394), _1260396), _1260398)), hAPP(_1260400, _1260392))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1260402, _1260394), tc_prod(_1260402, _1260394))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1260402, _1260394), tc_prod(_1260402, _1260394)), hAPP(hAPP(c_Product__Type_OPair(_1260402, _1260394), _1260392), _1260396)), hAPP(hAPP(c_Product__Type_OPair(_1260402, _1260394), _1260392), _1260398))), c_Recdef_Osame__fst(_1260402, _1260394, _1260390, _1260400))))], (26944 ^ _779448) ^ [_1260695, _1260697, _1260699] : [class_Orderings_Olinorder(_1260695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260695), _1260697)), hBOOL(hAPP(hAPP(c_member(_1260695), _1260699), _1260697)), 26955 ^ _779448 : [(26956 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260695, tc_HOL_Obool)), _1260697), hAPP(hAPP(c_Set_Oinsert(_1260695), _1260699), c_Orderings_Obot__class_Obot(tc_fun(_1260695, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1260695, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1260695, _1260697) = _1260699)], (26962 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260695, tc_HOL_Obool)), _1260697), hAPP(hAPP(c_Set_Oinsert(_1260695), _1260699), c_Orderings_Obot__class_Obot(tc_fun(_1260695, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1260695, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1260695, _1260697) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1260695), _1260699), c_Big__Operators_Olinorder__class_OMax(_1260695, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260695, tc_HOL_Obool)), _1260697), hAPP(hAPP(c_Set_Oinsert(_1260695), _1260699), c_Orderings_Obot__class_Obot(tc_fun(_1260695, tc_HOL_Obool)))))))]]], (26968 ^ _779448) ^ [_1261201, _1261203] : [class_Orderings_Olinorder(_1261201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1261201), _1261203)), -(_1261203 = c_Orderings_Obot__class_Obot(tc_fun(_1261201, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261201), c_Big__Operators_Olattice_OInf__fin(_1261201, c_Orderings_Oord__class_Omin(_1261201), _1261203)), c_Big__Operators_Olattice_OSup__fin(_1261201, c_Orderings_Oord__class_Omax(_1261201), _1261203))))], (26982 ^ _779448) ^ [_1261399, _1261401, _1261403] : [class_Orderings_Olinorder(_1261399), hBOOL(hAPP(c_Finite__Set_Ofinite(_1261399), _1261401)), hBOOL(hAPP(hAPP(c_member(_1261399), _1261403), _1261401)), 26993 ^ _779448 : [(26994 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261399, tc_HOL_Obool)), _1261401), hAPP(hAPP(c_Set_Oinsert(_1261399), _1261403), c_Orderings_Obot__class_Obot(tc_fun(_1261399, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1261399, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1261399, c_Orderings_Oord__class_Omax(_1261399), _1261401) = _1261403)], (27000 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261399, tc_HOL_Obool)), _1261401), hAPP(hAPP(c_Set_Oinsert(_1261399), _1261403), c_Orderings_Obot__class_Obot(tc_fun(_1261399, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1261399, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1261399, c_Orderings_Oord__class_Omax(_1261399), _1261401) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1261399), _1261403), c_Big__Operators_Olattice_OSup__fin(_1261399, c_Orderings_Oord__class_Omax(_1261399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1261399, tc_HOL_Obool)), _1261401), hAPP(hAPP(c_Set_Oinsert(_1261399), _1261403), c_Orderings_Obot__class_Obot(tc_fun(_1261399, tc_HOL_Obool)))))))]]], (27006 ^ _779448) ^ [_1261923, _1261925, _1261927, _1261929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261923), _1261925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1261927), _1261929)), -(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), _1261923), _1261927)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1261925), _1261929))), c_FunDef_Opair__less)))], (27016 ^ _779448) ^ [_1262126, _1262128] : [class_Orderings_Olinorder(_1262126), -(c_Big__Operators_Olinorder__class_OMax(_1262126, hAPP(hAPP(c_Set_Oinsert(_1262126), _1262128), c_Orderings_Obot__class_Obot(tc_fun(_1262126, tc_HOL_Obool)))) = _1262128)], (27022 ^ _779448) ^ [_1262233, _1262235, _1262237] : [class_Orderings_Olinorder(_1262233), hBOOL(hAPP(c_Finite__Set_Ofinite(_1262233), _1262235)), hBOOL(hAPP(hAPP(c_member(_1262233), _1262237), _1262235)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1262233), _1262237), c_Big__Operators_Olattice_OSup__fin(_1262233, c_Orderings_Oord__class_Omax(_1262233), _1262235)) = c_Big__Operators_Olattice_OSup__fin(_1262233, c_Orderings_Oord__class_Omax(_1262233), _1262235))], (27036 ^ _779448) ^ [_1262480, _1262482, _1262484] : [class_Orderings_Olinorder(_1262480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1262480), _1262482)), hBOOL(hAPP(hAPP(c_member(_1262480), _1262484), _1262482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262480), _1262484), c_Big__Operators_Olinorder__class_OMax(_1262480, _1262482))))], (27050 ^ _779448) ^ [_1262707, _1262709] : [class_Orderings_Olinorder(_1262707), -(c_Big__Operators_Olattice_OSup__fin(_1262707, c_Orderings_Oord__class_Omax(_1262707), hAPP(hAPP(c_Set_Oinsert(_1262707), _1262709), c_Orderings_Obot__class_Obot(tc_fun(_1262707, tc_HOL_Obool)))) = _1262709)], (27056 ^ _779448) ^ [_1262820, _1262822] : [class_Orderings_Olinorder(_1262820), hBOOL(hAPP(c_Finite__Set_Ofinite(_1262820), _1262822)), -(_1262822 = c_Orderings_Obot__class_Obot(tc_fun(_1262820, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1262820), c_Big__Operators_Olinorder__class_OMax(_1262820, _1262822)), _1262822)))], (27070 ^ _779448) ^ [_1263000, _1263002, _1263004] : [class_Orderings_Olinorder(_1263000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263000), _1263002)), hBOOL(hAPP(hAPP(c_member(_1263000), _1263004), _1263002)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1263000), _1263004), c_Big__Operators_Olinorder__class_OMax(_1263000, _1263002)) = c_Big__Operators_Olinorder__class_OMax(_1263000, _1263002))], (27084 ^ _779448) ^ [_1263235, _1263237] : [class_Orderings_Olinorder(_1263235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263235), _1263237)), -(c_Big__Operators_Olattice_OSup__fin(_1263235, c_Orderings_Oord__class_Omax(_1263235), _1263237) = hAPP(c_Finite__Set_Ofold1(_1263235, c_Orderings_Oord__class_Omax(_1263235)), _1263237))], (27094 ^ _779448) ^ [_1263398, _1263400] : [class_Orderings_Olinorder(_1263398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263398), _1263400)), -(c_Big__Operators_Olinorder__class_OMax(_1263398, _1263400) = hAPP(c_Finite__Set_Ofold1(_1263398, c_Orderings_Oord__class_Omax(_1263398)), _1263400))], (27104 ^ _779448) ^ [_1263555, _1263557, _1263559] : [class_Orderings_Olinorder(_1263555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263555), _1263557)), -(_1263557 = c_Orderings_Obot__class_Obot(tc_fun(_1263555, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1263555, c_Orderings_Oord__class_Omax(_1263555), hAPP(hAPP(c_Set_Oinsert(_1263555), _1263559), _1263557)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1263555), _1263559), c_Big__Operators_Olattice_OSup__fin(_1263555, c_Orderings_Oord__class_Omax(_1263555), _1263557)))], (27118 ^ _779448) ^ [_1263775, _1263777, _1263779] : [class_Orderings_Olinorder(_1263775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263775), _1263777)), -(_1263779 = c_Orderings_Obot__class_Obot(tc_fun(_1263775, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263775, tc_HOL_Obool)), _1263779), _1263777)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1263775), c_Big__Operators_Olattice_OSup__fin(_1263775, c_Orderings_Oord__class_Omax(_1263775), _1263779)), c_Big__Operators_Olattice_OSup__fin(_1263775, c_Orderings_Oord__class_Omax(_1263775), _1263777)) = c_Big__Operators_Olattice_OSup__fin(_1263775, c_Orderings_Oord__class_Omax(_1263775), _1263777))], (27136 ^ _779448) ^ [_1264107, _1264109, _1264111] : [class_Orderings_Olinorder(_1264107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264107), _1264109)), hBOOL(hAPP(hAPP(c_member(_1264107), _1264111), _1264109)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1264107), _1264111), c_Big__Operators_Olattice_OSup__fin(_1264107, c_Orderings_Oord__class_Omax(_1264107), _1264109)) = _1264111)], (27150 ^ _779448) ^ [_1264342, _1264344, _1264346, _1264348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1264342), _1264344)), -(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), _1264342), _1264346)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1264344), _1264348))), c_FunDef_Opair__less)))], (27156 ^ _779448) ^ [_1264479, _1264481, _1264483] : [class_Orderings_Olinorder(_1264479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264479, tc_HOL_Obool)), _1264481), _1264483)), -(_1264481 = c_Orderings_Obot__class_Obot(tc_fun(_1264479, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264479), _1264483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264479), c_Big__Operators_Olinorder__class_OMax(_1264479, _1264481)), c_Big__Operators_Olinorder__class_OMax(_1264479, _1264483))))], (27174 ^ _779448) ^ [_1264785, _1264787, _1264789] : [class_Orderings_Olinorder(_1264785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264785), _1264787)), -(c_Big__Operators_Olattice_OSup__fin(_1264785, c_Orderings_Oord__class_Omax(_1264785), hAPP(hAPP(c_Set_Oinsert(_1264785), _1264789), _1264787)) = hAPP(hAPP(c_Finite__Set_Ofold(_1264785, _1264785, c_Orderings_Oord__class_Omax(_1264785)), _1264789), _1264787))], (27184 ^ _779448) ^ [_1264976, _1264978, _1264980] : [class_Orderings_Olinorder(_1264976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264976), _1264978)), -(_1264978 = c_Orderings_Obot__class_Obot(tc_fun(_1264976, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1264976, hAPP(hAPP(c_Set_Oinsert(_1264976), _1264980), _1264978)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1264976), _1264980), c_Big__Operators_Olinorder__class_OMax(_1264976, _1264978)))], (27198 ^ _779448) ^ [_1265184, _1265186, _1265188] : [class_Orderings_Olinorder(_1265184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265184), _1265186)), -(_1265188 = c_Orderings_Obot__class_Obot(tc_fun(_1265184, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1265184, tc_HOL_Obool)), _1265188), _1265186)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1265184), c_Big__Operators_Olinorder__class_OMax(_1265184, _1265188)), c_Big__Operators_Olinorder__class_OMax(_1265184, _1265186)) = c_Big__Operators_Olinorder__class_OMax(_1265184, _1265186))], (27216 ^ _779448) ^ [_1265498, _1265500, _1265502] : [class_Orderings_Olinorder(_1265498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265498), _1265500)), -(c_Big__Operators_Olinorder__class_OMax(_1265498, hAPP(hAPP(c_Set_Oinsert(_1265498), _1265502), _1265500)) = hAPP(hAPP(c_Finite__Set_Ofold(_1265498, _1265498, c_Orderings_Oord__class_Omax(_1265498)), _1265502), _1265500))], (27226 ^ _779448) ^ [_1265683, _1265685, _1265687] : [class_Orderings_Olinorder(_1265683), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265683), _1265685)), -(hBOOL(hAPP(hAPP(c_member(_1265683), _1265687), _1265685))), -(_1265685 = c_Orderings_Obot__class_Obot(tc_fun(_1265683, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1265683, c_Orderings_Oord__class_Omax(_1265683), hAPP(hAPP(c_Set_Oinsert(_1265683), _1265687), _1265685)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1265683), _1265687), c_Big__Operators_Olattice_OSup__fin(_1265683, c_Orderings_Oord__class_Omax(_1265683), _1265685)))], (27244 ^ _779448) ^ [_1265932, _1265934, _1265936] : [class_Orderings_Olinorder(_1265932), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265932), _1265934)), 27251 ^ _779448 : [(27252 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265932, tc_HOL_Obool)), _1265934), hAPP(hAPP(c_Set_Oinsert(_1265932), _1265936), c_Orderings_Obot__class_Obot(tc_fun(_1265932, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1265932, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1265932, c_Orderings_Oord__class_Omax(_1265932), hAPP(hAPP(c_Set_Oinsert(_1265932), _1265936), _1265934)) = _1265936)], (27258 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265932, tc_HOL_Obool)), _1265934), hAPP(hAPP(c_Set_Oinsert(_1265932), _1265936), c_Orderings_Obot__class_Obot(tc_fun(_1265932, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1265932, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1265932, c_Orderings_Oord__class_Omax(_1265932), hAPP(hAPP(c_Set_Oinsert(_1265932), _1265936), _1265934)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1265932), _1265936), c_Big__Operators_Olattice_OSup__fin(_1265932, c_Orderings_Oord__class_Omax(_1265932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1265932, tc_HOL_Obool)), _1265934), hAPP(hAPP(c_Set_Oinsert(_1265932), _1265936), c_Orderings_Obot__class_Obot(tc_fun(_1265932, tc_HOL_Obool)))))))]]], (27264 ^ _779448) ^ [_1266420, _1266422, _1266424] : [class_Orderings_Olinorder(_1266420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266420), _1266422)), -(hBOOL(hAPP(hAPP(c_member(_1266420), _1266424), _1266422))), -(c_Big__Operators_Olattice_OSup__fin(_1266420, c_Orderings_Oord__class_Omax(_1266420), hAPP(hAPP(c_Set_Oinsert(_1266420), _1266424), _1266422)) = hAPP(hAPP(c_Finite__Set_Ofold(_1266420, _1266420, c_Orderings_Oord__class_Omax(_1266420)), _1266424), _1266422))], (27278 ^ _779448) ^ [_1266640, _1266642, _1266644] : [class_Orderings_Olinorder(_1266640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266640), _1266642)), -(hBOOL(hAPP(hAPP(c_member(_1266640), _1266644), _1266642))), -(_1266642 = c_Orderings_Obot__class_Obot(tc_fun(_1266640, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1266640, hAPP(hAPP(c_Set_Oinsert(_1266640), _1266644), _1266642)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1266640), _1266644), c_Big__Operators_Olinorder__class_OMax(_1266640, _1266642)))], (27296 ^ _779448) ^ [_1266877, _1266879, _1266881] : [class_Orderings_Olinorder(_1266877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266877), _1266879)), 27303 ^ _779448 : [(27304 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266877, tc_HOL_Obool)), _1266879), hAPP(hAPP(c_Set_Oinsert(_1266877), _1266881), c_Orderings_Obot__class_Obot(tc_fun(_1266877, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1266877, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1266877, hAPP(hAPP(c_Set_Oinsert(_1266877), _1266881), _1266879)) = _1266881)], (27310 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266877, tc_HOL_Obool)), _1266879), hAPP(hAPP(c_Set_Oinsert(_1266877), _1266881), c_Orderings_Obot__class_Obot(tc_fun(_1266877, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1266877, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1266877, hAPP(hAPP(c_Set_Oinsert(_1266877), _1266881), _1266879)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1266877), _1266881), c_Big__Operators_Olinorder__class_OMax(_1266877, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266877, tc_HOL_Obool)), _1266879), hAPP(hAPP(c_Set_Oinsert(_1266877), _1266881), c_Orderings_Obot__class_Obot(tc_fun(_1266877, tc_HOL_Obool)))))))]]], (27316 ^ _779448) ^ [_1267347, _1267349, _1267351] : [class_Orderings_Olinorder(_1267347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267347), _1267349)), -(hBOOL(hAPP(hAPP(c_member(_1267347), _1267351), _1267349))), -(c_Big__Operators_Olinorder__class_OMax(_1267347, hAPP(hAPP(c_Set_Oinsert(_1267347), _1267351), _1267349)) = hAPP(hAPP(c_Finite__Set_Ofold(_1267347, _1267347, c_Orderings_Oord__class_Omax(_1267347)), _1267351), _1267349))], (27330 ^ _779448) ^ [_1267561, _1267563] : [class_Groups_Olinordered__ab__group__add(_1267561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267561), _1267563)), -(_1267563 = c_Orderings_Obot__class_Obot(tc_fun(_1267561, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1267561), c_Big__Operators_Olinorder__class_OMax(_1267561, _1267563)) = c_Big__Operators_Olinorder__class_OMin(_1267561, hAPP(c_Set_Oimage(_1267561, _1267561, c_Groups_Ouminus__class_Ouminus(_1267561)), _1267563)))], (27344 ^ _779448) ^ [_1267761, _1267763] : [class_Groups_Olinordered__ab__group__add(_1267761), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267761), _1267763)), -(_1267763 = c_Orderings_Obot__class_Obot(tc_fun(_1267761, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1267761), c_Big__Operators_Olinorder__class_OMin(_1267761, _1267763)) = c_Big__Operators_Olinorder__class_OMax(_1267761, hAPP(c_Set_Oimage(_1267761, _1267761, c_Groups_Ouminus__class_Ouminus(_1267761)), _1267763)))], (27358 ^ _779448) ^ [_1267961, _1267963, _1267965, _1267967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267961), _1267963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1267965), _1267967)), -(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), _1267961), _1267965)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1267963), _1267967))), c_FunDef_Opair__leq)))], (27368 ^ _779448) ^ [_1268164, _1268166, _1268168, _1268170] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1268164), _1268166)), 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)), _1268164), _1268168)), 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)), _1268166), _1268170)), 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)), _1268166), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1268168), _1268170))), c_FunDef_Omin__strict)))], (27382 ^ _779448) ^ [_1268445, _1268447, _1268449, _1268451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1268445), _1268447)), 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)), _1268449), _1268445)), 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)), _1268451), _1268447)), 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)), _1268449), _1268451)), _1268447)), c_FunDef_Omax__strict)))], (27396 ^ _779448) ^ [_1268726, _1268728, _1268730, _1268732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1268726), _1268728)), -(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), _1268726), _1268730)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1268728), _1268732))), c_FunDef_Opair__leq)))], (27402 ^ _779448) ^ [_1268863, _1268865] : [class_Orderings_Olinorder(_1268863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268863), _1268865)), -(_1268865 = c_Orderings_Obot__class_Obot(tc_fun(_1268863, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1268863), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268863), 27415 ^ [_1268863, _1268865]), 27416 ^ [_1268863, _1268865])), hAPP(hAPP(c_Set_Oinsert(_1268863), 27415 ^ [_1268863, _1268865]), hAPP(hAPP(c_Set_Oinsert(_1268863), 27416 ^ [_1268863, _1268865]), c_Orderings_Obot__class_Obot(tc_fun(_1268863, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1268863), c_Big__Operators_Olattice_OSup__fin(_1268863, c_Orderings_Oord__class_Omax(_1268863), _1268865)), _1268865)))], (27422 ^ _779448) ^ [_1269313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1269313)), -(_1269313 = 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))), _1269313)), c_FunDef_Omax__strict)))], (27432 ^ _779448) ^ [_1269419] : [-(_1269419 = 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)), _1269419), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (27438 ^ _779448) ^ [_1269464, _1269466, _1269468, _1269470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1269464), _1269466)), 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)), _1269468), _1269464)), 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)), _1269470), _1269466)), c_FunDef_Omax__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1269468), _1269470)), _1269466)), c_FunDef_Omax__weak)))], (27452 ^ _779448) ^ [_1269745, _1269747, _1269749, _1269751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1269745), _1269747)), 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)), _1269745), _1269749)), 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)), _1269747), _1269751)), 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)), _1269747), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1269749), _1269751))), c_FunDef_Omin__weak)))], (27466 ^ _779448) ^ [_1270026, _1270028] : [class_Orderings_Olinorder(_1270026), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270026), _1270028)), -(_1270028 = c_Orderings_Obot__class_Obot(tc_fun(_1270026, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1270026), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270026), 27479 ^ [_1270026, _1270028]), 27480 ^ [_1270026, _1270028])), hAPP(hAPP(c_Set_Oinsert(_1270026), 27479 ^ [_1270026, _1270028]), hAPP(hAPP(c_Set_Oinsert(_1270026), 27480 ^ [_1270026, _1270028]), c_Orderings_Obot__class_Obot(tc_fun(_1270026, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1270026), c_Big__Operators_Olinorder__class_OMax(_1270026, _1270028)), _1270028)))], (27486 ^ _779448) ^ [_1270470] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1270470)), -(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))), _1270470)), c_FunDef_Omax__weak)))], (27492 ^ _779448) ^ [_1270565] : [-(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)), _1270565), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (27494 ^ _779448) ^ [] : [-(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)))], (27496 ^ _779448) ^ [] : [-(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)))], (27498 ^ _779448) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (27500 ^ _779448) ^ [_1270668, _1270670] : [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), _1270668), _1270670)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270668), _1270670)))], (27506 ^ _779448) ^ [_1270773, _1270775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270773), _1270775)), -(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), _1270773), _1270775)), c_Wellfounded_Oless__than)))], (27512 ^ _779448) ^ [_1270905, _1270907, _1270909, _1270911] : [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), _1270905), _1270907)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1270909), _1270911))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1270905), _1270911) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1270909), _1270907))], (27518 ^ _779448) ^ [_1271052, _1271054, _1271056, _1271058] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271052), _1271058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1271056), _1271054), -(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), _1271052), _1271054)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1271056), _1271058))), c_Int_Ointrel)))], (27524 ^ _779448) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (27526 ^ _779448) ^ [_1271223, _1271225, _1271227] : [-(c_Wellfounded_Omlex__prod(_1271223, _1271225, _1271227) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1271223), _1271223), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1271223, c_Wellfounded_Oless__than, _1271227)), hAPP(hAPP(c_COMBS(_1271223, _1271223, tc_prod(tc_Nat_Onat, _1271223)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1271223, tc_prod(tc_Nat_Onat, _1271223)), _1271223), c_Product__Type_OPair(tc_Nat_Onat, _1271223)), _1271225)), c_COMBI(_1271223))))], (27528 ^ _779448) ^ [] : [-(c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__leq)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)))))], (27530 ^ _779448) ^ [_1271323, _1271325, _1271327, _1271329] : [c_FunDef_Oreduction__pair(_1271323, _1271325), -(c_FunDef_Oreduction__pair(_1271327, hAPP(hAPP(c_FunDef_Orp__inv__image(_1271323, _1271327), _1271325), _1271329)))], (27536 ^ _779448) ^ [_1271422, _1271424, _1271426] : [class_Orderings_Olinorder(_1271422), hAPP(_1271424, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271422), 27541 ^ [_1271422, _1271424, _1271426]), 27542 ^ [_1271422, _1271424, _1271426])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271422), hAPP(_1271424, 27541 ^ [_1271422, _1271424, _1271426])), hAPP(_1271424, 27542 ^ [_1271422, _1271424, _1271426])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271422), _1271426)), -(_1271426 = c_Orderings_Obot__class_Obot(tc_fun(_1271422, tc_HOL_Obool))), -(hAPP(_1271424, c_Big__Operators_Olattice_OSup__fin(_1271422, c_Orderings_Oord__class_Omax(_1271422), _1271426)) = c_Big__Operators_Olattice_OSup__fin(_1271422, c_Orderings_Oord__class_Omax(_1271422), hAPP(c_Set_Oimage(_1271422, _1271422, _1271424), _1271426)))], (27556 ^ _779448) ^ [_1271837, _1271839, _1271841] : [class_Orderings_Olinorder(_1271837), hAPP(_1271839, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1271837), 27561 ^ [_1271837, _1271839, _1271841]), 27562 ^ [_1271837, _1271839, _1271841])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1271837), hAPP(_1271839, 27561 ^ [_1271837, _1271839, _1271841])), hAPP(_1271839, 27562 ^ [_1271837, _1271839, _1271841])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271837), _1271841)), -(_1271841 = c_Orderings_Obot__class_Obot(tc_fun(_1271837, tc_HOL_Obool))), -(hAPP(_1271839, c_Big__Operators_Olattice_OInf__fin(_1271837, c_Orderings_Oord__class_Omin(_1271837), _1271841)) = c_Big__Operators_Olattice_OInf__fin(_1271837, c_Orderings_Oord__class_Omin(_1271837), hAPP(c_Set_Oimage(_1271837, _1271837, _1271839), _1271841)))], (27576 ^ _779448) ^ [_1272252, _1272254, _1272256, _1272258] : [27577 ^ _779448 : [(27578 ^ _779448) ^ [] : [hBOOL(hAPP(_1272252, _1272254))], (27580 ^ _779448) ^ [] : [hBOOL(hAPP(_1272256, _1272254))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272258, tc_HOL_Obool)), _1272256), _1272252), _1272254)))], (27584 ^ _779448) ^ [_1272407, _1272409, _1272411, _1272413] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272407, tc_HOL_Obool)), _1272409), _1272411), _1272413)), -(hBOOL(hAPP(_1272409, _1272413))), -(hBOOL(hAPP(_1272411, _1272413)))], (27594 ^ _779448) ^ [_1272537, _1272539, _1272541, _1272543] : [27595 ^ _779448 : [(27596 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272537), _1272539), _1272541))], (27598 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1272537), _1272539), _1272543))]], -(hBOOL(hAPP(hAPP(c_member(_1272537), _1272539), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272537, tc_HOL_Obool)), _1272543), _1272541))))], (27602 ^ _779448) ^ [_1272722, _1272724, _1272726, _1272728] : [hBOOL(hAPP(hAPP(c_member(_1272722), _1272724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272722, tc_HOL_Obool)), _1272726), _1272728))), -(hBOOL(hAPP(hAPP(c_member(_1272722), _1272724), _1272726))), -(hBOOL(hAPP(hAPP(c_member(_1272722), _1272724), _1272728)))], (27612 ^ _779448) ^ [_1272882, _1272884, _1272886, _1272888] : [hBOOL(hAPP(hAPP(c_member(_1272882), _1272884), _1272886)), -(hBOOL(hAPP(hAPP(c_member(_1272882), _1272884), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272882, tc_HOL_Obool)), _1272888), _1272886))))], (27618 ^ _779448) ^ [_1273013, _1273015, _1273017, _1273019] : [hBOOL(hAPP(hAPP(c_member(_1273013), _1273015), _1273017)), -(hBOOL(hAPP(hAPP(c_member(_1273013), _1273015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273013, tc_HOL_Obool)), _1273017), _1273019))))], (27634 ^ _779448) ^ [_1273319, _1273321, _1273323, _1273325] : [27635 ^ _779448 : [(27636 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1273319), _1273321), _1273323))], (27638 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1273319), _1273321), _1273325))]], -(hBOOL(hAPP(hAPP(c_member(_1273319), _1273321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273319, tc_HOL_Obool)), _1273323), _1273325))))], (27624 ^ _779448) ^ [_1273165, _1273167, _1273169, _1273171] : [hBOOL(hAPP(hAPP(c_member(_1273165), _1273167), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273165, tc_HOL_Obool)), _1273169), _1273171))), -(hBOOL(hAPP(hAPP(c_member(_1273165), _1273167), _1273169))), -(hBOOL(hAPP(hAPP(c_member(_1273165), _1273167), _1273171)))], (27642 ^ _779448) ^ [_1273504, _1273506, _1273508, _1273510] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273504, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1273504), _1273506), _1273508)), _1273510) = hAPP(hAPP(c_Set_Oinsert(_1273504), _1273506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273504, tc_HOL_Obool)), _1273508), _1273510)))], (27644 ^ _779448) ^ [_1273571, _1273573, _1273575, _1273577] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273571, tc_HOL_Obool)), _1273573), hAPP(hAPP(c_Set_Oinsert(_1273571), _1273575), _1273577)) = hAPP(hAPP(c_Set_Oinsert(_1273571), _1273575), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273571, tc_HOL_Obool)), _1273573), _1273577)))], (27646 ^ _779448) ^ [_1273638] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1273638) = c_Orderings_Oord__class_Omax(_1273638)), class_Lattices_Osemilattice__sup(_1273638), class_Orderings_Olinorder(_1273638)], (27656 ^ _779448) ^ [_1273767, _1273769, _1273771] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273767, tc_HOL_Obool)), _1273769), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273767, tc_HOL_Obool)), _1273771), _1273769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273767, tc_HOL_Obool)), _1273769), _1273771))], (27658 ^ _779448) ^ [_1273827, _1273829, _1273831] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273827, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273827, tc_HOL_Obool)), _1273829), _1273831)), _1273831) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273827, tc_HOL_Obool)), _1273829), _1273831))], (27660 ^ _779448) ^ [_1273887, _1273889, _1273891, _1273893] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273887, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273887, tc_HOL_Obool)), _1273889), _1273891)), _1273893) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273887, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273887, tc_HOL_Obool)), _1273889), _1273893)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273887, tc_HOL_Obool)), _1273891), _1273893)))], (27662 ^ _779448) ^ [_1273971, _1273973, _1273975, _1273977, _1273979] : [class_Lattices_Olattice(_1273971), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273973, _1273971)), _1273975), _1273977), _1273979) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273971), hAPP(_1273975, _1273979)), hAPP(_1273977, _1273979)))], (27668 ^ _779448) ^ [_1274108, _1274110, _1274112, _1274114, _1274116] : [-(hAPP(c_Set_Oimage(_1274108, _1274110, _1274112), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274108, tc_HOL_Obool)), _1274114), _1274116)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274110, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1274108, _1274110, _1274112), _1274114)), hAPP(c_Set_Oimage(_1274108, _1274110, _1274112), _1274116)))], (27670 ^ _779448) ^ [_1274182, _1274184, _1274186, _1274188, _1274190] : [class_Lattices_Olattice(_1274182), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274184, _1274182)), _1274186), _1274188), _1274190) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274182), hAPP(_1274186, _1274190)), hAPP(_1274188, _1274190)))], (27676 ^ _779448) ^ [_1274319, _1274321, _1274323, _1274325] : [class_Lattices_Osemilattice__sup(_1274319), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274319), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274319), _1274321), _1274323)), _1274325) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274319), _1274321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274319), _1274323), _1274325)))], (27682 ^ _779448) ^ [_1274462, _1274464, _1274466, _1274468] : [class_Lattices_Olattice(_1274462), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274462), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274462), _1274464), _1274466)), _1274468) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274462), _1274464), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274462), _1274466), _1274468)))], (27688 ^ _779448) ^ [_1274605, _1274607, _1274609, _1274611] : [class_Lattices_Osemilattice__sup(_1274605), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274605), _1274607), _1274609)), _1274611) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274605), _1274607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274605), _1274609), _1274611)))], (27694 ^ _779448) ^ [_1274748, _1274750, _1274752, _1274754] : [class_Lattices_Osemilattice__sup(_1274748), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274748), _1274750), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274748), _1274752), _1274754)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274748), _1274752), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274748), _1274750), _1274754)))], (27700 ^ _779448) ^ [_1274891, _1274893, _1274895, _1274897] : [class_Lattices_Olattice(_1274891), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274891), _1274893), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274891), _1274895), _1274897)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274891), _1274895), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1274891), _1274893), _1274897)))], (27706 ^ _779448) ^ [_1275034, _1275036, _1275038, _1275040] : [class_Lattices_Osemilattice__sup(_1275034), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275034), _1275036), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275034), _1275038), _1275040)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275034), _1275038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275034), _1275036), _1275040)))], (27712 ^ _779448) ^ [_1275177, _1275179, _1275181] : [class_Lattices_Osemilattice__sup(_1275177), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275177), _1275179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275177), _1275179), _1275181)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275177), _1275179), _1275181))], (27718 ^ _779448) ^ [_1275302, _1275304, _1275306] : [class_Lattices_Olattice(_1275302), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275302), _1275304), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275302), _1275304), _1275306)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275302), _1275304), _1275306))], (27724 ^ _779448) ^ [_1275427, _1275429, _1275431] : [class_Lattices_Osemilattice__sup(_1275427), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275427), _1275429), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275427), _1275429), _1275431)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275427), _1275429), _1275431))], (27730 ^ _779448) ^ [_1275552, _1275554, _1275556] : [class_Lattices_Osemilattice__sup(_1275552), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275552), _1275554), _1275556) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275552), _1275556), _1275554))], (27736 ^ _779448) ^ [_1275661, _1275663, _1275665] : [class_Lattices_Olattice(_1275661), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275661), _1275663), _1275665) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275661), _1275665), _1275663))], (27742 ^ _779448) ^ [_1275770, _1275772, _1275774] : [class_Lattices_Osemilattice__sup(_1275770), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275770), _1275772), _1275774) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275770), _1275774), _1275772))], (27748 ^ _779448) ^ [_1275879, _1275881] : [class_Lattices_Osemilattice__sup(_1275879), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275879), _1275881), _1275881) = _1275881)], (27754 ^ _779448) ^ [_1275970, _1275972] : [class_Lattices_Osemilattice__sup(_1275970), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1275970), _1275972), _1275972) = _1275972)], (27760 ^ _779448) ^ [_1276061, _1276063, _1276065, _1276067] : [hBOOL(hAPP(_1276061, _1276063)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276065, tc_HOL_Obool)), _1276067), _1276061), _1276063)))], (27766 ^ _779448) ^ [_1276172, _1276174, _1276176, _1276178] : [hBOOL(hAPP(_1276172, _1276174)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276176, tc_HOL_Obool)), _1276172), _1276178), _1276174)))], (27791 ^ _779448) ^ [_1276726, _1276728, _1276730, _1276732] : [27795 ^ _779448 : [(27796 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276726), 27794 ^ [_1276726, _1276728, _1276730, _1276732]), _1276728)))], (27798 ^ _779448) ^ [] : [hBOOL(hAPP(_1276732, 27794 ^ [_1276726, _1276728, _1276730, _1276732]))]], 27800 ^ _779448 : [(27801 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276726), 27799 ^ [_1276726, _1276728, _1276730, _1276732]), _1276730)))], (27803 ^ _779448) ^ [] : [hBOOL(hAPP(_1276732, 27799 ^ [_1276726, _1276728, _1276730, _1276732]))]], 27804 ^ _779448 : [(27805 ^ _779448) ^ [_1277059] : [hBOOL(hAPP(hAPP(c_member(_1276726), _1277059), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276726, tc_HOL_Obool)), _1276728), _1276730))), -(hBOOL(hAPP(_1276732, _1277059)))]]], (27772 ^ _779448) ^ [_1276304, _1276306, _1276308, _1276310] : [27774 ^ _779448 : [(27775 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1276304), 27773 ^ [_1276304, _1276306, _1276308, _1276310]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276304, tc_HOL_Obool)), _1276306), _1276308))))], (27777 ^ _779448) ^ [] : [hBOOL(hAPP(_1276310, 27773 ^ [_1276304, _1276306, _1276308, _1276310]))]], 27778 ^ _779448 : [(27779 ^ _779448) ^ [_1276524] : [hBOOL(hAPP(hAPP(c_member(_1276304), _1276524), _1276306)), -(hBOOL(hAPP(_1276310, _1276524)))], (27785 ^ _779448) ^ [_1276621] : [hBOOL(hAPP(hAPP(c_member(_1276304), _1276621), _1276308)), -(hBOOL(hAPP(_1276310, _1276621)))]]], (27811 ^ _779448) ^ [_1277211, _1277213, _1277215, _1277217] : [27812 ^ _779448 : [(27813 ^ _779448) ^ [_1277321] : [hBOOL(hAPP(hAPP(c_member(_1277211), _1277321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277211, tc_HOL_Obool)), _1277213), _1277215))), hBOOL(hAPP(_1277217, _1277321))]], 27821 ^ _779448 : [(27822 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277211), 27820 ^ [_1277211, _1277213, _1277215, _1277217]), _1277213)))], (27824 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1277217, 27820 ^ [_1277211, _1277213, _1277215, _1277217])))]], 27826 ^ _779448 : [(27827 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277211), 27825 ^ [_1277211, _1277213, _1277215, _1277217]), _1277215)))], (27829 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1277217, 27825 ^ [_1277211, _1277213, _1277215, _1277217])))]]], (27831 ^ _779448) ^ [_1277610, _1277612, _1277614, _1277616] : [27845 ^ _779448 : [(27846 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1277610), 27844 ^ [_1277610, _1277612, _1277614, _1277616]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277610, tc_HOL_Obool)), _1277612), _1277614))))], (27848 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1277616, 27844 ^ [_1277610, _1277612, _1277614, _1277616])))]], 27832 ^ _779448 : [(27833 ^ _779448) ^ [_1277723] : [hBOOL(hAPP(hAPP(c_member(_1277610), _1277723), _1277612)), hBOOL(hAPP(_1277616, _1277723))], (27839 ^ _779448) ^ [_1277819] : [hBOOL(hAPP(hAPP(c_member(_1277610), _1277819), _1277614)), hBOOL(hAPP(_1277616, _1277819))]]], (27850 ^ _779448) ^ [_1278013, _1278015, _1278017, _1278019] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278013, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278013, tc_HOL_Obool)), _1278015), _1278017)), _1278019) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278013, tc_HOL_Obool)), _1278015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278013, tc_HOL_Obool)), _1278017), _1278019)))], (27852 ^ _779448) ^ [_1278086, _1278088, _1278090, _1278092] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278086, tc_HOL_Obool)), _1278088), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278086, tc_HOL_Obool)), _1278090), _1278092)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278086, tc_HOL_Obool)), _1278090), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278086, tc_HOL_Obool)), _1278088), _1278092)))], (27854 ^ _779448) ^ [_1278159, _1278161, _1278163] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278159, tc_HOL_Obool)), _1278161), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278159, tc_HOL_Obool)), _1278161), _1278163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278159, tc_HOL_Obool)), _1278161), _1278163))], (27856 ^ _779448) ^ [_1278219, _1278221, _1278223] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278219, tc_HOL_Obool)), _1278221), _1278223) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278219, tc_HOL_Obool)), _1278223), _1278221))], (27858 ^ _779448) ^ [_1278268, _1278270] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278268, tc_HOL_Obool)), _1278270), _1278270) = _1278270)], (27860 ^ _779448) ^ [_1278304, _1278306, _1278308, _1278310] : [class_Lattices_Osemilattice__sup(_1278304), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278304), _1278306), _1278308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278304), _1278306), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278304), _1278310), _1278308))))], (27870 ^ _779448) ^ [_1278483, _1278485, _1278487, _1278489] : [class_Lattices_Osemilattice__sup(_1278483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278483), _1278485), _1278487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278483), _1278485), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278483), _1278487), _1278489))))], (27880 ^ _779448) ^ [_1278662, _1278664] : [class_Lattices_Olattice(_1278662), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278662), _1278664), _1278664) = _1278664)], (27886 ^ _779448) ^ [_1278753, _1278755, _1278757, _1278759] : [class_Lattices_Osemilattice__sup(_1278753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278753), _1278755), _1278757)), _1278759)), 27893 ^ _779448 : [(27894 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278753), _1278755), _1278759)))], (27896 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278753), _1278757), _1278759)))]]], (27898 ^ _779448) ^ [_1278976, _1278978, _1278980, _1278982, _1278984] : [class_Lattices_Osemilattice__sup(_1278976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278976), _1278978), _1278980)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278976), _1278982), _1278984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278976), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278976), _1278978), _1278982)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278976), _1278980), _1278984))))], (27912 ^ _779448) ^ [_1279247, _1279249, _1279251, _1279253] : [class_Lattices_Osemilattice__sup(_1279247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279247), _1279249), _1279251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279247), _1279253), _1279251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279247), _1279249), _1279253)), _1279251)))], (27926 ^ _779448) ^ [_1279496, _1279498, _1279500, _1279502] : [class_Lattices_Osemilattice__sup(_1279496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279496), _1279498), _1279500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279496), _1279502), _1279500)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279496), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279496), _1279498), _1279502)), _1279500)))], (27940 ^ _779448) ^ [_1279745, _1279747, _1279749] : [class_Lattices_Osemilattice__sup(_1279745), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279745), _1279747), _1279749)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279745), _1279749), _1279747) = _1279749)], (27950 ^ _779448) ^ [_1279906, _1279908, _1279910] : [class_Lattices_Osemilattice__sup(_1279906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279906), _1279908), _1279910)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1279906), _1279908), _1279910) = _1279910)], (27960 ^ _779448) ^ [_1280067, _1280069, _1280071, _1280073] : [class_Lattices_Osemilattice__sup(_1280067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280067), _1280069), _1280071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280067), _1280069), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280067), _1280073), _1280071))))], (27970 ^ _779448) ^ [_1280246, _1280248, _1280250, _1280252] : [class_Lattices_Osemilattice__sup(_1280246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280246), _1280248), _1280250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280246), _1280248), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280246), _1280250), _1280252))))], (27980 ^ _779448) ^ [_1280425, _1280427, _1280429, _1280431] : [class_Lattices_Osemilattice__sup(_1280425), 27983 ^ _779448 : [(27984 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280425), _1280427), _1280429)), _1280431)), 27987 ^ _779448 : [(27988 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), _1280427), _1280431)))], (27990 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), _1280429), _1280431)))]]], (27992 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280425), _1280427), _1280429)), _1280431))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), _1280427), _1280431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280425), _1280429), _1280431))]]], (28002 ^ _779448) ^ [_1280805, _1280807, _1280809] : [class_Lattices_Osemilattice__sup(_1280805), 28005 ^ _779448 : [(28006 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280805), _1280807), _1280809)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280805), _1280807), _1280809) = _1280809)], (28012 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280805), _1280807), _1280809) = _1280809, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280805), _1280807), _1280809)))]]], (28018 ^ _779448) ^ [_1281061, _1281063, _1281065] : [class_Lattices_Osemilattice__sup(_1281061), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281061), _1281063), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281061), _1281065), _1281063))))], (28024 ^ _779448) ^ [_1281168, _1281170, _1281172] : [class_Lattices_Olattice(_1281168), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281168), _1281170), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281168), _1281172), _1281170))))], (28030 ^ _779448) ^ [_1281275, _1281277, _1281279] : [class_Lattices_Osemilattice__sup(_1281275), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281275), _1281277), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281275), _1281277), _1281279))))], (28036 ^ _779448) ^ [_1281382, _1281384, _1281386] : [class_Lattices_Olattice(_1281382), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281382), _1281384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1281382), _1281384), _1281386))))], (28042 ^ _779448) ^ [_1281489, _1281491, _1281493] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281489, tc_HOL_Obool)), _1281491), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281489, tc_HOL_Obool)), _1281491), _1281493))))], (28044 ^ _779448) ^ [_1281537, _1281539, _1281541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281537, tc_HOL_Obool)), _1281539), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281537, tc_HOL_Obool)), _1281541), _1281539))))], (28046 ^ _779448) ^ [_1281603, _1281605, _1281607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281603, tc_HOL_Obool)), _1281605), _1281607)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281603, tc_HOL_Obool)), _1281605), _1281607) = _1281607)], (28052 ^ _779448) ^ [_1281720, _1281722, _1281724] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281720, tc_HOL_Obool)), _1281722), _1281724) = _1281724, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281720, tc_HOL_Obool)), _1281722), _1281724)))], (28058 ^ _779448) ^ [_1281843, _1281845, _1281847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281843, tc_HOL_Obool)), _1281845), _1281847)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281843, tc_HOL_Obool)), _1281845), _1281847) = _1281847)], (28064 ^ _779448) ^ [_1281964, _1281966, _1281968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1281964, tc_HOL_Obool)), _1281966), _1281968)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281964, tc_HOL_Obool)), _1281968), _1281966) = _1281968)], (28070 ^ _779448) ^ [_1282085, _1282087, _1282089, _1282091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282085, tc_HOL_Obool)), _1282087), _1282089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282085, tc_HOL_Obool)), _1282091), _1282089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282085, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282085, tc_HOL_Obool)), _1282087), _1282091)), _1282089)))], (28080 ^ _779448) ^ [_1282304, _1282306, _1282308, _1282310, _1282312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282304, tc_HOL_Obool)), _1282306), _1282308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282304, tc_HOL_Obool)), _1282310), _1282312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282304, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282304, tc_HOL_Obool)), _1282306), _1282310)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282304, tc_HOL_Obool)), _1282308), _1282312))))], (28090 ^ _779448) ^ [_1282549, _1282551] : [class_Lattices_Obounded__lattice__bot(_1282549), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282549), c_Orderings_Obot__class_Obot(_1282549)), _1282551) = _1282551)], (28096 ^ _779448) ^ [_1282644, _1282646] : [class_Lattices_Obounded__lattice__bot(_1282644), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282644), _1282646), c_Orderings_Obot__class_Obot(_1282644)) = _1282646)], (28102 ^ _779448) ^ [_1282739, _1282741, _1282743] : [class_Lattices_Obounded__lattice__bot(_1282739), 28105 ^ _779448 : [(28106 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282739), _1282741), _1282743) = c_Orderings_Obot__class_Obot(_1282739), 28109 ^ _779448 : [(28110 ^ _779448) ^ [] : [-(_1282741 = c_Orderings_Obot__class_Obot(_1282739))], (28112 ^ _779448) ^ [] : [-(_1282743 = c_Orderings_Obot__class_Obot(_1282739))]]], (28114 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1282739), _1282741), _1282743) = c_Orderings_Obot__class_Obot(_1282739)), _1282741 = c_Orderings_Obot__class_Obot(_1282739), _1282743 = c_Orderings_Obot__class_Obot(_1282739)]]], (28124 ^ _779448) ^ [_1283066, _1283068, _1283070] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283066), _1283068)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283066), _1283070)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283066), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283066, tc_HOL_Obool)), _1283068), _1283070))))], (28134 ^ _779448) ^ [_1283263, _1283265, _1283267] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283263, tc_HOL_Obool)), _1283265), _1283267))), 28137 ^ _779448 : [(28138 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283263), _1283265)))], (28140 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283263), _1283267)))]]], (28142 ^ _779448) ^ [_1283410, _1283412, _1283414] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283410), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283410, tc_HOL_Obool)), _1283412), _1283414)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283410), _1283412)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283410), _1283414))], (28152 ^ _779448) ^ [_1283609, _1283611, _1283613] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283609, tc_HOL_Obool)), _1283611), _1283613) = c_Orderings_Obot__class_Obot(tc_fun(_1283609, tc_HOL_Obool)), 28155 ^ _779448 : [(28156 ^ _779448) ^ [] : [-(_1283611 = c_Orderings_Obot__class_Obot(tc_fun(_1283609, tc_HOL_Obool)))], (28158 ^ _779448) ^ [] : [-(_1283613 = c_Orderings_Obot__class_Obot(tc_fun(_1283609, tc_HOL_Obool)))]]], (28160 ^ _779448) ^ [_1283762, _1283764, _1283766] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283762, tc_HOL_Obool)), _1283764), _1283766) = c_Orderings_Obot__class_Obot(tc_fun(_1283762, tc_HOL_Obool))), _1283764 = c_Orderings_Obot__class_Obot(tc_fun(_1283762, tc_HOL_Obool)), _1283766 = c_Orderings_Obot__class_Obot(tc_fun(_1283762, tc_HOL_Obool))], (28170 ^ _779448) ^ [_1283949, _1283951] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283949, tc_HOL_Obool)), _1283951), c_Orderings_Obot__class_Obot(tc_fun(_1283949, tc_HOL_Obool))) = _1283951)], (28172 ^ _779448) ^ [_1283990, _1283992] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283990, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1283990, tc_HOL_Obool))), _1283992) = _1283992)], (28174 ^ _779448) ^ [_1284031] : [class_Lattices_Osemilattice__sup(_1284031), -(c_Finite__Set_Ofun__left__comm__idem(_1284031, _1284031, c_Lattices_Osemilattice__sup__class_Osup(_1284031)))], (28180 ^ _779448) ^ [_1284131, _1284133, _1284135, _1284137] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284131, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1284131, tc_fun(_1284131, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284131)), _1284133)), hAPP(hAPP(c_COMBC(_1284131, tc_fun(_1284131, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284131)), _1284135)), _1284137)), -(hBOOL(hAPP(hAPP(c_member(_1284131), _1284137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284131, tc_HOL_Obool)), _1284133), _1284135))))], (28186 ^ _779448) ^ [_1284330, _1284332, _1284334, _1284336] : [hBOOL(hAPP(hAPP(c_member(_1284330), _1284336), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284330, tc_HOL_Obool)), _1284332), _1284334))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284330, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1284330, tc_fun(_1284330, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284330)), _1284332)), hAPP(hAPP(c_COMBC(_1284330, tc_fun(_1284330, tc_HOL_Obool), tc_HOL_Obool), c_member(_1284330)), _1284334)), _1284336)))], (28192 ^ _779448) ^ [_1284535, _1284537, _1284539] : [-(hAPP(hAPP(c_Set_Oinsert(_1284535), _1284537), _1284539) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284535, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1284535), _1284537), c_Orderings_Obot__class_Obot(tc_fun(_1284535, tc_HOL_Obool)))), _1284539))], (28194 ^ _779448) ^ [_1284615, _1284617, _1284619, _1284621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284615, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284615, tc_HOL_Obool)), _1284617), _1284619)), _1284621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284615, tc_HOL_Obool)), _1284617), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284615, tc_HOL_Obool)), _1284619), _1284621))))], (28200 ^ _779448) ^ [_1284776, _1284778, _1284780, _1284782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284776, tc_HOL_Obool)), _1284778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284776, tc_HOL_Obool)), _1284780), _1284782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284776, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284776, tc_HOL_Obool)), _1284778), _1284780)), _1284782)))], (28206 ^ _779448) ^ [_1284943, _1284945, _1284947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284943, tc_HOL_Obool)), _1284945), _1284947)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284943, tc_HOL_Obool)), _1284945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284943, tc_HOL_Obool)), _1284947), _1284945)) = _1284947)], (28212 ^ _779448) ^ [_1285086, _1285088, _1285090, _1285092, _1285094] : [c_Fun_Oinj__on(_1285086, _1285088, _1285090, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285086, tc_HOL_Obool)), _1285092), _1285094)), 28215 ^ _779448 : [(28216 ^ _779448) ^ [] : [hAPP(c_Set_Oimage(_1285086, _1285088, _1285090), _1285092) = hAPP(c_Set_Oimage(_1285086, _1285088, _1285090), _1285094), -(_1285092 = _1285094)], (28222 ^ _779448) ^ [] : [_1285092 = _1285094, -(hAPP(c_Set_Oimage(_1285086, _1285088, _1285090), _1285092) = hAPP(c_Set_Oimage(_1285086, _1285088, _1285090), _1285094))]]], (28228 ^ _779448) ^ [_1285379, _1285381, _1285383] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285379, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1285379, tc_HOL_Obool)), _1285381), _1285383)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285379, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1285379, tc_HOL_Obool)), _1285381)), _1285383))], (28230 ^ _779448) ^ [_1285444, _1285446] : [-(c_FunDef_Orp__inv__image(_1285444, _1285446) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))))), tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))), tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)), tc_fun(tc_fun(_1285446, _1285444), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool)), c_COMBS(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)), tc_fun(tc_fun(_1285446, _1285444), tc_fun(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), tc_fun(tc_prod(_1285444, _1285444), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool))), tc_fun(_1285446, _1285444)), c_Product__Type_OPair(tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool), tc_fun(tc_prod(_1285446, _1285446), tc_HOL_Obool)))), c_Relation_Oinv__image(_1285444, _1285446))))), c_Relation_Oinv__image(_1285444, _1285446))))], (28232 ^ _779448) ^ [_1285957, _1285959, _1285961, _1285963, _1285965, _1285967, _1285969, _1285971] : [c_Finite__Set_Ofolding__image__simple__idem(_1285957, _1285959, _1285961, _1285963, _1285965, _1285967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285959), _1285969)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285959), _1285971)), -(hAPP(_1285967, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285959, tc_HOL_Obool)), _1285969), _1285971)) = hAPP(hAPP(_1285961, hAPP(_1285967, _1285969)), hAPP(_1285967, _1285971)))], (28246 ^ _779448) ^ [_1286250, _1286252, _1286254, _1286256] : [class_Lattices_Osemilattice__sup(_1286250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286250), _1286252)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1286250, _1286250, c_Lattices_Osemilattice__sup__class_Osup(_1286250)), _1286254), hAPP(hAPP(c_Set_Oinsert(_1286250), _1286256), _1286252)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1286250), _1286256), hAPP(hAPP(c_Finite__Set_Ofold(_1286250, _1286250, c_Lattices_Osemilattice__sup__class_Osup(_1286250)), _1286254), _1286252)))], (28256 ^ _779448) ^ [_1286473, _1286475, _1286477, _1286479, _1286481] : [c_Finite__Set_Ofolding__one__idem(_1286473, _1286475, _1286477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286473), _1286479)), -(_1286479 = c_Orderings_Obot__class_Obot(tc_fun(_1286473, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286473), _1286481)), -(_1286481 = c_Orderings_Obot__class_Obot(tc_fun(_1286473, tc_HOL_Obool))), -(hAPP(_1286477, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286473, tc_HOL_Obool)), _1286479), _1286481)) = hAPP(hAPP(_1286475, hAPP(_1286477, _1286479)), hAPP(_1286477, _1286481)))], (28278 ^ _779448) ^ [_1286838, _1286840, _1286842, _1286844, _1286846, _1286848] : [c_Finite__Set_Ofolding__idem(_1286838, _1286840, _1286842, _1286844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286838), _1286846)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286838), _1286848)), -(hAPP(_1286844, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286838, tc_HOL_Obool)), _1286846), _1286848)) = hAPP(c_Fun_Ocomp(_1286840, _1286840, _1286840, hAPP(_1286844, _1286846)), hAPP(_1286844, _1286848)))], (28292 ^ _779448) ^ [_1287119, _1287121, _1287123, _1287125] : [class_Lattices_Osemilattice__sup(_1287119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287119), _1287121)), hBOOL(hAPP(hAPP(c_member(_1287119), _1287123), _1287121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287119), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1287119), _1287123), _1287125)), hAPP(hAPP(c_Finite__Set_Ofold(_1287119, _1287119, c_Lattices_Osemilattice__sup__class_Osup(_1287119)), _1287125), _1287121))))], (28306 ^ _779448) ^ [_1287386, _1287388, _1287390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1287386), _1287388)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287386, tc_HOL_Obool)), _1287388), _1287390) = hAPP(hAPP(c_Finite__Set_Ofold(_1287386, tc_fun(_1287386, tc_HOL_Obool), c_Set_Oinsert(_1287386)), _1287390), _1287388))], (28312 ^ _779448) ^ [_1287525, _1287527, _1287529] : [class_Lattices_Oab__semigroup__idem__mult(_1287525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287525), _1287527)), -(_1287527 = c_Orderings_Obot__class_Obot(tc_fun(_1287525, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287525), _1287529)), -(_1287529 = c_Orderings_Obot__class_Obot(tc_fun(_1287525, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1287525, c_Groups_Otimes__class_Otimes(_1287525)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287525, tc_HOL_Obool)), _1287527), _1287529)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287525), hAPP(c_Finite__Set_Ofold1(_1287525, c_Groups_Otimes__class_Otimes(_1287525)), _1287527)), hAPP(c_Finite__Set_Ofold1(_1287525, c_Groups_Otimes__class_Otimes(_1287525)), _1287529)))], (28334 ^ _779448) ^ [_1287904, _1287906, _1287908] : [class_Orderings_Olinorder(_1287904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287904), _1287906)), -(_1287906 = c_Orderings_Obot__class_Obot(tc_fun(_1287904, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1287904), _1287908)), -(_1287908 = c_Orderings_Obot__class_Obot(tc_fun(_1287904, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1287904, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287904, tc_HOL_Obool)), _1287906), _1287908)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287904), c_Big__Operators_Olinorder__class_OMin(_1287904, _1287906)), c_Big__Operators_Olinorder__class_OMin(_1287904, _1287908)))], (28356 ^ _779448) ^ [_1288253, _1288255, _1288257] : [class_Orderings_Olinorder(_1288253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288253), _1288255)), -(_1288255 = c_Orderings_Obot__class_Obot(tc_fun(_1288253, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288253), _1288257)), -(_1288257 = c_Orderings_Obot__class_Obot(tc_fun(_1288253, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1288253, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288253, tc_HOL_Obool)), _1288255), _1288257)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288253), c_Big__Operators_Olinorder__class_OMax(_1288253, _1288255)), c_Big__Operators_Olinorder__class_OMax(_1288253, _1288257)))], (28378 ^ _779448) ^ [_1288602, _1288604, _1288606] : [class_Orderings_Olinorder(_1288602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288602), _1288604)), -(_1288604 = c_Orderings_Obot__class_Obot(tc_fun(_1288602, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288602), _1288606)), -(_1288606 = c_Orderings_Obot__class_Obot(tc_fun(_1288602, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1288602, c_Orderings_Oord__class_Omin(_1288602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288602, tc_HOL_Obool)), _1288604), _1288606)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288602), c_Big__Operators_Olattice_OInf__fin(_1288602, c_Orderings_Oord__class_Omin(_1288602), _1288604)), c_Big__Operators_Olattice_OInf__fin(_1288602, c_Orderings_Oord__class_Omin(_1288602), _1288606)))], (28400 ^ _779448) ^ [_1288969, _1288971, _1288973] : [class_Orderings_Olinorder(_1288969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288969), _1288971)), -(_1288971 = c_Orderings_Obot__class_Obot(tc_fun(_1288969, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288969), _1288973)), -(_1288973 = c_Orderings_Obot__class_Obot(tc_fun(_1288969, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1288969, c_Orderings_Oord__class_Omax(_1288969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288969, tc_HOL_Obool)), _1288971), _1288973)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288969), c_Big__Operators_Olattice_OSup__fin(_1288969, c_Orderings_Oord__class_Omax(_1288969), _1288971)), c_Big__Operators_Olattice_OSup__fin(_1288969, c_Orderings_Oord__class_Omax(_1288969), _1288973)))], (28422 ^ _779448) ^ [_1289336, _1289338, _1289340, _1289342] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1289336), _1289338)), -(hAPP(c_Set_Oimage(_1289336, _1289340, _1289342), _1289338) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1289340, tc_HOL_Obool), _1289336, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289340, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1289336, tc_fun(_1289340, tc_HOL_Obool), tc_fun(_1289340, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1289340, tc_fun(tc_fun(_1289340, tc_HOL_Obool), tc_fun(_1289340, tc_HOL_Obool)), _1289336), c_Set_Oinsert(_1289340)), _1289342)), c_Orderings_Obot__class_Obot(tc_fun(_1289340, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1289340, tc_HOL_Obool))), _1289338))], (28428 ^ _779448) ^ [] : [-(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)))))], (28430 ^ _779448) ^ [_1289620, _1289622, _1289624, _1289626, _1289628, _1289630] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1289620, _1289620)), hAPP(hAPP(c_Product__Type_OPair(_1289620, _1289620), _1289622), _1289624)), hAPP(hAPP(c_Relation_Oinv__image(_1289626, _1289620), _1289628), _1289630))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1289626, _1289626)), hAPP(hAPP(c_Product__Type_OPair(_1289626, _1289626), hAPP(_1289630, _1289622)), hAPP(_1289630, _1289624))), _1289628)))], (28436 ^ _779448) ^ [_1289807, _1289809, _1289811, _1289813, _1289815, _1289817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1289813, _1289813)), hAPP(hAPP(c_Product__Type_OPair(_1289813, _1289813), hAPP(_1289817, _1289809)), hAPP(_1289817, _1289811))), _1289815)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1289807, _1289807)), hAPP(hAPP(c_Product__Type_OPair(_1289807, _1289807), _1289809), _1289811)), hAPP(hAPP(c_Relation_Oinv__image(_1289813, _1289807), _1289815), _1289817))))], (28442 ^ _779448) ^ [_1290000, _1290002, _1290004] : [class_Orderings_Olinorder(_1290000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290000), _1290002), _1290004)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290000, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1290000, _1290002, _1290004)), hAPP(hAPP(c_Set_Oinsert(_1290000), _1290004), c_Orderings_Obot__class_Obot(tc_fun(_1290000, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1290000, _1290002, _1290004))], (28452 ^ _779448) ^ [_1290209, _1290211, _1290213] : [class_Lattices_Olattice(_1290209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290209), _1290211)), hBOOL(hAPP(hAPP(c_member(_1290209), _1290213), _1290211)), 28463 ^ _779448 : [(28464 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290209, tc_HOL_Obool)), _1290211), hAPP(hAPP(c_Set_Oinsert(_1290209), _1290213), c_Orderings_Obot__class_Obot(tc_fun(_1290209, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1290209, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1290209, _1290211) = _1290213)], (28470 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290209, tc_HOL_Obool)), _1290211), hAPP(hAPP(c_Set_Oinsert(_1290209), _1290213), c_Orderings_Obot__class_Obot(tc_fun(_1290209, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1290209, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1290209, _1290211) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290209), _1290213), c_Big__Operators_Olattice__class_OSup__fin(_1290209, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290209, tc_HOL_Obool)), _1290211), hAPP(hAPP(c_Set_Oinsert(_1290209), _1290213), c_Orderings_Obot__class_Obot(tc_fun(_1290209, tc_HOL_Obool)))))))]]], (28476 ^ _779448) ^ [_1290715, _1290717, _1290719] : [class_Orderings_Olinorder(_1290715), hAPP(_1290717, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290715), 28481 ^ [_1290715, _1290717, _1290719]), 28482 ^ [_1290715, _1290717, _1290719])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290715), hAPP(_1290717, 28481 ^ [_1290715, _1290717, _1290719])), hAPP(_1290717, 28482 ^ [_1290715, _1290717, _1290719])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290715), _1290719)), -(_1290719 = c_Orderings_Obot__class_Obot(tc_fun(_1290715, tc_HOL_Obool))), -(hAPP(_1290717, c_Big__Operators_Olinorder__class_OMax(_1290715, _1290719)) = c_Big__Operators_Olinorder__class_OMax(_1290715, hAPP(c_Set_Oimage(_1290715, _1290715, _1290717), _1290719)))], (28496 ^ _779448) ^ [_1291118, _1291120] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1291118, _1291120))))], (28498 ^ _779448) ^ [_1291149, _1291151] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1291149, _1291151))))], (28500 ^ _779448) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (28502 ^ _779448) ^ [_1291198, _1291200] : [c_Nat__Transfer_Onat__set(_1291198), c_Nat__Transfer_Onat__set(_1291200), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1291198), _1291200)))], (28512 ^ _779448) ^ [_1291333, _1291335] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1291333), _1291335) = 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)), _1291333)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1291335))))], (28514 ^ _779448) ^ [_1291379, _1291381] : [class_Lattices_Olattice(_1291379), -(c_Big__Operators_Olattice__class_OSup__fin(_1291379, hAPP(hAPP(c_Set_Oinsert(_1291379), _1291381), c_Orderings_Obot__class_Obot(tc_fun(_1291379, tc_HOL_Obool)))) = _1291381)], (28520 ^ _779448) ^ [_1291486, _1291488] : [c_Nat__Transfer_Onat__set(_1291486), c_Nat__Transfer_Onat__set(_1291488), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1291486), _1291488) = 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), _1291486)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1291488))))], (28530 ^ _779448) ^ [_1291653, _1291655, _1291657] : [class_Orderings_Oorder(_1291653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291653), _1291655), _1291657)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1291653, _1291657, _1291655) = c_Orderings_Obot__class_Obot(tc_fun(_1291653, tc_HOL_Obool)))], (28540 ^ _779448) ^ [_1291816, _1291818, _1291820] : [class_Orderings_Oorder(_1291816), 28543 ^ _779448 : [(28544 ^ _779448) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1291816, _1291818, _1291820) = c_Orderings_Obot__class_Obot(tc_fun(_1291816, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291816), _1291818), _1291820))], (28550 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291816), _1291818), _1291820))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1291816, _1291818, _1291820) = c_Orderings_Obot__class_Obot(tc_fun(_1291816, tc_HOL_Obool)))]]], (28556 ^ _779448) ^ [_1292035, _1292037, _1292039] : [class_Orderings_Oorder(_1292035), 28559 ^ _779448 : [(28560 ^ _779448) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1292035, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1292035, _1292037, _1292039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292035), _1292037), _1292039))], (28566 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292035), _1292037), _1292039))), -(c_Orderings_Obot__class_Obot(tc_fun(_1292035, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1292035, _1292037, _1292039))]]], (28572 ^ _779448) ^ [_1292254, _1292256, _1292258, _1292260] : [class_Orderings_Olinorder(_1292254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292254), _1292256), _1292258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292254), _1292258), _1292260)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292254, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292254, _1292256, _1292258)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292254, _1292258, _1292260)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1292254, _1292256, _1292260))], (28586 ^ _779448) ^ [_1292519, _1292521] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1292519, _1292521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1292521), _1292519))], (28588 ^ _779448) ^ [_1292584, _1292586, _1292588, _1292590, _1292592, _1292594] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292584, tc_fun(_1292586, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1292584, tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_fun(_1292586, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292586, tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_fun(_1292586, tc_HOL_Obool)), _1292584), c_COMBC(_1292586, tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292586, tc_prod(_1292584, _1292586)), tc_fun(_1292586, tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), _1292584), hAPP(c_COMBB(tc_prod(_1292584, _1292586), tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool), _1292586), c_member(tc_prod(_1292584, _1292586)))), c_Product__Type_OPair(_1292584, _1292586)))), _1292588)), hAPP(hAPP(c_COMBC(_1292584, tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_fun(_1292586, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292586, tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_fun(_1292586, tc_HOL_Obool)), _1292584), c_COMBC(_1292586, tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1292586, tc_prod(_1292584, _1292586)), tc_fun(_1292586, tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool)), _1292584), hAPP(c_COMBB(tc_prod(_1292584, _1292586), tc_fun(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool), tc_HOL_Obool), _1292586), c_member(tc_prod(_1292584, _1292586)))), c_Product__Type_OPair(_1292584, _1292586)))), _1292590)), _1292592), _1292594)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1292584, _1292586)), hAPP(hAPP(c_Product__Type_OPair(_1292584, _1292586), _1292592), _1292594)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1292584, _1292586), tc_HOL_Obool)), _1292588), _1292590))))], (28594 ^ _779448) ^ [_1293241, _1293243, _1293245, _1293247, _1293249, _1293251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293241, _1293243)), hAPP(hAPP(c_Product__Type_OPair(_1293241, _1293243), _1293249), _1293251)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool)), _1293245), _1293247))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293241, tc_fun(_1293243, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1293241, tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_fun(_1293243, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293243, tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_fun(_1293243, tc_HOL_Obool)), _1293241), c_COMBC(_1293243, tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293243, tc_prod(_1293241, _1293243)), tc_fun(_1293243, tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), _1293241), hAPP(c_COMBB(tc_prod(_1293241, _1293243), tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool), _1293243), c_member(tc_prod(_1293241, _1293243)))), c_Product__Type_OPair(_1293241, _1293243)))), _1293245)), hAPP(hAPP(c_COMBC(_1293241, tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_fun(_1293243, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293243, tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_fun(_1293243, tc_HOL_Obool)), _1293241), c_COMBC(_1293243, tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1293243, tc_prod(_1293241, _1293243)), tc_fun(_1293243, tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool)), _1293241), hAPP(c_COMBB(tc_prod(_1293241, _1293243), tc_fun(tc_fun(tc_prod(_1293241, _1293243), tc_HOL_Obool), tc_HOL_Obool), _1293243), c_member(tc_prod(_1293241, _1293243)))), c_Product__Type_OPair(_1293241, _1293243)))), _1293247)), _1293249), _1293251)))], (28600 ^ _779448) ^ [_1293904, _1293906, _1293908] : [class_Lattices_Olattice(_1293904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293904), _1293906)), hBOOL(hAPP(hAPP(c_member(_1293904), _1293908), _1293906)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293904), _1293908), c_Big__Operators_Olattice__class_OSup__fin(_1293904, _1293906)) = c_Big__Operators_Olattice__class_OSup__fin(_1293904, _1293906))], (28614 ^ _779448) ^ [_1294139, _1294141] : [class_Lattices_Olattice(_1294139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294139), _1294141)), -(c_Big__Operators_Olattice__class_OSup__fin(_1294139, _1294141) = hAPP(c_Finite__Set_Ofold1(_1294139, c_Lattices_Osemilattice__sup__class_Osup(_1294139)), _1294141))], (28624 ^ _779448) ^ [_1294296, _1294298, _1294300] : [class_Lattices_Olattice(_1294296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294296), _1294298)), -(_1294298 = c_Orderings_Obot__class_Obot(tc_fun(_1294296, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1294296, hAPP(hAPP(c_Set_Oinsert(_1294296), _1294300), _1294298)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294296), _1294300), c_Big__Operators_Olattice__class_OSup__fin(_1294296, _1294298)))], (28638 ^ _779448) ^ [_1294504, _1294506, _1294508] : [class_Lattices_Olattice(_1294504), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294504), _1294506)), -(_1294508 = c_Orderings_Obot__class_Obot(tc_fun(_1294504, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1294504, tc_HOL_Obool)), _1294508), _1294506)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294504), c_Big__Operators_Olattice__class_OSup__fin(_1294504, _1294508)), c_Big__Operators_Olattice__class_OSup__fin(_1294504, _1294506)) = c_Big__Operators_Olattice__class_OSup__fin(_1294504, _1294506))], (28656 ^ _779448) ^ [_1294818, _1294820] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1294818, _1294820)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1294820), _1294818)))], (28658 ^ _779448) ^ [_1294859, _1294861, _1294863] : [class_Lattices_Olattice(_1294859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294859), _1294861)), -(_1294861 = c_Orderings_Obot__class_Obot(tc_fun(_1294859, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294859), _1294863)), -(_1294863 = c_Orderings_Obot__class_Obot(tc_fun(_1294859, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1294859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1294859, tc_HOL_Obool)), _1294861), _1294863)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294859), c_Big__Operators_Olattice__class_OSup__fin(_1294859, _1294861)), c_Big__Operators_Olattice__class_OSup__fin(_1294859, _1294863)))], (28680 ^ _779448) ^ [_1295208, _1295210, _1295212] : [class_Lattices_Olattice(_1295208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295208), _1295210)), -(c_Big__Operators_Olattice__class_OSup__fin(_1295208, hAPP(hAPP(c_Set_Oinsert(_1295208), _1295212), _1295210)) = hAPP(hAPP(c_Finite__Set_Ofold(_1295208, _1295208, c_Lattices_Osemilattice__sup__class_Osup(_1295208)), _1295212), _1295210))], (28690 ^ _779448) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (28692 ^ _779448) ^ [_1295411, _1295413, _1295415, _1295417] : [class_Orderings_Olinorder(_1295411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295411), _1295413), _1295415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1295411), _1295415), _1295417)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295411, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1295411, _1295413, _1295415)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1295411, _1295415, _1295417)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1295411, _1295413, _1295417))], (28706 ^ _779448) ^ [_1295676] : [-(c_Wellfounded_Omeasure(_1295676) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1295676), c_Wellfounded_Oless__than))], (28708 ^ _779448) ^ [_1295707, _1295709, _1295711] : [class_Lattices_Olattice(_1295707), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295707), _1295709)), -(hBOOL(hAPP(hAPP(c_member(_1295707), _1295711), _1295709))), -(_1295709 = c_Orderings_Obot__class_Obot(tc_fun(_1295707, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1295707, hAPP(hAPP(c_Set_Oinsert(_1295707), _1295711), _1295709)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295707), _1295711), c_Big__Operators_Olattice__class_OSup__fin(_1295707, _1295709)))], (28726 ^ _779448) ^ [_1295944, _1295946, _1295948] : [class_Lattices_Olattice(_1295944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295944), _1295946)), 28733 ^ _779448 : [(28734 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295944, tc_HOL_Obool)), _1295946), hAPP(hAPP(c_Set_Oinsert(_1295944), _1295948), c_Orderings_Obot__class_Obot(tc_fun(_1295944, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1295944, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1295944, hAPP(hAPP(c_Set_Oinsert(_1295944), _1295948), _1295946)) = _1295948)], (28740 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295944, tc_HOL_Obool)), _1295946), hAPP(hAPP(c_Set_Oinsert(_1295944), _1295948), c_Orderings_Obot__class_Obot(tc_fun(_1295944, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1295944, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1295944, hAPP(hAPP(c_Set_Oinsert(_1295944), _1295948), _1295946)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295944), _1295948), c_Big__Operators_Olattice__class_OSup__fin(_1295944, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1295944, tc_HOL_Obool)), _1295946), hAPP(hAPP(c_Set_Oinsert(_1295944), _1295948), c_Orderings_Obot__class_Obot(tc_fun(_1295944, tc_HOL_Obool)))))))]]], (28746 ^ _779448) ^ [_1296414, _1296416, _1296418] : [class_Lattices_Olattice(_1296414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296414), _1296416)), -(hBOOL(hAPP(hAPP(c_member(_1296414), _1296418), _1296416))), -(c_Big__Operators_Olattice__class_OSup__fin(_1296414, hAPP(hAPP(c_Set_Oinsert(_1296414), _1296418), _1296416)) = hAPP(hAPP(c_Finite__Set_Ofold(_1296414, _1296414, c_Lattices_Osemilattice__sup__class_Osup(_1296414)), _1296418), _1296416))], (28760 ^ _779448) ^ [_1296628, _1296630, _1296632, _1296634, _1296636, _1296638] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool)), _1296630), _1296632)), c_Wellfounded_Omax__ext(_1296628, _1296634))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool)), _1296636), _1296638)), c_Wellfounded_Omax__ext(_1296628, _1296634))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1296628, tc_HOL_Obool), tc_fun(_1296628, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296628, tc_HOL_Obool)), _1296630), _1296636)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296628, tc_HOL_Obool)), _1296632), _1296638))), c_Wellfounded_Omax__ext(_1296628, _1296634))))], (28770 ^ _779448) ^ [_1297042, _1297044, _1297046, _1297048] : [c_Wellfounded_Omax__extp(_1297042, hAPP(hAPP(c_COMBC(_1297042, tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_fun(_1297042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297042, tc_fun(tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_fun(_1297042, tc_HOL_Obool)), _1297042), c_COMBC(_1297042, tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297042, tc_prod(_1297042, _1297042)), tc_fun(_1297042, tc_fun(tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_HOL_Obool)), _1297042), hAPP(c_COMBB(tc_prod(_1297042, _1297042), tc_fun(tc_fun(tc_prod(_1297042, _1297042), tc_HOL_Obool), tc_HOL_Obool), _1297042), c_member(tc_prod(_1297042, _1297042)))), c_Product__Type_OPair(_1297042, _1297042)))), _1297044), _1297046, _1297048), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1297042, tc_HOL_Obool), tc_fun(_1297042, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1297042, tc_HOL_Obool), tc_fun(_1297042, tc_HOL_Obool)), _1297046), _1297048)), c_Wellfounded_Omax__ext(_1297042, _1297044))))], (28776 ^ _779448) ^ [_1297427, _1297429, _1297431, _1297433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1297427, tc_HOL_Obool), tc_fun(_1297427, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1297427, tc_HOL_Obool), tc_fun(_1297427, tc_HOL_Obool)), _1297431), _1297433)), c_Wellfounded_Omax__ext(_1297427, _1297429))), -(c_Wellfounded_Omax__extp(_1297427, hAPP(hAPP(c_COMBC(_1297427, tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_fun(_1297427, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297427, tc_fun(tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_fun(_1297427, tc_HOL_Obool)), _1297427), c_COMBC(_1297427, tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1297427, tc_prod(_1297427, _1297427)), tc_fun(_1297427, tc_fun(tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_HOL_Obool)), _1297427), hAPP(c_COMBB(tc_prod(_1297427, _1297427), tc_fun(tc_fun(tc_prod(_1297427, _1297427), tc_HOL_Obool), tc_HOL_Obool), _1297427), c_member(tc_prod(_1297427, _1297427)))), c_Product__Type_OPair(_1297427, _1297427)))), _1297429), _1297431, _1297433))], (28782 ^ _779448) ^ [_1297833, _1297835] : [c_Relation_Oirrefl(_1297833, _1297835), 28785 ^ _779448 : [(28786 ^ _779448) ^ [_1297915] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1297833, _1297833)), hAPP(hAPP(c_Product__Type_OPair(_1297833, _1297833), _1297915), _1297915)), _1297835))]]], (28788 ^ _779448) ^ [_1297955, _1297957] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1297955, _1297955)), hAPP(hAPP(c_Product__Type_OPair(_1297955, _1297955), 28789 ^ [_1297955, _1297957]), 28789 ^ [_1297955, _1297957])), _1297957))), -(c_Relation_Oirrefl(_1297955, _1297957))], (28795 ^ _779448) ^ [_1298026, _1298028, _1298030, _1298032] : [-(hAPP(c_Relation_OField(_1298026), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1298026, _1298026)), hAPP(hAPP(c_Product__Type_OPair(_1298026, _1298026), _1298028), _1298030)), _1298032)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298026, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1298026), _1298028), hAPP(hAPP(c_Set_Oinsert(_1298026), _1298030), c_Orderings_Obot__class_Obot(tc_fun(_1298026, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1298026), _1298032)))], (28797 ^ _779448) ^ [_1298117, _1298119] : [class_Lattices_Olattice(_1298117), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298117), _1298119)), -(_1298119 = c_Orderings_Obot__class_Obot(tc_fun(_1298117, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1298117), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1298117), 28810 ^ [_1298117, _1298119]), 28811 ^ [_1298117, _1298119])), hAPP(hAPP(c_Set_Oinsert(_1298117), 28810 ^ [_1298117, _1298119]), hAPP(hAPP(c_Set_Oinsert(_1298117), 28811 ^ [_1298117, _1298119]), c_Orderings_Obot__class_Obot(tc_fun(_1298117, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1298117), c_Big__Operators_Olattice__class_OSup__fin(_1298117, _1298119)), _1298119)))], (28817 ^ _779448) ^ [_1298561, _1298563, _1298565, _1298567, _1298569, _1298571] : [28818 ^ _779448 : [(28819 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1298561, _1298563), _1298565))], (28821 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1298567, _1298563), _1298565))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298569, tc_fun(_1298571, tc_HOL_Obool))), _1298567), _1298561), _1298563), _1298565)))], (28825 ^ _779448) ^ [_1298744, _1298746, _1298748, _1298750, _1298752, _1298754] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298744, tc_fun(_1298746, tc_HOL_Obool))), _1298748), _1298750), _1298752), _1298754)), -(hBOOL(hAPP(hAPP(_1298748, _1298752), _1298754))), -(hBOOL(hAPP(hAPP(_1298750, _1298752), _1298754)))], (28835 ^ _779448) ^ [_1298902, _1298904, _1298906, _1298908, _1298910, _1298912] : [hBOOL(hAPP(hAPP(_1298902, _1298904), _1298906)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298908, tc_fun(_1298910, tc_HOL_Obool))), _1298912), _1298902), _1298904), _1298906)))], (28841 ^ _779448) ^ [_1299035, _1299037, _1299039, _1299041, _1299043, _1299045] : [hBOOL(hAPP(hAPP(_1299035, _1299037), _1299039)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299041, tc_fun(_1299043, tc_HOL_Obool))), _1299035), _1299045), _1299037), _1299039)))], (28847 ^ _779448) ^ [_1299168] : [-(hAPP(c_Relation_OField(_1299168), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1299168, _1299168), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1299168, tc_HOL_Obool)))], (28849 ^ _779448) ^ [_1299209, _1299211, _1299213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1299209, _1299209), tc_HOL_Obool)), _1299211), _1299213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1299209, tc_HOL_Obool)), hAPP(c_Relation_OField(_1299209), _1299211)), hAPP(c_Relation_OField(_1299209), _1299213))))], (28855 ^ _779448) ^ [_1299354, _1299356, _1299358] : [-(hAPP(c_Relation_OField(_1299354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1299354, _1299354), tc_HOL_Obool)), _1299356), _1299358)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299354, tc_HOL_Obool)), hAPP(c_Relation_OField(_1299354), _1299356)), hAPP(c_Relation_OField(_1299354), _1299358)))], (28857 ^ _779448) ^ [_1299421, _1299423] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1299421, _1299421)), _1299423)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1299421), hAPP(c_Relation_OField(_1299421), _1299423))))], (28863 ^ _779448) ^ [_1299530, _1299532, _1299534] : [class_Orderings_Olinorder(_1299530), hAPP(_1299532, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299530), 28868 ^ [_1299530, _1299532, _1299534]), 28869 ^ [_1299530, _1299532, _1299534])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299530), hAPP(_1299532, 28868 ^ [_1299530, _1299532, _1299534])), hAPP(_1299532, 28869 ^ [_1299530, _1299532, _1299534])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299530), _1299534)), -(_1299534 = c_Orderings_Obot__class_Obot(tc_fun(_1299530, tc_HOL_Obool))), -(hAPP(_1299532, c_Big__Operators_Olinorder__class_OMin(_1299530, _1299534)) = c_Big__Operators_Olinorder__class_OMin(_1299530, hAPP(c_Set_Oimage(_1299530, _1299530, _1299532), _1299534)))], (28883 ^ _779448) ^ [_1299933, _1299935, _1299937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299933)), 28889 ^ _779448 : [(28890 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1299935, 28888 ^ [_1299933, _1299935, _1299937])))], (28892 ^ _779448) ^ [] : [hBOOL(hAPP(_1299935, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28888 ^ [_1299933, _1299935, _1299937]), _1299933)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299937)), 28897 ^ _779448 : [(28898 ^ _779448) ^ [_1300222] : [hBOOL(hAPP(_1299935, _1300222)), -(hBOOL(hAPP(_1299935, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1300222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1299937), _1299933)))))]]], (28904 ^ _779448) ^ [_1300345, _1300347, _1300349] : [class_Lattices_Olattice(_1300345), hAPP(_1300347, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1300345), 28909 ^ [_1300345, _1300347, _1300349]), 28910 ^ [_1300345, _1300347, _1300349])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1300345), hAPP(_1300347, 28909 ^ [_1300345, _1300347, _1300349])), hAPP(_1300347, 28910 ^ [_1300345, _1300347, _1300349])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300345), _1300349)), -(_1300349 = c_Orderings_Obot__class_Obot(tc_fun(_1300345, tc_HOL_Obool))), -(hAPP(_1300347, c_Big__Operators_Olattice__class_OSup__fin(_1300345, _1300349)) = c_Big__Operators_Olattice__class_OSup__fin(_1300345, hAPP(c_Set_Oimage(_1300345, _1300345, _1300347), _1300349)))], (28924 ^ _779448) ^ [_1300748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1300748), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1300748 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28927 ^ [_1300748]))))], (28931 ^ _779448) ^ [_1300861, _1300863, _1300865, _1300867] : [class_Complete__Lattice_Ocomplete__lattice(_1300861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300863), _1300865)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1300863, _1300861), _1300865), _1300867) = hAPP(hAPP(c_Finite__Set_Ofold(_1300863, _1300861, hAPP(hAPP(c_COMBB(_1300861, tc_fun(_1300861, _1300861), _1300863), c_Lattices_Osemilattice__sup__class_Osup(_1300861)), _1300867)), c_Orderings_Obot__class_Obot(_1300861)), _1300865))], (28941 ^ _779448) ^ [_1301076, _1301078, _1301080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301076)), 28947 ^ _779448 : [(28948 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1301078, 28946 ^ [_1301076, _1301078, _1301080])))], (28950 ^ _779448) ^ [] : [hBOOL(hAPP(_1301078, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28946 ^ [_1301076, _1301078, _1301080]), _1301076)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301080)), 28955 ^ _779448 : [(28956 ^ _779448) ^ [_1301365] : [hBOOL(hAPP(_1301078, _1301365)), -(hBOOL(hAPP(_1301078, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1301365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1301080), _1301076)))))]]], (28962 ^ _779448) ^ [_1301488, _1301490, _1301492, _1301494, _1301496, _1301498, _1301500, _1301502] : [class_Groups_Ocomm__monoid__mult(_1301488), c_Fun_Oinj__on(_1301490, _1301492, _1301494, _1301496), _1301498 = hAPP(c_Set_Oimage(_1301490, _1301492, _1301494), _1301496), 28976 ^ _779448 : [(28977 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1301490), 28975 ^ [_1301488, _1301490, _1301492, _1301494, _1301496, _1301498, _1301500, _1301502]), _1301496)))], (28979 ^ _779448) ^ [] : [hAPP(_1301500, 28975 ^ [_1301488, _1301490, _1301492, _1301494, _1301496, _1301498, _1301500, _1301502]) = hAPP(hAPP(c_Fun_Ocomp(_1301492, _1301488, _1301490, _1301502), _1301494), 28975 ^ [_1301488, _1301490, _1301492, _1301494, _1301496, _1301498, _1301500, _1301502])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301492, _1301488), _1301502), _1301498) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301490, _1301488), _1301500), _1301496))], (28983 ^ _779448) ^ [_1301996, _1301998, _1302000, _1302002, _1302004] : [class_Groups_Ocomm__monoid__mult(_1301996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301998), _1302000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301998, tc_HOL_Obool)), _1302002), _1302000)), 28997 ^ _779448 : [(28998 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1301998), 28996 ^ [_1301996, _1301998, _1302000, _1302002, _1302004]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1301998, tc_HOL_Obool)), _1302000), _1302002))))], (29000 ^ _779448) ^ [] : [hAPP(_1302004, 28996 ^ [_1301996, _1301998, _1302000, _1302002, _1302004]) = c_Groups_Oone__class_Oone(_1301996)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301998, _1301996), _1302004), _1302000) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301998, _1301996), _1302004), _1302002))], (29004 ^ _779448) ^ [_1302447, _1302449, _1302451, _1302453, _1302455, _1302457] : [hBOOL(hAPP(hAPP(c_member(_1302447), _1302449), _1302451)), hBOOL(hAPP(hAPP(_1302453, _1302449), _1302455)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1302447, tc_fun(_1302457, tc_HOL_Obool)), _1302451), _1302453), _1302455)))], (29014 ^ _779448) ^ [_1302644, _1302646, _1302648, _1302650, _1302652, _1302654, _1302656, _1302658] : [hBOOL(hAPP(hAPP(c_member(_1302644), _1302646), _1302648)), hBOOL(hAPP(hAPP(hAPP(_1302650, _1302646), _1302652), _1302654)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1302644, tc_fun(_1302656, tc_fun(_1302658, tc_HOL_Obool))), _1302648), _1302650), _1302652), _1302654)))], (29024 ^ _779448) ^ [_1302867, _1302869, _1302871, _1302873] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302867), _1302869)), 29027 ^ _779448 : [(29038 ^ _779448) ^ [] : [29040 ^ _779448 : [(29041 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1302867), 29039 ^ [_1302867, _1302869, _1302871, _1302873]), _1302869)))], (29043 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302871), hAPP(_1302873, 29039 ^ [_1302867, _1302869, _1302871, _1302873])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1302871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1302867, tc_fun(_1302871, tc_HOL_Obool)), _1302869), _1302873))))], (29028 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302871), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1302867, tc_fun(_1302871, tc_HOL_Obool)), _1302869), _1302873))), 29031 ^ _779448 : [(29032 ^ _779448) ^ [_1303051] : [hBOOL(hAPP(hAPP(c_member(_1302867), _1303051), _1302869)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1302871), hAPP(_1302873, _1303051))))]]]]], (29047 ^ _779448) ^ [_1303342, _1303344, _1303346, _1303348, _1303350, _1303352] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303342, tc_fun(_1303344, tc_HOL_Obool)), _1303346), hAPP(c_Fun_Ocomp(_1303348, tc_fun(_1303344, tc_HOL_Obool), _1303342, _1303350), _1303352)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303348, tc_fun(_1303344, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1303342, _1303348, _1303352), _1303346)), _1303350))], (29049 ^ _779448) ^ [_1303417, _1303419, _1303421, _1303423, _1303425] : [class_Complete__Lattice_Ocomplete__lattice(_1303417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303419), _1303421)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1303417), _1303423), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303419, _1303417), _1303421), _1303425)) = hAPP(hAPP(c_Finite__Set_Ofold(_1303419, _1303417, hAPP(hAPP(c_COMBB(_1303417, tc_fun(_1303417, _1303417), _1303419), c_Lattices_Osemilattice__sup__class_Osup(_1303417)), _1303425)), _1303423), _1303421))], (29059 ^ _779448) ^ [_1303648, _1303650, _1303652, _1303654] : [-(hAPP(c_Set_Oimage(_1303648, _1303650, _1303652), _1303654) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303648, tc_fun(_1303650, tc_HOL_Obool)), _1303654), hAPP(hAPP(c_COMBC(_1303648, tc_fun(_1303650, tc_HOL_Obool), tc_fun(_1303650, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1303650, tc_fun(tc_fun(_1303650, tc_HOL_Obool), tc_fun(_1303650, tc_HOL_Obool)), _1303648), c_Set_Oinsert(_1303650)), _1303652)), c_Orderings_Obot__class_Obot(tc_fun(_1303650, tc_HOL_Obool)))))], (29061 ^ _779448) ^ [_1303738, _1303740, _1303742, _1303744, _1303746, _1303748] : [hBOOL(hAPP(hAPP(c_member(_1303738), _1303740), _1303742)), hBOOL(hAPP(hAPP(c_member(_1303744), _1303746), hAPP(_1303748, _1303740))), -(hBOOL(hAPP(hAPP(c_member(_1303744), _1303746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303738, tc_fun(_1303744, tc_HOL_Obool)), _1303742), _1303748))))], (29071 ^ _779448) ^ [_1303955, _1303957, _1303959, _1303961, _1303963] : [class_Complete__Lattice_Ocomplete__lattice(_1303955), hBOOL(hAPP(hAPP(c_member(_1303957), _1303959), _1303961)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303955), hAPP(_1303963, _1303959)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1303957, _1303955), _1303961), _1303963))))], (29081 ^ _779448) ^ [_1304146, _1304148, _1304150, _1304152, _1304154] : [class_Complete__Lattice_Ocomplete__lattice(_1304146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304148, tc_HOL_Obool)), _1304150), _1304152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304146), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304148, _1304146), _1304150), _1304154)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304148, _1304146), _1304152), _1304154))))], (29091 ^ _779448) ^ [_1304355, _1304357, _1304359, _1304361, _1304363, _1304365] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304355, tc_fun(_1304357, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304359, tc_fun(_1304355, tc_HOL_Obool)), _1304361), _1304363)), _1304365) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304359, tc_fun(_1304357, tc_HOL_Obool)), _1304361), hAPP(hAPP(c_COMBC(_1304359, tc_fun(_1304355, tc_fun(_1304357, tc_HOL_Obool)), tc_fun(_1304357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1304355, tc_HOL_Obool), tc_fun(tc_fun(_1304355, tc_fun(_1304357, tc_HOL_Obool)), tc_fun(_1304357, tc_HOL_Obool)), _1304359), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304355, tc_fun(_1304357, tc_HOL_Obool))), _1304363)), _1304365)))], (29093 ^ _779448) ^ [_1304474, _1304476, _1304478, _1304480, _1304482, _1304484] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304474, tc_fun(_1304476, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304478, tc_fun(_1304474, tc_HOL_Obool)), _1304480), _1304482)), _1304484) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304478, tc_fun(_1304476, tc_HOL_Obool)), _1304480), hAPP(hAPP(c_COMBC(_1304478, tc_fun(_1304474, tc_fun(_1304476, tc_HOL_Obool)), tc_fun(_1304476, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1304474, tc_HOL_Obool), tc_fun(tc_fun(_1304474, tc_fun(_1304476, tc_HOL_Obool)), tc_fun(_1304476, tc_HOL_Obool)), _1304478), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304474, tc_fun(_1304476, tc_HOL_Obool))), _1304482)), _1304484)))], (29095 ^ _779448) ^ [_1304593, _1304595, _1304597, _1304599, _1304601, _1304603] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304593, tc_fun(_1304595, tc_HOL_Obool)), _1304597), hAPP(hAPP(c_COMBC(_1304593, tc_fun(_1304599, tc_fun(_1304595, tc_HOL_Obool)), tc_fun(_1304595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1304599, tc_HOL_Obool), tc_fun(tc_fun(_1304599, tc_fun(_1304595, tc_HOL_Obool)), tc_fun(_1304595, tc_HOL_Obool)), _1304593), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304599, tc_fun(_1304595, tc_HOL_Obool))), _1304601)), _1304603)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304599, tc_fun(_1304595, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304593, tc_fun(_1304599, tc_HOL_Obool)), _1304597), _1304601)), _1304603))], (29097 ^ _779448) ^ [_1304736, _1304738, _1304740, _1304742, _1304744] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304736, tc_fun(_1304738, tc_HOL_Obool)), _1304740), _1304742), _1304744)), 29101 ^ _779448 : [(29102 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304736), 29100 ^ [_1304736, _1304738, _1304740, _1304742, _1304744]), _1304740)))], (29104 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1304742, 29100 ^ [_1304736, _1304738, _1304740, _1304742, _1304744]), _1304744)))]]], (29106 ^ _779448) ^ [_1304924, _1304926, _1304928, _1304930, _1304932] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1304924, tc_fun(_1304926, tc_HOL_Obool)), _1304928), _1304930), _1304932))), 29107 ^ _779448 : [(29108 ^ _779448) ^ [_1304996] : [hBOOL(hAPP(hAPP(c_member(_1304924), _1304996), _1304928)), hBOOL(hAPP(hAPP(_1304930, _1304996), _1304932))]]], (29116 ^ _779448) ^ [_1305178, _1305180, _1305182, _1305184, _1305186, _1305188, _1305190] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305178, tc_fun(_1305180, tc_fun(_1305182, tc_HOL_Obool))), _1305184), _1305186), _1305188), _1305190)), 29120 ^ _779448 : [(29121 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305178), 29119 ^ [_1305178, _1305180, _1305182, _1305184, _1305186, _1305188, _1305190]), _1305184)))], (29123 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1305186, 29119 ^ [_1305178, _1305180, _1305182, _1305184, _1305186, _1305188, _1305190]), _1305188), _1305190)))]]], (29125 ^ _779448) ^ [_1305396, _1305398, _1305400, _1305402, _1305404, _1305406, _1305408] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305396, tc_fun(_1305398, tc_fun(_1305400, tc_HOL_Obool))), _1305402), _1305404), _1305406), _1305408))), 29126 ^ _779448 : [(29127 ^ _779448) ^ [_1305481] : [hBOOL(hAPP(hAPP(c_member(_1305396), _1305481), _1305402)), hBOOL(hAPP(hAPP(hAPP(_1305404, _1305481), _1305406), _1305408))]]], (29152 ^ _779448) ^ [_1306109, _1306111, _1306113, _1306115, _1306117] : [29154 ^ _779448 : [(29155 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1306111), 29153 ^ [_1306109, _1306111, _1306113, _1306115, _1306117]), _1306113)))], (29158 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1306109), 29156 ^ [_1306109, _1306111, _1306113, _1306115, _1306117]), hAPP(_1306115, 29153 ^ [_1306109, _1306111, _1306113, _1306115, _1306117]))))], (29160 ^ _779448) ^ [] : [hBOOL(hAPP(_1306117, 29156 ^ [_1306109, _1306111, _1306113, _1306115, _1306117]))]], 29161 ^ _779448 : [(29162 ^ _779448) ^ [_1306419] : [hBOOL(hAPP(hAPP(c_member(_1306109), _1306419), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1306111, tc_fun(_1306109, tc_HOL_Obool)), _1306113), _1306115))), -(hBOOL(hAPP(_1306117, _1306419)))]]], (29135 ^ _779448) ^ [_1305673, _1305675, _1305677, _1305679, _1305681] : [29137 ^ _779448 : [(29138 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305673), 29136 ^ [_1305673, _1305675, _1305677, _1305679, _1305681]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1305675, tc_fun(_1305673, tc_HOL_Obool)), _1305677), _1305679))))], (29140 ^ _779448) ^ [] : [hBOOL(hAPP(_1305681, 29136 ^ [_1305673, _1305675, _1305677, _1305679, _1305681]))]], 29141 ^ _779448 : [(29142 ^ _779448) ^ [_1305895] : [hBOOL(hAPP(hAPP(c_member(_1305675), _1305895), _1305677)), 29145 ^ _779448 : [(29146 ^ _779448) ^ [_1305992] : [hBOOL(hAPP(hAPP(c_member(_1305673), _1305992), hAPP(_1305679, _1305895))), -(hBOOL(hAPP(_1305681, _1305992)))]]]]], (29168 ^ _779448) ^ [_1306578, _1306580, _1306582, _1306584, _1306586] : [hBOOL(hAPP(hAPP(c_member(_1306578), _1306580), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1306582, tc_fun(_1306578, tc_HOL_Obool)), _1306584), _1306586))), 29172 ^ _779448 : [(29173 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1306582), 29171 ^ [_1306578, _1306580, _1306582, _1306584, _1306586]), _1306584)))], (29175 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1306578), _1306580), hAPP(_1306586, 29171 ^ [_1306578, _1306580, _1306582, _1306584, _1306586]))))]]], (29177 ^ _779448) ^ [_1306786, _1306788, _1306790, _1306792, _1306794] : [-(hBOOL(hAPP(hAPP(c_member(_1306786), _1306788), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1306790, tc_fun(_1306786, tc_HOL_Obool)), _1306792), _1306794)))), 29178 ^ _779448 : [(29179 ^ _779448) ^ [_1306868] : [hBOOL(hAPP(hAPP(c_member(_1306790), _1306868), _1306792)), hBOOL(hAPP(hAPP(c_member(_1306786), _1306788), hAPP(_1306794, _1306868)))]]], (29197 ^ _779448) ^ [_1307285, _1307287, _1307289, _1307291] : [29199 ^ _779448 : [(29200 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1307285), 29198 ^ [_1307285, _1307287, _1307289, _1307291]), _1307289)))], (29202 ^ _779448) ^ [] : [hAPP(_1307291, 29198 ^ [_1307285, _1307287, _1307289, _1307291]) = c_Orderings_Obot__class_Obot(tc_fun(_1307287, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307285, tc_fun(_1307287, tc_HOL_Obool)), _1307289), _1307291) = c_Orderings_Obot__class_Obot(tc_fun(_1307287, tc_HOL_Obool)))], (29187 ^ _779448) ^ [_1307056, _1307058, _1307060, _1307062] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307056, tc_fun(_1307058, tc_HOL_Obool)), _1307060), _1307062) = c_Orderings_Obot__class_Obot(tc_fun(_1307058, tc_HOL_Obool)), 29190 ^ _779448 : [(29191 ^ _779448) ^ [_1307172] : [hBOOL(hAPP(hAPP(c_member(_1307056), _1307172), _1307060)), -(hAPP(_1307062, _1307172) = c_Orderings_Obot__class_Obot(tc_fun(_1307058, tc_HOL_Obool)))]]], (29206 ^ _779448) ^ [_1307530, _1307532, _1307534, _1307536] : [_1307530 = c_Orderings_Obot__class_Obot(tc_fun(_1307532, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307532, tc_fun(_1307534, tc_HOL_Obool)), _1307530), hAPP(c_COMBK(tc_fun(_1307534, tc_HOL_Obool), _1307532), _1307536)) = c_Orderings_Obot__class_Obot(tc_fun(_1307534, tc_HOL_Obool)))], (29212 ^ _779448) ^ [_1307667, _1307669, _1307671, _1307673] : [-(_1307667 = c_Orderings_Obot__class_Obot(tc_fun(_1307669, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307669, tc_fun(_1307671, tc_HOL_Obool)), _1307667), hAPP(c_COMBK(tc_fun(_1307671, tc_HOL_Obool), _1307669), _1307673)) = _1307673)], (29218 ^ _779448) ^ [_1307735, _1307737, _1307739] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307735, tc_fun(_1307737, tc_HOL_Obool)), _1307739), hAPP(c_COMBK(tc_fun(_1307737, tc_HOL_Obool), _1307735), c_Orderings_Obot__class_Obot(tc_fun(_1307737, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307737, tc_HOL_Obool)))], (29230 ^ _779448) ^ [_1308043, _1308045, _1308047, _1308049] : [29232 ^ _779448 : [(29233 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1308045), 29231 ^ [_1308043, _1308045, _1308047, _1308049]), _1308047)))], (29235 ^ _779448) ^ [] : [hAPP(_1308049, 29231 ^ [_1308043, _1308045, _1308047, _1308049]) = c_Orderings_Obot__class_Obot(tc_fun(_1308043, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1308043, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308045, tc_fun(_1308043, tc_HOL_Obool)), _1308047), _1308049))], (29220 ^ _779448) ^ [_1307814, _1307816, _1307818, _1307820] : [c_Orderings_Obot__class_Obot(tc_fun(_1307814, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1307816, tc_fun(_1307814, tc_HOL_Obool)), _1307818), _1307820), 29223 ^ _779448 : [(29224 ^ _779448) ^ [_1307930] : [hBOOL(hAPP(hAPP(c_member(_1307816), _1307930), _1307818)), -(hAPP(_1307820, _1307930) = c_Orderings_Obot__class_Obot(tc_fun(_1307814, tc_HOL_Obool)))]]], (29249 ^ _779448) ^ [_1308555, _1308557, _1308559, _1308561, _1308563] : [29251 ^ _779448 : [(29252 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1308557), 29250 ^ [_1308555, _1308557, _1308559, _1308561, _1308563]), _1308559)))], (29254 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308555, tc_HOL_Obool)), hAPP(_1308561, 29250 ^ [_1308555, _1308557, _1308559, _1308561, _1308563])), _1308563))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308555, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308557, tc_fun(_1308555, tc_HOL_Obool)), _1308559), _1308561)), _1308563)))], (29239 ^ _779448) ^ [_1308297, _1308299, _1308301, _1308303, _1308305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308297, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308299, tc_fun(_1308297, tc_HOL_Obool)), _1308301), _1308303)), _1308305)), 29242 ^ _779448 : [(29243 ^ _779448) ^ [_1308430] : [hBOOL(hAPP(hAPP(c_member(_1308299), _1308430), _1308301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1308297, tc_HOL_Obool)), hAPP(_1308303, _1308430)), _1308305)))]]], (29258 ^ _779448) ^ [_1308818, _1308820, _1308822, _1308824, _1308826, _1308828] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308818, tc_fun(_1308820, tc_HOL_Obool)), _1308822), hAPP(hAPP(c_COMBB(_1308824, tc_fun(_1308820, tc_HOL_Obool), _1308818), _1308826), _1308828)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308824, tc_fun(_1308820, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1308818, _1308824, _1308828), _1308822)), _1308826))], (29260 ^ _779448) ^ [_1308895, _1308897, _1308899, _1308901, _1308903, _1308905] : [-(hAPP(c_Set_Oimage(_1308895, _1308897, _1308899), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308901, tc_fun(_1308895, tc_HOL_Obool)), _1308903), _1308905)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308901, tc_fun(_1308897, tc_HOL_Obool)), _1308903), hAPP(hAPP(c_COMBB(tc_fun(_1308895, tc_HOL_Obool), tc_fun(_1308897, tc_HOL_Obool), _1308901), c_Set_Oimage(_1308895, _1308897, _1308899)), _1308905)))], (29262 ^ _779448) ^ [_1308979, _1308981, _1308983, _1308985, _1308987, _1308989] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308979, tc_fun(_1308981, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1308983, _1308979, _1308985), _1308987)), _1308989) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1308983, tc_fun(_1308981, tc_HOL_Obool)), _1308987), hAPP(hAPP(c_COMBB(_1308979, tc_fun(_1308981, tc_HOL_Obool), _1308983), _1308989), _1308985)))], (29264 ^ _779448) ^ [_1309056, _1309058, _1309060, _1309062, _1309064] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309056, tc_fun(_1309058, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309056, tc_HOL_Obool)), _1309060), _1309062)), _1309064) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309058, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309056, tc_fun(_1309058, tc_HOL_Obool)), _1309060), _1309064)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309056, tc_fun(_1309058, tc_HOL_Obool)), _1309062), _1309064)))], (29266 ^ _779448) ^ [_1309145, _1309147, _1309149, _1309151, _1309153] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309145, tc_fun(_1309147, tc_HOL_Obool)), _1309149), hAPP(hAPP(c_COMBS(_1309145, tc_fun(_1309147, tc_HOL_Obool), tc_fun(_1309147, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309147, tc_HOL_Obool), tc_fun(tc_fun(_1309147, tc_HOL_Obool), tc_fun(_1309147, tc_HOL_Obool)), _1309145), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309147, tc_HOL_Obool))), _1309151)), _1309153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309147, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309145, tc_fun(_1309147, tc_HOL_Obool)), _1309149), _1309151)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309145, tc_fun(_1309147, tc_HOL_Obool)), _1309149), _1309153)))], (29268 ^ _779448) ^ [_1309266, _1309268, _1309270, _1309272, _1309274, _1309276] : [class_Complete__Lattice_Ocomplete__lattice(_1309266), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309268, _1309266), _1309270), hAPP(hAPP(c_COMBB(tc_fun(_1309272, _1309266), _1309266, _1309268), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309272, _1309266), _1309274)), _1309276)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309272, _1309266), _1309274), hAPP(hAPP(c_COMBB(tc_fun(_1309268, _1309266), _1309266, _1309272), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309268, _1309266), _1309270)), hAPP(c_COMBC(_1309268, _1309272, _1309266), _1309276))))], (29274 ^ _779448) ^ [_1309475, _1309477, _1309479, _1309481, _1309483, _1309485] : [class_Complete__Lattice_Ocomplete__lattice(_1309475), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309477, tc_fun(_1309479, _1309475)), _1309481), _1309483), _1309485) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309477, _1309475), _1309481), hAPP(hAPP(c_COMBC(_1309477, _1309479, _1309475), _1309483), _1309485)))], (29280 ^ _779448) ^ [_1309626, _1309628, _1309630, _1309632, _1309634] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309626, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309628, tc_fun(_1309626, tc_HOL_Obool)), _1309630), _1309632)), _1309634) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309628, tc_fun(_1309626, tc_HOL_Obool)), _1309630), hAPP(hAPP(c_COMBC(_1309628, tc_fun(_1309626, tc_HOL_Obool), tc_fun(_1309626, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309626, tc_HOL_Obool), tc_fun(tc_fun(_1309626, tc_HOL_Obool), tc_fun(_1309626, tc_HOL_Obool)), _1309628), c_Groups_Ominus__class_Ominus(tc_fun(_1309626, tc_HOL_Obool))), _1309632)), _1309634)))], (29282 ^ _779448) ^ [_1309735, _1309737, _1309739, _1309741, _1309743] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309735, tc_fun(_1309737, tc_HOL_Obool)), _1309739), hAPP(hAPP(c_COMBC(_1309735, tc_fun(_1309737, tc_HOL_Obool), tc_fun(_1309737, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1309737, tc_HOL_Obool), tc_fun(tc_fun(_1309737, tc_HOL_Obool), tc_fun(_1309737, tc_HOL_Obool)), _1309735), c_Groups_Ominus__class_Ominus(tc_fun(_1309737, tc_HOL_Obool))), _1309741)), _1309743)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309737, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309735, tc_fun(_1309737, tc_HOL_Obool)), _1309739), _1309741)), _1309743))], (29284 ^ _779448) ^ [_1309844, _1309846, _1309848, _1309850, _1309852, _1309854] : [hBOOL(hAPP(hAPP(c_member(_1309844), _1309846), _1309848)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309844, tc_fun(_1309850, tc_HOL_Obool)), _1309848), hAPP(hAPP(c_COMBB(tc_fun(_1309850, tc_HOL_Obool), tc_fun(_1309850, tc_HOL_Obool), _1309844), hAPP(c_Set_Oinsert(_1309850), _1309852)), _1309854)) = hAPP(hAPP(c_Set_Oinsert(_1309850), _1309852), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1309844, tc_fun(_1309850, tc_HOL_Obool)), _1309848), _1309854)))], (29290 ^ _779448) ^ [_1310049, _1310051, _1310053, _1310055, _1310057] : [hBOOL(hAPP(hAPP(c_member(_1310049), _1310051), _1310053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1310055, tc_HOL_Obool)), hAPP(_1310057, _1310051)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310049, tc_fun(_1310055, tc_HOL_Obool)), _1310053), _1310057))))], (29296 ^ _779448) ^ [_1310196, _1310198, _1310200, _1310202, _1310204] : [hBOOL(hAPP(hAPP(c_member(_1310196), _1310198), _1310200)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310202, tc_HOL_Obool)), hAPP(_1310204, _1310198)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310196, tc_fun(_1310202, tc_HOL_Obool)), _1310200), _1310204)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310196, tc_fun(_1310202, tc_HOL_Obool)), _1310200), _1310204))], (29302 ^ _779448) ^ [_1310387, _1310389, _1310391, _1310393, _1310395] : [_1310387 = c_Orderings_Obot__class_Obot(tc_fun(_1310389, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310389, tc_fun(_1310391, tc_HOL_Obool)), _1310387), hAPP(hAPP(c_COMBB(tc_fun(_1310391, tc_HOL_Obool), tc_fun(_1310391, tc_HOL_Obool), _1310389), hAPP(c_Set_Oinsert(_1310391), _1310393)), _1310395)) = c_Orderings_Obot__class_Obot(tc_fun(_1310391, tc_HOL_Obool)))], (29308 ^ _779448) ^ [_1310550, _1310552, _1310554, _1310556, _1310558] : [-(_1310550 = c_Orderings_Obot__class_Obot(tc_fun(_1310552, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310552, tc_fun(_1310554, tc_HOL_Obool)), _1310550), hAPP(hAPP(c_COMBB(tc_fun(_1310554, tc_HOL_Obool), tc_fun(_1310554, tc_HOL_Obool), _1310552), hAPP(c_Set_Oinsert(_1310554), _1310556)), _1310558)) = hAPP(hAPP(c_Set_Oinsert(_1310554), _1310556), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310552, tc_fun(_1310554, tc_HOL_Obool)), _1310550), _1310558)))], (29314 ^ _779448) ^ [_1310652, _1310654] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310652, tc_fun(_1310652, tc_HOL_Obool)), _1310654), hAPP(hAPP(c_COMBC(_1310652, tc_fun(_1310652, tc_HOL_Obool), tc_fun(_1310652, tc_HOL_Obool)), c_Set_Oinsert(_1310652)), c_Orderings_Obot__class_Obot(tc_fun(_1310652, tc_HOL_Obool)))) = _1310654)], (29316 ^ _779448) ^ [_1310730, _1310732, _1310734, _1310736, _1310738] : [_1310730 = c_Orderings_Obot__class_Obot(tc_fun(_1310732, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1310734), _1310736), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310732, tc_fun(_1310734, tc_HOL_Obool)), _1310730), _1310738)) = hAPP(hAPP(c_Set_Oinsert(_1310734), _1310736), c_Orderings_Obot__class_Obot(tc_fun(_1310734, tc_HOL_Obool))))], (29322 ^ _779448) ^ [_1310883, _1310885, _1310887, _1310889, _1310891] : [-(_1310883 = c_Orderings_Obot__class_Obot(tc_fun(_1310885, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1310887), _1310889), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310885, tc_fun(_1310887, tc_HOL_Obool)), _1310883), _1310891)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310885, tc_fun(_1310887, tc_HOL_Obool)), _1310883), hAPP(hAPP(c_COMBB(tc_fun(_1310887, tc_HOL_Obool), tc_fun(_1310887, tc_HOL_Obool), _1310885), hAPP(c_Set_Oinsert(_1310887), _1310889)), _1310891)))], (29328 ^ _779448) ^ [_1310985, _1310987, _1310989, _1310991, _1310993] : [class_Complete__Lattice_Ocomplete__lattice(_1310985), 29331 ^ _779448 : [(29342 ^ _779448) ^ [] : [29344 ^ _779448 : [(29345 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1310987), 29343 ^ [_1310985, _1310987, _1310989, _1310991, _1310993]), _1310989)))], (29347 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310985), hAPP(_1310991, 29343 ^ [_1310985, _1310987, _1310989, _1310991, _1310993])), _1310993))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310985), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310987, _1310985), _1310989), _1310991)), _1310993)))], (29332 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310985), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1310987, _1310985), _1310989), _1310991)), _1310993)), 29335 ^ _779448 : [(29336 ^ _779448) ^ [_1311166] : [hBOOL(hAPP(hAPP(c_member(_1310987), _1311166), _1310989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310985), hAPP(_1310991, _1311166)), _1310993)))]]]]], (29351 ^ _779448) ^ [_1311479, _1311481, _1311483, _1311485, _1311487] : [class_Complete__Lattice_Ocomplete__lattice(_1311479), class_Orderings_Olinorder(_1311479), 29358 ^ _779448 : [(29359 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311479), _1311481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1311483, _1311479), _1311485), _1311487))), 29363 ^ _779448 : [(29364 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1311483), 29362 ^ [_1311479, _1311481, _1311483, _1311485, _1311487]), _1311485)))], (29366 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311479), _1311481), hAPP(_1311487, 29362 ^ [_1311479, _1311481, _1311483, _1311485, _1311487]))))]]], (29368 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311479), _1311481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1311483, _1311479), _1311485), _1311487)))), 29369 ^ _779448 : [(29370 ^ _779448) ^ [_1311827] : [hBOOL(hAPP(hAPP(c_member(_1311483), _1311827), _1311485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1311479), _1311481), hAPP(_1311487, _1311827)))]]]]], (29378 ^ _779448) ^ [_1312015, _1312017, _1312019, _1312021, _1312023] : [_1312015 = c_Orderings_Obot__class_Obot(tc_fun(_1312017, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312019, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312017, tc_fun(_1312019, tc_HOL_Obool)), _1312015), _1312021)), _1312023) = _1312023)], (29384 ^ _779448) ^ [_1312148, _1312150, _1312152, _1312154, _1312156] : [-(_1312148 = c_Orderings_Obot__class_Obot(tc_fun(_1312150, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312152, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312150, tc_fun(_1312152, tc_HOL_Obool)), _1312148), _1312154)), _1312156) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312150, tc_fun(_1312152, tc_HOL_Obool)), _1312148), hAPP(hAPP(c_COMBC(_1312150, tc_fun(_1312152, tc_HOL_Obool), tc_fun(_1312152, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312152, tc_HOL_Obool), tc_fun(tc_fun(_1312152, tc_HOL_Obool), tc_fun(_1312152, tc_HOL_Obool)), _1312150), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312152, tc_HOL_Obool))), _1312154)), _1312156)))], (29390 ^ _779448) ^ [_1312293, _1312295, _1312297, _1312299, _1312301] : [_1312293 = c_Orderings_Obot__class_Obot(tc_fun(_1312295, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312297, tc_HOL_Obool)), _1312299), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312295, tc_fun(_1312297, tc_HOL_Obool)), _1312293), _1312301)) = _1312299)], (29396 ^ _779448) ^ [_1312426, _1312428, _1312430, _1312432, _1312434] : [-(_1312426 = c_Orderings_Obot__class_Obot(tc_fun(_1312428, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312430, tc_HOL_Obool)), _1312432), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312428, tc_fun(_1312430, tc_HOL_Obool)), _1312426), _1312434)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312428, tc_fun(_1312430, tc_HOL_Obool)), _1312426), hAPP(hAPP(c_COMBB(tc_fun(_1312430, tc_HOL_Obool), tc_fun(_1312430, tc_HOL_Obool), _1312428), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312430, tc_HOL_Obool)), _1312432)), _1312434)))], (29402 ^ _779448) ^ [_1312552, _1312554, _1312556, _1312558, _1312560] : [_1312552 = c_Orderings_Obot__class_Obot(tc_fun(_1312554, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312554, tc_fun(_1312556, tc_HOL_Obool)), _1312552), hAPP(hAPP(c_COMBC(_1312554, tc_fun(_1312556, tc_HOL_Obool), tc_fun(_1312556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312556, tc_HOL_Obool), tc_fun(tc_fun(_1312556, tc_HOL_Obool), tc_fun(_1312556, tc_HOL_Obool)), _1312554), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312556, tc_HOL_Obool))), _1312558)), _1312560)) = c_Orderings_Obot__class_Obot(tc_fun(_1312556, tc_HOL_Obool)))], (29408 ^ _779448) ^ [_1312759, _1312761, _1312763, _1312765, _1312767] : [-(_1312759 = c_Orderings_Obot__class_Obot(tc_fun(_1312761, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312761, tc_fun(_1312763, tc_HOL_Obool)), _1312759), hAPP(hAPP(c_COMBC(_1312761, tc_fun(_1312763, tc_HOL_Obool), tc_fun(_1312763, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312763, tc_HOL_Obool), tc_fun(tc_fun(_1312763, tc_HOL_Obool), tc_fun(_1312763, tc_HOL_Obool)), _1312761), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312763, tc_HOL_Obool))), _1312765)), _1312767)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312763, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312761, tc_fun(_1312763, tc_HOL_Obool)), _1312759), _1312765)), _1312767))], (29414 ^ _779448) ^ [_1312904, _1312906, _1312908, _1312910, _1312912] : [_1312904 = c_Orderings_Obot__class_Obot(tc_fun(_1312906, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1312906, tc_fun(_1312908, tc_HOL_Obool)), _1312904), hAPP(hAPP(c_COMBB(tc_fun(_1312908, tc_HOL_Obool), tc_fun(_1312908, tc_HOL_Obool), _1312906), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1312908, tc_HOL_Obool)), _1312910)), _1312912)) = c_Orderings_Obot__class_Obot(tc_fun(_1312908, tc_HOL_Obool)))], (29420 ^ _779448) ^ [_1313073, _1313075, _1313077, _1313079, _1313081] : [-(_1313073 = c_Orderings_Obot__class_Obot(tc_fun(_1313075, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1313075, tc_fun(_1313077, tc_HOL_Obool)), _1313073), hAPP(hAPP(c_COMBB(tc_fun(_1313077, tc_HOL_Obool), tc_fun(_1313077, tc_HOL_Obool), _1313075), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313077, tc_HOL_Obool)), _1313079)), _1313081)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313077, tc_HOL_Obool)), _1313079), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1313075, tc_fun(_1313077, tc_HOL_Obool)), _1313073), _1313081)))], (29426 ^ _779448) ^ [_1313181, _1313183, _1313185, _1313187, _1313189] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1313181, tc_fun(_1313183, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1313181), _1313185), _1313187)), _1313189) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313183, tc_HOL_Obool)), hAPP(_1313189, _1313185)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1313181, tc_fun(_1313183, tc_HOL_Obool)), _1313187), _1313189)))], (29428 ^ _779448) ^ [_1313258, _1313260, _1313262, _1313264] : [class_Complete__Lattice_Ocomplete__lattice(_1313258), -(_1313260 = c_Orderings_Obot__class_Obot(tc_fun(_1313262, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1313262, _1313258), _1313260), hAPP(c_COMBK(_1313258, _1313262), _1313264)) = _1313264)], (29438 ^ _779448) ^ [_1313392] : [-(hAPP(c_Int_Onat, _1313392) = 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, _1313392)), 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)))))))], (29440 ^ _779448) ^ [_1313430, _1313432, _1313434, _1313436, _1313438] : [class_Groups_Ocomm__monoid__mult(_1313430), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313432), _1313434)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313432, tc_HOL_Obool)), _1313436), _1313434)), 29454 ^ _779448 : [(29455 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1313432), 29453 ^ [_1313430, _1313432, _1313434, _1313436, _1313438]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313432, tc_HOL_Obool)), _1313434), _1313436))))], (29457 ^ _779448) ^ [] : [hAPP(_1313438, 29453 ^ [_1313430, _1313432, _1313434, _1313436, _1313438]) = c_Groups_Oone__class_Oone(_1313430)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1313432, _1313430), _1313438), _1313436) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1313432, _1313430), _1313438), _1313434))], (29461 ^ _779448) ^ [_1313881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313881)), 29465 ^ _779448 : [(29466 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29464 ^ [_1313881])))], (29468 ^ _779448) ^ [] : [-(_1313881 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 29464 ^ [_1313881]))]]], (29470 ^ _779448) ^ [_1314011, _1314013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1314011), _1314013)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1314011, tc_HOL_Obool)), hAPP(c_Set_OPow(_1314011), _1314013)) = 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(_1314011), _1314013)))], (29476 ^ _779448) ^ [_1314138, _1314140, _1314142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1314138, tc_HOL_Obool)), _1314140), _1314142)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1314138, tc_HOL_Obool)), _1314140), hAPP(c_Set_OPow(_1314138), _1314142))))], (29482 ^ _779448) ^ [_1314267] : [-(hAPP(c_Set_OPow(_1314267), c_Orderings_Obot__class_Obot(tc_fun(_1314267, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1314267, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1314267, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314267, tc_HOL_Obool), tc_HOL_Obool))))], (29484 ^ _779448) ^ [_1314324, _1314326] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1314324, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1314324, tc_HOL_Obool))), hAPP(c_Set_OPow(_1314324), _1314326))))], (29486 ^ _779448) ^ [_1314369, _1314371] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1314369, tc_HOL_Obool)), _1314371), hAPP(c_Set_OPow(_1314369), _1314371))))], (29488 ^ _779448) ^ [_1314424, _1314426] : [hAPP(c_Int_ORep__Integ, _1314424) = hAPP(c_Int_ORep__Integ, _1314426), -(_1314424 = _1314426)], (29494 ^ _779448) ^ [_1314509, _1314511] : [_1314509 = _1314511, -(hAPP(c_Int_ORep__Integ, _1314509) = hAPP(c_Int_ORep__Integ, _1314511))], (29500 ^ _779448) ^ [_1314616, _1314618, _1314620] : [hAPP(c_Set_Oimage(_1314618, tc_fun(_1314618, tc_HOL_Obool), _1314616), _1314620) = hAPP(c_Set_OPow(_1314618), _1314620)], (29502 ^ _779448) ^ [_1314670, _1314672] : [hAPP(c_Set_OPow(_1314670), _1314672) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1314670, tc_HOL_Obool), tc_HOL_Obool))], (29504 ^ _779448) ^ [_1314723, _1314725] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1314723, tc_HOL_Obool)), hAPP(c_Set_OPow(_1314723), _1314725))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1314723), _1314725)))], (29510 ^ _779448) ^ [_1314828, _1314830] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1314828), _1314830)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1314828, tc_HOL_Obool)), hAPP(c_Set_OPow(_1314828), _1314830))))], (29516 ^ _779448) ^ [_1314939, _1314941, _1314943] : [-(hAPP(c_Set_OPow(_1314939), hAPP(hAPP(c_Set_Oinsert(_1314939), _1314941), _1314943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1314939, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1314939), _1314943)), hAPP(c_Set_Oimage(tc_fun(_1314939, tc_HOL_Obool), tc_fun(_1314939, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1314939), _1314941)), hAPP(c_Set_OPow(_1314939), _1314943))))], (29518 ^ _779448) ^ [_1315039, _1315041, _1315043] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1315039, tc_HOL_Obool)), _1315041), hAPP(c_Set_OPow(_1315039), _1315043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315039, tc_HOL_Obool)), _1315041), _1315043)))], (29524 ^ _779448) ^ [_1315164, _1315166, _1315168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315164, tc_HOL_Obool)), _1315166), _1315168)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1315164, tc_HOL_Obool)), _1315166), hAPP(c_Set_OPow(_1315164), _1315168))))], (29530 ^ _779448) ^ [_1315295, _1315297, _1315299] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1315295, tc_HOL_Obool)), _1315297), hAPP(c_Set_OPow(_1315295), _1315299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315295, tc_HOL_Obool)), _1315297), _1315299)))], (29536 ^ _779448) ^ [_1315424, _1315426, _1315428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315424, tc_HOL_Obool)), _1315426), _1315428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1315424, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1315424), _1315426)), hAPP(c_Set_OPow(_1315424), _1315428))))], (29542 ^ _779448) ^ [_1315569, _1315571, _1315573, _1315575, _1315577] : [hAPP(c_Set_Oimage(_1315569, _1315571, _1315573), _1315575) = _1315577, -(hAPP(c_Set_Oimage(tc_fun(_1315569, tc_HOL_Obool), tc_fun(_1315571, tc_HOL_Obool), c_Set_Oimage(_1315569, _1315571, _1315573)), hAPP(c_Set_OPow(_1315569), _1315575)) = hAPP(c_Set_OPow(_1315571), _1315577))], (29548 ^ _779448) ^ [_1315720, _1315722, _1315724] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1315720, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1315720, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1315720), _1315722)), hAPP(c_Set_OPow(_1315720), _1315724))), hAPP(c_Set_OPow(_1315720), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315720, tc_HOL_Obool)), _1315722), _1315724)))))], (29550 ^ _779448) ^ [_1315800, _1315802, _1315804, _1315806] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1315800, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1315802, tc_fun(tc_fun(_1315800, tc_HOL_Obool), tc_HOL_Obool)), _1315804), hAPP(hAPP(c_COMBB(tc_fun(_1315800, tc_HOL_Obool), tc_fun(tc_fun(_1315800, tc_HOL_Obool), tc_HOL_Obool), _1315802), c_Set_OPow(_1315800)), _1315806))), hAPP(c_Set_OPow(_1315800), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1315802, tc_fun(_1315800, tc_HOL_Obool)), _1315804), _1315806)))))], (29552 ^ _779448) ^ [_1315895, _1315897, _1315899, _1315901, _1315903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315895, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1315897, _1315895, _1315899), _1315901)), _1315903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1315895, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1315897, tc_HOL_Obool), tc_fun(_1315895, tc_HOL_Obool), c_Set_Oimage(_1315897, _1315895, _1315899)), hAPP(c_Set_OPow(_1315897), _1315901))), hAPP(c_Set_OPow(_1315895), _1315903))))], (29558 ^ _779448) ^ [_1316110, _1316112, _1316114] : [hBOOL(hAPP(c_Predicate_OPowp(_1316110, hAPP(hAPP(c_COMBC(_1316110, tc_fun(_1316110, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316110)), _1316112)), _1316114)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1316110, tc_HOL_Obool)), _1316114), hAPP(c_Set_OPow(_1316110), _1316112))))], (29564 ^ _779448) ^ [_1316255, _1316257, _1316259] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1316255, tc_HOL_Obool)), _1316259), hAPP(c_Set_OPow(_1316255), _1316257))), -(hBOOL(hAPP(c_Predicate_OPowp(_1316255, hAPP(hAPP(c_COMBC(_1316255, tc_fun(_1316255, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316255)), _1316257)), _1316259)))], (29570 ^ _779448) ^ [_1316406, _1316408, _1316410, _1316412] : [class_Orderings_Olinorder(_1316406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316406), _1316408), _1316410)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316406), _1316410), _1316412)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316406, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1316406, _1316408, _1316410)), c_SetInterval_Oord__class_OatLeastAtMost(_1316406, _1316410, _1316412)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1316406, _1316408, _1316412))], (29584 ^ _779448) ^ [_1316686, _1316688] : [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)), _1316686), 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)), _1316688), 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)), _1316686), _1316688)), c_Int_Ointrel)))], (29590 ^ _779448) ^ [_1316817, _1316819] : [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)), _1316817), _1316819)), 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)), _1316817), 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)), _1316819), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (29596 ^ _779448) ^ [_1316954, _1316956, _1316958] : [class_Orderings_Olinorder(_1316954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1316954), _1316956), _1316958)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316954, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1316954), _1316956), c_Orderings_Obot__class_Obot(tc_fun(_1316954, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1316954, _1316956, _1316958)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1316954, _1316956), _1316958))], (29606 ^ _779448) ^ [_1317167, _1317169] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1317167), _1317169))))], (29608 ^ _779448) ^ [_1317200, _1317202] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317200, _1317202))))], (29610 ^ _779448) ^ [_1317231, _1317233] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1317231, _1317233))))], (29612 ^ _779448) ^ [_1317262, _1317264] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1317262), _1317264))))], (29614 ^ _779448) ^ [_1317295, _1317297, _1317299, _1317301, _1317303] : [-(hAPP(c_Relation_OImage(_1317295, _1317297, _1317299), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317295, tc_HOL_Obool)), _1317301), _1317303)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317297, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1317295, _1317297, _1317299), _1317301)), hAPP(c_Relation_OImage(_1317295, _1317297, _1317299), _1317303)))], (29616 ^ _779448) ^ [_1317369, _1317371, _1317373, _1317375] : [class_Orderings_Olinorder(_1317369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317369), _1317371), _1317373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317369), _1317373), _1317375)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317369, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317369, _1317371), _1317373)), c_SetInterval_Oord__class_OatLeastAtMost(_1317369, _1317373, _1317375)) = c_SetInterval_Oord__class_OatLeastAtMost(_1317369, _1317371, _1317375))], (29630 ^ _779448) ^ [_1317638, _1317640] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317638, _1317640)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1317638), hAPP(c_Nat_OSuc, _1317640)))], (29632 ^ _779448) ^ [_1317680, _1317682] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1317680), _1317682)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1317680)), hAPP(c_Nat_OSuc, _1317682)))], (29634 ^ _779448) ^ [_1317726, _1317728] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1317726), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1317728), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1317726, _1317728))], (29636 ^ _779448) ^ [_1317767, _1317769] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1317767), hAPP(c_Nat_OSuc, _1317769)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317767, _1317769))], (29638 ^ _779448) ^ [_1317805, _1317807, _1317809, _1317811, _1317813] : [class_Orderings_Olinorder(_1317805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317805), _1317807), _1317809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1317805), _1317811), _1317813)), 29649 ^ _779448 : [(29650 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317805, _1317807), _1317809) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317805, _1317811), _1317813), 29653 ^ _779448 : [(29654 ^ _779448) ^ [] : [-(_1317807 = _1317811)], (29656 ^ _779448) ^ [] : [-(_1317809 = _1317813)]]], (29658 ^ _779448) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317805, _1317807), _1317809) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317805, _1317811), _1317813)), _1317807 = _1317811, _1317809 = _1317813]]], (29668 ^ _779448) ^ [_1318286, _1318288, _1318290, _1318292, _1318294] : [class_Orderings_Olinorder(_1318286), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1318286, _1318288), _1318290) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1318286, _1318292), _1318294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318286), _1318288), _1318290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318286), _1318292), _1318294)), -(_1318288 = _1318292)], (29686 ^ _779448) ^ [_1318593, _1318595, _1318597, _1318599, _1318601] : [class_Orderings_Olinorder(_1318593), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1318593, _1318595), _1318597) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1318593, _1318599), _1318601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318593), _1318595), _1318597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318593), _1318599), _1318601)), -(_1318597 = _1318601)], (29704 ^ _779448) ^ [_1318900, _1318902, _1318904] : [-(hAPP(c_Relation_OImage(_1318900, _1318902, _1318904), c_Orderings_Obot__class_Obot(tc_fun(_1318900, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1318902, tc_HOL_Obool)))], (29706 ^ _779448) ^ [_1318944, _1318946, _1318948] : [-(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)), _1318944)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1318946), _1318948)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1318946), _1318944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1318948), _1318944)))], (29708 ^ _779448) ^ [_1319005, _1319007, _1319009] : [-(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)), _1319005)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1319007, _1319009)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1319007), _1319005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1319009), _1319005)))], (29710 ^ _779448) ^ [_1319062, _1319064] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1319062, _1319064) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1319062), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1319064))))], (29712 ^ _779448) ^ [_1319104, _1319106, _1319108, _1319110, _1319112, _1319114] : [-(hAPP(c_Relation_OImage(_1319104, _1319106, _1319108), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1319110, tc_fun(_1319104, tc_HOL_Obool)), _1319112), _1319114)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1319110, tc_fun(_1319106, tc_HOL_Obool)), _1319112), hAPP(hAPP(c_COMBB(tc_fun(_1319104, tc_HOL_Obool), tc_fun(_1319106, tc_HOL_Obool), _1319110), c_Relation_OImage(_1319104, _1319106, _1319108)), _1319114)))], (29714 ^ _779448) ^ [_1319188, _1319190] : [c_Nat__Transfer_Ois__nat(_1319188), c_Nat__Transfer_Ois__nat(_1319190), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1319188, _1319190) = 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, _1319188), hAPP(c_Int_Onat, _1319190))))], (29724 ^ _779448) ^ [_1319347] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1319347), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29726 ^ _779448) ^ [_1319376, _1319378, _1319380] : [class_Orderings_Olinorder(_1319376), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319376), _1319378), _1319380)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319376, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1319376, _1319378), _1319380)), hAPP(hAPP(c_Set_Oinsert(_1319376), _1319380), c_Orderings_Obot__class_Obot(tc_fun(_1319376, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1319376, _1319378, _1319380))], (29736 ^ _779448) ^ [_1319589, _1319591] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1319589), _1319591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1319591), _1319589))], (29738 ^ _779448) ^ [_1319629, _1319631, _1319633, _1319635, _1319637, _1319639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1319629, _1319631), tc_HOL_Obool)), _1319633), _1319635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319629, tc_HOL_Obool)), _1319637), _1319639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319631, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1319629, _1319631, _1319633), _1319637)), hAPP(c_Relation_OImage(_1319629, _1319631, _1319635), _1319639))))], (29748 ^ _779448) ^ [_1319868, _1319870, _1319872, _1319874, _1319876] : [-(hAPP(c_Relation_OImage(_1319868, _1319870, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1319868, _1319870), tc_HOL_Obool)), _1319872), _1319874)), _1319876) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319870, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1319868, _1319870, _1319872), _1319876)), hAPP(c_Relation_OImage(_1319868, _1319870, _1319874), _1319876)))], (29750 ^ _779448) ^ [_1319945, _1319947] : [c_Nat__Transfer_Ois__nat(_1319945), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1319945, _1319947)))], (29756 ^ _779448) ^ [_1320026, _1320028, _1320030, _1320032] : [class_Orderings_Olinorder(_1320026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320026), _1320028), _1320030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320026), _1320030), _1320032)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320026, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1320026, _1320028, _1320030)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1320026, _1320030, _1320032)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1320026, _1320028), _1320032))], (29770 ^ _779448) ^ [_1320295, _1320297, _1320299] : [class_Orderings_Oorder(_1320295), 29773 ^ _779448 : [(29774 ^ _779448) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1320295, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1320295, _1320297, _1320299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320295), _1320297), _1320299))], (29780 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320295), _1320297), _1320299))), -(c_Orderings_Obot__class_Obot(tc_fun(_1320295, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1320295, _1320297, _1320299))]]], (29786 ^ _779448) ^ [_1320514, _1320516, _1320518] : [class_Orderings_Oorder(_1320514), 29789 ^ _779448 : [(29790 ^ _779448) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1320514, _1320516, _1320518) = c_Orderings_Obot__class_Obot(tc_fun(_1320514, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320514), _1320516), _1320518))], (29796 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320514), _1320516), _1320518))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1320514, _1320516, _1320518) = c_Orderings_Obot__class_Obot(tc_fun(_1320514, tc_HOL_Obool)))]]], (29802 ^ _779448) ^ [_1320733, _1320735, _1320737] : [class_Orderings_Oorder(_1320733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1320733), _1320735), _1320737)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1320733, _1320737, _1320735) = c_Orderings_Obot__class_Obot(tc_fun(_1320733, tc_HOL_Obool)))], (29812 ^ _779448) ^ [_1320896, _1320898, _1320900, _1320902, _1320904] : [class_Orderings_Oorder(_1320896), 29815 ^ _779448 : [(29816 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320896, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1320896, _1320898, _1320900)), c_SetInterval_Oord__class_OatLeastAtMost(_1320896, _1320902, _1320904))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320898), _1320900)), 29823 ^ _779448 : [(29824 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320902), _1320898)))], (29826 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320900), _1320904)))]]], (29828 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320896, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1320896, _1320898, _1320900)), c_SetInterval_Oord__class_OatLeastAtMost(_1320896, _1320902, _1320904)))), 29829 ^ _779448 : [(29830 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320898), _1320900)))], (29832 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320902), _1320898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320896), _1320900), _1320904))]]]]], (29840 ^ _779448) ^ [_1321399, _1321401, _1321403] : [class_Orderings_Oorder(_1321399), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321399), _1321401), _1321403)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321399, _1321403), _1321401) = c_Orderings_Obot__class_Obot(tc_fun(_1321399, tc_HOL_Obool)))], (29850 ^ _779448) ^ [_1321566, _1321568, _1321570] : [class_Orderings_Oorder(_1321566), 29853 ^ _779448 : [(29854 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321566, _1321568), _1321570) = c_Orderings_Obot__class_Obot(tc_fun(_1321566, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321566), _1321568), _1321570))], (29860 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321566), _1321568), _1321570))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321566, _1321568), _1321570) = c_Orderings_Obot__class_Obot(tc_fun(_1321566, tc_HOL_Obool)))]]], (29866 ^ _779448) ^ [_1321791, _1321793, _1321795] : [class_Orderings_Oorder(_1321791), 29869 ^ _779448 : [(29870 ^ _779448) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1321791, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321791, _1321793), _1321795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321791), _1321793), _1321795))], (29876 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321791), _1321793), _1321795))), -(c_Orderings_Obot__class_Obot(tc_fun(_1321791, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321791, _1321793), _1321795))]]], (29882 ^ _779448) ^ [_1322016, _1322018] : [class_Orderings_Oorder(_1322016), -(c_SetInterval_Oord__class_OatLeastAtMost(_1322016, _1322018, _1322018) = hAPP(hAPP(c_Set_Oinsert(_1322016), _1322018), c_Orderings_Obot__class_Obot(tc_fun(_1322016, tc_HOL_Obool))))], (29888 ^ _779448) ^ [_1322125, _1322127, _1322129, _1322131] : [class_Orderings_Oorder(_1322125), 29891 ^ _779448 : [(29892 ^ _779448) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1322125, _1322127, _1322129) = hAPP(hAPP(c_Set_Oinsert(_1322125), _1322131), c_Orderings_Obot__class_Obot(tc_fun(_1322125, tc_HOL_Obool))), 29895 ^ _779448 : [(29896 ^ _779448) ^ [] : [-(_1322127 = _1322129)], (29898 ^ _779448) ^ [] : [-(_1322129 = _1322131)]]], (29900 ^ _779448) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1322125, _1322127, _1322129) = hAPP(hAPP(c_Set_Oinsert(_1322125), _1322131), c_Orderings_Obot__class_Obot(tc_fun(_1322125, tc_HOL_Obool)))), _1322127 = _1322129, _1322129 = _1322131]]], (29910 ^ _779448) ^ [_1322469, _1322471, _1322473] : [class_Orderings_Oorder(_1322469), _1322471 = _1322473, -(c_SetInterval_Oord__class_OatLeastAtMost(_1322469, _1322471, _1322473) = hAPP(hAPP(c_Set_Oinsert(_1322469), _1322471), c_Orderings_Obot__class_Obot(tc_fun(_1322469, tc_HOL_Obool))))], (29920 ^ _779448) ^ [_1322634, _1322636, _1322638, _1322640, _1322642] : [class_Orderings_Olinorder(_1322634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322634, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322634, _1322636), _1322638)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322634, _1322640), _1322642))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322634), _1322638), _1322636))), 29931 ^ _779448 : [(29932 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322634), _1322640), _1322636)))], (29934 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322634), _1322638), _1322642)))]]], (29936 ^ _779448) ^ [_1322915, _1322917, _1322919, _1322921] : [class_Orderings_Olinorder(_1322915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322915), _1322917), _1322919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322915), _1322919), _1322921)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322915, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322915, _1322917), _1322919)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322915, _1322919), _1322921)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1322915, _1322917), _1322921))], (29950 ^ _779448) ^ [_1323192, _1323194, _1323196] : [class_Groups_Oordered__ab__group__add(_1323192), -(hAPP(c_Set_Oimage(_1323192, _1323192, c_Groups_Ouminus__class_Ouminus(_1323192)), c_SetInterval_Oord__class_OatLeastAtMost(_1323192, _1323194, _1323196)) = c_SetInterval_Oord__class_OatLeastAtMost(_1323192, hAPP(c_Groups_Ouminus__class_Ouminus(_1323192), _1323196), hAPP(c_Groups_Ouminus__class_Ouminus(_1323192), _1323194)))], (29956 ^ _779448) ^ [_1323323, _1323325, _1323327, _1323329] : [class_Orderings_Olinorder(_1323323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323323), _1323325), _1323327)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323323, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1323323, _1323325), _1323329)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1323323, _1323325), _1323327)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1323323, _1323327), _1323329))], (29966 ^ _779448) ^ [_1323530, _1323532] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1323530)), _1323532) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1323530, _1323532))], (29968 ^ _779448) ^ [_1323568, _1323570] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1323568), _1323570) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1323568, _1323570))], (29970 ^ _779448) ^ [_1323604] : [-(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)), _1323604))))], (29972 ^ _779448) ^ [_1323632, _1323634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1323632)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1323632, _1323634)))], (29978 ^ _779448) ^ [_1323719, _1323721, _1323723, _1323725, _1323727, _1323729] : [hBOOL(hAPP(hAPP(c_member(_1323719), _1323721), _1323723)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1323719, _1323725)), hAPP(hAPP(c_Product__Type_OPair(_1323719, _1323725), _1323721), _1323727)), _1323729)), -(hBOOL(hAPP(hAPP(c_member(_1323725), _1323727), hAPP(c_Relation_OImage(_1323719, _1323725, _1323729), _1323723))))], (29988 ^ _779448) ^ [_1323968, _1323970, _1323972, _1323974, _1323976] : [hBOOL(hAPP(hAPP(c_member(_1323968), _1323970), hAPP(c_Relation_OImage(_1323972, _1323968, _1323974), _1323976))), 29992 ^ _779448 : [(29993 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1323972), 29991 ^ [_1323968, _1323970, _1323972, _1323974, _1323976]), _1323976)))], (29995 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1323972, _1323968)), hAPP(hAPP(c_Product__Type_OPair(_1323972, _1323968), 29991 ^ [_1323968, _1323970, _1323972, _1323974, _1323976]), _1323970)), _1323974)))]]], (29997 ^ _779448) ^ [_1324184, _1324186, _1324188, _1324190, _1324192] : [-(hBOOL(hAPP(hAPP(c_member(_1324184), _1324186), hAPP(c_Relation_OImage(_1324188, _1324184, _1324190), _1324192)))), 29998 ^ _779448 : [(29999 ^ _779448) ^ [_1324270] : [hBOOL(hAPP(hAPP(c_member(_1324188), _1324270), _1324192)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1324188, _1324184)), hAPP(hAPP(c_Product__Type_OPair(_1324188, _1324184), _1324270), _1324186)), _1324190))]]], (30007 ^ _779448) ^ [_1324450, _1324452] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1324450, _1324452)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1324452)), _1324450))], (30009 ^ _779448) ^ [_1324491, _1324493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1324491), hAPP(c_Nat_OSuc, _1324493))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1324491, hAPP(c_Nat_OSuc, _1324493)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1324493)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1324491, _1324493)))], (30015 ^ _779448) ^ [_1324624, _1324626, _1324628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324624, tc_HOL_Obool)), _1324626), _1324628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1324624, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1324624, _1324626)), c_Predicate_OPowp(_1324624, _1324628))))], (30021 ^ _779448) ^ [_1324761] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1324761), hAPP(c_Nat_OSuc, _1324761)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1324761), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (30023 ^ _779448) ^ [_1324799, _1324801, _1324803, _1324805] : [-(hAPP(c_Relation_OImage(_1324799, _1324801, _1324803), _1324805) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1324799, tc_fun(_1324801, tc_HOL_Obool)), _1324805), hAPP(hAPP(c_COMBB(tc_fun(_1324799, tc_HOL_Obool), tc_fun(_1324801, tc_HOL_Obool), _1324799), c_Relation_OImage(_1324799, _1324801, _1324803)), hAPP(hAPP(c_COMBC(_1324799, tc_fun(_1324799, tc_HOL_Obool), tc_fun(_1324799, tc_HOL_Obool)), c_Set_Oinsert(_1324799)), c_Orderings_Obot__class_Obot(tc_fun(_1324799, tc_HOL_Obool))))))], (30025 ^ _779448) ^ [_1324890, _1324892] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1324890), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1324892) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1324890, _1324892))], (30027 ^ _779448) ^ [_1324929, _1324931, _1324933, _1324935, _1324937] : [class_Orderings_Oorder(_1324929), 30030 ^ _779448 : [(30031 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324929, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1324929, _1324931, _1324933)), c_SetInterval_Oord__class_OatLeastAtMost(_1324929, _1324935, _1324937))), 30034 ^ _779448 : [(30049 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324935), _1324937)))], (30035 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324931), _1324933)), 30038 ^ _779448 : [(30039 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324935), _1324931)))], (30041 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324933), _1324937)))], (30043 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324929), _1324935), _1324931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324929), _1324933), _1324937)))]]]]], (30051 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1324929, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1324929, _1324931, _1324933)), c_SetInterval_Oord__class_OatLeastAtMost(_1324929, _1324935, _1324937)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324935), _1324937)), 30054 ^ _779448 : [(30055 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324931), _1324933)))], (30057 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324935), _1324931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324929), _1324933), _1324937)), 30064 ^ _779448 : [(30065 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324929), _1324935), _1324931))], (30067 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1324929), _1324933), _1324937))]]]]]]], (30073 ^ _779448) ^ [_1325700, _1325702, _1325704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1325700), _1325702)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1325700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1325702), _1325704)) = 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, _1325700), _1325702)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1325702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1325702), _1325704))))], (30079 ^ _779448) ^ [_1325861, _1325863, _1325865, _1325867] : [class_Orderings_Olinorder(_1325861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325861), _1325863), _1325865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325861), _1325865), _1325867)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325861, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1325861, _1325863, _1325865)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1325861, _1325865, _1325867)) = c_SetInterval_Oord__class_OatLeastAtMost(_1325861, _1325863, _1325867))], (30093 ^ _779448) ^ [_1326126, _1326128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1326126), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1326128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1326128), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1326126))))), -(_1326126 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1326128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1326128), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1326126))))], (30099 ^ _779448) ^ [_1326273, _1326275, _1326277] : [class_Groups_Oordered__ab__group__add(_1326273), -(hAPP(c_Set_Oimage(_1326273, _1326273, c_Groups_Ouminus__class_Ouminus(_1326273)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1326273, _1326275, _1326277)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1326273, hAPP(c_Groups_Ouminus__class_Ouminus(_1326273), _1326277)), hAPP(c_Groups_Ouminus__class_Ouminus(_1326273), _1326275)))], (30105 ^ _779448) ^ [_1326408, _1326410, _1326412] : [class_Groups_Oordered__ab__group__add(_1326408), -(hAPP(c_Set_Oimage(_1326408, _1326408, c_Groups_Ouminus__class_Ouminus(_1326408)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1326408, _1326410), _1326412)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1326408, hAPP(c_Groups_Ouminus__class_Ouminus(_1326408), _1326412), hAPP(c_Groups_Ouminus__class_Ouminus(_1326408), _1326410)))], (30111 ^ _779448) ^ [_1326543, _1326545] : [-(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)), _1326543)), 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), _1326545), _1326543))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1326543), _1326545))], (30113 ^ _779448) ^ [_1326593] : [-(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)), _1326593)) = hAPP(c_Int_Onat, _1326593))], (30115 ^ _779448) ^ [_1326625, _1326627] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1326625), _1326627)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1326627), _1326625)))], (30117 ^ _779448) ^ [_1326668, _1326670] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1326668), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1326670) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1326668, _1326670))], (30119 ^ _779448) ^ [_1326718, _1326720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1326718), _1326720)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1326718), hAPP(c_Nat_OSuc, _1326720)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1326720), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1326718), _1326720)))], (30125 ^ _779448) ^ [_1326841, _1326843] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1326841), _1326843))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1326841), hAPP(c_Nat_OSuc, _1326843)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30131 ^ _779448) ^ [_1326902, _1326904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326902), _1326904)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1326904, _1326902) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (30137 ^ _779448) ^ [_1326991, _1326993] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326991), _1326993))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1326993, _1326991) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1326993), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1326993), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1326991)))], (30143 ^ _779448) ^ [_1327054, _1327056, _1327058, _1327060] : [class_Orderings_Olinorder(_1327054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327054), _1327056), _1327058)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327054), _1327058), _1327060)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327054, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1327054, _1327056, _1327058)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1327054, _1327058), _1327060)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1327054, _1327056, _1327060))], (30157 ^ _779448) ^ [_1327347, _1327349, _1327351, _1327353, _1327355] : [hBOOL(hAPP(hAPP(c_member(_1327347), _1327349), hAPP(c_Relation_OImage(_1327351, _1327347, _1327353), hAPP(hAPP(c_Set_Oinsert(_1327351), _1327355), c_Orderings_Obot__class_Obot(tc_fun(_1327351, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1327351, _1327347)), hAPP(hAPP(c_Product__Type_OPair(_1327351, _1327347), _1327355), _1327349)), _1327353)))], (30163 ^ _779448) ^ [_1327518, _1327520, _1327522, _1327524, _1327526] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1327522, _1327518)), hAPP(hAPP(c_Product__Type_OPair(_1327522, _1327518), _1327526), _1327520)), _1327524)), -(hBOOL(hAPP(hAPP(c_member(_1327518), _1327520), hAPP(c_Relation_OImage(_1327522, _1327518, _1327524), hAPP(hAPP(c_Set_Oinsert(_1327522), _1327526), c_Orderings_Obot__class_Obot(tc_fun(_1327522, tc_HOL_Obool)))))))], (30169 ^ _779448) ^ [_1327695, _1327697] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1327695, _1327697)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1327697), _1327695)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30171 ^ _779448) ^ [_1327754, _1327756, _1327758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327754), _1327756)), -(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)), _1327754)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1327758), _1327756)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1327758), _1327754)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1327756), _1327754)))], (30177 ^ _779448) ^ [_1327906, _1327908, _1327910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327906), _1327908))), 30180 ^ _779448 : [(30181 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327910), _1327908)), -(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)), _1327906)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1327910), _1327908)) = 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))))], (30187 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1327910), _1327908))), -(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)), _1327906)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1327910), _1327908)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (30193 ^ _779448) ^ [_1328175, _1328177, _1328179] : [class_Orderings_Olinorder(_1328175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328175), _1328177), _1328179)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328175, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328175), _1328177), c_Orderings_Obot__class_Obot(tc_fun(_1328175, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1328175, _1328177, _1328179)) = c_SetInterval_Oord__class_OatLeastAtMost(_1328175, _1328177, _1328179))], (30203 ^ _779448) ^ [_1328384, _1328386, _1328388] : [class_Rings_Oring__1(_1328384), -(hAPP(c_Int_Oring__1__class_Oof__int(_1328384), 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), _1328386), _1328388)), 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(_1328384), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1328384), _1328386)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1328384), _1328388)))], (30209 ^ _779448) ^ [] : [-(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))))))], (30211 ^ _779448) ^ [_1328561, _1328563, _1328565, _1328567] : [-(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), _1328561), _1328563)), 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), _1328565), _1328567)), 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), _1328561), _1328565)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328563), _1328567))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328561), _1328567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328563), _1328565)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (30213 ^ _779448) ^ [_1328707, _1328709, _1328711, _1328713] : [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), _1328707), _1328709)), 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), _1328711), _1328713)), 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), _1328707), _1328713)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328711), _1328709))))], (30219 ^ _779448) ^ [_1328900, _1328902, _1328904, _1328906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328900), _1328906)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1328904), _1328902))), -(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), _1328900), _1328902)), 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), _1328904), _1328906)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (30225 ^ _779448) ^ [_1329099] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1329099)) = _1329099)], (30227 ^ _779448) ^ [_1329128, _1329130] : [-(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), _1329128), _1329130)), 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), _1329130), _1329128)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (30229 ^ _779448) ^ [] : [-(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))))))], (30231 ^ _779448) ^ [_1329210] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329210) = 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), _1329210), 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))))))], (30233 ^ _779448) ^ [_1329254, _1329256, _1329258, _1329260] : [-(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), _1329254), _1329256)), 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), _1329258), _1329260)), 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), _1329254), _1329258)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1329256), _1329260))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (30235 ^ _779448) ^ [_1329355, _1329357] : [-(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), _1329355), _1329357)), 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), _1329355), _1329357))], (30237 ^ _779448) ^ [_1329407] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329407) = 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, _1329407)), 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))))))))], (30239 ^ _779448) ^ [_1329466, _1329468, _1329470, _1329472] : [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), _1329466), _1329468)), 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), _1329470), _1329472)), 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), _1329466), _1329472)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1329470), _1329468))))], (30245 ^ _779448) ^ [_1329659, _1329661, _1329663, _1329665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1329659), _1329665)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1329663), _1329661))), -(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), _1329659), _1329661)), 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), _1329663), _1329665)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (30251 ^ _779448) ^ [_1329873, _1329875] : [30259 ^ _779448 : [(30260 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30258 ^ [_1329873, _1329875]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1329873))))], (30262 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1329875, 30258 ^ [_1329873, _1329875])))]], 30252 ^ _779448 : [(30253 ^ _779448) ^ [_1329942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1329942), _1329873)), hBOOL(hAPP(_1329875, _1329942))]]], (30264 ^ _779448) ^ [_1330103, _1330105] : [30272 ^ _779448 : [(30273 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30271 ^ [_1330103, _1330105]), _1330103)))], (30275 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1330105, 30271 ^ [_1330103, _1330105])))]], 30265 ^ _779448 : [(30266 ^ _779448) ^ [_1330172] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1330172), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1330103))), hBOOL(hAPP(_1330105, _1330172))]]], (30277 ^ _779448) ^ [_1330358, _1330360] : [30279 ^ _779448 : [(30280 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30278 ^ [_1330358, _1330360]), _1330358)))], (30282 ^ _779448) ^ [] : [hBOOL(hAPP(_1330360, 30278 ^ [_1330358, _1330360]))]], 30283 ^ _779448 : [(30284 ^ _779448) ^ [_1330509] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1330509), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1330358))), -(hBOOL(hAPP(_1330360, _1330509)))]]], (30290 ^ _779448) ^ [_1330612, _1330614] : [30292 ^ _779448 : [(30293 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30291 ^ [_1330612, _1330614]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1330612))))], (30295 ^ _779448) ^ [] : [hBOOL(hAPP(_1330614, 30291 ^ [_1330612, _1330614]))]], 30296 ^ _779448 : [(30297 ^ _779448) ^ [_1330767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1330767), _1330612)), -(hBOOL(hAPP(_1330614, _1330767)))]]], (30303 ^ _779448) ^ [_1330883, _1330885] : [30305 ^ _779448 : [(30306 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30304 ^ [_1330883, _1330885]), _1330883)))], (30308 ^ _779448) ^ [] : [hBOOL(hAPP(_1330885, 30304 ^ [_1330883, _1330885]))]], 30309 ^ _779448 : [(30310 ^ _779448) ^ [_1331033] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331033), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1330883))), -(hBOOL(hAPP(_1330885, _1331033)))]]], (30316 ^ _779448) ^ [_1331134, _1331136] : [30318 ^ _779448 : [(30319 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30317 ^ [_1331134, _1331136]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1331134))))], (30321 ^ _779448) ^ [] : [hBOOL(hAPP(_1331136, 30317 ^ [_1331134, _1331136]))]], 30322 ^ _779448 : [(30323 ^ _779448) ^ [_1331287] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1331287), _1331134)), -(hBOOL(hAPP(_1331136, _1331287)))]]], (30329 ^ _779448) ^ [_1331403, _1331405] : [30337 ^ _779448 : [(30338 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 30336 ^ [_1331403, _1331405]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1331403))))], (30340 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1331405, 30336 ^ [_1331403, _1331405])))]], 30330 ^ _779448 : [(30331 ^ _779448) ^ [_1331471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1331471), _1331403)), hBOOL(hAPP(_1331405, _1331471))]]], (30342 ^ _779448) ^ [_1331631, _1331633] : [30350 ^ _779448 : [(30351 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30349 ^ [_1331631, _1331633]), _1331631)))], (30353 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1331633, 30349 ^ [_1331631, _1331633])))]], 30343 ^ _779448 : [(30344 ^ _779448) ^ [_1331699] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1331699), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1331631))), hBOOL(hAPP(_1331633, _1331699))]]], (30355 ^ _779448) ^ [_1331868, _1331870, _1331872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331868)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1331870), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1331872)), 30362 ^ _779448 : [(30363 ^ _779448) ^ [_1332076] : [30365 ^ _779448 : [(30366 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30364 ^ [_1331868, _1331870, _1331872, _1332076]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1331868))))], (30369 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30367 ^ [_1331868, _1331870, _1331872, _1332076]), _1331872)))], (30371 ^ _779448) ^ [] : [-(_1332076 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30367 ^ [_1331868, _1331870, _1331872, _1332076]), 30364 ^ [_1331868, _1331870, _1331872, _1332076]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1331870), _1332076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1331870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332076), _1331868))))]]], (30379 ^ _779448) ^ [_1332352, _1332354, _1332356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332352)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332354), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1332356)), 30386 ^ _779448 : [(30387 ^ _779448) ^ [_1332560] : [30389 ^ _779448 : [(30390 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30388 ^ [_1332352, _1332354, _1332356, _1332560]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1332352))))], (30393 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30391 ^ [_1332352, _1332354, _1332356, _1332560]), _1332356)))], (30395 ^ _779448) ^ [] : [-(_1332560 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30391 ^ [_1332352, _1332354, _1332356, _1332560]), 30388 ^ [_1332352, _1332354, _1332356, _1332560]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332560), _1332354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332560), _1332352)), _1332354)))]]], (30403 ^ _779448) ^ [_1332836, _1332838, _1332840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332836)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332838), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1332840)), 30413 ^ _779448 : [(30414 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30412 ^ [_1332836, _1332838, _1332840]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1332836))))], (30417 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30415 ^ [_1332836, _1332838, _1332840]), _1332840)))], (30419 ^ _779448) ^ [] : [-(_1332838 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30415 ^ [_1332836, _1332838, _1332840]), 30412 ^ [_1332836, _1332838, _1332840]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332838), _1332836) = _1332838)], (30423 ^ _779448) ^ [_1333175, _1333177, _1333179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333175)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333177), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1333179)), 30433 ^ _779448 : [(30434 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30432 ^ [_1333175, _1333177, _1333179]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333175))))], (30437 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30435 ^ [_1333175, _1333177, _1333179]), _1333179)))], (30439 ^ _779448) ^ [] : [-(_1333177 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30435 ^ [_1333175, _1333177, _1333179]), 30432 ^ [_1333175, _1333177, _1333179]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333177), _1333175) = _1333177)], (30443 ^ _779448) ^ [_1333514, _1333516, _1333518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333514)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1333516), _1333518)), 30450 ^ _779448 : [(30451 ^ _779448) ^ [_1333704] : [30453 ^ _779448 : [(30454 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30452 ^ [_1333514, _1333516, _1333518, _1333704]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333514))))], (30457 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30455 ^ [_1333514, _1333516, _1333518, _1333704]), _1333518)))], (30459 ^ _779448) ^ [] : [-(_1333704 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30455 ^ [_1333514, _1333516, _1333518, _1333704]), 30452 ^ [_1333514, _1333516, _1333518, _1333704]))]], -(_1333704 = _1333516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333704), _1333514) = _1333516]]], (30467 ^ _779448) ^ [_1333964, _1333966, _1333968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333964)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1333966), _1333968)), 30474 ^ _779448 : [(30475 ^ _779448) ^ [_1334154] : [30477 ^ _779448 : [(30478 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30476 ^ [_1333964, _1333966, _1333968, _1334154]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333964))))], (30481 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30479 ^ [_1333964, _1333966, _1333968, _1334154]), _1333968)))], (30483 ^ _779448) ^ [] : [-(_1334154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30479 ^ [_1333964, _1333966, _1333968, _1334154]), 30476 ^ [_1333964, _1333966, _1333968, _1334154]))]], -(_1334154 = _1333966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334154), _1333964) = _1333966]]], (30491 ^ _779448) ^ [_1334414, _1334416, _1334418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334414)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1334416), _1334418)), 30498 ^ _779448 : [(30499 ^ _779448) ^ [_1334610] : [30501 ^ _779448 : [(30502 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30500 ^ [_1334414, _1334416, _1334418, _1334610]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1334414))))], (30505 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30503 ^ [_1334414, _1334416, _1334418, _1334610]), _1334418)))], (30507 ^ _779448) ^ [] : [-(_1334610 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30503 ^ [_1334414, _1334416, _1334418, _1334610]), 30500 ^ [_1334414, _1334416, _1334418, _1334610]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334416), _1334610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334610), _1334414))))]]], (30515 ^ _779448) ^ [_1334886, _1334888, _1334890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334886)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1334888), _1334890)), 30522 ^ _779448 : [(30523 ^ _779448) ^ [_1335082] : [30525 ^ _779448 : [(30526 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30524 ^ [_1334886, _1334888, _1334890, _1335082]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1334886))))], (30529 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30527 ^ [_1334886, _1334888, _1334890, _1335082]), _1334890)))], (30531 ^ _779448) ^ [] : [-(_1335082 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30527 ^ [_1334886, _1334888, _1334890, _1335082]), 30524 ^ [_1334886, _1334888, _1334890, _1335082]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335082), _1334888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1335082), _1334886)), _1334888)))]]], (30539 ^ _779448) ^ [_1335358, _1335360, _1335362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335358)), 30542 ^ _779448 : [(30543 ^ _779448) ^ [_1335492] : [30545 ^ _779448 : [(30546 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30544 ^ [_1335358, _1335360, _1335362, _1335492]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1335358))))], (30549 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30547 ^ [_1335358, _1335360, _1335362, _1335492]), _1335360)))], (30551 ^ _779448) ^ [] : [-(_1335492 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30547 ^ [_1335358, _1335360, _1335362, _1335492]), 30544 ^ [_1335358, _1335360, _1335362, _1335492]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335362), _1335492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1335492), _1335358))))]]], (30559 ^ _779448) ^ [_1335766, _1335768, _1335770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335766)), 30562 ^ _779448 : [(30563 ^ _779448) ^ [_1335900] : [30565 ^ _779448 : [(30566 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30564 ^ [_1335766, _1335768, _1335770, _1335900]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1335766))))], (30569 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30567 ^ [_1335766, _1335768, _1335770, _1335900]), _1335768)))], (30571 ^ _779448) ^ [] : [-(_1335900 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30567 ^ [_1335766, _1335768, _1335770, _1335900]), 30564 ^ [_1335766, _1335768, _1335770, _1335900]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335900), _1335770)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1335900), _1335766)), _1335770)))]]], (30581 ^ _779448) ^ [_1336174] : [-(_1336174 = 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), 30578 ^ [_1336174]), 30579 ^ [_1336174])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (30583 ^ _779448) ^ [_1336225, _1336227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336225)), 30592 ^ _779448 : [(30593 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1336227, 30588 ^ [_1336225, _1336227])))], (30595 ^ _779448) ^ [] : [hBOOL(hAPP(_1336227, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30588 ^ [_1336225, _1336227]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 30589 ^ [_1336225, _1336227]), _1336225))))]], 30596 ^ _779448 : [(30597 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1336227, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30588 ^ [_1336225, _1336227]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 30589 ^ [_1336225, _1336227]), _1336225)))))], (30599 ^ _779448) ^ [] : [hBOOL(hAPP(_1336227, 30588 ^ [_1336225, _1336227]))]], 30600 ^ _779448 : [(30601 ^ _779448) ^ [] : [30602 ^ _779448 : [(30603 ^ _779448) ^ [_1336657] : [hBOOL(hAPP(_1336227, _1336657))]], 30605 ^ _779448 : [(30606 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30604 ^ [_1336225, _1336227]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1336225))))], (30608 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1336227, 30604 ^ [_1336225, _1336227])))]]], (30610 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1336227, 30617 ^ [_1336225, _1336227]))), 30611 ^ _779448 : [(30612 ^ _779448) ^ [_1336772] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1336772), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1336225))), hBOOL(hAPP(_1336227, _1336772))]]]]], (30621 ^ _779448) ^ [_1336919, _1336921, _1336923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336919)), 30624 ^ _779448 : [(30625 ^ _779448) ^ [_1337053] : [30627 ^ _779448 : [(30628 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30626 ^ [_1336919, _1336921, _1336923, _1337053]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1336919))))], (30631 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30629 ^ [_1336919, _1336921, _1336923, _1337053]), _1336921)))], (30633 ^ _779448) ^ [] : [-(_1337053 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 30629 ^ [_1336919, _1336921, _1336923, _1337053]), 30626 ^ [_1336919, _1336921, _1336923, _1337053]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337053), _1336923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1337053), _1336919)), _1336923)))]]], (30641 ^ _779448) ^ [_1337327, _1337329, _1337331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337327)), 30644 ^ _779448 : [(30645 ^ _779448) ^ [_1337461] : [30647 ^ _779448 : [(30648 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30646 ^ [_1337327, _1337329, _1337331, _1337461]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1337327))))], (30651 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 30649 ^ [_1337327, _1337329, _1337331, _1337461]), _1337329)))], (30653 ^ _779448) ^ [] : [-(_1337461 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 30649 ^ [_1337327, _1337329, _1337331, _1337461]), 30646 ^ [_1337327, _1337329, _1337331, _1337461]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337331), _1337461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1337331), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1337461), _1337327))))]]], (30661 ^ _779448) ^ [_1337735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337735)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1337735) = 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, _1337735))))], (30667 ^ _779448) ^ [_1337838, _1337840] : [-(c_Relation_OId__on(_1337838, _1337840) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1337838, tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool)), _1337840), hAPP(hAPP(c_COMBC(_1337838, tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool), tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1337838, _1337838), tc_fun(tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool), tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool)), _1337838), c_Set_Oinsert(tc_prod(_1337838, _1337838))), hAPP(hAPP(c_COMBS(_1337838, _1337838, tc_prod(_1337838, _1337838)), c_Product__Type_OPair(_1337838, _1337838)), c_COMBI(_1337838)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1337838, _1337838), tc_HOL_Obool)))))], (30669 ^ _779448) ^ [_1337962] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1337962))))], (30671 ^ _779448) ^ [_1337990, _1337992, _1337994] : [class_Orderings_Olinorder(_1337990), 30674 ^ _779448 : [(30675 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1337990), _1337992) = hAPP(c_SetInterval_Oord__class_OlessThan(_1337990), _1337994), -(_1337992 = _1337994)], (30681 ^ _779448) ^ [] : [_1337992 = _1337994, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1337990), _1337992) = hAPP(c_SetInterval_Oord__class_OlessThan(_1337990), _1337994))]]], (30687 ^ _779448) ^ [_1338231] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1338231)) = _1338231)], (30689 ^ _779448) ^ [_1338260, _1338262] : [-(c_Relation_OId__on(_1338260, _1338262) = hAPP(c_Product__Type_Oprod_Oprod__case(_1338260, _1338260, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1338260, tc_HOL_Obool, tc_fun(_1338260, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1338260, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1338260, tc_HOL_Obool)), _1338260), c_COMBC(_1338260, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1338260, tc_HOL_Obool), tc_fun(_1338260, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1338260), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1338260), c_fconj)), c_fequal))), _1338262)))], (30691 ^ _779448) ^ [_1338354] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1338354) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1338354))], (30693 ^ _779448) ^ [] : [-(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)))], (30695 ^ _779448) ^ [_1338401] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1338401)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1338401), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1338401)))], (30697 ^ _779448) ^ [_1338439, _1338441, _1338443] : [class_Orderings_Oord(_1338439), 30700 ^ _779448 : [(30701 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1338439), _1338441), hAPP(c_SetInterval_Oord__class_OlessThan(_1338439), _1338443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338439), _1338441), _1338443)))], (30707 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338439), _1338441), _1338443)), -(hBOOL(hAPP(hAPP(c_member(_1338439), _1338441), hAPP(c_SetInterval_Oord__class_OlessThan(_1338439), _1338443))))]]], (30713 ^ _779448) ^ [_1338707, _1338709, _1338711] : [class_Orderings_Olinorder(_1338707), 30716 ^ _779448 : [(30717 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338707, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338707), _1338709)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338707), _1338711))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338707), _1338709), _1338711)))], (30723 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338707), _1338709), _1338711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338707, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338707), _1338709)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338707), _1338711))))]]], (30729 ^ _779448) ^ [_1338999, _1339001, _1339003] : [class_Orderings_Olinorder(_1338999), 30732 ^ _779448 : [(30733 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1338999, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338999), _1339001)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338999), _1339003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338999), _1339001), _1339003)))], (30739 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338999), _1339001), _1339003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1338999, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338999), _1339001)), hAPP(c_SetInterval_Oord__class_OlessThan(_1338999), _1339003))))]]], (30745 ^ _779448) ^ [_1339291] : [-(c_Relation_OId__on(_1339291, c_Orderings_Obot__class_Obot(tc_fun(_1339291, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1339291, _1339291), tc_HOL_Obool)))], (30747 ^ _779448) ^ [_1339330, _1339332] : [class_Orderings_Oorder(_1339330), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1339330, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1339330), _1339332), c_Orderings_Obot__class_Obot(tc_fun(_1339330, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1339330), _1339332)) = hAPP(hAPP(c_Set_Oinsert(_1339330), _1339332), c_Orderings_Obot__class_Obot(tc_fun(_1339330, tc_HOL_Obool))))], (30753 ^ _779448) ^ [_1339489, _1339491, _1339493, _1339495] : [_1339489 = _1339491, hBOOL(hAPP(hAPP(c_member(_1339493), _1339489), _1339495)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1339493, _1339493)), hAPP(hAPP(c_Product__Type_OPair(_1339493, _1339493), _1339489), _1339491)), c_Relation_OId__on(_1339493, _1339495))))], (30763 ^ _779448) ^ [_1339705, _1339707, _1339709, _1339711] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1339705, _1339705)), hAPP(hAPP(c_Product__Type_OPair(_1339705, _1339705), _1339707), _1339709)), c_Relation_OId__on(_1339705, _1339711))), 30766 ^ _779448 : [(30767 ^ _779448) ^ [] : [-(_1339707 = _1339709)], (30769 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339705), _1339707), _1339711)))]]], (30771 ^ _779448) ^ [_1339866, _1339868, _1339870, _1339872] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1339866, _1339866)), hAPP(hAPP(c_Product__Type_OPair(_1339866, _1339866), _1339868), _1339870)), c_Relation_OId__on(_1339866, _1339872)))), _1339868 = _1339870, hBOOL(hAPP(hAPP(c_member(_1339866), _1339868), _1339872))], (30781 ^ _779448) ^ [_1340063, _1340065, _1340067] : [class_Orderings_Olinorder(_1340063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340063), _1340065), _1340067)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340063, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1340063), _1340065)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1340063, _1340065), _1340067)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1340063), _1340067))], (30791 ^ _779448) ^ [_1340262] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1340262)) = 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), _1340262))))], (30793 ^ _779448) ^ [_1340300, _1340302, _1340304] : [-(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), _1340300)), 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))), _1340302))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1340304))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1340304)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340300), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340300), 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), _1340304), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1340302)))))], (30795 ^ _779448) ^ [_1340387, _1340389, _1340391] : [-(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), _1340387)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1340389))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1340391))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1340391), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1340387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1340387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1340391), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1340389)))))], (30797 ^ _779448) ^ [_1340468, _1340470, _1340472, _1340474] : [class_Rings_Ocomm__semiring__1(_1340468), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1340468), c_Groups_Oone__class_Oone(_1340468)), c_Groups_Oone__class_Oone(_1340468))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1340468), hAPP(hAPP(c_COMBB(_1340468, _1340468, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1340468), _1340470)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1340468, _1340468), hAPP(hAPP(c_COMBB(_1340468, tc_fun(_1340468, _1340468), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1340468)), c_Nat_Osemiring__1__class_Oof__nat(_1340468))), _1340472))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1340474))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340468), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1340468), _1340474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1340468), _1340470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1340468), _1340470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340468), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1340468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1340474), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1340472)))))], (30803 ^ _779448) ^ [_1340791, _1340793, _1340795] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1340791), _1340793), _1340795) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1340791, tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool)), _1340793), hAPP(hAPP(c_COMBC(_1340791, tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1340791, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool)), _1340791), c_Set_Oinsert(tc_fun(_1340791, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1340791, tc_HOL_Obool), tc_fun(_1340791, tc_HOL_Obool), _1340791), c_Relation_OImage(_1340791, _1340791, _1340795)), hAPP(hAPP(c_COMBC(_1340791, tc_fun(_1340791, tc_HOL_Obool), tc_fun(_1340791, tc_HOL_Obool)), c_Set_Oinsert(_1340791)), c_Orderings_Obot__class_Obot(tc_fun(_1340791, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1340791, tc_HOL_Obool), tc_HOL_Obool)))))], (30805 ^ _779448) ^ [_1340947, _1340949, _1340951, _1340953] : [class_Groups_Oab__group__add(_1340947), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1340949, _1340947), hAPP(hAPP(c_COMBB(_1340947, _1340947, _1340949), c_Groups_Ouminus__class_Ouminus(_1340947)), _1340951)), _1340953) = hAPP(c_Groups_Ouminus__class_Ouminus(_1340947), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1340949, _1340947), _1340951), _1340953)))], (30811 ^ _779448) ^ [_1341096, _1341098, _1341100] : [class_Groups_Ocomm__monoid__add(_1341096), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341098, _1341096), hAPP(c_COMBK(_1341096, _1341098), c_Groups_Ozero__class_Ozero(_1341096))), _1341100) = c_Groups_Ozero__class_Ozero(_1341096))], (30817 ^ _779448) ^ [_1341211, _1341213, _1341215, _1341217] : [class_Rings_Oring__1(_1341211), -(hAPP(c_Int_Oring__1__class_Oof__int(_1341211), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341213, tc_Int_Oint), _1341215), _1341217)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341213, _1341211), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1341211, _1341213), c_Int_Oring__1__class_Oof__int(_1341211)), _1341215)), _1341217))], (30823 ^ _779448) ^ [_1341360, _1341362, _1341364, _1341366, _1341368, _1341370] : [class_Groups_Ocomm__monoid__add(_1341360), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341362, _1341360), hAPP(hAPP(c_COMBC(_1341362, tc_fun(_1341364, tc_HOL_Obool), _1341360), hAPP(hAPP(c_COMBB(tc_fun(_1341364, _1341360), tc_fun(tc_fun(_1341364, tc_HOL_Obool), _1341360), _1341362), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341364, _1341360)), _1341366)), _1341368)), _1341370) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341364, _1341360), hAPP(hAPP(c_COMBC(_1341364, tc_fun(_1341362, tc_HOL_Obool), _1341360), hAPP(hAPP(c_COMBB(tc_fun(_1341362, _1341360), tc_fun(tc_fun(_1341362, tc_HOL_Obool), _1341360), _1341364), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341362, _1341360)), hAPP(c_COMBC(_1341362, _1341364, _1341360), _1341366))), _1341370)), _1341368))], (30829 ^ _779448) ^ [_1341633, _1341635, _1341637, _1341639] : [class_Rings_Osemiring__1(_1341633), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1341633), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341635, tc_Nat_Onat), _1341637), _1341639)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341635, _1341633), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1341633, _1341635), c_Nat_Osemiring__1__class_Oof__nat(_1341633)), _1341637)), _1341639))], (30835 ^ _779448) ^ [_1341782, _1341784, _1341786] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341782, tc_Nat_Onat), _1341784), _1341786)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341782, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1341782), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1341784)), _1341786))], (30837 ^ _779448) ^ [_1341840, _1341842, _1341844] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341840, tc_Nat_Onat), _1341842), _1341844) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341840, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1341840), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1341842)), _1341844)))], (30839 ^ _779448) ^ [_1341898, _1341900, _1341902, _1341904, _1341906] : [class_Groups_Oab__group__add(_1341898), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341900, _1341898), hAPP(hAPP(c_COMBS(_1341900, _1341898, _1341898), hAPP(hAPP(c_COMBB(_1341898, tc_fun(_1341898, _1341898), _1341900), c_Groups_Ominus__class_Ominus(_1341898)), _1341902)), _1341904)), _1341906) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1341898), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341900, _1341898), _1341902), _1341906)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341900, _1341898), _1341904), _1341906)))], (30845 ^ _779448) ^ [_1342099, _1342101, _1342103, _1342105, _1342107] : [class_Rings_Osemiring__0(_1342099), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342099), _1342101), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342103, _1342099), _1342105), _1342107)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342103, _1342099), hAPP(hAPP(c_COMBB(_1342099, _1342099, _1342103), hAPP(c_Groups_Otimes__class_Otimes(_1342099), _1342101)), _1342105)), _1342107))], (30851 ^ _779448) ^ [_1342262, _1342264, _1342266, _1342268, _1342270] : [class_Rings_Osemiring__0(_1342262), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342262), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342264, _1342262), _1342266), _1342268)), _1342270) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342264, _1342262), hAPP(hAPP(c_COMBC(_1342264, _1342262, _1342262), hAPP(hAPP(c_COMBB(_1342262, tc_fun(_1342262, _1342262), _1342264), c_Groups_Otimes__class_Otimes(_1342262)), _1342266)), _1342270)), _1342268))], (30857 ^ _779448) ^ [_1342445, _1342447, _1342449, _1342451, _1342453, _1342455, _1342457] : [class_Rings_Osemiring__0(_1342445), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342447, _1342445), _1342449), _1342451)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342453, _1342445), _1342455), _1342457)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342447, _1342445), hAPP(hAPP(c_COMBC(_1342447, tc_fun(_1342453, tc_HOL_Obool), _1342445), hAPP(hAPP(c_COMBB(tc_fun(_1342453, _1342445), tc_fun(tc_fun(_1342453, tc_HOL_Obool), _1342445), _1342447), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342453, _1342445)), hAPP(hAPP(c_COMBC(_1342447, tc_fun(_1342453, _1342445), tc_fun(_1342453, _1342445)), hAPP(hAPP(c_COMBB(tc_fun(_1342445, _1342445), tc_fun(tc_fun(_1342453, _1342445), tc_fun(_1342453, _1342445)), _1342447), c_COMBB(_1342445, _1342445, _1342453)), hAPP(hAPP(c_COMBB(_1342445, tc_fun(_1342445, _1342445), _1342447), c_Groups_Otimes__class_Otimes(_1342445)), _1342449))), _1342455))), _1342457)), _1342451))], (30863 ^ _779448) ^ [_1342784, _1342786, _1342788, _1342790, _1342792] : [class_Groups_Ocomm__monoid__add(_1342784), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342786, _1342784), hAPP(hAPP(c_COMBS(_1342786, _1342784, _1342784), hAPP(hAPP(c_COMBB(_1342784, tc_fun(_1342784, _1342784), _1342786), c_Groups_Oplus__class_Oplus(_1342784)), _1342788)), _1342790)), _1342792) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1342784), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342786, _1342784), _1342788), _1342792)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342786, _1342784), _1342790), _1342792)))], (30869 ^ _779448) ^ [_1342985, _1342987, _1342989, _1342991, _1342993] : [class_Fields_Ofield(_1342985), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1342985), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342987, _1342985), _1342989), _1342991)), _1342993) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1342987, _1342985), hAPP(hAPP(c_COMBC(_1342987, _1342985, _1342985), hAPP(hAPP(c_COMBB(_1342985, tc_fun(_1342985, _1342985), _1342987), c_Rings_Oinverse__class_Odivide(_1342985)), _1342989)), _1342993)), _1342991))], (30875 ^ _779448) ^ [_1343168, _1343170, _1343172] : [class_Groups_Ocomm__monoid__add(_1343168), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343170, _1343168), _1343172), c_Orderings_Obot__class_Obot(tc_fun(_1343170, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1343168))], (30881 ^ _779448) ^ [_1343277, _1343279, _1343281] : [class_Groups_Ocomm__monoid__add(_1343277), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343279, _1343277), _1343281), c_Orderings_Obot__class_Obot(tc_fun(_1343279, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1343277))], (30887 ^ _779448) ^ [_1343386, _1343388, _1343390, _1343392] : [class_Groups_Ocomm__monoid__add(_1343386), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1343388), _1343390))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343388, _1343386), _1343392), _1343390) = c_Groups_Ozero__class_Ozero(_1343386))], (30897 ^ _779448) ^ [_1343510, _1343512, _1343514, _1343516] : [class_Groups_Ocomm__monoid__add(_1343510), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1343512), _1343514))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343512, _1343510), _1343516), _1343514) = c_Groups_Ozero__class_Ozero(_1343510))], (30907 ^ _779448) ^ [_1343634, _1343636] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343634), c_Orderings_Obot__class_Obot(tc_fun(_1343634, tc_HOL_Obool))), _1343636) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343634, tc_HOL_Obool), tc_HOL_Obool)))], (30909 ^ _779448) ^ [_1343698, _1343700, _1343702] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343698, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343698), _1343700), _1343702), -(_1343700 = c_Orderings_Obot__class_Obot(tc_fun(_1343698, tc_HOL_Obool)))], (30915 ^ _779448) ^ [_1343815, _1343817, _1343819] : [_1343817 = c_Orderings_Obot__class_Obot(tc_fun(_1343815, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343815, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343815), _1343817), _1343819))], (30921 ^ _779448) ^ [_1343956, _1343958, _1343960] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1343956), _1343958), _1343960) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343956, tc_HOL_Obool), tc_HOL_Obool)), -(_1343958 = c_Orderings_Obot__class_Obot(tc_fun(_1343956, tc_HOL_Obool)))], (30927 ^ _779448) ^ [_1344073, _1344075, _1344077] : [_1344075 = c_Orderings_Obot__class_Obot(tc_fun(_1344073, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1344073), _1344075), _1344077) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1344073, tc_HOL_Obool), tc_HOL_Obool)))], (30933 ^ _779448) ^ [_1344196, _1344198, _1344200] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1344196), _1344198)), 30936 ^ _779448 : [(30947 ^ _779448) ^ [] : [30949 ^ _779448 : [(30950 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344196), 30948 ^ [_1344196, _1344198, _1344200]), _1344198)))], (30952 ^ _779448) ^ [] : [hAPP(_1344200, 30948 ^ [_1344196, _1344198, _1344200]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344196, tc_Nat_Onat), _1344200), _1344198) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30937 ^ _779448) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344196, tc_Nat_Onat), _1344200), _1344198) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 30940 ^ _779448 : [(30941 ^ _779448) ^ [_1344358] : [hBOOL(hAPP(hAPP(c_member(_1344196), _1344358), _1344198)), -(hAPP(_1344200, _1344358) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (30956 ^ _779448) ^ [_1344616, _1344618, _1344620, _1344622, _1344624] : [class_Groups_Ocomm__monoid__add(_1344616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344618), _1344620)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344618, _1344616), hAPP(hAPP(c_COMBS(_1344618, _1344616, _1344616), hAPP(hAPP(c_COMBB(_1344616, tc_fun(_1344616, _1344616), _1344618), c_Groups_Oplus__class_Oplus(_1344616)), _1344622)), _1344624)), _1344620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344616), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344618, _1344616), _1344622), _1344620)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344618, _1344616), _1344624), _1344620)))], (30966 ^ _779448) ^ [_1344883, _1344885] : [-(hAPP(c_Finite__Set_Ocard(_1344883), _1344885) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344883, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1344883), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1344885))], (30968 ^ _779448) ^ [_1344928, _1344930, _1344932, _1344934] : [class_Groups_Ocomm__monoid__add(_1344928), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1344928), _1344930), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1344932)), hAPP(c_Nat_OSuc, _1344934))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1344928), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1344928, tc_Nat_Onat), _1344930), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1344932), _1344934)))], (30974 ^ _779448) ^ [_1345099, _1345101, _1345103, _1345105, _1345107] : [class_Groups_Ocomm__monoid__add(_1345099), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345099), _1345101), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1345103), _1345105)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1345107), _1345105))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345099), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1345099, tc_Nat_Onat), _1345101), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1345105))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1345103), _1345107)))], (30980 ^ _779448) ^ [_1345290, _1345292, _1345294, _1345296] : [class_Groups_Ocomm__monoid__add(_1345290), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345290), _1345292), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1345294), hAPP(c_Nat_OSuc, _1345296))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345290), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1345290, tc_Nat_Onat), _1345292), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1345294, _1345296)))], (30986 ^ _779448) ^ [_1345453, _1345455, _1345457, _1345459, _1345461] : [class_Groups_Ocomm__monoid__add(_1345453), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345453), _1345455), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1345457), _1345459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1345461), _1345459))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1345453), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1345453, tc_Nat_Onat), _1345455), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1345459))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1345457, _1345461)))], (30992 ^ _779448) ^ [_1345636, _1345638, _1345640] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345636), _1345638)), 30995 ^ _779448 : [(30996 ^ _779448) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345636, tc_Nat_Onat), _1345640), _1345638) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31000 ^ _779448 : [(31001 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345636), 30999 ^ [_1345636, _1345638, _1345640]), _1345638)))], (31003 ^ _779448) ^ [] : [-(hAPP(_1345640, 30999 ^ [_1345636, _1345638, _1345640]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31005 ^ _779448) ^ [_1345956] : [hBOOL(hAPP(hAPP(c_member(_1345636), _1345956), _1345638)), -(30999 ^ [_1345636, _1345638, _1345640] = _1345956), -(hAPP(_1345640, _1345956) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31015 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345636, tc_Nat_Onat), _1345640), _1345638) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 31016 ^ _779448 : [(31017 ^ _779448) ^ [_1346117] : [hBOOL(hAPP(hAPP(c_member(_1345636), _1346117), _1345638)), hAPP(_1345640, _1346117) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31025 ^ _779448 : [(31026 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345636), 31024 ^ [_1345636, _1345638, _1345640, _1346117]), _1345638)))], (31028 ^ _779448) ^ [] : [_1346117 = 31024 ^ [_1345636, _1345638, _1345640, _1346117]], (31030 ^ _779448) ^ [] : [hAPP(_1345640, 31024 ^ [_1345636, _1345638, _1345640, _1346117]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (31034 ^ _779448) ^ [_1346470, _1346472, _1346474, _1346476, _1346478, _1346480] : [class_Groups_Ocomm__monoid__add(_1346470), c_Fun_Oinj__on(_1346472, _1346474, _1346476, _1346478), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346474, _1346470), _1346480), hAPP(c_Set_Oimage(_1346472, _1346474, _1346476), _1346478)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346472, _1346470), hAPP(c_Fun_Ocomp(_1346474, _1346470, _1346472, _1346480), _1346476)), _1346478))], (31044 ^ _779448) ^ [_1346683, _1346685, _1346687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1346683), _1346685)), 31047 ^ _779448 : [(31048 ^ _779448) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346683, tc_Nat_Onat), _1346687), _1346685) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31052 ^ _779448 : [(31053 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346683), 31051 ^ [_1346683, _1346685, _1346687]), _1346685)))], (31055 ^ _779448) ^ [] : [-(hAPP(_1346687, 31051 ^ [_1346683, _1346685, _1346687]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31057 ^ _779448) ^ [_1347003] : [hBOOL(hAPP(hAPP(c_member(_1346683), _1347003), _1346685)), -(31051 ^ [_1346683, _1346685, _1346687] = _1347003), -(hAPP(_1346687, _1347003) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31067 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346683, tc_Nat_Onat), _1346687), _1346685) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 31068 ^ _779448 : [(31069 ^ _779448) ^ [_1347164] : [hBOOL(hAPP(hAPP(c_member(_1346683), _1347164), _1346685)), hAPP(_1346687, _1347164) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31077 ^ _779448 : [(31078 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346683), 31076 ^ [_1346683, _1346685, _1346687, _1347164]), _1346685)))], (31080 ^ _779448) ^ [] : [_1347164 = 31076 ^ [_1346683, _1346685, _1346687, _1347164]], (31082 ^ _779448) ^ [] : [hAPP(_1346687, 31076 ^ [_1346683, _1346685, _1346687, _1347164]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (31086 ^ _779448) ^ [_1347517, _1347519, _1347521, _1347523, _1347525] : [class_Groups_Ocomm__monoid__add(_1347517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1347519), _1347521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1347521), _1347523)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347517), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347517), _1347525), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347519), _1347521))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347517), _1347525), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347521), _1347523))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347517), _1347525), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347519), _1347523)))], (31100 ^ _779448) ^ [_1347840, _1347842, _1347844, _1347846, _1347848] : [class_Groups_Oab__group__add(_1347840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1347842), _1347844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1347844), _1347846)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347840), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347840), _1347848), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347842), _1347846))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347840), _1347848), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347842), _1347844))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347840), _1347848), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347844), _1347846)))], (31114 ^ _779448) ^ [_1348163, _1348165] : [hAPP(_1348163, 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), _1348163), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1348165)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1348163), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1348165)))], (31120 ^ _779448) ^ [_1348286, _1348288, _1348290, _1348292, _1348294] : [class_Groups_Ocomm__monoid__add(_1348286), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348288), _1348290)), 31127 ^ _779448 : [(31128 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1348288), _1348292), _1348290)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348288, _1348286), hAPP(hAPP(c_COMBC(_1348288, _1348286, _1348286), hAPP(hAPP(c_COMBS(_1348288, _1348286, tc_fun(_1348286, _1348286)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1348286, tc_fun(_1348286, _1348286)), _1348288), c_If(_1348286)), hAPP(hAPP(c_COMBC(_1348288, _1348288, tc_HOL_Obool), c_fequal), _1348292))), _1348294)), c_Groups_Ozero__class_Ozero(_1348286))), _1348290) = hAPP(_1348294, _1348292))], (31134 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348288), _1348292), _1348290))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348288, _1348286), hAPP(hAPP(c_COMBC(_1348288, _1348286, _1348286), hAPP(hAPP(c_COMBS(_1348288, _1348286, tc_fun(_1348286, _1348286)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1348286, tc_fun(_1348286, _1348286)), _1348288), c_If(_1348286)), hAPP(hAPP(c_COMBC(_1348288, _1348288, tc_HOL_Obool), c_fequal), _1348292))), _1348294)), c_Groups_Ozero__class_Ozero(_1348286))), _1348290) = c_Groups_Ozero__class_Ozero(_1348286))]]], (31140 ^ _779448) ^ [_1348824, _1348826, _1348828, _1348830, _1348832] : [class_Groups_Ocomm__monoid__add(_1348824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1348826), _1348828)), 31147 ^ _779448 : [(31148 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1348826), _1348830), _1348828)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348826, _1348824), hAPP(hAPP(c_COMBC(_1348826, _1348824, _1348824), hAPP(hAPP(c_COMBS(_1348826, _1348824, tc_fun(_1348824, _1348824)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1348824, tc_fun(_1348824, _1348824)), _1348826), c_If(_1348824)), hAPP(c_fequal, _1348830))), _1348832)), c_Groups_Ozero__class_Ozero(_1348824))), _1348828) = hAPP(_1348832, _1348830))], (31154 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1348826), _1348830), _1348828))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348826, _1348824), hAPP(hAPP(c_COMBC(_1348826, _1348824, _1348824), hAPP(hAPP(c_COMBS(_1348826, _1348824, tc_fun(_1348824, _1348824)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1348824, tc_fun(_1348824, _1348824)), _1348826), c_If(_1348824)), hAPP(c_fequal, _1348830))), _1348832)), c_Groups_Ozero__class_Ozero(_1348824))), _1348828) = c_Groups_Ozero__class_Ozero(_1348824))]]], (31160 ^ _779448) ^ [_1349334, _1349336, _1349338, _1349340] : [class_Rings_Osemiring__1(_1349334), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349336, _1349334), hAPP(c_COMBK(_1349334, _1349336), _1349338)), _1349340) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349334), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1349334), hAPP(c_Finite__Set_Ocard(_1349336), _1349340))), _1349338))], (31166 ^ _779448) ^ [_1349479, _1349481, _1349483] : [class_Groups_Ocomm__monoid__add(_1349479), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349479), _1349481), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1349483))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349479), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349479), _1349481), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1349483))), hAPP(_1349481, _1349483)))], (31172 ^ _779448) ^ [_1349632, _1349634, _1349636, _1349638, _1349640] : [class_Groups_Ocomm__monoid__add(_1349632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349634), _1349636)), -(hBOOL(hAPP(hAPP(c_member(_1349634), _1349638), _1349636))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349634, _1349632), _1349640), hAPP(hAPP(c_Set_Oinsert(_1349634), _1349638), _1349636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349632), hAPP(_1349640, _1349638)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349634, _1349632), _1349640), _1349636)))], (31186 ^ _779448) ^ [_1349882, _1349884, _1349886, _1349888, _1349890] : [class_Groups_Ocomm__monoid__add(_1349882), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349884), _1349886)), -(hBOOL(hAPP(hAPP(c_member(_1349884), _1349888), _1349886))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349884, _1349882), _1349890), hAPP(hAPP(c_Set_Oinsert(_1349884), _1349888), _1349886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349882), hAPP(_1349890, _1349888)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349884, _1349882), _1349890), _1349886)))], (31200 ^ _779448) ^ [_1350132, _1350134, _1350136, _1350138, _1350140] : [class_Groups_Oab__group__add(_1350132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350134), _1350136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350134, tc_HOL_Obool)), _1350138), _1350136)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350134, _1350132), _1350140), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1350134, tc_HOL_Obool)), _1350136), _1350138)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1350132), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350134, _1350132), _1350140), _1350136)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350134, _1350132), _1350140), _1350138)))], (31214 ^ _779448) ^ [_1350449, _1350451, _1350453, _1350455, _1350457] : [class_Groups_Ocomm__monoid__add(_1350449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350451), _1350453)), c_Fun_Oinj__on(_1350451, _1350451, _1350455, _1350453), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350451, _1350449), _1350457), hAPP(c_Set_Oimage(_1350451, _1350451, _1350455), _1350453)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350451, _1350449), hAPP(c_Fun_Ocomp(_1350451, _1350449, _1350451, _1350457), _1350455)), _1350453))], (31228 ^ _779448) ^ [_1350724, _1350726, _1350728, _1350730] : [class_Groups_Ocomm__monoid__add(_1350724), 31231 ^ _779448 : [(31232 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350726), _1350728)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350726, _1350724), _1350730), _1350728) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350724, _1350726, c_Groups_Oplus__class_Oplus(_1350724)), _1350730), c_Groups_Ozero__class_Ozero(_1350724)), _1350728))], (31238 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1350726), _1350728))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350726, _1350724), _1350730), _1350728) = c_Groups_Ozero__class_Ozero(_1350724))]]], (31244 ^ _779448) ^ [_1350996, _1350998, _1351000, _1351002] : [class_Groups_Ocomm__monoid__add(_1350996), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350998), _1351000)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350998, _1350996), _1351002), _1351000) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1350996, _1350998, c_Groups_Oplus__class_Oplus(_1350996)), _1351002), c_Groups_Ozero__class_Ozero(_1350996)), _1351000))], (31254 ^ _779448) ^ [_1351191, _1351193, _1351195, _1351197] : [c_Fun_Oinj__on(_1351191, tc_fun(tc_fun(_1351191, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1351191, tc_fun(tc_prod(_1351191, _1351191), tc_HOL_Obool), tc_fun(tc_fun(_1351191, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1351191, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1351191, _1351191), tc_HOL_Obool), tc_fun(tc_fun(_1351191, tc_HOL_Obool), tc_HOL_Obool)), _1351191), c_Equiv__Relations_Oquotient(_1351191)), hAPP(hAPP(c_COMBC(_1351191, tc_fun(_1351191, tc_HOL_Obool), tc_fun(_1351191, tc_HOL_Obool)), c_Set_Oinsert(_1351191)), c_Orderings_Obot__class_Obot(tc_fun(_1351191, tc_HOL_Obool))))), _1351193), _1351195), hBOOL(hAPP(hAPP(c_member(_1351191), _1351197), _1351195)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1351191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351191, tc_HOL_Obool)), _1351195), hAPP(hAPP(c_Set_Oinsert(_1351191), _1351197), c_Orderings_Obot__class_Obot(tc_fun(_1351191, tc_HOL_Obool))))), _1351193) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1351191, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1351191), _1351195), _1351193)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1351191), hAPP(hAPP(c_Set_Oinsert(_1351191), _1351197), c_Orderings_Obot__class_Obot(tc_fun(_1351191, tc_HOL_Obool)))), _1351193)))], (31264 ^ _779448) ^ [_1351658, _1351660, _1351662, _1351664] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351658), _1351660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351658, tc_HOL_Obool)), _1351660), _1351662)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351658, tc_Nat_Onat), _1351664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351658, tc_HOL_Obool)), _1351662), _1351660)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351658, tc_Nat_Onat), _1351664), _1351662)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351658, tc_Nat_Onat), _1351664), _1351660)))], (31274 ^ _779448) ^ [_1351911, _1351913, _1351915] : [class_Groups_Ocomm__monoid__add(_1351911), hAPP(_1351913, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1351911), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1351911), _1351913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1351915)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1351911), _1351913), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1351915)))], (31284 ^ _779448) ^ [_1352100, _1352102, _1352104, _1352106] : [class_Groups_Ocomm__monoid__add(_1352100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1352102), _1352104)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352100), _1352106), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1352102), _1352104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352100), hAPP(_1352106, _1352102)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352100), _1352106), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1352102)), _1352104))))], (31294 ^ _779448) ^ [_1352333, _1352335, _1352337, _1352339] : [class_Groups_Ocomm__monoid__add(_1352333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1352335), _1352337)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352333), _1352339), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1352335, _1352337)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352333), hAPP(_1352339, _1352335)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352333), _1352339), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1352335), _1352337))))], (31304 ^ _779448) ^ [_1352558, _1352560, _1352562, _1352564] : [hBOOL(hAPP(hAPP(c_member(_1352558), _1352560), _1352562)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1352558, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1352558, _1352558, _1352564), hAPP(hAPP(c_Set_Oinsert(_1352558), _1352560), c_Orderings_Obot__class_Obot(tc_fun(_1352558, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1352558), _1352562), _1352564))))], (31310 ^ _779448) ^ [_1352729, _1352731, _1352733, _1352735, _1352737] : [class_Groups_Ocomm__monoid__add(_1352729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352731), _1352733)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352731, _1352729), _1352735), hAPP(hAPP(c_Set_Oinsert(_1352731), _1352737), _1352733)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352729), hAPP(_1352735, _1352737)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352731, _1352729), _1352735), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1352731, tc_HOL_Obool)), _1352733), hAPP(hAPP(c_Set_Oinsert(_1352731), _1352737), c_Orderings_Obot__class_Obot(tc_fun(_1352731, tc_HOL_Obool)))))))], (31320 ^ _779448) ^ [_1353013, _1353015, _1353017, _1353019] : [hBOOL(hAPP(hAPP(c_member(_1353013), _1353015), _1353017)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353013, tc_Nat_Onat), _1353019), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353013, tc_HOL_Obool)), _1353017), hAPP(hAPP(c_Set_Oinsert(_1353013), _1353015), c_Orderings_Obot__class_Obot(tc_fun(_1353013, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353013, tc_Nat_Onat), _1353019), _1353017)), hAPP(_1353019, _1353015)))], (31326 ^ _779448) ^ [_1353204, _1353206, _1353208, _1353210] : [-(hBOOL(hAPP(hAPP(c_member(_1353204), _1353206), _1353208))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353204, tc_Nat_Onat), _1353210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353204, tc_HOL_Obool)), _1353208), hAPP(hAPP(c_Set_Oinsert(_1353204), _1353206), c_Orderings_Obot__class_Obot(tc_fun(_1353204, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353204, tc_Nat_Onat), _1353210), _1353208))], (31332 ^ _779448) ^ [_1353295, _1353297, _1353299, _1353301] : [class_Groups_Ocomm__monoid__add(_1353295), 31335 ^ _779448 : [(31336 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353297), _1353299)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353295), _1353301), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1353299), hAPP(c_Nat_OSuc, _1353297))) = c_Groups_Ozero__class_Ozero(_1353295))], (31342 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1353297), _1353299))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353295), _1353301), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1353299), hAPP(c_Nat_OSuc, _1353297))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353295), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353295), _1353301), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1353299), _1353297))), hAPP(_1353301, _1353297)))]]], (31348 ^ _779448) ^ [_1353625, _1353627, _1353629, _1353631] : [class_Groups_Ocomm__monoid__add(_1353625), 31351 ^ _779448 : [(31352 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1353627)), _1353629)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353625), _1353631), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1353629, hAPP(c_Nat_OSuc, _1353627))) = c_Groups_Ozero__class_Ozero(_1353625))], (31358 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1353627)), _1353629))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353625), _1353631), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1353629, hAPP(c_Nat_OSuc, _1353627))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353625), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353625), _1353631), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1353629, _1353627))), hAPP(_1353631, hAPP(c_Nat_OSuc, _1353627))))]]], (31364 ^ _779448) ^ [_1353961, _1353963, _1353965, _1353967] : [class_Groups_Ocomm__monoid__add(_1353961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1353963), _1353965)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353961), _1353967), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1353963, _1353965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353961), hAPP(_1353967, _1353963)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1353961), _1353967), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1353963, _1353965))))], (31374 ^ _779448) ^ [_1354180, _1354182, _1354184, _1354186, _1354188] : [class_Groups_Ocomm__monoid__add(_1354180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1354182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1354184), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354180), _1354186), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354182, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1354184), _1354188))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354180), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354180), _1354186), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354182, _1354184))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354180), _1354186), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1354184), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1354184), _1354188)))))], (31384 ^ _779448) ^ [_1354471, _1354473, _1354475] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1354471), hAPP(hAPP(c_Set_Oinsert(_1354471), _1354473), c_Orderings_Obot__class_Obot(tc_fun(_1354471, tc_HOL_Obool)))), _1354475) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1354471, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1354471, _1354471, _1354475), hAPP(hAPP(c_Set_Oinsert(_1354471), _1354473), c_Orderings_Obot__class_Obot(tc_fun(_1354471, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1354471, tc_HOL_Obool), tc_HOL_Obool))))], (31386 ^ _779448) ^ [_1354558, _1354560, _1354562, _1354564, _1354566] : [class_Groups_Ocomm__monoid__add(_1354558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354560), _1354562)), hBOOL(hAPP(hAPP(c_member(_1354560), _1354564), _1354562)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354560, _1354558), _1354566), _1354562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354558), hAPP(_1354566, _1354564)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354560, _1354558), _1354566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354560, tc_HOL_Obool)), _1354562), hAPP(hAPP(c_Set_Oinsert(_1354560), _1354564), c_Orderings_Obot__class_Obot(tc_fun(_1354560, tc_HOL_Obool)))))))], (31400 ^ _779448) ^ [_1354883, _1354885, _1354887, _1354889, _1354891] : [class_Groups_Ocomm__monoid__add(_1354883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354885), _1354887)), hBOOL(hAPP(hAPP(c_member(_1354885), _1354889), _1354887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354885, _1354883), _1354891), _1354887) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354883), hAPP(_1354891, _1354889)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354885, _1354883), _1354891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1354885, tc_HOL_Obool)), _1354887), hAPP(hAPP(c_Set_Oinsert(_1354885), _1354889), c_Orderings_Obot__class_Obot(tc_fun(_1354885, tc_HOL_Obool)))))))], (31414 ^ _779448) ^ [_1355208, _1355210, _1355212, _1355214, _1355216] : [class_Rings_Oring(_1355208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355210), _1355212)), hBOOL(hAPP(hAPP(c_member(_1355210), _1355214), _1355212)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355210, _1355208), _1355216), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355210, tc_HOL_Obool)), _1355212), hAPP(hAPP(c_Set_Oinsert(_1355210), _1355214), c_Orderings_Obot__class_Obot(tc_fun(_1355210, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1355208), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355210, _1355208), _1355216), _1355212)), hAPP(_1355216, _1355214)))], (31428 ^ _779448) ^ [_1355533, _1355535, _1355537, _1355539, _1355541] : [class_Groups_Oab__group__add(_1355533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355535), _1355537)), 31435 ^ _779448 : [(31436 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1355535), _1355539), _1355537)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355535, _1355533), _1355541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355535, tc_HOL_Obool)), _1355537), hAPP(hAPP(c_Set_Oinsert(_1355535), _1355539), c_Orderings_Obot__class_Obot(tc_fun(_1355535, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1355533), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355535, _1355533), _1355541), _1355537)), hAPP(_1355541, _1355539)))], (31442 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1355535), _1355539), _1355537))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355535, _1355533), _1355541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355535, tc_HOL_Obool)), _1355537), hAPP(hAPP(c_Set_Oinsert(_1355535), _1355539), c_Orderings_Obot__class_Obot(tc_fun(_1355535, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355535, _1355533), _1355541), _1355537))]]], (31448 ^ _779448) ^ [_1356003, _1356005, _1356007] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1356003), _1356005)), c_Fun_Oinj__on(_1356003, tc_fun(tc_fun(_1356003, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1356003, tc_fun(tc_prod(_1356003, _1356003), tc_HOL_Obool), tc_fun(tc_fun(_1356003, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1356003, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1356003, _1356003), tc_HOL_Obool), tc_fun(tc_fun(_1356003, tc_HOL_Obool), tc_HOL_Obool)), _1356003), c_Equiv__Relations_Oquotient(_1356003)), hAPP(hAPP(c_COMBC(_1356003, tc_fun(_1356003, tc_HOL_Obool), tc_fun(_1356003, tc_HOL_Obool)), c_Set_Oinsert(_1356003)), c_Orderings_Obot__class_Obot(tc_fun(_1356003, tc_HOL_Obool))))), _1356007), _1356005), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1356003, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1356003), _1356005), _1356007)) = hAPP(c_Finite__Set_Ocard(_1356003), _1356005))], (31458 ^ _779448) ^ [_1356352, _1356354, _1356356] : [class_Fields_Ofield(_1356352), -(_1356354 = c_Groups_Oone__class_Oone(_1356352)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356352), hAPP(c_Power_Opower__class_Opower(_1356352), _1356354)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1356356)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356352), hAPP(hAPP(c_Power_Opower__class_Opower(_1356352), _1356354), _1356356)), c_Groups_Oone__class_Oone(_1356352))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356352), _1356354), c_Groups_Oone__class_Oone(_1356352))))], (31468 ^ _779448) ^ [_1356554, _1356556] : [class_Rings_Ocomm__semiring__1(_1356554), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356554), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356554), c_Groups_Oone__class_Oone(_1356554)), c_Groups_Oone__class_Oone(_1356554))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356554), c_Nat_Osemiring__1__class_Oof__nat(_1356554)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1356556))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356554), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356554), _1356556)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356554), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356554), _1356556)), c_Groups_Oone__class_Oone(_1356554))))], (31474 ^ _779448) ^ [_1356755, _1356757, _1356759, _1356761] : [class_Groups_Oab__group__add(_1356755), 31477 ^ _779448 : [(31478 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1356757), _1356759)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356755), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1356755, _1356755), hAPP(hAPP(c_COMBB(_1356755, tc_fun(_1356755, _1356755), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1356755)), _1356761)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356755, tc_Nat_Onat), _1356761), 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, _1356757, _1356759)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356755), hAPP(_1356761, _1356757)), hAPP(_1356761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356759), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (31484 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1356757), _1356759))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356755), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1356755, _1356755), hAPP(hAPP(c_COMBB(_1356755, tc_fun(_1356755, _1356755), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1356755)), _1356761)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356755, tc_Nat_Onat), _1356761), 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, _1356757, _1356759)) = c_Groups_Ozero__class_Ozero(_1356755))]]], (31490 ^ _779448) ^ [_1357193, _1357195, _1357197] : [31492 ^ _779448 : [(31493 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357193), 31491 ^ [_1357193, _1357195, _1357197]), _1357195)))], (31495 ^ _779448) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1357197, 31491 ^ [_1357193, _1357195, _1357197]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357193, tc_Int_Oint), _1357197), _1357195) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357193, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1357193), c_Int_Onat), _1357197)), _1357195)))], (31499 ^ _779448) ^ [_1357423, _1357425, _1357427, _1357429, _1357431] : [class_Groups_Oordered__comm__monoid__add(_1357423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357425), _1357427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357425, tc_HOL_Obool)), _1357429), _1357427)), 31513 ^ _779448 : [(31514 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357425), 31512 ^ [_1357423, _1357425, _1357427, _1357429, _1357431]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357425, tc_HOL_Obool)), _1357427), _1357429))))], (31516 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357423), c_Groups_Ozero__class_Ozero(_1357423)), hAPP(_1357431, 31512 ^ [_1357423, _1357425, _1357427, _1357429, _1357431])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357423), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357425, _1357423), _1357431), _1357429)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357425, _1357423), _1357431), _1357427))))], (31520 ^ _779448) ^ [_1357909, _1357911, _1357913, _1357915, _1357917] : [c_Equiv__Relations_Oequiv(_1357909, _1357911, _1357913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357909, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1357909, _1357909, _1357913), hAPP(hAPP(c_Set_Oinsert(_1357909), _1357915), c_Orderings_Obot__class_Obot(tc_fun(_1357909, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1357909, _1357909, _1357913), hAPP(hAPP(c_Set_Oinsert(_1357909), _1357917), c_Orderings_Obot__class_Obot(tc_fun(_1357909, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1357909), _1357915), _1357911)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1357909, _1357909)), hAPP(hAPP(c_Product__Type_OPair(_1357909, _1357909), _1357917), _1357915)), _1357913)))], (31534 ^ _779448) ^ [_1358262, _1358264, _1358266, _1358268] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1358262, tc_HOL_Obool)), _1358264), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1358262), _1358266), _1358268))), 31538 ^ _779448 : [(31539 ^ _779448) ^ [] : [-(_1358264 = hAPP(c_Relation_OImage(_1358262, _1358262, _1358268), hAPP(hAPP(c_Set_Oinsert(_1358262), 31537 ^ [_1358262, _1358264, _1358266, _1358268]), c_Orderings_Obot__class_Obot(tc_fun(_1358262, tc_HOL_Obool)))))], (31541 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358262), 31537 ^ [_1358262, _1358264, _1358266, _1358268]), _1358266)))]]], (31543 ^ _779448) ^ [_1358490, _1358492, _1358494] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358490), _1358492), _1358494) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1358490), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1358490, tc_Int_Oint), _1358492), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1358494))), class_Groups_Ocomm__monoid__add(_1358490), class_Groups_Ocomm__monoid__mult(_1358490)], (31553 ^ _779448) ^ [_1358681, _1358683, _1358685, _1358687] : [c_Equiv__Relations_Oequiv(_1358681, _1358683, _1358685), hBOOL(hAPP(hAPP(c_member(_1358681), _1358687), _1358683)), -(hBOOL(hAPP(hAPP(c_member(_1358681), _1358687), hAPP(c_Relation_OImage(_1358681, _1358681, _1358685), hAPP(hAPP(c_Set_Oinsert(_1358681), _1358687), c_Orderings_Obot__class_Obot(tc_fun(_1358681, tc_HOL_Obool)))))))], (31563 ^ _779448) ^ [_1358888, _1358890, _1358892] : [class_Groups_Ocomm__monoid__add(_1358888), class_Groups_Ocomm__monoid__mult(_1358888), c_Nat__Transfer_Onat__set(_1358890), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1358888), _1358892), _1358890) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1358888), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1358888, tc_Nat_Onat), _1358892), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1358890)))], (31577 ^ _779448) ^ [_1359133, _1359135, _1359137, _1359139, _1359141] : [c_Equiv__Relations_Oequiv(_1359133, _1359135, _1359137), hBOOL(hAPP(hAPP(c_member(tc_prod(_1359133, _1359133)), hAPP(hAPP(c_Product__Type_OPair(_1359133, _1359133), _1359139), _1359141)), _1359137)), -(hAPP(c_Relation_OImage(_1359133, _1359133, _1359137), hAPP(hAPP(c_Set_Oinsert(_1359133), _1359139), c_Orderings_Obot__class_Obot(tc_fun(_1359133, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1359133, _1359133, _1359137), hAPP(hAPP(c_Set_Oinsert(_1359133), _1359141), c_Orderings_Obot__class_Obot(tc_fun(_1359133, tc_HOL_Obool)))))], (31587 ^ _779448) ^ [_1359394, _1359396, _1359398, _1359400, _1359402, _1359404, _1359406] : [c_Equiv__Relations_Oequiv(_1359394, _1359396, _1359398), hBOOL(hAPP(hAPP(c_member(tc_fun(_1359394, tc_HOL_Obool)), _1359400), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1359394), _1359396), _1359398))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1359394, tc_HOL_Obool)), _1359402), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1359394), _1359396), _1359398))), hBOOL(hAPP(hAPP(c_member(_1359394), _1359404), _1359400)), hBOOL(hAPP(hAPP(c_member(_1359394), _1359406), _1359402)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1359394, _1359394)), hAPP(hAPP(c_Product__Type_OPair(_1359394, _1359394), _1359404), _1359406)), _1359398)), -(_1359400 = _1359402)], (31613 ^ _779448) ^ [_1359931, _1359933, _1359935, _1359937, _1359939, _1359941, _1359943] : [c_Equiv__Relations_Oequiv(_1359931, _1359933, _1359935), hBOOL(hAPP(hAPP(c_member(tc_fun(_1359931, tc_HOL_Obool)), _1359937), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1359931), _1359933), _1359935))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1359931, tc_HOL_Obool)), _1359939), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1359931), _1359933), _1359935))), hBOOL(hAPP(hAPP(c_member(_1359931), _1359941), _1359937)), hBOOL(hAPP(hAPP(c_member(_1359931), _1359943), _1359939)), 31632 ^ _779448 : [(31633 ^ _779448) ^ [] : [_1359937 = _1359939, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1359931, _1359931)), hAPP(hAPP(c_Product__Type_OPair(_1359931, _1359931), _1359941), _1359943)), _1359935)))], (31639 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1359931, _1359931)), hAPP(hAPP(c_Product__Type_OPair(_1359931, _1359931), _1359941), _1359943)), _1359935)), -(_1359937 = _1359939)]]], (31645 ^ _779448) ^ [_1360575, _1360577, _1360579, _1360581, _1360583] : [c_Equiv__Relations_Oequiv(_1360575, _1360577, _1360579), hBOOL(hAPP(hAPP(c_member(_1360575), _1360581), _1360577)), hBOOL(hAPP(hAPP(c_member(_1360575), _1360583), _1360577)), 31656 ^ _779448 : [(31657 ^ _779448) ^ [] : [hAPP(c_Relation_OImage(_1360575, _1360575, _1360579), hAPP(hAPP(c_Set_Oinsert(_1360575), _1360581), c_Orderings_Obot__class_Obot(tc_fun(_1360575, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1360575, _1360575, _1360579), hAPP(hAPP(c_Set_Oinsert(_1360575), _1360583), c_Orderings_Obot__class_Obot(tc_fun(_1360575, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1360575, _1360575)), hAPP(hAPP(c_Product__Type_OPair(_1360575, _1360575), _1360581), _1360583)), _1360579)))], (31663 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1360575, _1360575)), hAPP(hAPP(c_Product__Type_OPair(_1360575, _1360575), _1360581), _1360583)), _1360579)), -(hAPP(c_Relation_OImage(_1360575, _1360575, _1360579), hAPP(hAPP(c_Set_Oinsert(_1360575), _1360581), c_Orderings_Obot__class_Obot(tc_fun(_1360575, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1360575, _1360575, _1360579), hAPP(hAPP(c_Set_Oinsert(_1360575), _1360583), c_Orderings_Obot__class_Obot(tc_fun(_1360575, tc_HOL_Obool)))))]]], (31669 ^ _779448) ^ [_1361123, _1361125, _1361127, _1361129, _1361131] : [hAPP(c_Relation_OImage(_1361123, _1361123, _1361125), hAPP(hAPP(c_Set_Oinsert(_1361123), _1361127), c_Orderings_Obot__class_Obot(tc_fun(_1361123, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1361123, _1361123, _1361125), hAPP(hAPP(c_Set_Oinsert(_1361123), _1361129), c_Orderings_Obot__class_Obot(tc_fun(_1361123, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1361123, _1361131, _1361125), hBOOL(hAPP(hAPP(c_member(_1361123), _1361129), _1361131)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361123, _1361123)), hAPP(hAPP(c_Product__Type_OPair(_1361123, _1361123), _1361127), _1361129)), _1361125)))], (31683 ^ _779448) ^ [_1361456, _1361458, _1361460, _1361462, _1361464] : [c_Equiv__Relations_Oequiv(_1361456, _1361458, _1361460), 31686 ^ _779448 : [(31687 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1361456, _1361456)), hAPP(hAPP(c_Product__Type_OPair(_1361456, _1361456), _1361462), _1361464)), _1361460)), 31690 ^ _779448 : [(31691 ^ _779448) ^ [] : [-(hAPP(c_Relation_OImage(_1361456, _1361456, _1361460), hAPP(hAPP(c_Set_Oinsert(_1361456), _1361462), c_Orderings_Obot__class_Obot(tc_fun(_1361456, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1361456, _1361456, _1361460), hAPP(hAPP(c_Set_Oinsert(_1361456), _1361464), c_Orderings_Obot__class_Obot(tc_fun(_1361456, tc_HOL_Obool)))))], (31693 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361456), _1361462), _1361458)))], (31695 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361456), _1361464), _1361458)))]]], (31697 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1361456, _1361456)), hAPP(hAPP(c_Product__Type_OPair(_1361456, _1361456), _1361462), _1361464)), _1361460))), hAPP(c_Relation_OImage(_1361456, _1361456, _1361460), hAPP(hAPP(c_Set_Oinsert(_1361456), _1361462), c_Orderings_Obot__class_Obot(tc_fun(_1361456, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1361456, _1361456, _1361460), hAPP(hAPP(c_Set_Oinsert(_1361456), _1361464), c_Orderings_Obot__class_Obot(tc_fun(_1361456, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1361456), _1361462), _1361458)), hBOOL(hAPP(hAPP(c_member(_1361456), _1361464), _1361458))]]], (31711 ^ _779448) ^ [_1362056, _1362058, _1362060, _1362062, _1362064] : [c_Equiv__Relations_Oequiv(_1362056, _1362058, _1362060), hBOOL(hAPP(hAPP(c_member(tc_prod(_1362056, _1362056)), hAPP(hAPP(c_Product__Type_OPair(_1362056, _1362056), _1362062), _1362064)), _1362060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1362056, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1362056, _1362056, _1362060), hAPP(hAPP(c_Set_Oinsert(_1362056), _1362062), c_Orderings_Obot__class_Obot(tc_fun(_1362056, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1362056, _1362056, _1362060), hAPP(hAPP(c_Set_Oinsert(_1362056), _1362064), c_Orderings_Obot__class_Obot(tc_fun(_1362056, tc_HOL_Obool)))))))], (31721 ^ _779448) ^ [_1362337, _1362339, _1362341, _1362343, _1362345] : [c_Equiv__Relations_Oequiv(_1362337, _1362339, _1362341), hBOOL(hAPP(hAPP(c_member(_1362337), _1362343), _1362339)), hBOOL(hAPP(hAPP(c_member(_1362337), _1362345), _1362339)), 31732 ^ _779448 : [(31733 ^ _779448) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1362337), hAPP(hAPP(c_Set_Oinsert(_1362337), _1362343), c_Orderings_Obot__class_Obot(tc_fun(_1362337, tc_HOL_Obool)))), _1362341) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1362337), hAPP(hAPP(c_Set_Oinsert(_1362337), _1362345), c_Orderings_Obot__class_Obot(tc_fun(_1362337, tc_HOL_Obool)))), _1362341), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1362337, _1362337)), hAPP(hAPP(c_Product__Type_OPair(_1362337, _1362337), _1362343), _1362345)), _1362341)))], (31739 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1362337, _1362337)), hAPP(hAPP(c_Product__Type_OPair(_1362337, _1362337), _1362343), _1362345)), _1362341)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1362337), hAPP(hAPP(c_Set_Oinsert(_1362337), _1362343), c_Orderings_Obot__class_Obot(tc_fun(_1362337, tc_HOL_Obool)))), _1362341) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1362337), hAPP(hAPP(c_Set_Oinsert(_1362337), _1362345), c_Orderings_Obot__class_Obot(tc_fun(_1362337, tc_HOL_Obool)))), _1362341))]]], (31745 ^ _779448) ^ [_1362891, _1362893, _1362895, _1362897, _1362899, _1362901, _1362903, _1362905, _1362907, _1362909] : [c_Equiv__Relations_Oequiv(_1362891, _1362893, _1362895), c_Equiv__Relations_Oequiv(_1362897, _1362899, _1362901), c_Equiv__Relations_Ocongruent2(_1362891, _1362897, tc_fun(_1362903, tc_HOL_Obool), _1362895, _1362901, _1362905), hBOOL(hAPP(hAPP(c_member(_1362891), _1362907), _1362893)), hBOOL(hAPP(hAPP(c_member(_1362897), _1362909), _1362899)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362891, tc_fun(_1362903, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1362891, _1362891, _1362895), hAPP(hAPP(c_Set_Oinsert(_1362891), _1362907), c_Orderings_Obot__class_Obot(tc_fun(_1362891, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1362897, tc_fun(_1362903, tc_HOL_Obool)), tc_fun(_1362903, tc_HOL_Obool), _1362891), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1362897, tc_fun(_1362903, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1362897, _1362897, _1362901), hAPP(hAPP(c_Set_Oinsert(_1362897), _1362909), c_Orderings_Obot__class_Obot(tc_fun(_1362897, tc_HOL_Obool)))))), _1362905)) = hAPP(hAPP(_1362905, _1362907), _1362909))], (31767 ^ _779448) ^ [_1363474, _1363476, _1363478, _1363480, _1363482, _1363484] : [c_Equiv__Relations_Oequiv(_1363474, _1363476, _1363478), c_Equiv__Relations_Ocongruent(_1363474, tc_fun(_1363480, tc_HOL_Obool), _1363478, _1363482), hBOOL(hAPP(hAPP(c_member(_1363474), _1363484), _1363476)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1363474, tc_fun(_1363480, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1363474, _1363474, _1363478), hAPP(hAPP(c_Set_Oinsert(_1363474), _1363484), c_Orderings_Obot__class_Obot(tc_fun(_1363474, tc_HOL_Obool))))), _1363482) = hAPP(_1363482, _1363484))], (31781 ^ _779448) ^ [_1363775, _1363777, _1363779, _1363781, _1363783] : [class_Groups_Oordered__ab__semigroup__add(_1363775), class_Rings_Osemiring__1(_1363775), 31791 ^ _779448 : [(31792 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1363777), 31790 ^ [_1363775, _1363777, _1363779, _1363781, _1363783]), _1363779)))], (31794 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363775), hAPP(_1363781, 31790 ^ [_1363775, _1363777, _1363779, _1363781, _1363783])), _1363783))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363775), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363777, _1363775), _1363781), _1363779)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363775), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363775), hAPP(c_Finite__Set_Ocard(_1363777), _1363779))), _1363783))))], (31798 ^ _779448) ^ [_1364165, _1364167, _1364169, _1364171, _1364173] : [class_Groups_Ocomm__monoid__add(_1364165), class_Groups_Oordered__ab__semigroup__add(_1364165), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364167), _1364169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1364167, tc_HOL_Obool)), _1364171), _1364169)), 31816 ^ _779448 : [(31817 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364167), 31815 ^ [_1364165, _1364167, _1364169, _1364171, _1364173]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1364167, tc_HOL_Obool)), _1364169), _1364171))))], (31819 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364165), c_Groups_Ozero__class_Ozero(_1364165)), hAPP(_1364173, 31815 ^ [_1364165, _1364167, _1364169, _1364171, _1364173])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364165), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364167, _1364165), _1364173), _1364171)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364167, _1364165), _1364173), _1364169))))], (31823 ^ _779448) ^ [_1364709, _1364711, _1364713, _1364715, _1364717, _1364719, _1364721, _1364723] : [c_Equiv__Relations_Oequiv(_1364709, _1364711, _1364713), c_Equiv__Relations_Ocongruent2(_1364709, _1364715, _1364717, _1364713, _1364719, _1364721), hBOOL(hAPP(hAPP(c_member(_1364709), _1364723), _1364711)), -(c_Equiv__Relations_Ocongruent(_1364715, _1364717, _1364719, hAPP(_1364721, _1364723)))], (31837 ^ _779448) ^ [_1364960, _1364962, _1364964, _1364966, _1364968, _1364970, _1364972, _1364974, _1364976, _1364978] : [c_Equiv__Relations_Ocongruent2(_1364960, _1364962, _1364964, _1364966, _1364968, _1364970), hBOOL(hAPP(hAPP(c_member(tc_prod(_1364960, _1364960)), hAPP(hAPP(c_Product__Type_OPair(_1364960, _1364960), _1364972), _1364974)), _1364966)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1364962, _1364962)), hAPP(hAPP(c_Product__Type_OPair(_1364962, _1364962), _1364976), _1364978)), _1364968)), -(hAPP(hAPP(_1364970, _1364972), _1364976) = hAPP(hAPP(_1364970, _1364974), _1364978))], (31851 ^ _779448) ^ [_1365297, _1365299, _1365301, _1365303, _1365305, _1365307] : [c_Equiv__Relations_Ocongruent(_1365297, _1365299, _1365301, _1365303), hBOOL(hAPP(hAPP(c_member(tc_prod(_1365297, _1365297)), hAPP(hAPP(c_Product__Type_OPair(_1365297, _1365297), _1365305), _1365307)), _1365301)), -(hAPP(_1365303, _1365305) = hAPP(_1365303, _1365307))], (31861 ^ _779448) ^ [_1365496, _1365498, _1365500, _1365502, _1365504, _1365506, _1365508, _1365510, _1365512] : [c_Equiv__Relations_Oequiv(_1365496, _1365498, _1365500), c_Equiv__Relations_Oequiv(_1365502, _1365504, _1365506), c_Equiv__Relations_Ocongruent2(_1365496, _1365502, tc_fun(_1365508, tc_HOL_Obool), _1365500, _1365506, _1365510), hBOOL(hAPP(hAPP(c_member(_1365502), _1365512), _1365504)), -(c_Equiv__Relations_Ocongruent(_1365496, tc_fun(_1365508, tc_HOL_Obool), _1365500, hAPP(hAPP(c_COMBB(tc_fun(_1365502, tc_fun(_1365508, tc_HOL_Obool)), tc_fun(_1365508, tc_HOL_Obool), _1365496), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365502, tc_fun(_1365508, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1365502, _1365502, _1365506), hAPP(hAPP(c_Set_Oinsert(_1365502), _1365512), c_Orderings_Obot__class_Obot(tc_fun(_1365502, tc_HOL_Obool)))))), _1365510)))], (31879 ^ _779448) ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935] : [c_Equiv__Relations_Oequiv(_1365923, _1365925, _1365927), c_Equiv__Relations_Ocongruent(_1365923, tc_fun(_1365929, tc_HOL_Obool), _1365927, _1365931), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365923, tc_fun(_1365929, tc_HOL_Obool)), _1365933), _1365931) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1365923, tc_fun(_1365929, tc_HOL_Obool)), _1365935), _1365931), hBOOL(hAPP(hAPP(c_member(tc_fun(_1365923, tc_HOL_Obool)), _1365933), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1365923), _1365925), _1365927))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1365923, tc_HOL_Obool)), _1365935), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1365923), _1365925), _1365927))), 31901 ^ _779448 : [(31902 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365923), 31900 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935]), _1365925)))], (31905 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365923), 31903 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935]), _1365925)))], (31907 ^ _779448) ^ [] : [-(hAPP(_1365931, 31900 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935]) = hAPP(_1365931, 31903 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935]))], (31909 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1365923, _1365923)), hAPP(hAPP(c_Product__Type_OPair(_1365923, _1365923), 31900 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935]), 31903 ^ [_1365923, _1365925, _1365927, _1365929, _1365931, _1365933, _1365935])), _1365927))]], -(_1365933 = _1365935)], (31913 ^ _779448) ^ [_1366893, _1366895, _1366897, _1366899, _1366901, _1366903, _1366905, _1366907, _1366909, _1366911, _1366913] : [c_Equiv__Relations_Oequiv(_1366893, _1366895, _1366897), c_Equiv__Relations_Oequiv(_1366899, _1366901, _1366903), c_Equiv__Relations_Ocongruent2(_1366893, _1366899, tc_fun(_1366905, tc_HOL_Obool), _1366897, _1366903, _1366907), hBOOL(hAPP(hAPP(c_member(tc_fun(_1366893, tc_HOL_Obool)), _1366909), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1366893), _1366895), _1366897))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1366899, tc_HOL_Obool)), _1366911), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1366899), _1366901), _1366903))), 31935 ^ _779448 : [(31936 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366893), 31934 ^ [_1366893, _1366895, _1366897, _1366899, _1366901, _1366903, _1366905, _1366907, _1366909, _1366911, _1366913]), _1366895)))], (31939 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366899), 31937 ^ [_1366893, _1366895, _1366897, _1366899, _1366901, _1366903, _1366905, _1366907, _1366909, _1366911, _1366913]), _1366901)))], (31941 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1366905, tc_HOL_Obool)), hAPP(hAPP(_1366907, 31934 ^ [_1366893, _1366895, _1366897, _1366899, _1366901, _1366903, _1366905, _1366907, _1366909, _1366911, _1366913]), 31937 ^ [_1366893, _1366895, _1366897, _1366899, _1366901, _1366903, _1366905, _1366907, _1366909, _1366911, _1366913])), _1366913))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1366905, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1366893, tc_fun(_1366905, tc_HOL_Obool)), _1366909), hAPP(hAPP(c_COMBB(tc_fun(_1366899, tc_fun(_1366905, tc_HOL_Obool)), tc_fun(_1366905, tc_HOL_Obool), _1366893), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1366899, tc_fun(_1366905, tc_HOL_Obool)), _1366911)), _1366907))), _1366913)))], (31945 ^ _779448) ^ [_1367895, _1367897, _1367899, _1367901, _1367903, _1367905, _1367907] : [c_Equiv__Relations_Oequiv(_1367895, _1367897, _1367899), c_Equiv__Relations_Ocongruent(_1367895, tc_fun(_1367901, tc_HOL_Obool), _1367899, _1367903), hBOOL(hAPP(hAPP(c_member(tc_fun(_1367895, tc_HOL_Obool)), _1367905), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1367895), _1367897), _1367899))), 31959 ^ _779448 : [(31960 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1367895), 31958 ^ [_1367895, _1367897, _1367899, _1367901, _1367903, _1367905, _1367907]), _1367897)))], (31962 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1367901, tc_HOL_Obool)), hAPP(_1367903, 31958 ^ [_1367895, _1367897, _1367899, _1367901, _1367903, _1367905, _1367907])), _1367907))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1367901, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1367895, tc_fun(_1367901, tc_HOL_Obool)), _1367905), _1367903)), _1367907)))], (31966 ^ _779448) ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416] : [class_Groups_Ocomm__monoid__add(_1368406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368408), _1368410)), 31976 ^ _779448 : [(31977 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1368408), 31975 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416]), _1368410)))], (31980 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1368408), 31978 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416]), _1368410)))], (31982 ^ _779448) ^ [] : [31975 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416] = 31978 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416]], (31984 ^ _779448) ^ [] : [-(hAPP(_1368412, 31975 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416]) = hAPP(_1368412, 31978 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416]))], (31986 ^ _779448) ^ [] : [hAPP(_1368414, hAPP(_1368412, 31975 ^ [_1368406, _1368408, _1368410, _1368412, _1368414, _1368416])) = c_Groups_Ozero__class_Ozero(_1368406)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368416, _1368406), _1368414), hAPP(c_Set_Oimage(_1368408, _1368416, _1368412), _1368410)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1368408, _1368406), hAPP(c_Fun_Ocomp(_1368416, _1368406, _1368408, _1368414), _1368412)), _1368410))], (31990 ^ _779448) ^ [_1369143, _1369145, _1369147, _1369149, _1369151, _1369153] : [c_Equiv__Relations_Oequiv(_1369143, _1369145, _1369147), hBOOL(hAPP(hAPP(c_member(_1369143), _1369149), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1369143, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1369143, _1369143, _1369147), hAPP(hAPP(c_Set_Oinsert(_1369143), _1369151), c_Orderings_Obot__class_Obot(tc_fun(_1369143, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1369143, _1369143, _1369147), hAPP(hAPP(c_Set_Oinsert(_1369143), _1369153), c_Orderings_Obot__class_Obot(tc_fun(_1369143, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1369143, _1369143)), hAPP(hAPP(c_Product__Type_OPair(_1369143, _1369143), _1369151), _1369153)), _1369147)))], (32000 ^ _779448) ^ [_1369444] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1369444) = 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), _1369444))))], (32002 ^ _779448) ^ [_1369480, _1369482, _1369484] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1369480, _1369480)), _1369482), c_Relation_OId__on(_1369480, _1369484))), 32006 ^ _779448 : [(32007 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369480), 32005 ^ [_1369480, _1369482, _1369484]), _1369484)))], (32009 ^ _779448) ^ [] : [-(_1369482 = hAPP(hAPP(c_Product__Type_OPair(_1369480, _1369480), 32005 ^ [_1369480, _1369482, _1369484]), 32005 ^ [_1369480, _1369482, _1369484]))]]], (32011 ^ _779448) ^ [_1369679, _1369681, _1369683, _1369685, _1369687] : [class_Groups_Oordered__ab__group__add(_1369679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369681), _1369683)), 32021 ^ _779448 : [(32022 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1369681), 32020 ^ [_1369679, _1369681, _1369683, _1369685, _1369687]), _1369683)))], (32024 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369679), c_Groups_Ozero__class_Ozero(_1369679)), hAPP(_1369685, 32020 ^ [_1369679, _1369681, _1369683, _1369685, _1369687])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1369681, _1369679), _1369685), _1369683) = c_Groups_Ozero__class_Ozero(_1369679), hBOOL(hAPP(hAPP(c_member(_1369681), _1369687), _1369683)), -(hAPP(_1369685, _1369687) = c_Groups_Ozero__class_Ozero(_1369679))], (32036 ^ _779448) ^ [_1370177, _1370179, _1370181, _1370183] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370177, tc_HOL_Obool)), _1370179), _1370181), _1370183)), 32039 ^ _779448 : [(32040 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1370179, _1370183)))], (32042 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1370181, _1370183)))]]], (32044 ^ _779448) ^ [_1370322, _1370324, _1370326, _1370328] : [hBOOL(hAPP(_1370322, _1370324)), hBOOL(hAPP(_1370326, _1370324)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370328, tc_HOL_Obool)), _1370322), _1370326), _1370324)))], (32054 ^ _779448) ^ [_1370493, _1370495, _1370497, _1370499] : [hBOOL(hAPP(hAPP(c_member(_1370493), _1370495), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370493, tc_HOL_Obool)), _1370497), _1370499))), 32057 ^ _779448 : [(32058 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370493), _1370495), _1370497)))], (32060 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370493), _1370495), _1370499)))]]], (32062 ^ _779448) ^ [_1370668, _1370670, _1370672, _1370674] : [hBOOL(hAPP(hAPP(c_member(_1370668), _1370670), _1370672)), hBOOL(hAPP(hAPP(c_member(_1370668), _1370670), _1370674)), -(hBOOL(hAPP(hAPP(c_member(_1370668), _1370670), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370668, tc_HOL_Obool)), _1370672), _1370674))))], (32072 ^ _779448) ^ [_1370869, _1370871, _1370873] : [32073 ^ _779448 : [(32074 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370869), _1370871))], (32076 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1370869), _1370873))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1370869), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370869, tc_HOL_Obool)), _1370871), _1370873))))], (32080 ^ _779448) ^ [_1371032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1371032))))], (32082 ^ _779448) ^ [_1371060, _1371062, _1371064, _1371066, _1371068] : [c_Fun_Oinj__on(_1371060, _1371062, _1371064, _1371066), c_Fun_Oinj__on(_1371060, _1371062, _1371064, _1371068), -(c_Fun_Oinj__on(_1371060, _1371062, _1371064, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371060, tc_HOL_Obool)), _1371066), _1371068)))], (32092 ^ _779448) ^ [_1371235, _1371237, _1371239, _1371241] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371235, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371235, tc_HOL_Obool)), _1371237), _1371239)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371235, tc_HOL_Obool)), _1371241), _1371239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371235, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371235, tc_HOL_Obool)), _1371237), _1371239)), _1371241))], (32094 ^ _779448) ^ [_1371319, _1371321, _1371323, _1371325] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371319, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371319, tc_HOL_Obool)), _1371321), _1371323)), _1371325) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371319, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371319, tc_HOL_Obool)), _1371321), _1371325)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371319, tc_HOL_Obool)), _1371323), _1371325)))], (32096 ^ _779448) ^ [_1371403, _1371405, _1371407, _1371409] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371403, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371403, tc_HOL_Obool)), _1371405), _1371407)), _1371409) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371403, tc_HOL_Obool)), _1371405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371403, tc_HOL_Obool)), _1371407), _1371409)))], (32098 ^ _779448) ^ [_1371476, _1371478, _1371480, _1371482] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371476, tc_HOL_Obool)), _1371478), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371476, tc_HOL_Obool)), _1371480), _1371482)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371476, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371476, tc_HOL_Obool)), _1371478), _1371480)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1371476, tc_HOL_Obool)), _1371478), _1371482)))], (32100 ^ _779448) ^ [_1371560, _1371562, _1371564, _1371566] : [class_Lattices_Odistrib__lattice(_1371560), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371560), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371560), _1371562), _1371564)), _1371566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371560), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371560), _1371562), _1371566)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371560), _1371564), _1371566)))], (32106 ^ _779448) ^ [_1371719, _1371721, _1371723, _1371725] : [class_Lattices_Odistrib__lattice(_1371719), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371719), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371719), _1371721), _1371723)), _1371725) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371719), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371719), _1371721), _1371725)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371719), _1371723), _1371725)))], (32112 ^ _779448) ^ [_1371878, _1371880, _1371882, _1371884] : [class_Lattices_Odistrib__lattice(_1371878), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371878), _1371880), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371878), _1371882), _1371884)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371878), _1371880), _1371882)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371878), _1371880), _1371884)))], (32118 ^ _779448) ^ [_1372037, _1372039, _1372041, _1372043] : [class_Lattices_Odistrib__lattice(_1372037), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372037), _1372039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372037), _1372041), _1372043)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372037), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372037), _1372039), _1372041)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372037), _1372039), _1372043)))], (32124 ^ _779448) ^ [_1372196, _1372198, _1372200] : [class_Lattices_Olattice(_1372196), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372196), _1372198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372196), _1372198), _1372200)) = _1372198)], (32130 ^ _779448) ^ [_1372305, _1372307, _1372309] : [class_Lattices_Olattice(_1372305), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1372305), _1372307), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372305), _1372307), _1372309)) = _1372307)], (32136 ^ _779448) ^ [_1372414, _1372416, _1372418, _1372420] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372414, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372414, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372414, tc_HOL_Obool)), _1372416), _1372418)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372414, tc_HOL_Obool)), _1372418), _1372420))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372414, tc_HOL_Obool)), _1372420), _1372416)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372414, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372414, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372414, tc_HOL_Obool)), _1372416), _1372418)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372414, tc_HOL_Obool)), _1372418), _1372420))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372414, tc_HOL_Obool)), _1372420), _1372416)))], (32138 ^ _779448) ^ [_1372553, _1372555, _1372557, _1372559] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372553, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372553, tc_HOL_Obool)), _1372555), _1372557)), _1372559) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372553, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372553, tc_HOL_Obool)), _1372555), _1372559)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372553, tc_HOL_Obool)), _1372557), _1372559)))], (32140 ^ _779448) ^ [_1372637, _1372639, _1372641, _1372643] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372637, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372637, tc_HOL_Obool)), _1372639), _1372641)), _1372643) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372637, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372637, tc_HOL_Obool)), _1372639), _1372643)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372637, tc_HOL_Obool)), _1372641), _1372643)))], (32142 ^ _779448) ^ [_1372721, _1372723, _1372725, _1372727] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372721, tc_HOL_Obool)), _1372723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372721, tc_HOL_Obool)), _1372725), _1372727)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372721, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372721, tc_HOL_Obool)), _1372723), _1372725)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372721, tc_HOL_Obool)), _1372723), _1372727)))], (32144 ^ _779448) ^ [_1372805, _1372807, _1372809, _1372811] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372805, tc_HOL_Obool)), _1372807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372805, tc_HOL_Obool)), _1372809), _1372811)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372805, tc_HOL_Obool)), _1372807), _1372809)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372805, tc_HOL_Obool)), _1372807), _1372811)))], (32146 ^ _779448) ^ [_1372889, _1372891, _1372893] : [class_Orderings_Oorder(_1372889), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1372889, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1372889), _1372891)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1372889, _1372891, _1372893)) = c_Orderings_Obot__class_Obot(tc_fun(_1372889, tc_HOL_Obool)))], (32152 ^ _779448) ^ [_1373016, _1373018] : [class_Lattices_Obounded__lattice__bot(_1373016), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373016), c_Orderings_Obot__class_Obot(_1373016)), _1373018) = c_Orderings_Obot__class_Obot(_1373016))], (32158 ^ _779448) ^ [_1373115, _1373117] : [class_Lattices_Obounded__lattice__bot(_1373115), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373115), _1373117), c_Orderings_Obot__class_Obot(_1373115)) = c_Orderings_Obot__class_Obot(_1373115))], (32178 ^ _779448) ^ [_1373546, _1373548, _1373550] : [32180 ^ _779448 : [(32181 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373546), 32179 ^ [_1373546, _1373548, _1373550]), _1373548)))], (32184 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373546), 32182 ^ [_1373546, _1373548, _1373550]), _1373550)))], (32186 ^ _779448) ^ [] : [-(32179 ^ [_1373546, _1373548, _1373550] = 32182 ^ [_1373546, _1373548, _1373550])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373546, tc_HOL_Obool)), _1373548), _1373550) = c_Orderings_Obot__class_Obot(tc_fun(_1373546, tc_HOL_Obool)))], (32164 ^ _779448) ^ [_1373232, _1373234, _1373236] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373232, tc_HOL_Obool)), _1373234), _1373236) = c_Orderings_Obot__class_Obot(tc_fun(_1373232, tc_HOL_Obool)), 32167 ^ _779448 : [(32168 ^ _779448) ^ [_1373356] : [hBOOL(hAPP(hAPP(c_member(_1373232), _1373356), _1373234)), 32171 ^ _779448 : [(32172 ^ _779448) ^ [_1373446] : [hBOOL(hAPP(hAPP(c_member(_1373232), _1373446), _1373236)), _1373356 = _1373446]]]]], (32190 ^ _779448) ^ [_1373707, _1373709] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373707, tc_HOL_Obool)), _1373709), c_Orderings_Obot__class_Obot(tc_fun(_1373707, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1373707, tc_HOL_Obool)))], (32192 ^ _779448) ^ [_1373753, _1373755] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373753, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1373753, tc_HOL_Obool))), _1373755) = c_Orderings_Obot__class_Obot(tc_fun(_1373753, tc_HOL_Obool)))], (32194 ^ _779448) ^ [_1373799, _1373801, _1373803] : [class_Orderings_Oorder(_1373799), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373799, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1373799), _1373801)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1373799, _1373801, _1373803)) = c_Orderings_Obot__class_Obot(tc_fun(_1373799, tc_HOL_Obool)))], (32200 ^ _779448) ^ [_1373926, _1373928, _1373930] : [class_Lattices_Olattice(_1373926), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373926), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373926), _1373928), _1373930)), _1373928)))], (32206 ^ _779448) ^ [_1374033, _1374035, _1374037] : [class_Lattices_Osemilattice__inf(_1374033), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374033), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374033), _1374035), _1374037)), _1374035)))], (32212 ^ _779448) ^ [_1374140, _1374142, _1374144] : [class_Lattices_Olattice(_1374140), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374140), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374140), _1374142), _1374144)), _1374144)))], (32218 ^ _779448) ^ [_1374247, _1374249, _1374251] : [class_Lattices_Osemilattice__inf(_1374247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374247), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374247), _1374249), _1374251)), _1374251)))], (32224 ^ _779448) ^ [_1374354, _1374356, _1374358] : [class_Lattices_Osemilattice__inf(_1374354), 32227 ^ _779448 : [(32228 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374354), _1374356), _1374358)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374354), _1374356), _1374358) = _1374356)], (32234 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374354), _1374356), _1374358) = _1374356, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374354), _1374356), _1374358)))]]], (32240 ^ _779448) ^ [_1374610, _1374612, _1374614, _1374616] : [class_Lattices_Osemilattice__inf(_1374610), 32243 ^ _779448 : [(32244 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374610), _1374614), _1374616))), 32247 ^ _779448 : [(32248 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), _1374614)))], (32250 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), _1374616)))]]], (32252 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374610), _1374614), _1374616)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), _1374614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374610), _1374612), _1374616))]]], (32262 ^ _779448) ^ [_1374990, _1374992, _1374994, _1374996] : [class_Lattices_Osemilattice__inf(_1374990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374990), _1374992), _1374994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374990), _1374992), _1374996)), _1374994)))], (32272 ^ _779448) ^ [_1375169, _1375171, _1375173, _1375175] : [class_Lattices_Osemilattice__inf(_1375169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375169), _1375171), _1375173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1375169), _1375175), _1375171)), _1375173)))], (32282 ^ _779448) ^ [_1375348, _1375350, _1375352] : [class_Lattices_Osemilattice__inf(_1375348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375348), _1375350), _1375352)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1375348), _1375350), _1375352) = _1375350)], (32292 ^ _779448) ^ [_1375509, _1375511, _1375513] : [class_Lattices_Osemilattice__inf(_1375509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375509), _1375511), _1375513)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1375509), _1375513), _1375511) = _1375511)], (32302 ^ _779448) ^ [_1375670, _1375672, _1375674, _1375676] : [class_Lattices_Osemilattice__inf(_1375670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375670), _1375672), _1375674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375670), _1375672), _1375676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375670), _1375672), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1375670), _1375674), _1375676))))], (32316 ^ _779448) ^ [_1375919, _1375921, _1375923, _1375925] : [class_Lattices_Osemilattice__inf(_1375919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375919), _1375921), _1375923)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375919), _1375921), _1375925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375919), _1375921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1375919), _1375923), _1375925))))], (32330 ^ _779448) ^ [_1376168, _1376170, _1376172, _1376174, _1376176] : [class_Lattices_Osemilattice__inf(_1376168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376168), _1376170), _1376172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376168), _1376174), _1376176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376168), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1376168), _1376170), _1376174)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1376168), _1376172), _1376176))))], (32344 ^ _779448) ^ [_1376439, _1376441, _1376443, _1376445] : [class_Lattices_Osemilattice__inf(_1376439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376439), _1376441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1376439), _1376443), _1376445))), 32351 ^ _779448 : [(32352 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376439), _1376441), _1376443)))], (32354 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376439), _1376441), _1376445)))]]], (32356 ^ _779448) ^ [_1376662, _1376664, _1376666, _1376668, _1376670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376662, tc_HOL_Obool)), _1376664), _1376666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376662, tc_HOL_Obool)), _1376668), _1376670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376662, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376662, tc_HOL_Obool)), _1376664), _1376668)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376662, tc_HOL_Obool)), _1376666), _1376670))))], (32366 ^ _779448) ^ [_1376907, _1376909, _1376911, _1376913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376907, tc_HOL_Obool)), _1376909), _1376911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376907, tc_HOL_Obool)), _1376909), _1376913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1376907, tc_HOL_Obool)), _1376909), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376907, tc_HOL_Obool)), _1376911), _1376913))))], (32376 ^ _779448) ^ [_1377126, _1377128, _1377130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377126, tc_HOL_Obool)), _1377128), _1377130)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377126, tc_HOL_Obool)), _1377130), _1377128) = _1377128)], (32382 ^ _779448) ^ [_1377247, _1377249, _1377251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377247, tc_HOL_Obool)), _1377249), _1377251)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377247, tc_HOL_Obool)), _1377249), _1377251) = _1377249)], (32388 ^ _779448) ^ [_1377368, _1377370, _1377372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377368, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377368, tc_HOL_Obool)), _1377370), _1377372)), _1377372)))], (32390 ^ _779448) ^ [_1377416, _1377418, _1377420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1377416, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377416, tc_HOL_Obool)), _1377418), _1377420)), _1377418)))], (32392 ^ _779448) ^ [_1377485, _1377487, _1377489, _1377491] : [hBOOL(hAPP(hAPP(c_member(_1377485), _1377487), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377485, tc_HOL_Obool)), _1377489), _1377491))), 32395 ^ _779448 : [(32396 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377485), _1377487), _1377489)))], (32398 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377485), _1377487), _1377491)))]]], (32400 ^ _779448) ^ [_1377652, _1377654, _1377656, _1377658] : [-(hBOOL(hAPP(hAPP(c_member(_1377652), _1377654), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377652, tc_HOL_Obool)), _1377656), _1377658)))), hBOOL(hAPP(hAPP(c_member(_1377652), _1377654), _1377656)), hBOOL(hAPP(hAPP(c_member(_1377652), _1377654), _1377658))], (32410 ^ _779448) ^ [_1377855, _1377857, _1377859, _1377861] : [hBOOL(hAPP(hAPP(c_member(_1377855), _1377857), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377855, tc_HOL_Obool)), _1377859), _1377861))), -(hBOOL(hAPP(hAPP(c_member(_1377855), _1377857), _1377859)))], (32416 ^ _779448) ^ [_1377986, _1377988, _1377990, _1377992] : [hBOOL(hAPP(hAPP(c_member(_1377986), _1377988), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1377986, tc_HOL_Obool)), _1377990), _1377992))), -(hBOOL(hAPP(hAPP(c_member(_1377986), _1377988), _1377992)))], (32422 ^ _779448) ^ [_1378117] : [class_Lattices_Osemilattice__inf(_1378117), -(c_Finite__Set_Ofun__left__comm__idem(_1378117, _1378117, c_Lattices_Osemilattice__inf__class_Oinf(_1378117)))], (32428 ^ _779448) ^ [_1378196, _1378198] : [c_Nat__Transfer_Onat__set(_1378196), c_Nat__Transfer_Onat__set(_1378198), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1378196), _1378198)))], (32438 ^ _779448) ^ [_1378331, _1378333, _1378335, _1378337, _1378339] : [class_Lattices_Olattice(_1378331), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378333, _1378331)), _1378335), _1378337), _1378339) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378331), hAPP(_1378335, _1378339)), hAPP(_1378337, _1378339)))], (32444 ^ _779448) ^ [_1378468, _1378470, _1378472, _1378474, _1378476] : [class_Lattices_Olattice(_1378468), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378470, _1378468)), _1378472), _1378474), _1378476) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378468), hAPP(_1378472, _1378476)), hAPP(_1378474, _1378476)))], (32450 ^ _779448) ^ [_1378605, _1378607, _1378609, _1378611] : [class_Lattices_Osemilattice__inf(_1378605), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378605), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378605), _1378607), _1378609)), _1378611) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378605), _1378607), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378605), _1378609), _1378611)))], (32456 ^ _779448) ^ [_1378748, _1378750, _1378752, _1378754] : [class_Lattices_Olattice(_1378748), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378748), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378748), _1378750), _1378752)), _1378754) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378748), _1378750), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378748), _1378752), _1378754)))], (32462 ^ _779448) ^ [_1378891, _1378893, _1378895, _1378897] : [class_Lattices_Osemilattice__inf(_1378891), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378891), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378891), _1378893), _1378895)), _1378897) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378891), _1378893), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1378891), _1378895), _1378897)))], (32468 ^ _779448) ^ [_1379034, _1379036, _1379038, _1379040] : [class_Lattices_Osemilattice__inf(_1379034), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379034), _1379036), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379034), _1379038), _1379040)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379034), _1379038), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379034), _1379036), _1379040)))], (32474 ^ _779448) ^ [_1379177, _1379179, _1379181, _1379183] : [class_Lattices_Olattice(_1379177), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379177), _1379179), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379177), _1379181), _1379183)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379177), _1379181), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379177), _1379179), _1379183)))], (32480 ^ _779448) ^ [_1379320, _1379322, _1379324, _1379326] : [class_Lattices_Osemilattice__inf(_1379320), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379320), _1379322), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379320), _1379324), _1379326)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379320), _1379324), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379320), _1379322), _1379326)))], (32486 ^ _779448) ^ [_1379463, _1379465, _1379467] : [class_Lattices_Osemilattice__inf(_1379463), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379463), _1379465), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379463), _1379465), _1379467)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379463), _1379465), _1379467))], (32492 ^ _779448) ^ [_1379588, _1379590, _1379592] : [class_Lattices_Olattice(_1379588), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379588), _1379590), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379588), _1379590), _1379592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379588), _1379590), _1379592))], (32498 ^ _779448) ^ [_1379713, _1379715, _1379717] : [class_Lattices_Osemilattice__inf(_1379713), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379713), _1379715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379713), _1379715), _1379717)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379713), _1379715), _1379717))], (32504 ^ _779448) ^ [_1379838, _1379840, _1379842] : [class_Lattices_Osemilattice__inf(_1379838), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379838), _1379840), _1379842) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379838), _1379842), _1379840))], (32510 ^ _779448) ^ [_1379947, _1379949, _1379951] : [class_Lattices_Olattice(_1379947), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379947), _1379949), _1379951) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1379947), _1379951), _1379949))], (32516 ^ _779448) ^ [_1380056, _1380058, _1380060] : [class_Lattices_Osemilattice__inf(_1380056), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1380056), _1380058), _1380060) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1380056), _1380060), _1380058))], (32522 ^ _779448) ^ [_1380165, _1380167] : [class_Lattices_Osemilattice__inf(_1380165), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1380165), _1380167), _1380167) = _1380167)], (32528 ^ _779448) ^ [_1380256, _1380258] : [class_Lattices_Osemilattice__inf(_1380256), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1380256), _1380258), _1380258) = _1380258)], (32534 ^ _779448) ^ [_1380347, _1380349, _1380351, _1380353] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380347, tc_HOL_Obool)), _1380349), _1380351), _1380353)), -(hBOOL(hAPP(_1380351, _1380353)))], (32540 ^ _779448) ^ [_1380458, _1380460, _1380462, _1380464] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380458, tc_HOL_Obool)), _1380460), _1380462), _1380464)), -(hBOOL(hAPP(_1380460, _1380464)))], (32546 ^ _779448) ^ [_1380569, _1380571, _1380573, _1380575] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380569, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380569, tc_HOL_Obool)), _1380571), _1380573)), _1380575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380569, tc_HOL_Obool)), _1380571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380569, tc_HOL_Obool)), _1380573), _1380575)))], (32548 ^ _779448) ^ [_1380642, _1380644, _1380646, _1380648] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380642, tc_HOL_Obool)), _1380644), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380642, tc_HOL_Obool)), _1380646), _1380648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380642, tc_HOL_Obool)), _1380646), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380642, tc_HOL_Obool)), _1380644), _1380648)))], (32550 ^ _779448) ^ [_1380715, _1380717, _1380719] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380715, tc_HOL_Obool)), _1380717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380715, tc_HOL_Obool)), _1380717), _1380719)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380715, tc_HOL_Obool)), _1380717), _1380719))], (32552 ^ _779448) ^ [_1380775, _1380777, _1380779] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380775, tc_HOL_Obool)), _1380777), _1380779) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380775, tc_HOL_Obool)), _1380779), _1380777))], (32554 ^ _779448) ^ [_1380824, _1380826] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380824, tc_HOL_Obool)), _1380826), _1380826) = _1380826)], (32556 ^ _779448) ^ [_1380860, _1380862, _1380864] : [class_Orderings_Olinorder(_1380860), 32559 ^ _779448 : [(32560 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1380860), _1380862) = hAPP(c_SetInterval_Oord__class_OatMost(_1380860), _1380864), -(_1380862 = _1380864)], (32566 ^ _779448) ^ [] : [_1380862 = _1380864, -(hAPP(c_SetInterval_Oord__class_OatMost(_1380860), _1380862) = hAPP(c_SetInterval_Oord__class_OatMost(_1380860), _1380864))]]], (32572 ^ _779448) ^ [_1381101, _1381103, _1381105, _1381107] : [class_Lattices_Osemilattice__inf(_1381101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381101), _1381103), _1381105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381101), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1381101), _1381107), _1381103)), _1381105)))], (32582 ^ _779448) ^ [_1381280, _1381282, _1381284, _1381286] : [class_Lattices_Osemilattice__inf(_1381280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381280), _1381282), _1381284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381280), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1381280), _1381282), _1381286)), _1381284)))], (32592 ^ _779448) ^ [_1381459, _1381461] : [class_Lattices_Olattice(_1381459), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1381459), _1381461), _1381461) = _1381461)], (32598 ^ _779448) ^ [_1381550] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1381550) = c_Orderings_Oord__class_Omin(_1381550)), class_Lattices_Osemilattice__inf(_1381550), class_Orderings_Olinorder(_1381550)], (32608 ^ _779448) ^ [_1381679, _1381681, _1381683] : [-(hAPP(c_Set_OPow(_1381679), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381679, tc_HOL_Obool)), _1381681), _1381683)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1381679, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1381679), _1381681)), hAPP(c_Set_OPow(_1381679), _1381683)))], (32610 ^ _779448) ^ [_1381746, _1381748, _1381750, _1381752] : [class_Orderings_Olinorder(_1381746), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381746, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1381746, _1381748, _1381750)), hAPP(c_SetInterval_Oord__class_OatMost(_1381746), _1381752)) = c_SetInterval_Oord__class_OatLeastAtMost(_1381746, _1381748, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381746), _1381750), _1381752)))], (32616 ^ _779448) ^ [_1381889, _1381891, _1381893, _1381895] : [class_Orderings_Olinorder(_1381889), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381889, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1381889), _1381891)), c_SetInterval_Oord__class_OatLeastAtMost(_1381889, _1381893, _1381895)) = c_SetInterval_Oord__class_OatLeastAtMost(_1381889, _1381893, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381889), _1381891), _1381895)))], (32622 ^ _779448) ^ [_1382032, _1382034, _1382036, _1382038] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382032, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1382032), _1382034), _1382036)), hAPP(hAPP(c_Set_Oinsert(_1382032), _1382034), _1382038)) = hAPP(hAPP(c_Set_Oinsert(_1382032), _1382034), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382032, tc_HOL_Obool)), _1382036), _1382038)))], (32624 ^ _779448) ^ [_1382128, _1382130, _1382132, _1382134] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382128, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1382128, tc_fun(_1382128, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382128)), _1382130)), hAPP(hAPP(c_COMBC(_1382128, tc_fun(_1382128, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382128)), _1382132)), _1382134)), -(hBOOL(hAPP(hAPP(c_member(_1382128), _1382134), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382128, tc_HOL_Obool)), _1382130), _1382132))))], (32630 ^ _779448) ^ [_1382327, _1382329, _1382331, _1382333] : [hBOOL(hAPP(hAPP(c_member(_1382327), _1382333), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382327, tc_HOL_Obool)), _1382329), _1382331))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382327, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1382327, tc_fun(_1382327, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382327)), _1382329)), hAPP(hAPP(c_COMBC(_1382327, tc_fun(_1382327, tc_HOL_Obool), tc_HOL_Obool), c_member(_1382327)), _1382331)), _1382333)))], (32636 ^ _779448) ^ [_1382532, _1382534, _1382536, _1382538, _1382540] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382532, tc_fun(_1382534, tc_HOL_Obool)), _1382536), hAPP(hAPP(c_COMBB(tc_fun(_1382534, tc_HOL_Obool), tc_fun(_1382534, tc_HOL_Obool), _1382532), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382534, tc_HOL_Obool)), _1382538)), _1382540)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382534, tc_HOL_Obool)), _1382538), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382532, tc_fun(_1382534, tc_HOL_Obool)), _1382536), _1382540)))], (32638 ^ _779448) ^ [_1382622, _1382624, _1382626, _1382628, _1382630] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382622, tc_fun(_1382624, tc_HOL_Obool)), _1382626), hAPP(hAPP(c_COMBC(_1382622, tc_fun(_1382624, tc_HOL_Obool), tc_fun(_1382624, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382624, tc_HOL_Obool), tc_fun(tc_fun(_1382624, tc_HOL_Obool), tc_fun(_1382624, tc_HOL_Obool)), _1382622), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382624, tc_HOL_Obool))), _1382628)), _1382630)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382624, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382622, tc_fun(_1382624, tc_HOL_Obool)), _1382626), _1382628)), _1382630))], (32640 ^ _779448) ^ [_1382731, _1382733, _1382735, _1382737, _1382739] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382731, tc_HOL_Obool)), _1382733), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382735, tc_fun(_1382731, tc_HOL_Obool)), _1382737), _1382739)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382735, tc_fun(_1382731, tc_HOL_Obool)), _1382737), hAPP(hAPP(c_COMBB(tc_fun(_1382731, tc_HOL_Obool), tc_fun(_1382731, tc_HOL_Obool), _1382735), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382731, tc_HOL_Obool)), _1382733)), _1382739)))], (32642 ^ _779448) ^ [_1382821, _1382823, _1382825, _1382827, _1382829] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382821, tc_HOL_Obool)), _1382823), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382825, tc_fun(_1382821, tc_HOL_Obool)), _1382827), _1382829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382825, tc_fun(_1382821, tc_HOL_Obool)), _1382827), hAPP(hAPP(c_COMBB(tc_fun(_1382821, tc_HOL_Obool), tc_fun(_1382821, tc_HOL_Obool), _1382825), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382821, tc_HOL_Obool)), _1382823)), _1382829)))], (32644 ^ _779448) ^ [_1382911, _1382913, _1382915, _1382917, _1382919] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382911, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382913, tc_fun(_1382911, tc_HOL_Obool)), _1382915), _1382917)), _1382919) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1382913, tc_fun(_1382911, tc_HOL_Obool)), _1382915), hAPP(hAPP(c_COMBC(_1382913, tc_fun(_1382911, tc_HOL_Obool), tc_fun(_1382911, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1382911, tc_HOL_Obool), tc_fun(tc_fun(_1382911, tc_HOL_Obool), tc_fun(_1382911, tc_HOL_Obool)), _1382913), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382911, tc_HOL_Obool))), _1382917)), _1382919)))], (32646 ^ _779448) ^ [_1383020, _1383022, _1383024, _1383026, _1383028, _1383030, _1383032] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383020, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383022, tc_fun(_1383020, tc_HOL_Obool)), _1383024), _1383026)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383028, tc_fun(_1383020, tc_HOL_Obool)), _1383030), _1383032)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383022, tc_fun(_1383020, tc_HOL_Obool)), _1383024), hAPP(hAPP(c_COMBB(tc_fun(_1383028, tc_fun(_1383020, tc_HOL_Obool)), tc_fun(_1383020, tc_HOL_Obool), _1383022), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1383028, tc_fun(_1383020, tc_HOL_Obool)), _1383030)), hAPP(hAPP(c_COMBC(_1383022, tc_fun(_1383028, tc_fun(_1383020, tc_HOL_Obool)), tc_fun(_1383028, tc_fun(_1383020, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1383020, tc_HOL_Obool), tc_fun(_1383020, tc_HOL_Obool)), tc_fun(tc_fun(_1383028, tc_fun(_1383020, tc_HOL_Obool)), tc_fun(_1383028, tc_fun(_1383020, tc_HOL_Obool))), _1383022), c_COMBB(tc_fun(_1383020, tc_HOL_Obool), tc_fun(_1383020, tc_HOL_Obool), _1383028)), hAPP(hAPP(c_COMBB(tc_fun(_1383020, tc_HOL_Obool), tc_fun(tc_fun(_1383020, tc_HOL_Obool), tc_fun(_1383020, tc_HOL_Obool)), _1383022), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1383020, tc_HOL_Obool))), _1383026))), _1383032))))], (32648 ^ _779448) ^ [_1383223, _1383225, _1383227, _1383229] : [class_Lattices_Olattice(_1383223), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383223), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383223), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383223), _1383225), _1383227)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383223), _1383225), _1383229))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383223), _1383225), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383223), _1383227), _1383229)))))], (32654 ^ _779448) ^ [_1383396, _1383398, _1383400, _1383402] : [class_Lattices_Olattice(_1383396), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383396), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383396), _1383398), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383396), _1383400), _1383402))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383396), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383396), _1383398), _1383400)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383396), _1383398), _1383402)))))], (32660 ^ _779448) ^ [_1383569, _1383571] : [class_Lattices_Oboolean__algebra(_1383569), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383569), _1383571), hAPP(c_Groups_Ouminus__class_Ouminus(_1383569), _1383571)) = c_Orderings_Obot__class_Obot(_1383569))], (32666 ^ _779448) ^ [_1383674, _1383676] : [class_Lattices_Oboolean__algebra(_1383674), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383674), hAPP(c_Groups_Ouminus__class_Ouminus(_1383674), _1383676)), _1383676) = c_Orderings_Obot__class_Obot(_1383674))], (32672 ^ _779448) ^ [_1383779, _1383781, _1383783] : [class_Lattices_Oboolean__algebra(_1383779), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383779), _1383781), _1383783) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383779), _1383781), hAPP(c_Groups_Ouminus__class_Ouminus(_1383779), _1383783)))], (32678 ^ _779448) ^ [_1383898, _1383900, _1383902] : [class_Lattices_Oboolean__algebra(_1383898), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1383898), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1383898), _1383900), _1383902)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1383898), hAPP(c_Groups_Ouminus__class_Ouminus(_1383898), _1383900)), hAPP(c_Groups_Ouminus__class_Ouminus(_1383898), _1383902)))], (32684 ^ _779448) ^ [_1384037, _1384039, _1384041] : [class_Lattices_Oboolean__algebra(_1384037), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1384037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1384037), _1384039), _1384041)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1384037), hAPP(c_Groups_Ouminus__class_Ouminus(_1384037), _1384039)), hAPP(c_Groups_Ouminus__class_Ouminus(_1384037), _1384041)))], (32690 ^ _779448) ^ [_1384176, _1384178, _1384180, _1384182] : [hBOOL(hAPP(hAPP(c_member(_1384176), _1384178), _1384180)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384176, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1384176), _1384178), _1384182)), _1384180) = hAPP(hAPP(c_Set_Oinsert(_1384176), _1384178), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384176, tc_HOL_Obool)), _1384182), _1384180)))], (32696 ^ _779448) ^ [_1384347, _1384349, _1384351, _1384353] : [hBOOL(hAPP(hAPP(c_member(_1384347), _1384349), _1384351)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384347, tc_HOL_Obool)), _1384351), hAPP(hAPP(c_Set_Oinsert(_1384347), _1384349), _1384353)) = hAPP(hAPP(c_Set_Oinsert(_1384347), _1384349), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384347, tc_HOL_Obool)), _1384351), _1384353)))], (32702 ^ _779448) ^ [_1384514, _1384516, _1384518, _1384520] : [-(hBOOL(hAPP(hAPP(c_member(_1384514), _1384516), _1384518))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384514, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1384514), _1384516), _1384520)), _1384518) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384514, tc_HOL_Obool)), _1384520), _1384518))], (32708 ^ _779448) ^ [_1384587, _1384589, _1384591, _1384593] : [-(hBOOL(hAPP(hAPP(c_member(_1384587), _1384589), _1384591))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384587, tc_HOL_Obool)), _1384591), hAPP(hAPP(c_Set_Oinsert(_1384587), _1384589), _1384593)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384587, tc_HOL_Obool)), _1384591), _1384593))], (32714 ^ _779448) ^ [_1384679, _1384681, _1384683, _1384685] : [hBOOL(hAPP(hAPP(c_member(_1384679), _1384681), _1384683)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384679, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1384679), _1384681), _1384685)), _1384683) = hAPP(hAPP(c_Set_Oinsert(_1384679), _1384681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384679, tc_HOL_Obool)), _1384685), _1384683)))], (32720 ^ _779448) ^ [_1384844, _1384846, _1384848, _1384850] : [-(hBOOL(hAPP(hAPP(c_member(_1384844), _1384846), _1384848))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384844, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1384844), _1384846), _1384850)), _1384848) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384844, tc_HOL_Obool)), _1384850), _1384848))], (32726 ^ _779448) ^ [_1384938, _1384940, _1384942, _1384944] : [hBOOL(hAPP(hAPP(c_member(_1384938), _1384940), _1384942)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384938, tc_HOL_Obool)), _1384942), hAPP(hAPP(c_Set_Oinsert(_1384938), _1384940), _1384944)) = hAPP(hAPP(c_Set_Oinsert(_1384938), _1384940), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384938, tc_HOL_Obool)), _1384942), _1384944)))], (32732 ^ _779448) ^ [_1385103, _1385105, _1385107, _1385109] : [-(hBOOL(hAPP(hAPP(c_member(_1385103), _1385105), _1385107))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385103, tc_HOL_Obool)), _1385107), hAPP(hAPP(c_Set_Oinsert(_1385103), _1385105), _1385109)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385103, tc_HOL_Obool)), _1385107), _1385109))], (32738 ^ _779448) ^ [_1385182, _1385184, _1385186, _1385188, _1385190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385182, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1385184, _1385182, _1385186), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385184, tc_HOL_Obool)), _1385188), _1385190))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385182, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1385184, _1385182, _1385186), _1385188)), hAPP(c_Set_Oimage(_1385184, _1385182, _1385186), _1385190)))))], (32740 ^ _779448) ^ [_1385266, _1385268, _1385270] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385266, tc_HOL_Obool)), _1385268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385266, tc_HOL_Obool)), _1385270), _1385268)) = c_Orderings_Obot__class_Obot(tc_fun(_1385266, tc_HOL_Obool)))], (32742 ^ _779448) ^ [_1385320, _1385322, _1385324] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385320, tc_HOL_Obool)), _1385322), _1385324) = c_Orderings_Obot__class_Obot(tc_fun(_1385320, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385320, tc_HOL_Obool)), _1385322), _1385324) = _1385322)], (32748 ^ _779448) ^ [_1385474, _1385476, _1385478, _1385480] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385474, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385474, tc_HOL_Obool)), _1385476), _1385478)), _1385480) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385474, tc_HOL_Obool)), _1385476), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385474, tc_HOL_Obool)), _1385478), _1385480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385474, tc_HOL_Obool)), _1385480), _1385476)))], (32754 ^ _779448) ^ [_1385659, _1385661, _1385663, _1385665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1385659, tc_HOL_Obool)), _1385665), _1385661)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385659, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385659, tc_HOL_Obool)), _1385661), _1385663)), _1385665) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385659, tc_HOL_Obool)), _1385661), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385659, tc_HOL_Obool)), _1385663), _1385665)))], (32760 ^ _779448) ^ [_1385850, _1385852, _1385854, _1385856] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385850, tc_HOL_Obool)), _1385852), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385850, tc_HOL_Obool)), _1385854), _1385856)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385850, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385850, tc_HOL_Obool)), _1385852), _1385854)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385850, tc_HOL_Obool)), _1385852), _1385856)))], (32762 ^ _779448) ^ [_1385934, _1385936, _1385938, _1385940] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385934, tc_HOL_Obool)), _1385936), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1385934, tc_HOL_Obool)), _1385938), _1385940)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1385934, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385934, tc_HOL_Obool)), _1385936), _1385938)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1385934, tc_HOL_Obool)), _1385936), _1385940)))], (32764 ^ _779448) ^ [_1386018, _1386020, _1386022] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386018, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386018, tc_HOL_Obool)), _1386020), _1386022)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386018, tc_HOL_Obool)), _1386020), _1386022)) = _1386020)], (32766 ^ _779448) ^ [_1386078, _1386080, _1386082, _1386084] : [class_Orderings_Oorder(_1386078), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386078, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1386078, _1386080), _1386082)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1386078, _1386082), _1386084)) = c_Orderings_Obot__class_Obot(tc_fun(_1386078, tc_HOL_Obool)))], (32772 ^ _779448) ^ [_1386213, _1386215] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1386213), _1386215) = 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)), _1386213)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1386215))))], (32774 ^ _779448) ^ [_1386259, _1386261] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386259, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386259, tc_HOL_Obool)), _1386261)), _1386261) = c_Orderings_Obot__class_Obot(tc_fun(_1386259, tc_HOL_Obool)))], (32776 ^ _779448) ^ [_1386308, _1386310] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386308, tc_HOL_Obool)), _1386310), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386308, tc_HOL_Obool)), _1386310)) = c_Orderings_Obot__class_Obot(tc_fun(_1386308, tc_HOL_Obool)))], (32778 ^ _779448) ^ [_1386357, _1386359, _1386361, _1386363, _1386365] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1386357, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1386359, _1386357, _1386361), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386359, tc_HOL_Obool)), _1386363), _1386365))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386357, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1386359, _1386357, _1386361), _1386363)), hAPP(c_Relation_OImage(_1386359, _1386357, _1386361), _1386365)))))], (32780 ^ _779448) ^ [_1386441, _1386443, _1386445] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386441, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386441, tc_HOL_Obool)), _1386443), _1386445)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386441, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386441, tc_HOL_Obool)), _1386443)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386441, tc_HOL_Obool)), _1386445)))], (32782 ^ _779448) ^ [_1386514, _1386516, _1386518] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386514, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1386514, tc_HOL_Obool)), _1386516), _1386518)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386514, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386514, tc_HOL_Obool)), _1386516)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386514, tc_HOL_Obool)), _1386518)))], (32784 ^ _779448) ^ [_1386587, _1386589, _1386591] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386587, tc_HOL_Obool)), _1386589), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386587, tc_HOL_Obool)), _1386591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386587, tc_HOL_Obool)), _1386589), _1386591))], (32786 ^ _779448) ^ [_1386644, _1386646, _1386648] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1386644, tc_HOL_Obool)), _1386646), _1386648) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386644, tc_HOL_Obool)), _1386646), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1386644, tc_HOL_Obool)), _1386648)))], (32788 ^ _779448) ^ [_1386701, _1386703, _1386705, _1386707] : [class_Orderings_Oorder(_1386701), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386701, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1386701, _1386703, _1386705)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1386701, _1386705, _1386707)) = c_Orderings_Obot__class_Obot(tc_fun(_1386701, tc_HOL_Obool)))], (32794 ^ _779448) ^ [_1386828, _1386830, _1386832] : [-(hAPP(c_Relation_OImage(_1386828, _1386828, c_Relation_OId__on(_1386828, _1386830)), _1386832) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1386828, tc_HOL_Obool)), _1386830), _1386832))], (32796 ^ _779448) ^ [_1386876, _1386878] : [c_Nat__Transfer_Onat__set(_1386876), c_Nat__Transfer_Onat__set(_1386878), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1386876), _1386878) = 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), _1386876)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1386878))))], (32806 ^ _779448) ^ [_1387043] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1387043) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1387043))], (32808 ^ _779448) ^ [_1387073] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1387073)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1387073))], (32810 ^ _779448) ^ [_1387105] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1387105)) = hAPP(c_Nat_OSuc, _1387105))], (32812 ^ _779448) ^ [_1387137] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1387137)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1387137)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1387137)))], (32814 ^ _779448) ^ [_1387178, _1387180, _1387182] : [class_Orderings_Oord(_1387178), 32817 ^ _779448 : [(32818 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1387178), _1387180), hAPP(c_SetInterval_Oord__class_OatMost(_1387178), _1387182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387178), _1387180), _1387182)))], (32824 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387178), _1387180), _1387182)), -(hBOOL(hAPP(hAPP(c_member(_1387178), _1387180), hAPP(c_SetInterval_Oord__class_OatMost(_1387178), _1387182))))]]], (32830 ^ _779448) ^ [_1387446, _1387448, _1387450, _1387452] : [class_Lattices_Osemilattice__inf(_1387446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387446), _1387448)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1387446, _1387446, c_Lattices_Osemilattice__inf__class_Oinf(_1387446)), _1387450), hAPP(hAPP(c_Set_Oinsert(_1387446), _1387452), _1387448)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387446), _1387452), hAPP(hAPP(c_Finite__Set_Ofold(_1387446, _1387446, c_Lattices_Osemilattice__inf__class_Oinf(_1387446)), _1387450), _1387448)))], (32840 ^ _779448) ^ [_1387669, _1387671, _1387673] : [class_Lattices_Olattice(_1387669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387669), _1387671)), hBOOL(hAPP(hAPP(c_member(_1387669), _1387673), _1387671)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1387669), _1387673), c_Big__Operators_Olattice__class_OSup__fin(_1387669, _1387671)) = _1387673)], (32854 ^ _779448) ^ [_1387898, _1387900, _1387902] : [class_Orderings_Oorder(_1387898), 32857 ^ _779448 : [(32858 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387898, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1387898), _1387900)), hAPP(c_SetInterval_Oord__class_OatMost(_1387898), _1387902))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387898), _1387900), _1387902)))], (32864 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387898), _1387900), _1387902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1387898, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1387898), _1387900)), hAPP(c_SetInterval_Oord__class_OatMost(_1387898), _1387902))))]]], (32870 ^ _779448) ^ [_1388190, _1388192, _1388194, _1388196, _1388198, _1388200] : [c_Fun_Oinj__on(_1388190, _1388192, _1388194, _1388196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388190, tc_HOL_Obool)), _1388198), _1388196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388190, tc_HOL_Obool)), _1388200), _1388196)), -(hAPP(c_Set_Oimage(_1388190, _1388192, _1388194), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388190, tc_HOL_Obool)), _1388198), _1388200)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388192, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1388190, _1388192, _1388194), _1388198)), hAPP(c_Set_Oimage(_1388190, _1388192, _1388194), _1388200)))], (32884 ^ _779448) ^ [_1388543, _1388545, _1388547] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388543, tc_HOL_Obool)), _1388545), _1388547) = c_Orderings_Obot__class_Obot(tc_fun(_1388543, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388543, tc_HOL_Obool)), _1388545), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388543, tc_HOL_Obool)), _1388547))))], (32890 ^ _779448) ^ [_1388686, _1388688, _1388690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1388686, tc_HOL_Obool)), _1388688), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1388686, tc_HOL_Obool)), _1388690))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388686, tc_HOL_Obool)), _1388688), _1388690) = c_Orderings_Obot__class_Obot(tc_fun(_1388686, tc_HOL_Obool)))], (32896 ^ _779448) ^ [_1388835, _1388837, _1388839, _1388841] : [class_Orderings_Oorder(_1388835), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388835, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1388835, _1388837), _1388839)), c_SetInterval_Oord__class_OatLeastAtMost(_1388835, _1388839, _1388841)) = c_Orderings_Obot__class_Obot(tc_fun(_1388835, tc_HOL_Obool)))], (32902 ^ _779448) ^ [_1388966, _1388968, _1388970, _1388972, _1388974] : [class_Orderings_Olinorder(_1388966), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1388966, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1388966, _1388968, _1388970)), c_SetInterval_Oord__class_OatLeastAtMost(_1388966, _1388972, _1388974)) = c_SetInterval_Oord__class_OatLeastAtMost(_1388966, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1388966), _1388968), _1388972), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388966), _1388970), _1388974)))], (32908 ^ _779448) ^ [_1389125, _1389127, _1389129, _1389131, _1389133] : [class_Orderings_Olinorder(_1389125), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389125, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1389125, _1389127), _1389129)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1389125, _1389131), _1389133)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1389125, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389125), _1389127), _1389131)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1389125), _1389129), _1389133)))], (32914 ^ _779448) ^ [_1389296, _1389298, _1389300, _1389302] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1389296, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1389298)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1389296, tc_HOL_Obool), tc_Nat_Onat), _1389300), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1389302))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1389296, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1389302, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1389298), _1389302))), _1389300))], (32916 ^ _779448) ^ [_1389378, _1389380, _1389382] : [class_Orderings_Oorder(_1389378), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389378, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1389378), _1389380)), c_SetInterval_Oord__class_OatLeastAtMost(_1389378, _1389380, _1389382)) = c_Orderings_Obot__class_Obot(tc_fun(_1389378, tc_HOL_Obool)))], (32922 ^ _779448) ^ [_1389505, _1389507, _1389509] : [class_Orderings_Oorder(_1389505), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389505, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1389505), _1389507)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1389505, _1389507), _1389509)) = c_Orderings_Obot__class_Obot(tc_fun(_1389505, tc_HOL_Obool)))], (32928 ^ _779448) ^ [_1389636, _1389638, _1389640, _1389642] : [class_Orderings_Oorder(_1389636), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389636, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1389636, _1389638, _1389640)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1389636, _1389640, _1389642)) = c_Orderings_Obot__class_Obot(tc_fun(_1389636, tc_HOL_Obool)))], (32934 ^ _779448) ^ [_1389763, _1389765, _1389767, _1389769] : [class_Orderings_Oorder(_1389763), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389763, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1389763, _1389765, _1389767)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1389763, _1389767, _1389769)) = c_Orderings_Obot__class_Obot(tc_fun(_1389763, tc_HOL_Obool)))], (32940 ^ _779448) ^ [_1389890, _1389892, _1389894, _1389896] : [class_Orderings_Oorder(_1389890), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1389890, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1389890, _1389892, _1389894)), c_SetInterval_Oord__class_OatLeastAtMost(_1389890, _1389894, _1389896)) = c_Orderings_Obot__class_Obot(tc_fun(_1389890, tc_HOL_Obool)))], (32946 ^ _779448) ^ [_1390017, _1390019, _1390021, _1390023, _1390025] : [class_Orderings_Olinorder(_1390017), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390017, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1390017, _1390019, _1390021)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1390017, _1390023, _1390025)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1390017, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1390017), _1390019), _1390023), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1390017), _1390021), _1390025)))], (32952 ^ _779448) ^ [_1390176, _1390178, _1390180, _1390182] : [class_Orderings_Oorder(_1390176), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390176, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1390176, _1390178, _1390180)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1390176, _1390180), _1390182)) = c_Orderings_Obot__class_Obot(tc_fun(_1390176, tc_HOL_Obool)))], (32958 ^ _779448) ^ [_1390307, _1390309, _1390311, _1390313, _1390315] : [class_Orderings_Olinorder(_1390307), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390307, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1390307, _1390309, _1390311)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1390307, _1390313, _1390315)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1390307, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1390307), _1390309), _1390313), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1390307), _1390311), _1390315)))], (32964 ^ _779448) ^ [_1390466, _1390468, _1390470, _1390472] : [class_Orderings_Oorder(_1390466), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390466, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1390466, _1390468, _1390470)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1390466, _1390470, _1390472)) = c_Orderings_Obot__class_Obot(tc_fun(_1390466, tc_HOL_Obool)))], (32970 ^ _779448) ^ [_1390593, _1390595, _1390597, _1390599, _1390601, _1390603, _1390605, _1390607] : [c_Finite__Set_Ofolding__image__simple(_1390593, _1390595, _1390597, _1390599, _1390601, _1390603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390595), _1390605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390595), _1390607)), -(hAPP(hAPP(_1390597, hAPP(_1390603, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1390595, tc_HOL_Obool)), _1390605), _1390607))), hAPP(_1390603, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1390595, tc_HOL_Obool)), _1390605), _1390607))) = hAPP(hAPP(_1390597, hAPP(_1390603, _1390605)), hAPP(_1390603, _1390607)))], (32984 ^ _779448) ^ [_1390926, _1390928, _1390930, _1390932] : [class_Lattices_Osemilattice__inf(_1390926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390926), _1390928)), hBOOL(hAPP(hAPP(c_member(_1390926), _1390930), _1390928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1390926), hAPP(hAPP(c_Finite__Set_Ofold(_1390926, _1390926, c_Lattices_Osemilattice__inf__class_Oinf(_1390926)), _1390932), _1390928)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1390926), _1390930), _1390932))))], (32998 ^ _779448) ^ [_1391193, _1391195, _1391197] : [class_Lattices_Osemilattice__inf(_1391193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391193), _1391195)), hBOOL(hAPP(hAPP(c_member(_1391193), _1391197), _1391195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391193), hAPP(c_Finite__Set_Ofold1(_1391193, c_Lattices_Osemilattice__inf__class_Oinf(_1391193)), _1391195)), _1391197)))], (33012 ^ _779448) ^ [_1391430, _1391432, _1391434] : [class_Lattices_Osemilattice__inf(_1391430), hBOOL(hAPP(c_Finite__Set_Ofinite(_1391430), _1391432)), -(_1391432 = c_Orderings_Obot__class_Obot(tc_fun(_1391430, tc_HOL_Obool))), 33023 ^ _779448 : [(33034 ^ _779448) ^ [] : [33036 ^ _779448 : [(33037 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391430), 33035 ^ [_1391430, _1391432, _1391434]), _1391432)))], (33039 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391430), _1391434), 33035 ^ [_1391430, _1391432, _1391434]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391430), _1391434), hAPP(c_Finite__Set_Ofold1(_1391430, c_Lattices_Osemilattice__inf__class_Oinf(_1391430)), _1391432))))], (33024 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391430), _1391434), hAPP(c_Finite__Set_Ofold1(_1391430, c_Lattices_Osemilattice__inf__class_Oinf(_1391430)), _1391432))), 33027 ^ _779448 : [(33028 ^ _779448) ^ [_1391723] : [hBOOL(hAPP(hAPP(c_member(_1391430), _1391723), _1391432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391430), _1391434), _1391723)))]]]]], (33043 ^ _779448) ^ [_1392008, _1392010, _1392012, _1392014, _1392016] : [class_Groups_Ocomm__monoid__add(_1392008), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392010), _1392012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392010), _1392014)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392008), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392010, _1392008), _1392016), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392010, tc_HOL_Obool)), _1392012), _1392014))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392010, _1392008), _1392016), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392010, tc_HOL_Obool)), _1392012), _1392014))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1392008), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392010, _1392008), _1392016), _1392012)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1392010, _1392008), _1392016), _1392014)))], (33057 ^ _779448) ^ [_1392369, _1392371, _1392373, _1392375, _1392377] : [class_Groups_Ocomm__monoid__mult(_1392369), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392371), _1392373)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392371), _1392375)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392369), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392371, _1392369), _1392377), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392371, tc_HOL_Obool)), _1392373), _1392375))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392371, _1392369), _1392377), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392371, tc_HOL_Obool)), _1392373), _1392375))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392369), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392371, _1392369), _1392377), _1392373)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392371, _1392369), _1392377), _1392375)))], (33071 ^ _779448) ^ [_1392730, _1392732, _1392734, _1392736, _1392738] : [class_Groups_Ocomm__monoid__mult(_1392730), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392732), _1392734)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1392732), _1392736)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392730), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392732, _1392730), _1392738), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392732, tc_HOL_Obool)), _1392734), _1392736))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392732, _1392730), _1392738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392732, tc_HOL_Obool)), _1392734), _1392736))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392730), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392732, _1392730), _1392738), _1392734)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1392732, _1392730), _1392738), _1392736)))], (33085 ^ _779448) ^ [_1393091, _1393093, _1393095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393091), _1393093)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393091), _1393095)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1393091, tc_HOL_Obool)), _1393093), _1393095))), hAPP(c_Finite__Set_Ocard(_1393091), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393091, tc_HOL_Obool)), _1393093), _1393095))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393091), _1393093)), hAPP(c_Finite__Set_Ocard(_1393091), _1393095)))], (33095 ^ _779448) ^ [_1393348, _1393350, _1393352] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393348), _1393350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393348), _1393352)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393348), _1393350)), hAPP(c_Finite__Set_Ocard(_1393348), _1393352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393348), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1393348, tc_HOL_Obool)), _1393350), _1393352))), hAPP(c_Finite__Set_Ocard(_1393348), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393348, tc_HOL_Obool)), _1393350), _1393352))))], (33105 ^ _779448) ^ [_1393605, _1393607, _1393609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393605), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393605, tc_HOL_Obool)), _1393607), _1393609))), -(hAPP(c_Finite__Set_Ocard(_1393605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1393605, tc_HOL_Obool)), _1393607), _1393609)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1393605), _1393607)), hAPP(c_Finite__Set_Ocard(_1393605), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393605, tc_HOL_Obool)), _1393607), _1393609))))], (33111 ^ _779448) ^ [_1393800, _1393802, _1393804, _1393806, _1393808] : [class_Groups_Ocomm__monoid__add(_1393800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1393802), _1393804)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1393802, _1393800), _1393806), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1393802, tc_HOL_Obool)), _1393804), _1393808)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1393802, _1393800), hAPP(hAPP(c_COMBC(_1393802, _1393800, _1393800), hAPP(hAPP(c_COMBS(_1393802, _1393800, tc_fun(_1393800, _1393800)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1393800, tc_fun(_1393800, _1393800)), _1393802), c_If(_1393800)), hAPP(hAPP(c_COMBC(_1393802, tc_fun(_1393802, tc_HOL_Obool), tc_HOL_Obool), c_member(_1393802)), _1393808))), _1393806)), c_Groups_Ozero__class_Ozero(_1393800))), _1393804))], (33121 ^ _779448) ^ [_1394121, _1394123, _1394125] : [class_Groups_Ocomm__monoid__add(_1394121), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1394121), _1394123), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1394125))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1394121), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1394121), _1394123), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1394125))), hAPP(_1394123, hAPP(c_Nat_OSuc, _1394125))))], (33127 ^ _779448) ^ [] : [-(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))))], (33129 ^ _779448) ^ [_1394298, _1394300, _1394302, _1394304, _1394306, _1394308] : [c_Finite__Set_Ofolding(_1394298, _1394300, _1394302, _1394304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394298), _1394306)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394298), _1394308)), -(hAPP(c_Fun_Ocomp(_1394300, _1394300, _1394300, hAPP(_1394304, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1394298, tc_HOL_Obool)), _1394306), _1394308))), hAPP(_1394304, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394298, tc_HOL_Obool)), _1394306), _1394308))) = hAPP(c_Fun_Ocomp(_1394300, _1394300, _1394300, hAPP(_1394304, _1394306)), hAPP(_1394304, _1394308)))], (33143 ^ _779448) ^ [_1394623, _1394625, _1394627, _1394629, _1394631] : [c_Equiv__Relations_Oequiv(_1394623, _1394625, _1394627), hBOOL(hAPP(hAPP(c_member(tc_fun(_1394623, tc_HOL_Obool)), _1394629), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1394623), _1394625), _1394627))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1394623, tc_HOL_Obool)), _1394631), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1394623), _1394625), _1394627))), -(_1394629 = _1394631), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394623, tc_HOL_Obool)), _1394629), _1394631) = c_Orderings_Obot__class_Obot(tc_fun(_1394623, tc_HOL_Obool)))], (33161 ^ _779448) ^ [_1394941, _1394943, _1394945, _1394947, _1394949, _1394951, _1394953, _1394955] : [c_Finite__Set_Ofolding__image__simple(_1394941, _1394943, _1394945, _1394947, _1394949, _1394951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394943), _1394953)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1394943), _1394955)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1394943, tc_HOL_Obool)), _1394953), _1394955) = c_Orderings_Obot__class_Obot(tc_fun(_1394943, tc_HOL_Obool)), -(hAPP(_1394951, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1394943, tc_HOL_Obool)), _1394953), _1394955)) = hAPP(hAPP(_1394945, hAPP(_1394951, _1394953)), hAPP(_1394951, _1394955)))], (33179 ^ _779448) ^ [_1395330, _1395332, _1395334, _1395336, _1395338] : [c_Finite__Set_Ofolding__one(_1395330, _1395332, _1395334), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395330), _1395336)), -(_1395336 = c_Orderings_Obot__class_Obot(tc_fun(_1395330, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395330), _1395338)), -(_1395338 = c_Orderings_Obot__class_Obot(tc_fun(_1395330, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395330, tc_HOL_Obool)), _1395336), _1395338) = c_Orderings_Obot__class_Obot(tc_fun(_1395330, tc_HOL_Obool)), -(hAPP(_1395334, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395330, tc_HOL_Obool)), _1395336), _1395338)) = hAPP(hAPP(_1395332, hAPP(_1395334, _1395336)), hAPP(_1395334, _1395338)))], (33205 ^ _779448) ^ [_1395831, _1395833, _1395835, _1395837, _1395839] : [c_Finite__Set_Ofolding__one(_1395831, _1395833, _1395835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395831), _1395837)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395831), _1395839)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395831, tc_HOL_Obool)), _1395837), _1395839) = c_Orderings_Obot__class_Obot(tc_fun(_1395831, tc_HOL_Obool))), -(hAPP(hAPP(_1395833, hAPP(_1395835, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1395831, tc_HOL_Obool)), _1395837), _1395839))), hAPP(_1395835, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1395831, tc_HOL_Obool)), _1395837), _1395839))) = hAPP(hAPP(_1395833, hAPP(_1395835, _1395837)), hAPP(_1395835, _1395839)))], (33223 ^ _779448) ^ [_1396187, _1396189, _1396191] : [class_Orderings_Olinorder(_1396187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396187), _1396189), _1396191)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396187, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1396187), _1396189)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1396187, _1396189, _1396191)) = hAPP(c_SetInterval_Oord__class_OatMost(_1396187), _1396191))], (33233 ^ _779448) ^ [_1396382, _1396384, _1396386, _1396388, _1396390] : [class_Groups_Ocomm__monoid__add(_1396382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396384), _1396386)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396384), _1396388)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396384, tc_HOL_Obool)), _1396386), _1396388) = c_Orderings_Obot__class_Obot(tc_fun(_1396384, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396384, _1396382), _1396390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396384, tc_HOL_Obool)), _1396386), _1396388)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1396382), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396384, _1396382), _1396390), _1396386)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396384, _1396382), _1396390), _1396388)))], (33251 ^ _779448) ^ [_1396777, _1396779, _1396781, _1396783, _1396785] : [class_Groups_Oab__group__add(_1396777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396779), _1396781)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1396779), _1396783)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396779, _1396777), _1396785), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1396779, tc_HOL_Obool)), _1396781), _1396783)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1396777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1396777), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396779, _1396777), _1396785), _1396781)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396779, _1396777), _1396785), _1396783))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1396779, _1396777), _1396785), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396779, tc_HOL_Obool)), _1396781), _1396783))))], (33265 ^ _779448) ^ [_1397138, _1397140, _1397142, _1397144, _1397146] : [class_Groups_Ocomm__monoid__mult(_1397138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397140), _1397142)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397140), _1397144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397140, tc_HOL_Obool)), _1397142), _1397144) = c_Orderings_Obot__class_Obot(tc_fun(_1397140, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397140, _1397138), _1397146), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397140, tc_HOL_Obool)), _1397142), _1397144)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397138), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397140, _1397138), _1397146), _1397142)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397140, _1397138), _1397146), _1397144)))], (33283 ^ _779448) ^ [_1397533, _1397535, _1397537, _1397539, _1397541] : [class_Groups_Ocomm__monoid__mult(_1397533), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397535), _1397537)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397535), _1397539)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397535, tc_HOL_Obool)), _1397537), _1397539) = c_Orderings_Obot__class_Obot(tc_fun(_1397535, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397535, _1397533), _1397541), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397535, tc_HOL_Obool)), _1397537), _1397539)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397533), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397535, _1397533), _1397541), _1397537)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397535, _1397533), _1397541), _1397539)))], (33301 ^ _779448) ^ [_1397928, _1397930, _1397932] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1397928), _1397930)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1397928), _1397932)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397928, tc_HOL_Obool)), _1397930), _1397932) = c_Orderings_Obot__class_Obot(tc_fun(_1397928, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1397928), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397928, tc_HOL_Obool)), _1397930), _1397932)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1397928), _1397930)), hAPP(c_Finite__Set_Ocard(_1397928), _1397932)))], (33315 ^ _779448) ^ [_1398251, _1398253, _1398255, _1398257, _1398259] : [c_Fun_Oinj__on(_1398251, _1398253, _1398255, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398251, tc_HOL_Obool)), _1398257), _1398259)), 33318 ^ _779448 : [(33319 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_1398251, _1398253, _1398255, _1398257))], (33321 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_1398251, _1398253, _1398255, _1398259))], (33323 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398253, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398251, _1398253, _1398255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398251, tc_HOL_Obool)), _1398257), _1398259))), hAPP(c_Set_Oimage(_1398251, _1398253, _1398255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398251, tc_HOL_Obool)), _1398259), _1398257))) = c_Orderings_Obot__class_Obot(tc_fun(_1398253, tc_HOL_Obool)))]]], (33325 ^ _779448) ^ [_1398518, _1398520, _1398522, _1398524, _1398526] : [-(c_Fun_Oinj__on(_1398518, _1398520, _1398522, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398518, tc_HOL_Obool)), _1398524), _1398526))), c_Fun_Oinj__on(_1398518, _1398520, _1398522, _1398524), c_Fun_Oinj__on(_1398518, _1398520, _1398522, _1398526), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398520, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1398518, _1398520, _1398522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398518, tc_HOL_Obool)), _1398524), _1398526))), hAPP(c_Set_Oimage(_1398518, _1398520, _1398522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398518, tc_HOL_Obool)), _1398526), _1398524))) = c_Orderings_Obot__class_Obot(tc_fun(_1398520, tc_HOL_Obool))], (33339 ^ _779448) ^ [_1398857, _1398859, _1398861, _1398863, _1398865] : [class_Groups_Ocomm__monoid__mult(_1398857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398859), _1398861)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1398859), _1398863)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398857), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1398857, _1398859, c_Groups_Otimes__class_Otimes(_1398857)), _1398865), c_Groups_Oone__class_Oone(_1398857)), _1398861)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1398857, _1398859, c_Groups_Otimes__class_Otimes(_1398857)), _1398865), c_Groups_Oone__class_Oone(_1398857)), _1398863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1398857), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1398857, _1398859, c_Groups_Otimes__class_Otimes(_1398857)), _1398865), c_Groups_Oone__class_Oone(_1398857)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398859, tc_HOL_Obool)), _1398861), _1398863))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1398857, _1398859, c_Groups_Otimes__class_Otimes(_1398857)), _1398865), c_Groups_Oone__class_Oone(_1398857)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1398859, tc_HOL_Obool)), _1398861), _1398863))))], (33353 ^ _779448) ^ [_1399282, _1399284, _1399286] : [class_Groups_Oab__semigroup__mult(_1399282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399282), _1399284)), -(_1399284 = c_Orderings_Obot__class_Obot(tc_fun(_1399282, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399282), _1399286)), -(_1399286 = c_Orderings_Obot__class_Obot(tc_fun(_1399282, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399282, tc_HOL_Obool)), _1399284), _1399286) = c_Orderings_Obot__class_Obot(tc_fun(_1399282, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1399282, c_Groups_Otimes__class_Otimes(_1399282)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399282, tc_HOL_Obool)), _1399284), _1399286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399282), hAPP(c_Finite__Set_Ofold1(_1399282, c_Groups_Otimes__class_Otimes(_1399282)), _1399284)), hAPP(c_Finite__Set_Ofold1(_1399282, c_Groups_Otimes__class_Otimes(_1399282)), _1399286)))], (33379 ^ _779448) ^ [_1399789, _1399791, _1399793] : [class_Lattices_Olattice(_1399789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399789), _1399791)), -(_1399791 = c_Orderings_Obot__class_Obot(tc_fun(_1399789, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1399789), _1399793)), -(_1399793 = c_Orderings_Obot__class_Obot(tc_fun(_1399789, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1399789, tc_HOL_Obool)), _1399791), _1399793) = c_Orderings_Obot__class_Obot(tc_fun(_1399789, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1399789, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1399789, tc_HOL_Obool)), _1399791), _1399793)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1399789), c_Big__Operators_Olattice__class_OSup__fin(_1399789, _1399791)), c_Big__Operators_Olattice__class_OSup__fin(_1399789, _1399793)))], (33405 ^ _779448) ^ [_1400266, _1400268, _1400270] : [class_Lattices_Olattice(_1400266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400266), _1400268)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400266), _1400270)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400266, tc_HOL_Obool)), _1400268), _1400270) = c_Orderings_Obot__class_Obot(tc_fun(_1400266, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1400266), c_Big__Operators_Olattice__class_OSup__fin(_1400266, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400266, tc_HOL_Obool)), _1400268), _1400270))), c_Big__Operators_Olattice__class_OSup__fin(_1400266, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400266, tc_HOL_Obool)), _1400268), _1400270))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1400266), c_Big__Operators_Olattice__class_OSup__fin(_1400266, _1400268)), c_Big__Operators_Olattice__class_OSup__fin(_1400266, _1400270)))], (33423 ^ _779448) ^ [_1400614, _1400616, _1400618] : [class_Orderings_Olinorder(_1400614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400614), _1400616)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400614), _1400618)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400614, tc_HOL_Obool)), _1400616), _1400618) = c_Orderings_Obot__class_Obot(tc_fun(_1400614, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400614), c_Big__Operators_Olinorder__class_OMin(_1400614, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400614, tc_HOL_Obool)), _1400616), _1400618))), c_Big__Operators_Olinorder__class_OMin(_1400614, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400614, tc_HOL_Obool)), _1400616), _1400618))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400614), c_Big__Operators_Olinorder__class_OMin(_1400614, _1400616)), c_Big__Operators_Olinorder__class_OMin(_1400614, _1400618)))], (33441 ^ _779448) ^ [_1400962, _1400964, _1400966] : [class_Orderings_Olinorder(_1400962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400962), _1400964)), -(_1400964 = c_Orderings_Obot__class_Obot(tc_fun(_1400962, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1400962), _1400966)), -(_1400966 = c_Orderings_Obot__class_Obot(tc_fun(_1400962, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1400962, tc_HOL_Obool)), _1400964), _1400966) = c_Orderings_Obot__class_Obot(tc_fun(_1400962, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1400962, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400962, tc_HOL_Obool)), _1400964), _1400966)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1400962), c_Big__Operators_Olinorder__class_OMin(_1400962, _1400964)), c_Big__Operators_Olinorder__class_OMin(_1400962, _1400966)))], (33467 ^ _779448) ^ [_1401439, _1401441, _1401443] : [class_Orderings_Olinorder(_1401439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401439), _1401441)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401439), _1401443)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401439, tc_HOL_Obool)), _1401441), _1401443) = c_Orderings_Obot__class_Obot(tc_fun(_1401439, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401439), c_Big__Operators_Olinorder__class_OMax(_1401439, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401439, tc_HOL_Obool)), _1401441), _1401443))), c_Big__Operators_Olinorder__class_OMax(_1401439, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401439, tc_HOL_Obool)), _1401441), _1401443))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401439), c_Big__Operators_Olinorder__class_OMax(_1401439, _1401441)), c_Big__Operators_Olinorder__class_OMax(_1401439, _1401443)))], (33485 ^ _779448) ^ [_1401787, _1401789, _1401791] : [class_Orderings_Olinorder(_1401787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401787), _1401789)), -(_1401789 = c_Orderings_Obot__class_Obot(tc_fun(_1401787, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401787), _1401791)), -(_1401791 = c_Orderings_Obot__class_Obot(tc_fun(_1401787, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1401787, tc_HOL_Obool)), _1401789), _1401791) = c_Orderings_Obot__class_Obot(tc_fun(_1401787, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1401787, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1401787, tc_HOL_Obool)), _1401789), _1401791)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1401787), c_Big__Operators_Olinorder__class_OMax(_1401787, _1401789)), c_Big__Operators_Olinorder__class_OMax(_1401787, _1401791)))], (33511 ^ _779448) ^ [_1402264, _1402266, _1402268] : [class_Orderings_Olinorder(_1402264), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402264), _1402266)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402264), _1402268)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402264, tc_HOL_Obool)), _1402266), _1402268) = c_Orderings_Obot__class_Obot(tc_fun(_1402264, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402264), c_Big__Operators_Olattice_OInf__fin(_1402264, c_Orderings_Oord__class_Omin(_1402264), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402264, tc_HOL_Obool)), _1402266), _1402268))), c_Big__Operators_Olattice_OInf__fin(_1402264, c_Orderings_Oord__class_Omin(_1402264), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402264, tc_HOL_Obool)), _1402266), _1402268))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402264), c_Big__Operators_Olattice_OInf__fin(_1402264, c_Orderings_Oord__class_Omin(_1402264), _1402266)), c_Big__Operators_Olattice_OInf__fin(_1402264, c_Orderings_Oord__class_Omin(_1402264), _1402268)))], (33529 ^ _779448) ^ [_1402636, _1402638, _1402640] : [class_Orderings_Olinorder(_1402636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402636), _1402638)), -(_1402638 = c_Orderings_Obot__class_Obot(tc_fun(_1402636, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402636), _1402640)), -(_1402640 = c_Orderings_Obot__class_Obot(tc_fun(_1402636, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402636, tc_HOL_Obool)), _1402638), _1402640) = c_Orderings_Obot__class_Obot(tc_fun(_1402636, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1402636, c_Orderings_Oord__class_Omin(_1402636), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402636, tc_HOL_Obool)), _1402638), _1402640)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402636), c_Big__Operators_Olattice_OInf__fin(_1402636, c_Orderings_Oord__class_Omin(_1402636), _1402638)), c_Big__Operators_Olattice_OInf__fin(_1402636, c_Orderings_Oord__class_Omin(_1402636), _1402640)))], (33555 ^ _779448) ^ [_1403131, _1403133, _1403135] : [class_Orderings_Olinorder(_1403131), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403131), _1403133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403131), _1403135)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403131, tc_HOL_Obool)), _1403133), _1403135) = c_Orderings_Obot__class_Obot(tc_fun(_1403131, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1403131), c_Big__Operators_Olattice_OSup__fin(_1403131, c_Orderings_Oord__class_Omax(_1403131), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403131, tc_HOL_Obool)), _1403133), _1403135))), c_Big__Operators_Olattice_OSup__fin(_1403131, c_Orderings_Oord__class_Omax(_1403131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403131, tc_HOL_Obool)), _1403133), _1403135))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1403131), c_Big__Operators_Olattice_OSup__fin(_1403131, c_Orderings_Oord__class_Omax(_1403131), _1403133)), c_Big__Operators_Olattice_OSup__fin(_1403131, c_Orderings_Oord__class_Omax(_1403131), _1403135)))], (33573 ^ _779448) ^ [_1403503, _1403505, _1403507] : [class_Orderings_Olinorder(_1403503), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403503), _1403505)), -(_1403505 = c_Orderings_Obot__class_Obot(tc_fun(_1403503, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403503), _1403507)), -(_1403507 = c_Orderings_Obot__class_Obot(tc_fun(_1403503, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403503, tc_HOL_Obool)), _1403505), _1403507) = c_Orderings_Obot__class_Obot(tc_fun(_1403503, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1403503, c_Orderings_Oord__class_Omax(_1403503), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403503, tc_HOL_Obool)), _1403505), _1403507)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1403503), c_Big__Operators_Olattice_OSup__fin(_1403503, c_Orderings_Oord__class_Omax(_1403503), _1403505)), c_Big__Operators_Olattice_OSup__fin(_1403503, c_Orderings_Oord__class_Omax(_1403503), _1403507)))], (33599 ^ _779448) ^ [_1403998, _1404000, _1404002, _1404004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1403998), _1404000)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403998), _1404002)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1403998, tc_Nat_Onat), _1404004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1403998, tc_HOL_Obool)), _1404000), _1404002)) = 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(_1403998, tc_Nat_Onat), _1404004), _1404000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1403998, tc_Nat_Onat), _1404004), _1404002))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1403998, tc_Nat_Onat), _1404004), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1403998, tc_HOL_Obool)), _1404000), _1404002))))], (33609 ^ _779448) ^ [_1404291, _1404293, _1404295, _1404297, _1404299, _1404301] : [c_Finite__Set_Ofolding(_1404291, _1404293, _1404295, _1404297), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404291), _1404299)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404291), _1404301)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404291, tc_HOL_Obool)), _1404299), _1404301) = c_Orderings_Obot__class_Obot(tc_fun(_1404291, tc_HOL_Obool)), -(hAPP(_1404297, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404291, tc_HOL_Obool)), _1404299), _1404301)) = hAPP(c_Fun_Ocomp(_1404293, _1404293, _1404293, hAPP(_1404297, _1404299)), hAPP(_1404297, _1404301)))], (33627 ^ _779448) ^ [_1404664, _1404666, _1404668] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404664, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1404666)), _1404668) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404664, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404664, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1404666)), _1404668)), hAPP(_1404668, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33629 ^ _779448) ^ [_1404736, _1404738] : [class_Orderings_Olinorder(_1404736), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404736, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1404736), _1404738)), hAPP(hAPP(c_Set_Oinsert(_1404736), _1404738), c_Orderings_Obot__class_Obot(tc_fun(_1404736, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1404736), _1404738))], (33635 ^ _779448) ^ [_1404879, _1404881, _1404883, _1404885, _1404887] : [class_Groups_Ocomm__monoid__mult(_1404879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404881), _1404883)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404881), _1404885)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404881, tc_HOL_Obool)), _1404883), _1404885) = c_Orderings_Obot__class_Obot(tc_fun(_1404881, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1404879, _1404881, c_Groups_Otimes__class_Otimes(_1404879)), _1404887), c_Groups_Oone__class_Oone(_1404879)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404881, tc_HOL_Obool)), _1404883), _1404885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1404879), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1404879, _1404881, c_Groups_Otimes__class_Otimes(_1404879)), _1404887), c_Groups_Oone__class_Oone(_1404879)), _1404883)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1404879, _1404881, c_Groups_Otimes__class_Otimes(_1404879)), _1404887), c_Groups_Oone__class_Oone(_1404879)), _1404885)))], (33653 ^ _779448) ^ [_1405322, _1405324, _1405326] : [class_Orderings_Olinorder(_1405322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405322), _1405324), _1405326)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405322, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1405322), _1405324)), c_SetInterval_Oord__class_OatLeastAtMost(_1405322, _1405324, _1405326)) = hAPP(c_SetInterval_Oord__class_OatMost(_1405322), _1405326))], (33663 ^ _779448) ^ [_1405517, _1405519, _1405521] : [class_Orderings_Olinorder(_1405517), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405517), _1405519), _1405521)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405517, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1405517), _1405519)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1405517, _1405519, _1405521)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1405517), _1405521))], (33673 ^ _779448) ^ [_1405712, _1405714, _1405716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1405712), _1405714)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405712), _1405716)), 33683 ^ _779448 : [(33684 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405712), 33682 ^ [_1405712, _1405714, _1405716]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1405712, tc_HOL_Obool)), _1405714), _1405716))))], (33686 ^ _779448) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1405712), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405712, tc_HOL_Obool)), _1405714), _1405716)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1405712), _1405714)), hAPP(c_Finite__Set_Ocard(_1405712), _1405716)))], (33690 ^ _779448) ^ [_1406056, _1406058, _1406060, _1406062, _1406064] : [class_Fields_Ofield(_1406056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406058), _1406060)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406058), _1406062)), 33704 ^ _779448 : [(33705 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406058), 33703 ^ [_1406056, _1406058, _1406060, _1406062, _1406064]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406058, tc_HOL_Obool)), _1406060), _1406062))))], (33707 ^ _779448) ^ [] : [-(hAPP(_1406064, 33703 ^ [_1406056, _1406058, _1406060, _1406062, _1406064]) = c_Groups_Ozero__class_Ozero(_1406056))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406058, _1406056), _1406064), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406058, tc_HOL_Obool)), _1406060), _1406062)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1406056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1406056), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406058, _1406056), _1406064), _1406060)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406058, _1406056), _1406064), _1406062))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1406058, _1406056), _1406064), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406058, tc_HOL_Obool)), _1406060), _1406062))))], (33711 ^ _779448) ^ [_1406552, _1406554, _1406556, _1406558, _1406560] : [class_Groups_Ocomm__monoid__mult(_1406552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406554), _1406556)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406554), _1406558)), 33725 ^ _779448 : [(33726 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406554), 33724 ^ [_1406552, _1406554, _1406556, _1406558, _1406560]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406554, tc_HOL_Obool)), _1406556), _1406558))))], (33728 ^ _779448) ^ [] : [hAPP(_1406560, 33724 ^ [_1406552, _1406554, _1406556, _1406558, _1406560]) = c_Groups_Oone__class_Oone(_1406552)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406552, _1406554, c_Groups_Otimes__class_Otimes(_1406552)), _1406560), c_Groups_Oone__class_Oone(_1406552)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406554, tc_HOL_Obool)), _1406556), _1406558)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1406552), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406552, _1406554, c_Groups_Otimes__class_Otimes(_1406552)), _1406560), c_Groups_Oone__class_Oone(_1406552)), _1406556)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406552, _1406554, c_Groups_Otimes__class_Otimes(_1406552)), _1406560), c_Groups_Oone__class_Oone(_1406552)), _1406558)))], (33732 ^ _779448) ^ [_1407095, _1407097, _1407099, _1407101, _1407103] : [class_Groups_Ocomm__monoid__mult(_1407095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407097), _1407099)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407097), _1407101)), 33746 ^ _779448 : [(33747 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407097), 33745 ^ [_1407095, _1407097, _1407099, _1407101, _1407103]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407097, tc_HOL_Obool)), _1407099), _1407101))))], (33749 ^ _779448) ^ [] : [hAPP(_1407103, 33745 ^ [_1407095, _1407097, _1407099, _1407101, _1407103]) = c_Groups_Oone__class_Oone(_1407095)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407097, _1407095), _1407103), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1407097, tc_HOL_Obool)), _1407099), _1407101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407095), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407097, _1407095), _1407103), _1407099)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1407097, _1407095), _1407103), _1407101)))], (33753 ^ _779448) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (33755 ^ _779448) ^ [_1407635, _1407637, _1407639, _1407641, _1407643, _1407645] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1407635, tc_fun(_1407637, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1407635, tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_fun(_1407637, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407637, tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_fun(_1407637, tc_HOL_Obool)), _1407635), c_COMBC(_1407637, tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407637, tc_prod(_1407635, _1407637)), tc_fun(_1407637, tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), _1407635), hAPP(c_COMBB(tc_prod(_1407635, _1407637), tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool), _1407637), c_member(tc_prod(_1407635, _1407637)))), c_Product__Type_OPair(_1407635, _1407637)))), _1407639)), hAPP(hAPP(c_COMBC(_1407635, tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_fun(_1407637, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407637, tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_fun(_1407637, tc_HOL_Obool)), _1407635), c_COMBC(_1407637, tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407637, tc_prod(_1407635, _1407637)), tc_fun(_1407637, tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool)), _1407635), hAPP(c_COMBB(tc_prod(_1407635, _1407637), tc_fun(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool), tc_HOL_Obool), _1407637), c_member(tc_prod(_1407635, _1407637)))), c_Product__Type_OPair(_1407635, _1407637)))), _1407641)), _1407643), _1407645)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1407635, _1407637)), hAPP(hAPP(c_Product__Type_OPair(_1407635, _1407637), _1407643), _1407645)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1407635, _1407637), tc_HOL_Obool)), _1407639), _1407641))))], (33761 ^ _779448) ^ [_1408292, _1408294, _1408296, _1408298, _1408300, _1408302] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1408292, _1408294)), hAPP(hAPP(c_Product__Type_OPair(_1408292, _1408294), _1408300), _1408302)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool)), _1408296), _1408298))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408292, tc_fun(_1408294, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1408292, tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_fun(_1408294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408294, tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_fun(_1408294, tc_HOL_Obool)), _1408292), c_COMBC(_1408294, tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408294, tc_prod(_1408292, _1408294)), tc_fun(_1408294, tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), _1408292), hAPP(c_COMBB(tc_prod(_1408292, _1408294), tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool), _1408294), c_member(tc_prod(_1408292, _1408294)))), c_Product__Type_OPair(_1408292, _1408294)))), _1408296)), hAPP(hAPP(c_COMBC(_1408292, tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_fun(_1408294, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408294, tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_fun(_1408294, tc_HOL_Obool)), _1408292), c_COMBC(_1408294, tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408294, tc_prod(_1408292, _1408294)), tc_fun(_1408294, tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool)), _1408292), hAPP(c_COMBB(tc_prod(_1408292, _1408294), tc_fun(tc_fun(tc_prod(_1408292, _1408294), tc_HOL_Obool), tc_HOL_Obool), _1408294), c_member(tc_prod(_1408292, _1408294)))), c_Product__Type_OPair(_1408292, _1408294)))), _1408298)), _1408300), _1408302)))], (33767 ^ _779448) ^ [_1408955, _1408957, _1408959, _1408961, _1408963] : [class_Groups_Ocomm__monoid__mult(_1408955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408957), _1408959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408957), _1408961)), 33781 ^ _779448 : [(33782 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408957), 33780 ^ [_1408955, _1408957, _1408959, _1408961, _1408963]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408957, tc_HOL_Obool)), _1408959), _1408961))))], (33784 ^ _779448) ^ [] : [hAPP(_1408963, 33780 ^ [_1408955, _1408957, _1408959, _1408961, _1408963]) = c_Groups_Oone__class_Oone(_1408955)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408957, _1408955), _1408963), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408957, tc_HOL_Obool)), _1408959), _1408961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408955), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408957, _1408955), _1408963), _1408959)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1408957, _1408955), _1408963), _1408961)))], (33788 ^ _779448) ^ [_1409450, _1409452, _1409454, _1409456, _1409458] : [class_Groups_Ocomm__monoid__add(_1409450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409452), _1409454)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409452), _1409456)), 33802 ^ _779448 : [(33803 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409452), 33801 ^ [_1409450, _1409452, _1409454, _1409456, _1409458]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409452, tc_HOL_Obool)), _1409454), _1409456))))], (33805 ^ _779448) ^ [] : [hAPP(_1409458, 33801 ^ [_1409450, _1409452, _1409454, _1409456, _1409458]) = c_Groups_Ozero__class_Ozero(_1409450)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409452, _1409450), _1409458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409452, tc_HOL_Obool)), _1409454), _1409456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409450), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409452, _1409450), _1409458), _1409454)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409452, _1409450), _1409458), _1409456)))], (33809 ^ _779448) ^ [_1409945, _1409947, _1409949, _1409951, _1409953] : [class_Groups_Ocomm__monoid__add(_1409945), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409947), _1409949)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409947), _1409951)), 33823 ^ _779448 : [(33824 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1409947), 33822 ^ [_1409945, _1409947, _1409949, _1409951, _1409953]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409947, tc_HOL_Obool)), _1409949), _1409951))))], (33826 ^ _779448) ^ [] : [hAPP(_1409953, 33822 ^ [_1409945, _1409947, _1409949, _1409951, _1409953]) = c_Groups_Ozero__class_Ozero(_1409945)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409947, _1409945), _1409953), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409947, tc_HOL_Obool)), _1409949), _1409951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409945), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409947, _1409945), _1409953), _1409949)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1409947, _1409945), _1409953), _1409951)))], (33830 ^ _779448) ^ [_1410440, _1410442, _1410444, _1410446, _1410448, _1410450] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410440, tc_fun(_1410442, tc_HOL_Obool))), _1410444), _1410446), _1410448), _1410450)), 33833 ^ _779448 : [(33834 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1410444, _1410448), _1410450)))], (33836 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1410446, _1410448), _1410450)))]]], (33838 ^ _779448) ^ [_1410613, _1410615, _1410617, _1410619, _1410621, _1410623] : [hBOOL(hAPP(hAPP(_1410613, _1410615), _1410617)), hBOOL(hAPP(hAPP(_1410619, _1410615), _1410617)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410621, tc_fun(_1410623, tc_HOL_Obool))), _1410613), _1410619), _1410615), _1410617)))], (33848 ^ _779448) ^ [_1410816, _1410818, _1410820, _1410822, _1410824, _1410826] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410816, tc_fun(_1410818, tc_HOL_Obool))), _1410820), _1410822), _1410824), _1410826)), -(hBOOL(hAPP(hAPP(_1410822, _1410824), _1410826)))], (33854 ^ _779448) ^ [_1410949, _1410951, _1410953, _1410955, _1410957, _1410959] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410949, tc_fun(_1410951, tc_HOL_Obool))), _1410953), _1410955), _1410957), _1410959)), -(hBOOL(hAPP(hAPP(_1410953, _1410957), _1410959)))], (33860 ^ _779448) ^ [_1411082, _1411084, _1411086] : [class_Lattices_Olattice(_1411082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411082), _1411084)), hBOOL(hAPP(hAPP(c_member(_1411082), _1411086), _1411084)), 33871 ^ _779448 : [(33872 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411082, tc_HOL_Obool)), _1411084), hAPP(hAPP(c_Set_Oinsert(_1411082), _1411086), c_Orderings_Obot__class_Obot(tc_fun(_1411082, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1411082, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1411082, _1411084) = _1411086)], (33878 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411082, tc_HOL_Obool)), _1411084), hAPP(hAPP(c_Set_Oinsert(_1411082), _1411086), c_Orderings_Obot__class_Obot(tc_fun(_1411082, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1411082, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1411082, _1411084) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1411082), _1411086), c_Big__Operators_Olattice__class_OInf__fin(_1411082, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1411082, tc_HOL_Obool)), _1411084), hAPP(hAPP(c_Set_Oinsert(_1411082), _1411086), c_Orderings_Obot__class_Obot(tc_fun(_1411082, tc_HOL_Obool)))))))]]], (33884 ^ _779448) ^ [_1411588, _1411590, _1411592, _1411594, _1411596, _1411598] : [class_Groups_Oordered__ab__group__add(_1411588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1411590), _1411592)), 33894 ^ _779448 : [(33895 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411590), 33893 ^ [_1411588, _1411590, _1411592, _1411594, _1411596, _1411598]), _1411592)))], (33897 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411588), c_Groups_Ozero__class_Ozero(_1411588)), hAPP(_1411594, 33893 ^ [_1411588, _1411590, _1411592, _1411594, _1411596, _1411598])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1411590, _1411588), _1411594), _1411592) = _1411596, hBOOL(hAPP(hAPP(c_member(_1411590), _1411598), _1411592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411588), hAPP(_1411594, _1411598)), _1411596)))], (33909 ^ _779448) ^ [_1412108, _1412110, _1412112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1412108, 33910 ^ [_1412108, _1412110, _1412112])), hAPP(_1412110, 33910 ^ [_1412108, _1412110, _1412112]))), -(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), _1412110), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412112))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1412108), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412112))) = 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)), _1412110)), _1412108)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1412112)))], (33916 ^ _779448) ^ [_1412341, _1412343] : [class_Lattices_Olattice(_1412341), -(c_Big__Operators_Olattice__class_OInf__fin(_1412341, hAPP(hAPP(c_Set_Oinsert(_1412341), _1412343), c_Orderings_Obot__class_Obot(tc_fun(_1412341, tc_HOL_Obool)))) = _1412343)], (33922 ^ _779448) ^ [_1412448, _1412450, _1412452] : [class_Lattices_Olattice(_1412448), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412448), _1412450)), hBOOL(hAPP(hAPP(c_member(_1412448), _1412452), _1412450)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1412448), _1412452), c_Big__Operators_Olattice__class_OInf__fin(_1412448, _1412450)) = _1412452)], (33936 ^ _779448) ^ [_1412677, _1412679, _1412681] : [class_Lattices_Olattice(_1412677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412677), _1412679)), hBOOL(hAPP(hAPP(c_member(_1412677), _1412681), _1412679)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1412677), _1412681), c_Big__Operators_Olattice__class_OInf__fin(_1412677, _1412679)) = c_Big__Operators_Olattice__class_OInf__fin(_1412677, _1412679))], (33950 ^ _779448) ^ [_1412912, _1412914] : [class_Lattices_Olattice(_1412912), hBOOL(hAPP(c_Finite__Set_Ofinite(_1412912), _1412914)), -(c_Big__Operators_Olattice__class_OInf__fin(_1412912, _1412914) = hAPP(c_Finite__Set_Ofold1(_1412912, c_Lattices_Osemilattice__inf__class_Oinf(_1412912)), _1412914))], (33960 ^ _779448) ^ [_1413069, _1413071, _1413073] : [class_Lattices_Olattice(_1413069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413069), _1413071)), -(_1413071 = c_Orderings_Obot__class_Obot(tc_fun(_1413069, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1413069, hAPP(hAPP(c_Set_Oinsert(_1413069), _1413073), _1413071)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413069), _1413073), c_Big__Operators_Olattice__class_OInf__fin(_1413069, _1413071)))], (33974 ^ _779448) ^ [_1413277, _1413279, _1413281] : [class_Lattices_Olattice(_1413277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413277), _1413279)), -(_1413281 = c_Orderings_Obot__class_Obot(tc_fun(_1413277, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413277, tc_HOL_Obool)), _1413281), _1413279)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413277), c_Big__Operators_Olattice__class_OInf__fin(_1413277, _1413281)), c_Big__Operators_Olattice__class_OInf__fin(_1413277, _1413279)) = c_Big__Operators_Olattice__class_OInf__fin(_1413277, _1413279))], (33992 ^ _779448) ^ [_1413591, _1413593, _1413595] : [class_Lattices_Olattice(_1413591), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413591), _1413593)), -(_1413593 = c_Orderings_Obot__class_Obot(tc_fun(_1413591, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413591), _1413595)), -(_1413595 = c_Orderings_Obot__class_Obot(tc_fun(_1413591, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1413591, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413591, tc_HOL_Obool)), _1413593), _1413595)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1413591), c_Big__Operators_Olattice__class_OInf__fin(_1413591, _1413593)), c_Big__Operators_Olattice__class_OInf__fin(_1413591, _1413595)))], (34014 ^ _779448) ^ [_1413940, _1413942] : [class_Lattices_Olattice(_1413940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1413940), _1413942)), -(_1413942 = c_Orderings_Obot__class_Obot(tc_fun(_1413940, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413940), c_Big__Operators_Olattice__class_OInf__fin(_1413940, _1413942)), c_Big__Operators_Olattice__class_OSup__fin(_1413940, _1413942))))], (34028 ^ _779448) ^ [_1414126, _1414128, _1414130] : [class_Lattices_Olattice(_1414126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414126), _1414128)), -(c_Big__Operators_Olattice__class_OInf__fin(_1414126, hAPP(hAPP(c_Set_Oinsert(_1414126), _1414130), _1414128)) = hAPP(hAPP(c_Finite__Set_Ofold(_1414126, _1414126, c_Lattices_Osemilattice__inf__class_Oinf(_1414126)), _1414130), _1414128))], (34038 ^ _779448) ^ [_1414311, _1414313, _1414315] : [class_Lattices_Olattice(_1414311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414311), _1414313)), -(hBOOL(hAPP(hAPP(c_member(_1414311), _1414315), _1414313))), -(_1414313 = c_Orderings_Obot__class_Obot(tc_fun(_1414311, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1414311, hAPP(hAPP(c_Set_Oinsert(_1414311), _1414315), _1414313)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414311), _1414315), c_Big__Operators_Olattice__class_OInf__fin(_1414311, _1414313)))], (34056 ^ _779448) ^ [_1414548, _1414550, _1414552] : [class_Lattices_Olattice(_1414548), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414548), _1414550)), 34063 ^ _779448 : [(34064 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414548, tc_HOL_Obool)), _1414550), hAPP(hAPP(c_Set_Oinsert(_1414548), _1414552), c_Orderings_Obot__class_Obot(tc_fun(_1414548, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1414548, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1414548, hAPP(hAPP(c_Set_Oinsert(_1414548), _1414552), _1414550)) = _1414552)], (34070 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414548, tc_HOL_Obool)), _1414550), hAPP(hAPP(c_Set_Oinsert(_1414548), _1414552), c_Orderings_Obot__class_Obot(tc_fun(_1414548, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1414548, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1414548, hAPP(hAPP(c_Set_Oinsert(_1414548), _1414552), _1414550)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1414548), _1414552), c_Big__Operators_Olattice__class_OInf__fin(_1414548, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414548, tc_HOL_Obool)), _1414550), hAPP(hAPP(c_Set_Oinsert(_1414548), _1414552), c_Orderings_Obot__class_Obot(tc_fun(_1414548, tc_HOL_Obool)))))))]]], (34076 ^ _779448) ^ [_1415018, _1415020, _1415022] : [class_Lattices_Olattice(_1415018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415018), _1415020)), -(_1415020 = c_Orderings_Obot__class_Obot(tc_fun(_1415018, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415018), _1415022)), -(_1415022 = c_Orderings_Obot__class_Obot(tc_fun(_1415018, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415018, tc_HOL_Obool)), _1415020), _1415022) = c_Orderings_Obot__class_Obot(tc_fun(_1415018, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1415018, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415018, tc_HOL_Obool)), _1415020), _1415022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415018), c_Big__Operators_Olattice__class_OInf__fin(_1415018, _1415020)), c_Big__Operators_Olattice__class_OInf__fin(_1415018, _1415022)))], (34102 ^ _779448) ^ [_1415495, _1415497, _1415499] : [class_Lattices_Olattice(_1415495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415495), _1415497)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415495), _1415499)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415495, tc_HOL_Obool)), _1415497), _1415499) = c_Orderings_Obot__class_Obot(tc_fun(_1415495, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415495), c_Big__Operators_Olattice__class_OInf__fin(_1415495, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1415495, tc_HOL_Obool)), _1415497), _1415499))), c_Big__Operators_Olattice__class_OInf__fin(_1415495, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1415495, tc_HOL_Obool)), _1415497), _1415499))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1415495), c_Big__Operators_Olattice__class_OInf__fin(_1415495, _1415497)), c_Big__Operators_Olattice__class_OInf__fin(_1415495, _1415499)))], (34120 ^ _779448) ^ [_1415843, _1415845, _1415847] : [class_Lattices_Olattice(_1415843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1415843), _1415845)), -(hBOOL(hAPP(hAPP(c_member(_1415843), _1415847), _1415845))), -(c_Big__Operators_Olattice__class_OInf__fin(_1415843, hAPP(hAPP(c_Set_Oinsert(_1415843), _1415847), _1415845)) = hAPP(hAPP(c_Finite__Set_Ofold(_1415843, _1415843, c_Lattices_Osemilattice__inf__class_Oinf(_1415843)), _1415847), _1415845))], (34134 ^ _779448) ^ [_1416057, _1416059] : [class_Lattices_Olattice(_1416057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416057), _1416059)), -(_1416059 = c_Orderings_Obot__class_Obot(tc_fun(_1416057, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1416057), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416057), 34147 ^ [_1416057, _1416059]), 34148 ^ [_1416057, _1416059])), hAPP(hAPP(c_Set_Oinsert(_1416057), 34147 ^ [_1416057, _1416059]), hAPP(hAPP(c_Set_Oinsert(_1416057), 34148 ^ [_1416057, _1416059]), c_Orderings_Obot__class_Obot(tc_fun(_1416057, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1416057), c_Big__Operators_Olattice__class_OInf__fin(_1416057, _1416059)), _1416059)))], (34154 ^ _779448) ^ [_1416501, _1416503, _1416505] : [class_Lattices_Olattice(_1416501), hAPP(_1416503, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416501), 34159 ^ [_1416501, _1416503, _1416505]), 34160 ^ [_1416501, _1416503, _1416505])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1416501), hAPP(_1416503, 34159 ^ [_1416501, _1416503, _1416505])), hAPP(_1416503, 34160 ^ [_1416501, _1416503, _1416505])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1416501), _1416505)), -(_1416505 = c_Orderings_Obot__class_Obot(tc_fun(_1416501, tc_HOL_Obool))), -(hAPP(_1416503, c_Big__Operators_Olattice__class_OInf__fin(_1416501, _1416505)) = c_Big__Operators_Olattice__class_OInf__fin(_1416501, hAPP(c_Set_Oimage(_1416501, _1416501, _1416503), _1416505)))], (34174 ^ _779448) ^ [_1416904, _1416906, _1416908, _1416910, _1416912] : [hBOOL(hAPP(hAPP(c_member(_1416904), _1416906), hAPP(c_Relation_OImage(_1416908, _1416904, _1416910), _1416912))), 34178 ^ _779448 : [(34179 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1416908, _1416904)), hAPP(hAPP(c_Product__Type_OPair(_1416908, _1416904), 34177 ^ [_1416904, _1416906, _1416908, _1416910, _1416912]), _1416906)), _1416910)))], (34181 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416908), 34177 ^ [_1416904, _1416906, _1416908, _1416910, _1416912]), _1416912)))]]], (34183 ^ _779448) ^ [_1417128, _1417130, _1417132, _1417134, _1417136] : [class_Groups_Ocomm__monoid__add(_1417128), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417130), _1417132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417130, tc_HOL_Obool)), _1417134), _1417132)), 34197 ^ _779448 : [(34198 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417130), 34196 ^ [_1417128, _1417130, _1417132, _1417134, _1417136]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417130, tc_HOL_Obool)), _1417132), _1417134))))], (34200 ^ _779448) ^ [] : [hAPP(_1417136, 34196 ^ [_1417128, _1417130, _1417132, _1417134, _1417136]) = c_Groups_Ozero__class_Ozero(_1417128)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417130, _1417128), _1417136), _1417134) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417130, _1417128), _1417136), _1417132))], (34204 ^ _779448) ^ [_1417579, _1417581, _1417583, _1417585, _1417587] : [class_Groups_Ocomm__monoid__add(_1417579), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417581), _1417583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1417581, tc_HOL_Obool)), _1417585), _1417583)), 34218 ^ _779448 : [(34219 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417581), 34217 ^ [_1417579, _1417581, _1417583, _1417585, _1417587]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417581, tc_HOL_Obool)), _1417583), _1417585))))], (34221 ^ _779448) ^ [] : [hAPP(_1417587, 34217 ^ [_1417579, _1417581, _1417583, _1417585, _1417587]) = c_Groups_Ozero__class_Ozero(_1417579)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417581, _1417579), _1417587), _1417583) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1417581, _1417579), _1417587), _1417585))], (34225 ^ _779448) ^ [_1418030, _1418032, _1418034, _1418036, _1418038] : [class_Groups_Ocomm__monoid__add(_1418030), class_Groups_Oordered__cancel__ab__semigroup__add(_1418030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418032), _1418034)), -(_1418034 = c_Orderings_Obot__class_Obot(tc_fun(_1418032, tc_HOL_Obool))), 34243 ^ _779448 : [(34244 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418032), 34242 ^ [_1418030, _1418032, _1418034, _1418036, _1418038]), _1418034)))], (34246 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418030), hAPP(_1418036, 34242 ^ [_1418030, _1418032, _1418034, _1418036, _1418038])), hAPP(_1418038, 34242 ^ [_1418030, _1418032, _1418034, _1418036, _1418038])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418030), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418032, _1418030), _1418036), _1418034)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1418032, _1418030), _1418038), _1418034))))], (34250 ^ _779448) ^ [_1418561, _1418563] : [class_Orderings_Oorder(_1418561), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418561, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1418561), _1418563)), hAPP(c_SetInterval_Oord__class_OatLeast(_1418561), _1418563)) = hAPP(hAPP(c_Set_Oinsert(_1418561), _1418563), c_Orderings_Obot__class_Obot(tc_fun(_1418561, tc_HOL_Obool))))], (34256 ^ _779448) ^ [_1418704, _1418706, _1418708] : [class_Fields_Olinordered__field__inverse__zero(_1418704), 34262 ^ _779448 : [(34263 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418704), c_Groups_Ozero__class_Ozero(_1418704)), 34261 ^ [_1418704, _1418706, _1418708])))], (34265 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418704), 34261 ^ [_1418704, _1418706, _1418708]), c_Groups_Oone__class_Oone(_1418704))))], (34267 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1418704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418704), 34261 ^ [_1418704, _1418706, _1418708]), _1418706)), _1418708))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1418704), _1418706), _1418708)))], (34271 ^ _779448) ^ [_1419053, _1419055, _1419057, _1419059, _1419061] : [class_Groups_Ocomm__monoid__add(_1419053), class_Groups_Ocomm__monoid__mult(_1419053), _1419055 = _1419057, c_Nat__Transfer_Onat__set(_1419057), 34289 ^ _779448 : [(34290 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34288 ^ [_1419053, _1419055, _1419057, _1419059, _1419061])))], (34292 ^ _779448) ^ [] : [hAPP(_1419059, 34288 ^ [_1419053, _1419055, _1419057, _1419059, _1419061]) = hAPP(_1419061, 34288 ^ [_1419053, _1419055, _1419057, _1419059, _1419061])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1419053), _1419059), _1419055) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1419053), _1419061), _1419057))], (34296 ^ _779448) ^ [_1419516, _1419518, _1419520] : [class_Orderings_Olinorder(_1419516), 34299 ^ _779448 : [(34300 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1419516), _1419518) = hAPP(c_SetInterval_Oord__class_OatLeast(_1419516), _1419520), -(_1419518 = _1419520)], (34306 ^ _779448) ^ [] : [_1419518 = _1419520, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1419516), _1419518) = hAPP(c_SetInterval_Oord__class_OatLeast(_1419516), _1419520))]]], (34312 ^ _779448) ^ [_1419757, _1419759, _1419761] : [class_Orderings_Oord(_1419757), 34315 ^ _779448 : [(34316 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1419757), _1419759), hAPP(c_SetInterval_Oord__class_OatLeast(_1419757), _1419761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419757), _1419761), _1419759)))], (34322 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419757), _1419761), _1419759)), -(hBOOL(hAPP(hAPP(c_member(_1419757), _1419759), hAPP(c_SetInterval_Oord__class_OatLeast(_1419757), _1419761))))]]], (34328 ^ _779448) ^ [_1420025, _1420027, _1420029] : [class_Orderings_Oorder(_1420025), 34331 ^ _779448 : [(34332 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420025, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420025), _1420027)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420025), _1420029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420025), _1420029), _1420027)))], (34338 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420025), _1420029), _1420027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420025, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420025), _1420027)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420025), _1420029))))]]], (34344 ^ _779448) ^ [_1420317, _1420319] : [class_Orderings_Olinorder(_1420317), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1420317, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420317), _1420319)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1420317), _1420319))], (34350 ^ _779448) ^ [_1420428, _1420430] : [class_Orderings_Olinorder(_1420428), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1420428, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1420428), _1420430)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1420428), _1420430))], (34356 ^ _779448) ^ [_1420539, _1420541, _1420543] : [class_Orderings_Olinorder(_1420539), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420539), _1420541), _1420543)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420539, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1420539, _1420541), _1420543)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420539), _1420543)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1420539), _1420541))], (34366 ^ _779448) ^ [_1420738, _1420740, _1420742] : [class_Orderings_Oorder(_1420738), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420738, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1420738, _1420740), _1420742)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420738), _1420742)) = c_Orderings_Obot__class_Obot(tc_fun(_1420738, tc_HOL_Obool)))], (34372 ^ _779448) ^ [_1420869, _1420871, _1420873, _1420875] : [class_Orderings_Olinorder(_1420869), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420869, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1420869, _1420871, _1420873)), hAPP(c_SetInterval_Oord__class_OatLeast(_1420869), _1420875)) = c_SetInterval_Oord__class_OatLeastAtMost(_1420869, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1420869), _1420871), _1420875), _1420873))], (34378 ^ _779448) ^ [_1421012, _1421014, _1421016, _1421018] : [class_Orderings_Olinorder(_1421012), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421012, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1421012), _1421014)), c_SetInterval_Oord__class_OatLeastAtMost(_1421012, _1421016, _1421018)) = c_SetInterval_Oord__class_OatLeastAtMost(_1421012, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1421012), _1421014), _1421016), _1421018))], (34384 ^ _779448) ^ [_1421155, _1421157, _1421159] : [class_Orderings_Oorder(_1421155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421155, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1421155, _1421157, _1421159)), hAPP(c_SetInterval_Oord__class_OatLeast(_1421155), _1421159)) = c_Orderings_Obot__class_Obot(tc_fun(_1421155, tc_HOL_Obool)))], (34390 ^ _779448) ^ [_1421282, _1421284] : [class_Groups_Oordered__ab__group__add(_1421282), -(hAPP(c_Set_Oimage(_1421282, _1421282, c_Groups_Ouminus__class_Ouminus(_1421282)), hAPP(c_SetInterval_Oord__class_OatMost(_1421282), _1421284)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1421282), hAPP(c_Groups_Ouminus__class_Ouminus(_1421282), _1421284)))], (34396 ^ _779448) ^ [_1421405, _1421407] : [class_Groups_Oordered__ab__group__add(_1421405), -(hAPP(c_Set_Oimage(_1421405, _1421405, c_Groups_Ouminus__class_Ouminus(_1421405)), hAPP(c_SetInterval_Oord__class_OatLeast(_1421405), _1421407)) = hAPP(c_SetInterval_Oord__class_OatMost(_1421405), hAPP(c_Groups_Ouminus__class_Ouminus(_1421405), _1421407)))], (34402 ^ _779448) ^ [_1421528] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1421528)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1421528), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (34404 ^ _779448) ^ [_1421572, _1421574, _1421576] : [class_Orderings_Olinorder(_1421572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421572), _1421574), _1421576)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421572, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1421572, _1421574, _1421576)), hAPP(c_SetInterval_Oord__class_OatLeast(_1421572), _1421576)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1421572), _1421574))], (34414 ^ _779448) ^ [_1421767, _1421769, _1421771] : [class_Orderings_Olinorder(_1421767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421767), _1421769), _1421771)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421767, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1421767, _1421769, _1421771)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1421767), _1421771)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1421767), _1421769))], (34424 ^ _779448) ^ [_1421962, _1421964] : [class_Orderings_Olinorder(_1421962), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1421962, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1421962), _1421964), c_Orderings_Obot__class_Obot(tc_fun(_1421962, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1421962), _1421964)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1421962), _1421964))], (34430 ^ _779448) ^ [_1422105] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1422105)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1422105))], (34432 ^ _779448) ^ [_1422137, _1422139, _1422141] : [class_Orderings_Olinorder(_1422137), 34435 ^ _779448 : [(34436 ^ _779448) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422137), _1422139) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422137), _1422141), -(_1422139 = _1422141)], (34442 ^ _779448) ^ [] : [_1422139 = _1422141, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422137), _1422139) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422137), _1422141))]]], (34448 ^ _779448) ^ [_1422378, _1422380, _1422382] : [class_Orderings_Oord(_1422378), 34451 ^ _779448 : [(34452 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1422378), _1422380), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422378), _1422382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422378), _1422382), _1422380)))], (34458 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422378), _1422382), _1422380)), -(hBOOL(hAPP(hAPP(c_member(_1422378), _1422380), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422378), _1422382))))]]], (34464 ^ _779448) ^ [_1422646, _1422648, _1422650] : [class_Orderings_Olinorder(_1422646), 34467 ^ _779448 : [(34468 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422646, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422646), _1422648)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422646), _1422650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422646), _1422650), _1422648)))], (34474 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422646), _1422650), _1422648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1422646, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422646), _1422648)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422646), _1422650))))]]], (34480 ^ _779448) ^ [_1422938, _1422940] : [class_Orderings_Olinorder(_1422938), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1422938, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1422938), _1422940)) = hAPP(c_SetInterval_Oord__class_OatMost(_1422938), _1422940))], (34486 ^ _779448) ^ [_1423049, _1423051] : [class_Orderings_Olinorder(_1423049), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423049, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1423049), _1423051)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423049), _1423051))], (34492 ^ _779448) ^ [_1423160, _1423162, _1423164] : [class_Orderings_Oorder(_1423160), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423160, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1423160, _1423162, _1423164)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423160), _1423164)) = c_Orderings_Obot__class_Obot(tc_fun(_1423160, tc_HOL_Obool)))], (34498 ^ _779448) ^ [_1423287, _1423289, _1423291] : [class_Orderings_Olinorder(_1423287), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423287), _1423289), _1423291)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1423287, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1423287, _1423289, _1423291)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423287), _1423291)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423287), _1423289))], (34508 ^ _779448) ^ [_1423482, _1423484] : [class_Groups_Oordered__ab__group__add(_1423482), -(hAPP(c_Set_Oimage(_1423482, _1423482, c_Groups_Ouminus__class_Ouminus(_1423482)), hAPP(c_SetInterval_Oord__class_OlessThan(_1423482), _1423484)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423482), hAPP(c_Groups_Ouminus__class_Ouminus(_1423482), _1423484)))], (34514 ^ _779448) ^ [_1423605, _1423607] : [class_Groups_Oordered__ab__group__add(_1423605), -(hAPP(c_Set_Oimage(_1423605, _1423605, c_Groups_Ouminus__class_Ouminus(_1423605)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423605), _1423607)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1423605), hAPP(c_Groups_Ouminus__class_Ouminus(_1423605), _1423607)))], (34520 ^ _779448) ^ [_1423728, _1423730, _1423732] : [class_Orderings_Oorder(_1423728), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423728, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1423728, _1423730, _1423732)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1423728), _1423732)) = c_Orderings_Obot__class_Obot(tc_fun(_1423728, tc_HOL_Obool)))], (34526 ^ _779448) ^ [_1423855] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423855)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1423855)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423855)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (34528 ^ _779448) ^ [_1423902, _1423904] : [class_Rings_Olinordered__idom(_1423902), 34531 ^ _779448 : [(34532 ^ _779448) ^ [] : [c_Groups_Osgn__class_Osgn(_1423902, _1423904) = hAPP(c_Groups_Ouminus__class_Ouminus(_1423902), c_Groups_Oone__class_Oone(_1423902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423902), _1423904), c_Groups_Ozero__class_Ozero(_1423902))))], (34538 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423902), _1423904), c_Groups_Ozero__class_Ozero(_1423902))), -(c_Groups_Osgn__class_Osgn(_1423902, _1423904) = hAPP(c_Groups_Ouminus__class_Ouminus(_1423902), c_Groups_Oone__class_Oone(_1423902)))]]], (34544 ^ _779448) ^ [_1424164, _1424166] : [class_Rings_Olinordered__idom(_1424164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424164), _1424166), c_Groups_Ozero__class_Ozero(_1424164))), -(c_Groups_Osgn__class_Osgn(_1424164, _1424166) = hAPP(c_Groups_Ouminus__class_Ouminus(_1424164), c_Groups_Oone__class_Oone(_1424164)))], (34554 ^ _779448) ^ [_1424329, _1424331] : [class_Groups_Osgn__if(_1424329), 34557 ^ _779448 : [(34558 ^ _779448) ^ [] : [_1424331 = c_Groups_Ozero__class_Ozero(_1424329), -(c_Groups_Osgn__class_Osgn(_1424329, _1424331) = c_Groups_Ozero__class_Ozero(_1424329))], (34564 ^ _779448) ^ [] : [-(_1424331 = c_Groups_Ozero__class_Ozero(_1424329)), 34567 ^ _779448 : [(34568 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424329), c_Groups_Ozero__class_Ozero(_1424329)), _1424331)), -(c_Groups_Osgn__class_Osgn(_1424329, _1424331) = c_Groups_Oone__class_Oone(_1424329))], (34574 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1424329), c_Groups_Ozero__class_Ozero(_1424329)), _1424331))), -(c_Groups_Osgn__class_Osgn(_1424329, _1424331) = hAPP(c_Groups_Ouminus__class_Ouminus(_1424329), c_Groups_Oone__class_Oone(_1424329)))]]]]], (34580 ^ _779448) ^ [_1424726, _1424728] : [class_Rings_Olinordered__idom(_1424726), -(c_Groups_Osgn__class_Osgn(_1424726, c_Groups_Osgn__class_Osgn(_1424726, _1424728)) = c_Groups_Osgn__class_Osgn(_1424726, _1424728))], (34586 ^ _779448) ^ [_1424819, _1424821] : [class_Rings_Olinordered__idom(_1424819), 34589 ^ _779448 : [(34590 ^ _779448) ^ [] : [c_Groups_Osgn__class_Osgn(_1424819, _1424821) = c_Groups_Ozero__class_Ozero(_1424819), -(_1424821 = c_Groups_Ozero__class_Ozero(_1424819))], (34596 ^ _779448) ^ [] : [_1424821 = c_Groups_Ozero__class_Ozero(_1424819), -(c_Groups_Osgn__class_Osgn(_1424819, _1424821) = c_Groups_Ozero__class_Ozero(_1424819))]]], (34602 ^ _779448) ^ [_1425045] : [class_Groups_Osgn__if(_1425045), -(c_Groups_Osgn__class_Osgn(_1425045, c_Groups_Ozero__class_Ozero(_1425045)) = c_Groups_Ozero__class_Ozero(_1425045))], (34608 ^ _779448) ^ [_1425132, _1425134, _1425136] : [class_Rings_Olinordered__idom(_1425132), -(c_Groups_Osgn__class_Osgn(_1425132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425132), _1425134), _1425136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425132), c_Groups_Osgn__class_Osgn(_1425132, _1425134)), c_Groups_Osgn__class_Osgn(_1425132, _1425136)))], (34614 ^ _779448) ^ [_1425259, _1425261] : [class_Rings_Olinordered__idom(_1425259), 34617 ^ _779448 : [(34618 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425259), c_Groups_Ozero__class_Ozero(_1425259)), c_Groups_Osgn__class_Osgn(_1425259, _1425261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425259), c_Groups_Ozero__class_Ozero(_1425259)), _1425261)))], (34624 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425259), c_Groups_Ozero__class_Ozero(_1425259)), _1425261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425259), c_Groups_Ozero__class_Ozero(_1425259)), c_Groups_Osgn__class_Osgn(_1425259, _1425261))))]]], (34630 ^ _779448) ^ [_1425527, _1425529] : [class_Rings_Olinordered__idom(_1425527), 34633 ^ _779448 : [(34634 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425527), c_Groups_Osgn__class_Osgn(_1425527, _1425529)), c_Groups_Ozero__class_Ozero(_1425527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425527), _1425529), c_Groups_Ozero__class_Ozero(_1425527))))], (34640 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425527), _1425529), c_Groups_Ozero__class_Ozero(_1425527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425527), c_Groups_Osgn__class_Osgn(_1425527, _1425529)), c_Groups_Ozero__class_Ozero(_1425527))))]]], (34646 ^ _779448) ^ [_1425795, _1425797] : [class_Rings_Olinordered__idom(_1425795), 34649 ^ _779448 : [(34650 ^ _779448) ^ [] : [c_Groups_Osgn__class_Osgn(_1425795, _1425797) = c_Groups_Oone__class_Oone(_1425795), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425795), c_Groups_Ozero__class_Ozero(_1425795)), _1425797)))], (34656 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425795), c_Groups_Ozero__class_Ozero(_1425795)), _1425797)), -(c_Groups_Osgn__class_Osgn(_1425795, _1425797) = c_Groups_Oone__class_Oone(_1425795))]]], (34662 ^ _779448) ^ [_1426042, _1426044] : [class_Rings_Olinordered__idom(_1426042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1426042), c_Groups_Ozero__class_Ozero(_1426042)), _1426044)), -(c_Groups_Osgn__class_Osgn(_1426042, _1426044) = c_Groups_Oone__class_Oone(_1426042))], (34672 ^ _779448) ^ [_1426203] : [_1426203 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1426203) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34678 ^ _779448) ^ [_1426279] : [-(_1426279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34681 ^ _779448 : [(34682 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1426279)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1426279) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34688 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1426279))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1426279) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (34694 ^ _779448) ^ [_1426471, _1426473, _1426475, _1426477] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1426471, _1426473, _1426475, c_Code__Numeral_OSuc__code__numeral(_1426477)) = hAPP(_1426475, _1426477))], (34696 ^ _779448) ^ [_1426510, _1426512, _1426514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1426510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1426512), 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), _1426512), _1426514))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1426510))), _1426514)))], (34702 ^ _779448) ^ [_1426657, _1426659, _1426661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1426657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426659), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426661), 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), _1426661), _1426659))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1426657)))))], (34708 ^ _779448) ^ [_1426804, _1426806, _1426808, _1426810] : [class_Groups_Oordered__ab__group__add__abs(_1426804), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1426804), hAPP(c_Groups_Oabs__class_Oabs(_1426804), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426806, _1426804), _1426808), _1426810))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426806, _1426804), hAPP(hAPP(c_COMBB(_1426804, _1426804, _1426806), c_Groups_Oabs__class_Oabs(_1426804)), _1426808)), _1426810))))], (34714 ^ _779448) ^ [_1426967, _1426969, _1426971, _1426973] : [class_Groups_Oordered__ab__group__add__abs(_1426967), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1426967), c_Groups_Ozero__class_Ozero(_1426967)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426969, _1426967), hAPP(hAPP(c_COMBB(_1426967, _1426967, _1426969), c_Groups_Oabs__class_Oabs(_1426967)), _1426971)), _1426973))))], (34720 ^ _779448) ^ [_1427106, _1427108, _1427110, _1427112] : [class_Groups_Oordered__ab__group__add__abs(_1427106), -(hAPP(c_Groups_Oabs__class_Oabs(_1427106), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427108, _1427106), hAPP(hAPP(c_COMBB(_1427106, _1427106, _1427108), c_Groups_Oabs__class_Oabs(_1427106)), _1427110)), _1427112)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427108, _1427106), hAPP(hAPP(c_COMBB(_1427106, _1427106, _1427108), c_Groups_Oabs__class_Oabs(_1427106)), _1427110)), _1427112))], (34726 ^ _779448) ^ [_1427279, _1427281, _1427283] : [class_Groups_Oordered__ab__group__add__abs(_1427279), -(hAPP(c_Groups_Oabs__class_Oabs(_1427279), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427279), hAPP(c_Groups_Oabs__class_Oabs(_1427279), _1427281)), hAPP(c_Groups_Oabs__class_Oabs(_1427279), _1427283))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427279), hAPP(c_Groups_Oabs__class_Oabs(_1427279), _1427281)), hAPP(c_Groups_Oabs__class_Oabs(_1427279), _1427283)))], (34732 ^ _779448) ^ [_1427438, _1427440, _1427442] : [class_Rings_Olinordered__idom(_1427438), -(hAPP(c_Groups_Oabs__class_Oabs(_1427438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427438), _1427440), _1427442)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427438), hAPP(c_Groups_Oabs__class_Oabs(_1427438), _1427440)), hAPP(c_Groups_Oabs__class_Oabs(_1427438), _1427442)))], (34738 ^ _779448) ^ [_1427577, _1427579] : [class_Rings_Olinordered__idom(_1427577), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427577), hAPP(c_Groups_Oabs__class_Oabs(_1427577), _1427579)), hAPP(c_Groups_Oabs__class_Oabs(_1427577), _1427579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427577), _1427579), _1427579))], (34744 ^ _779448) ^ [_1427704] : [class_Rings_Olinordered__idom(_1427704), -(hAPP(c_Groups_Oabs__class_Oabs(_1427704), c_Groups_Oone__class_Oone(_1427704)) = c_Groups_Oone__class_Oone(_1427704))], (34750 ^ _779448) ^ [_1427795, _1427797] : [class_Groups_Oordered__ab__group__add__abs(_1427795), -(hAPP(c_Groups_Oabs__class_Oabs(_1427795), hAPP(c_Groups_Ouminus__class_Ouminus(_1427795), _1427797)) = hAPP(c_Groups_Oabs__class_Oabs(_1427795), _1427797))], (34756 ^ _779448) ^ [_1427900, _1427902] : [class_Groups_Oordered__ab__group__add__abs(_1427900), -(hAPP(c_Groups_Oabs__class_Oabs(_1427900), hAPP(c_Groups_Oabs__class_Oabs(_1427900), _1427902)) = hAPP(c_Groups_Oabs__class_Oabs(_1427900), _1427902))], (34762 ^ _779448) ^ [_1428005, _1428007] : [class_Groups_Oordered__ab__group__add__abs(_1428005), 34765 ^ _779448 : [(34766 ^ _779448) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1428005), _1428007) = c_Groups_Ozero__class_Ozero(_1428005), -(_1428007 = c_Groups_Ozero__class_Ozero(_1428005))], (34772 ^ _779448) ^ [] : [_1428007 = c_Groups_Ozero__class_Ozero(_1428005), -(hAPP(c_Groups_Oabs__class_Oabs(_1428005), _1428007) = c_Groups_Ozero__class_Ozero(_1428005))]]], (34778 ^ _779448) ^ [_1428237] : [class_Groups_Oordered__ab__group__add__abs(_1428237), -(hAPP(c_Groups_Oabs__class_Oabs(_1428237), c_Groups_Ozero__class_Ozero(_1428237)) = c_Groups_Ozero__class_Ozero(_1428237))], (34784 ^ _779448) ^ [_1428328, _1428330, _1428332] : [class_Rings_Olinordered__idom(_1428328), -(hAPP(c_Groups_Oabs__class_Oabs(_1428328), hAPP(hAPP(c_Power_Opower__class_Opower(_1428328), _1428330), _1428332)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1428328), hAPP(c_Groups_Oabs__class_Oabs(_1428328), _1428330)), _1428332))], (34790 ^ _779448) ^ [_1428457, _1428459] : [class_Rings_Olinordered__idom(_1428457), -(hAPP(c_Groups_Oabs__class_Oabs(_1428457), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1428457), _1428459)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1428457), _1428459))], (34796 ^ _779448) ^ [_1428562] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428562)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428562))], (34798 ^ _779448) ^ [_1428594, _1428596, _1428598] : [class_Fields_Olinordered__field__inverse__zero(_1428594), -(hAPP(c_Groups_Oabs__class_Oabs(_1428594), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1428594), _1428596), _1428598)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1428594), hAPP(c_Groups_Oabs__class_Oabs(_1428594), _1428596)), hAPP(c_Groups_Oabs__class_Oabs(_1428594), _1428598)))], (34804 ^ _779448) ^ [_1428733, _1428735, _1428737] : [class_Groups_Oordered__ab__group__add__abs(_1428733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428733), hAPP(c_Groups_Oabs__class_Oabs(_1428733), _1428735)), _1428737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428733), _1428735), _1428737)))], (34814 ^ _779448) ^ [_1428902, _1428904] : [class_Groups_Oordered__ab__group__add__abs(_1428902), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428902), _1428904), hAPP(c_Groups_Oabs__class_Oabs(_1428902), _1428904))))], (34820 ^ _779448) ^ [_1429001, _1429003, _1429005, _1429007] : [class_Fields_Olinordered__field(_1429001), -(hAPP(c_Groups_Oabs__class_Oabs(_1429001), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1429003, _1429001), _1429005), _1429007)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1429003, _1429001), hAPP(hAPP(c_COMBB(_1429001, _1429001, _1429003), c_Groups_Oabs__class_Oabs(_1429001)), _1429005)), _1429007))], (34826 ^ _779448) ^ [_1429150, _1429152, _1429154] : [class_Groups_Oordered__ab__group__add__abs(_1429150), -(hAPP(c_Groups_Oabs__class_Oabs(_1429150), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1429150), _1429152), _1429154)) = hAPP(c_Groups_Oabs__class_Oabs(_1429150), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1429150), _1429154), _1429152)))], (34832 ^ _779448) ^ [_1429279, _1429281] : [class_Groups_Oordered__ab__group__add__abs(_1429279), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429279), c_Groups_Ozero__class_Ozero(_1429279)), hAPP(c_Groups_Oabs__class_Oabs(_1429279), _1429281))))], (34838 ^ _779448) ^ [_1429382, _1429384] : [class_Groups_Oordered__ab__group__add__abs(_1429382), 34841 ^ _779448 : [(34842 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429382), hAPP(c_Groups_Oabs__class_Oabs(_1429382), _1429384)), c_Groups_Ozero__class_Ozero(_1429382))), -(_1429384 = c_Groups_Ozero__class_Ozero(_1429382))], (34848 ^ _779448) ^ [] : [_1429384 = c_Groups_Ozero__class_Ozero(_1429382), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429382), hAPP(c_Groups_Oabs__class_Oabs(_1429382), _1429384)), c_Groups_Ozero__class_Ozero(_1429382))))]]], (34854 ^ _779448) ^ [_1429635, _1429637] : [class_Groups_Oordered__ab__group__add__abs(_1429635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1429635), c_Groups_Ozero__class_Ozero(_1429635)), _1429637)), -(hAPP(c_Groups_Oabs__class_Oabs(_1429635), _1429637) = _1429637)], (34864 ^ _779448) ^ [_1429790, _1429792] : [class_Groups_Oordered__ab__group__add__abs(_1429790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429790), c_Groups_Ozero__class_Ozero(_1429790)), _1429792)), -(hAPP(c_Groups_Oabs__class_Oabs(_1429790), _1429792) = _1429792)], (34874 ^ _779448) ^ [_1429945, _1429947] : [class_Groups_Oordered__ab__group__add__abs(_1429945), 34877 ^ _779448 : [(34878 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429945), c_Groups_Ozero__class_Ozero(_1429945)), hAPP(c_Groups_Oabs__class_Oabs(_1429945), _1429947))), _1429947 = c_Groups_Ozero__class_Ozero(_1429945)], (34884 ^ _779448) ^ [] : [-(_1429947 = c_Groups_Ozero__class_Ozero(_1429945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429945), c_Groups_Ozero__class_Ozero(_1429945)), hAPP(c_Groups_Oabs__class_Oabs(_1429945), _1429947))))]]], (34890 ^ _779448) ^ [_1430160, _1430162] : [class_Groups_Oordered__ab__group__add__abs(_1430160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430160), hAPP(c_Groups_Oabs__class_Oabs(_1430160), _1430162)), c_Groups_Ozero__class_Ozero(_1430160)))], (34896 ^ _779448) ^ [_1430264, _1430266, _1430268] : [class_Groups_Oordered__ab__group__add__abs(_1430264), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430264), hAPP(c_Groups_Oabs__class_Oabs(_1430264), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430264), _1430266), _1430268))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430264), hAPP(c_Groups_Oabs__class_Oabs(_1430264), _1430266)), hAPP(c_Groups_Oabs__class_Oabs(_1430264), _1430268)))))], (34902 ^ _779448) ^ [_1430417, _1430419, _1430421, _1430423, _1430425] : [class_Rings_Olinordered__idom(_1430417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430417), hAPP(c_Groups_Oabs__class_Oabs(_1430417), _1430419)), _1430421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430417), hAPP(c_Groups_Oabs__class_Oabs(_1430417), _1430423)), _1430425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430417), hAPP(c_Groups_Oabs__class_Oabs(_1430417), _1430419)), hAPP(c_Groups_Oabs__class_Oabs(_1430417), _1430423))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430417), _1430421), _1430425))))], (34916 ^ _779448) ^ [_1430728, _1430730, _1430732] : [class_Groups_Oordered__ab__group__add__abs(_1430728), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430728), hAPP(c_Groups_Oabs__class_Oabs(_1430728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430728), hAPP(c_Groups_Oabs__class_Oabs(_1430728), _1430730)), hAPP(c_Groups_Oabs__class_Oabs(_1430728), _1430732)))), hAPP(c_Groups_Oabs__class_Oabs(_1430728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430728), _1430730), _1430732)))))], (34922 ^ _779448) ^ [_1430891, _1430893, _1430895] : [class_Groups_Oordered__ab__group__add__abs(_1430891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430891), hAPP(c_Groups_Oabs__class_Oabs(_1430891), _1430893)), hAPP(c_Groups_Oabs__class_Oabs(_1430891), _1430895))), hAPP(c_Groups_Oabs__class_Oabs(_1430891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430891), _1430893), _1430895)))))], (34928 ^ _779448) ^ [_1431044, _1431046, _1431048] : [class_Groups_Oordered__ab__group__add__abs(_1431044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431044), hAPP(c_Groups_Oabs__class_Oabs(_1431044), _1431046)), hAPP(c_Groups_Oabs__class_Oabs(_1431044), _1431048))), hAPP(c_Groups_Oabs__class_Oabs(_1431044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1431044), _1431048), _1431046)))))], (34934 ^ _779448) ^ [_1431197, _1431199] : [class_Groups_Oordered__ab__group__add__abs(_1431197), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431197), hAPP(c_Groups_Ouminus__class_Ouminus(_1431197), _1431199)), hAPP(c_Groups_Oabs__class_Oabs(_1431197), _1431199))))], (34940 ^ _779448) ^ [_1431306, _1431308, _1431310] : [class_Groups_Oordered__ab__group__add__abs(_1431306), 34943 ^ _779448 : [(34944 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), hAPP(c_Groups_Oabs__class_Oabs(_1431306), _1431308)), _1431310)), 34947 ^ _779448 : [(34948 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), _1431308), _1431310)))], (34950 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), hAPP(c_Groups_Ouminus__class_Ouminus(_1431306), _1431308)), _1431310)))]]], (34952 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), hAPP(c_Groups_Oabs__class_Oabs(_1431306), _1431308)), _1431310))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), _1431308), _1431310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431306), hAPP(c_Groups_Ouminus__class_Ouminus(_1431306), _1431308)), _1431310))]]], (34962 ^ _779448) ^ [_1431684, _1431686, _1431688] : [class_Groups_Oordered__ab__group__add__abs(_1431684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431684), _1431686), _1431688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431684), hAPP(c_Groups_Ouminus__class_Ouminus(_1431684), _1431686)), _1431688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431684), hAPP(c_Groups_Oabs__class_Oabs(_1431684), _1431686)), _1431688)))], (34976 ^ _779448) ^ [_1431931, _1431933, _1431935] : [class_Groups_Oordered__ab__group__add__abs(_1431931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431931), hAPP(c_Groups_Oabs__class_Oabs(_1431931), _1431933)), _1431935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431931), hAPP(c_Groups_Ouminus__class_Ouminus(_1431931), _1431933)), _1431935)))], (34986 ^ _779448) ^ [_1432110, _1432112, _1432114] : [class_Rings_Olinordered__idom(_1432110), 34989 ^ _779448 : [(34990 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), hAPP(c_Groups_Oabs__class_Oabs(_1432110), _1432112)), _1432114)), 34993 ^ _779448 : [(34994 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), _1432112), _1432114)))], (34996 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), hAPP(c_Groups_Ouminus__class_Ouminus(_1432110), _1432112)), _1432114)))]]], (34998 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), hAPP(c_Groups_Oabs__class_Oabs(_1432110), _1432112)), _1432114))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), _1432112), _1432114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1432110), hAPP(c_Groups_Ouminus__class_Ouminus(_1432110), _1432112)), _1432114))]]], (35008 ^ _779448) ^ [_1432488, _1432490, _1432492] : [class_Fields_Olinordered__field(_1432488), -(_1432490 = c_Groups_Ozero__class_Ozero(_1432488)), -(hAPP(c_Groups_Oabs__class_Oabs(_1432488), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432488), _1432492), _1432490)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1432488), hAPP(c_Groups_Oabs__class_Oabs(_1432488), _1432492)), hAPP(c_Groups_Oabs__class_Oabs(_1432488), _1432490)))], (35018 ^ _779448) ^ [_1432646, _1432648, _1432650] : [class_Rings_Olinordered__idom(_1432646), -(hAPP(c_Groups_Oabs__class_Oabs(_1432646), hAPP(hAPP(c_Power_Opower__class_Opower(_1432646), hAPP(c_Groups_Ouminus__class_Ouminus(_1432646), _1432648)), _1432650)) = hAPP(c_Groups_Oabs__class_Oabs(_1432646), hAPP(hAPP(c_Power_Opower__class_Opower(_1432646), _1432648), _1432650)))], (35024 ^ _779448) ^ [_1432785, _1432787] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1432785), _1432787)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1432785) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35030 ^ _779448) ^ [_1432886, _1432888] : [class_Rings_Olinordered__idom(_1432886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432886), c_Groups_Osgn__class_Osgn(_1432886, _1432888)), hAPP(c_Groups_Oabs__class_Oabs(_1432886), _1432888)) = _1432888)], (35036 ^ _779448) ^ [_1432993, _1432995] : [class_Rings_Olinordered__idom(_1432993), -(hAPP(c_Groups_Oabs__class_Oabs(_1432993), _1432995) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432993), _1432995), c_Groups_Osgn__class_Osgn(_1432993, _1432995)))], (35042 ^ _779448) ^ [_1433100, _1433102, _1433104] : [class_Rings_Olinordered__idom(_1433100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433100), c_Groups_Ozero__class_Ozero(_1433100)), _1433102)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433100), hAPP(c_Groups_Oabs__class_Oabs(_1433100), _1433104)), _1433102) = hAPP(c_Groups_Oabs__class_Oabs(_1433100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433100), _1433104), _1433102)))], (35052 ^ _779448) ^ [_1433301, _1433303, _1433305] : [class_Rings_Oordered__ring__abs(_1433301), -(hAPP(c_Groups_Oabs__class_Oabs(_1433301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433301), _1433303), _1433305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433301), hAPP(c_Groups_Oabs__class_Oabs(_1433301), _1433303)), hAPP(c_Groups_Oabs__class_Oabs(_1433301), _1433305))), 35059 ^ _779448 : [(35060 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433301), c_Groups_Ozero__class_Ozero(_1433301)), _1433303))], (35062 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433301), _1433303), c_Groups_Ozero__class_Ozero(_1433301)))]], 35063 ^ _779448 : [(35064 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433301), c_Groups_Ozero__class_Ozero(_1433301)), _1433305))], (35066 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433301), _1433305), c_Groups_Ozero__class_Ozero(_1433301)))]]], (35070 ^ _779448) ^ [_1433696, _1433698, _1433700] : [class_Groups_Oordered__ab__group__add__abs(_1433696), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433696), hAPP(c_Groups_Oabs__class_Oabs(_1433696), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1433696), _1433698), _1433700))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433696), hAPP(c_Groups_Oabs__class_Oabs(_1433696), _1433698)), hAPP(c_Groups_Oabs__class_Oabs(_1433696), _1433700)))))], (35076 ^ _779448) ^ [_1433849, _1433851, _1433853, _1433855, _1433857] : [class_Groups_Oordered__ab__group__add__abs(_1433849), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433849), hAPP(c_Groups_Oabs__class_Oabs(_1433849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1433849), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433849), _1433851), _1433853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433849), _1433855), _1433857)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433849), hAPP(c_Groups_Oabs__class_Oabs(_1433849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1433849), _1433851), _1433855))), hAPP(c_Groups_Oabs__class_Oabs(_1433849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1433849), _1433853), _1433857))))))], (35082 ^ _779448) ^ [_1434070, _1434072] : [class_Groups_Oordered__ab__group__add__abs(_1434070), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434070), hAPP(c_Groups_Ouminus__class_Ouminus(_1434070), hAPP(c_Groups_Oabs__class_Oabs(_1434070), _1434072))), c_Groups_Ozero__class_Ozero(_1434070))))], (35088 ^ _779448) ^ [_1434183, _1434185] : [class_Groups_Oordered__ab__group__add__abs(_1434183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434183), _1434185), c_Groups_Ozero__class_Ozero(_1434183))), -(hAPP(c_Groups_Oabs__class_Oabs(_1434183), _1434185) = hAPP(c_Groups_Ouminus__class_Ouminus(_1434183), _1434185))], (35098 ^ _779448) ^ [_1434348, _1434350] : [class_Groups_Oabs__if(_1434348), 35101 ^ _779448 : [(35102 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434348), _1434350), c_Groups_Ozero__class_Ozero(_1434348))), -(hAPP(c_Groups_Oabs__class_Oabs(_1434348), _1434350) = hAPP(c_Groups_Ouminus__class_Ouminus(_1434348), _1434350))], (35108 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434348), _1434350), c_Groups_Ozero__class_Ozero(_1434348)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1434348), _1434350) = _1434350)]]], (35114 ^ _779448) ^ [_1434588, _1434590] : [class_Groups_Oordered__ab__group__add__abs(_1434588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434588), _1434590), c_Groups_Ozero__class_Ozero(_1434588))), -(hAPP(c_Groups_Oabs__class_Oabs(_1434588), _1434590) = hAPP(c_Groups_Ouminus__class_Ouminus(_1434588), _1434590))], (35124 ^ _779448) ^ [_1434753, _1434755, _1434757] : [class_Rings_Olinordered__idom(_1434753), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1434753), c_Groups_Ozero__class_Ozero(_1434753)), hAPP(hAPP(c_Power_Opower__class_Opower(_1434753), hAPP(c_Groups_Oabs__class_Oabs(_1434753), _1434755)), _1434757))))], (35130 ^ _779448) ^ [_1434874, _1434876, _1434878] : [class_Fields_Olinordered__field__inverse__zero(_1434874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434874), c_Groups_Ozero__class_Ozero(_1434874)), _1434876)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434874), hAPP(c_Groups_Oabs__class_Oabs(_1434874), _1434878)), _1434876) = hAPP(c_Groups_Oabs__class_Oabs(_1434874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1434874), _1434878), _1434876)))], (35140 ^ _779448) ^ [_1435075] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1435075), hAPP(c_Int_Onumber__class_Onumber__of(_1435075), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1435075)), class_Int_Onumber__ring(_1435075), class_Rings_Olinordered__idom(_1435075)], (35150 ^ _779448) ^ [_1435232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1435232)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1435232 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35156 ^ _779448) ^ [_1435319] : [_1435319 = 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), _1435319)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35162 ^ _779448) ^ [_1435418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435418), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1435418) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435418))], (35168 ^ _779448) ^ [_1435509] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435509), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1435509) = _1435509)], (35174 ^ _779448) ^ [_1435553, _1435555] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1435553), _1435555))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1435553))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1435555))))], (35176 ^ _779448) ^ [_1435608, _1435610] : [-(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), _1435608)), _1435610))))], (35178 ^ _779448) ^ [_1435644, _1435646] : [class_Int_Onumber__ring(_1435644), class_Rings_Olinordered__idom(_1435644), 35185 ^ _779448 : [(35186 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435644), hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646)), c_Groups_Ozero__class_Ozero(_1435644))), -(hAPP(c_Groups_Oabs__class_Oabs(_1435644), hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1435644), hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646)))], (35192 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435644), hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646)), c_Groups_Ozero__class_Ozero(_1435644)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1435644), hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646)) = hAPP(c_Int_Onumber__class_Onumber__of(_1435644), _1435646))]]], (35198 ^ _779448) ^ [_1435996, _1435998] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1435996), hAPP(hAPP(c_Power_Opower__class_Opower(_1435996), hAPP(c_Int_Onumber__class_Onumber__of(_1435996), c_Int_OMin)), _1435998)) = c_Groups_Oone__class_Oone(_1435996)), class_Int_Onumber__ring(_1435996), class_Rings_Olinordered__idom(_1435996)], (35218 ^ _779448) ^ [_1436325, _1436327] : [35219 ^ _779448 : [(35220 ^ _779448) ^ [] : [-(_1436325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35222 ^ _779448) ^ [] : [_1436327 = 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), _1436325)), _1436327))))], (35208 ^ _779448) ^ [_1436176, _1436178] : [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), _1436176)), _1436178))), _1436176 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1436178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35226 ^ _779448) ^ [_1436461, _1436463] : [class_Rings_Olinordered__idom(_1436461), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436461), hAPP(c_Groups_Oabs__class_Oabs(_1436461), _1436463)), 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(_1436461), _1436463), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35232 ^ _779448) ^ [_1436578, _1436580] : [class_Rings_Olinordered__idom(_1436578), -(hAPP(c_Groups_Oabs__class_Oabs(_1436578), hAPP(hAPP(c_Power_Opower__class_Opower(_1436578), _1436580), 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(_1436578), _1436580), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35238 ^ _779448) ^ [_1436695, _1436697, _1436699] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1436695, _1436697, _1436699, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1436697)], (35240 ^ _779448) ^ [_1436736, _1436738] : [_1436736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1436736, _1436738) = 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)))], (35246 ^ _779448) ^ [_1436814, _1436816] : [-(_1436814 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35249 ^ _779448 : [(35250 ^ _779448) ^ [] : [_1436816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1436814, _1436816) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436814))], (35256 ^ _779448) ^ [] : [-(_1436816 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1436814, _1436816) = 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, _1436816))), 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)), _1436816)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1436814))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436816), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1436814), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1436814, _1436816)), 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), _1436816))))), c_Divides_Opdivmod(_1436814, _1436816)))))]]], (35262 ^ _779448) ^ [_1437174, _1437176] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1437174), _1437176) = 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), _1437174)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1437176)))))], (35264 ^ _779448) ^ [_1437232, _1437234] : [_1437232 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1437232, _1437234) = 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)))], (35270 ^ _779448) ^ [_1437310, _1437312] : [-(_1437310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35273 ^ _779448 : [(35274 ^ _779448) ^ [] : [_1437312 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1437310, _1437312) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1437310))], (35280 ^ _779448) ^ [] : [-(_1437312 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1437310, _1437312) = 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, _1437312))), 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, _1437310)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1437312))), c_Divides_Opdivmod(_1437310, _1437312)), 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), _1437312))))), c_Divides_Opdivmod(_1437310, _1437312)))))]]], (35286 ^ _779448) ^ [_1437622, _1437624, _1437626, _1437628, _1437630, _1437632] : [-(hAPP(c_Product__Type_Oapsnd(_1437622, _1437624, _1437626, _1437628), hAPP(hAPP(c_Product__Type_OPair(_1437626, _1437622), _1437630), _1437632)) = hAPP(hAPP(c_Product__Type_OPair(_1437626, _1437624), _1437630), hAPP(_1437628, _1437632)))], (35288 ^ _779448) ^ [_1437684, _1437686, _1437688, _1437690, _1437692, _1437694, _1437696] : [-(hAPP(c_Product__Type_Oapsnd(_1437684, _1437686, _1437688, _1437690), hAPP(c_Product__Type_Oapsnd(_1437692, _1437684, _1437688, _1437694), _1437696)) = hAPP(c_Product__Type_Oapsnd(_1437692, _1437686, _1437688, hAPP(c_Fun_Ocomp(_1437684, _1437686, _1437692, _1437690), _1437694)), _1437696))], (35290 ^ _779448) ^ [_1437751, _1437753, _1437755, _1437757, _1437759] : [-(hAPP(c_Product__Type_Ofst(_1437751, _1437753), hAPP(c_Product__Type_Oapsnd(_1437755, _1437753, _1437751, _1437757), _1437759)) = hAPP(c_Product__Type_Ofst(_1437751, _1437755), _1437759))], (35292 ^ _779448) ^ [_1437829, _1437831, _1437833, _1437835, _1437837, _1437839] : [hAPP(c_Product__Type_Oapsnd(_1437829, _1437831, _1437833, _1437835), _1437837) = hAPP(c_Product__Type_Oapsnd(_1437829, _1437831, _1437833, _1437839), _1437837), -(hAPP(_1437835, hAPP(c_Product__Type_Osnd(_1437833, _1437829), _1437837)) = hAPP(_1437839, hAPP(c_Product__Type_Osnd(_1437833, _1437829), _1437837)))], (35298 ^ _779448) ^ [_1437978, _1437980, _1437982, _1437984, _1437986, _1437988] : [hAPP(_1437984, hAPP(c_Product__Type_Osnd(_1437982, _1437978), _1437986)) = hAPP(_1437988, hAPP(c_Product__Type_Osnd(_1437982, _1437978), _1437986)), -(hAPP(c_Product__Type_Oapsnd(_1437978, _1437980, _1437982, _1437984), _1437986) = hAPP(c_Product__Type_Oapsnd(_1437978, _1437980, _1437982, _1437988), _1437986))], (35304 ^ _779448) ^ [_1438133, _1438135, _1438137, _1438139, _1438141] : [-(hAPP(c_Product__Type_Osnd(_1438133, _1438135), hAPP(c_Product__Type_Oapsnd(_1438137, _1438135, _1438133, _1438139), _1438141)) = hAPP(_1438139, hAPP(c_Product__Type_Osnd(_1438133, _1438137), _1438141)))], (35306 ^ _779448) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (35308 ^ _779448) ^ [_1438214, _1438216] : [_1438214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1438216, _1438214) = _1438216)], (35314 ^ _779448) ^ [_1438291, _1438293] : [-(_1438291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1438293, _1438291) = c_Nitpick_Onat__gcd(_1438291, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1438293, _1438291)))], (35320 ^ _779448) ^ [_1438339, _1438341] : [-(c_Divides_Opdivmod(_1438339, _1438341) = 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), _1438339)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438341))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438339), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438341))))], (35322 ^ _779448) ^ [_1438404, _1438406] : [_1438404 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1438406, _1438404) = 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), _1438406)))], (35328 ^ _779448) ^ [_1438493, _1438495] : [-(_1438493 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1438495, _1438493) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438495), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438493)))], (35334 ^ _779448) ^ [_1438543, _1438545] : [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), _1438543), _1438545))), 35337 ^ _779448 : [(35338 ^ _779448) ^ [] : [_1438545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1438543, _1438545) = _1438543)], (35344 ^ _779448) ^ [] : [-(_1438545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1438543, _1438545) = c_Nitpick_Onat__gcd(_1438545, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1438543, _1438545)))]]], (35350 ^ _779448) ^ [_1438761, _1438763] : [-(c_Nitpick_Onat__lcm(_1438761, _1438763) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1438761), _1438763)), c_Nitpick_Onat__gcd(_1438761, _1438763)))], (35352 ^ _779448) ^ [_1438804, _1438806] : [-(c_Nitpick_Oint__lcm(_1438804, _1438806) = 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), _1438804)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1438806)))))], (35354 ^ _779448) ^ [_1438850, _1438852, _1438854] : [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), _1438850), _1438852))), -(hBOOL(hAPP(hAPP(_1438854, _1438850), _1438852))), 35361 ^ _779448 : [(35362 ^ _779448) ^ [] : [-(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), 35359 ^ [_1438850, _1438852, _1438854]), 35360 ^ [_1438850, _1438852, _1438854]))))], (35370 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1438854, 35359 ^ [_1438850, _1438852, _1438854]), 35360 ^ [_1438850, _1438852, _1438854]))], (35364 ^ _779448) ^ [] : [-(35360 ^ [_1438850, _1438852, _1438854] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1438854, 35360 ^ [_1438850, _1438852, _1438854]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 35359 ^ [_1438850, _1438852, _1438854], 35360 ^ [_1438850, _1438852, _1438854]))))]]], (35374 ^ _779448) ^ [_1439272, _1439274, _1439276, _1439278, _1439280, _1439282, _1439284] : [-(hAPP(c_Product__Type_Oapsnd(_1439272, _1439274, _1439276, _1439278), hAPP(c_Product__Type_Oapfst(_1439280, _1439276, _1439272, _1439282), _1439284)) = hAPP(hAPP(c_Product__Type_OPair(_1439276, _1439274), hAPP(_1439282, hAPP(c_Product__Type_Ofst(_1439280, _1439272), _1439284))), hAPP(_1439278, hAPP(c_Product__Type_Osnd(_1439280, _1439272), _1439284))))], (35376 ^ _779448) ^ [_1439350, _1439352, _1439354, _1439356, _1439358, _1439360, _1439362] : [-(hAPP(c_Product__Type_Oapfst(_1439350, _1439352, _1439354, _1439356), hAPP(c_Product__Type_Oapsnd(_1439358, _1439354, _1439350, _1439360), _1439362)) = hAPP(hAPP(c_Product__Type_OPair(_1439352, _1439354), hAPP(_1439356, hAPP(c_Product__Type_Ofst(_1439350, _1439358), _1439362))), hAPP(_1439360, hAPP(c_Product__Type_Osnd(_1439350, _1439358), _1439362))))], (35378 ^ _779448) ^ [_1439428, _1439430, _1439432, _1439434, _1439436, _1439438, _1439440] : [-(hAPP(c_Product__Type_Oapfst(_1439428, _1439430, _1439432, _1439434), hAPP(c_Product__Type_Oapfst(_1439436, _1439428, _1439432, _1439438), _1439440)) = hAPP(c_Product__Type_Oapfst(_1439436, _1439430, _1439432, hAPP(c_Fun_Ocomp(_1439428, _1439430, _1439436, _1439434), _1439438)), _1439440))], (35380 ^ _779448) ^ [_1439495, _1439497, _1439499, _1439501, _1439503, _1439505] : [-(hAPP(c_Product__Type_Oapfst(_1439495, _1439497, _1439499, _1439501), hAPP(hAPP(c_Product__Type_OPair(_1439495, _1439499), _1439503), _1439505)) = hAPP(hAPP(c_Product__Type_OPair(_1439497, _1439499), hAPP(_1439501, _1439503)), _1439505))], (35382 ^ _779448) ^ [_1439584, _1439586, _1439588, _1439590, _1439592, _1439594] : [hAPP(c_Product__Type_Oapfst(_1439584, _1439586, _1439588, _1439590), _1439592) = hAPP(c_Product__Type_Oapfst(_1439584, _1439586, _1439588, _1439594), _1439592), -(hAPP(_1439590, hAPP(c_Product__Type_Ofst(_1439584, _1439588), _1439592)) = hAPP(_1439594, hAPP(c_Product__Type_Ofst(_1439584, _1439588), _1439592)))], (35388 ^ _779448) ^ [_1439733, _1439735, _1439737, _1439739, _1439741, _1439743] : [hAPP(_1439739, hAPP(c_Product__Type_Ofst(_1439733, _1439737), _1439741)) = hAPP(_1439743, hAPP(c_Product__Type_Ofst(_1439733, _1439737), _1439741)), -(hAPP(c_Product__Type_Oapfst(_1439733, _1439735, _1439737, _1439739), _1439741) = hAPP(c_Product__Type_Oapfst(_1439733, _1439735, _1439737, _1439743), _1439741))], (35394 ^ _779448) ^ [_1439888, _1439890, _1439892, _1439894, _1439896] : [-(hAPP(c_Product__Type_Ofst(_1439888, _1439890), hAPP(c_Product__Type_Oapfst(_1439892, _1439888, _1439890, _1439894), _1439896)) = hAPP(_1439894, hAPP(c_Product__Type_Ofst(_1439892, _1439890), _1439896)))], (35396 ^ _779448) ^ [_1439942, _1439944, _1439946, _1439948, _1439950] : [-(hAPP(c_Product__Type_Osnd(_1439942, _1439944), hAPP(c_Product__Type_Oapfst(_1439946, _1439942, _1439944, _1439948), _1439950)) = hAPP(c_Product__Type_Osnd(_1439946, _1439944), _1439950))], (35398 ^ _779448) ^ [_1439993, _1439995, _1439997, _1439999, _1440001, _1440003, _1440005] : [-(hAPP(c_Product__Type_Oapsnd(_1439993, _1439995, _1439997, _1439999), hAPP(c_Product__Type_Oapfst(_1440001, _1439997, _1439993, _1440003), _1440005)) = hAPP(c_Product__Type_Oapfst(_1440001, _1439997, _1439995, _1440003), hAPP(c_Product__Type_Oapsnd(_1439993, _1439995, _1440001, _1439999), _1440005)))], (35400 ^ _779448) ^ [_1440060, _1440062, _1440064] : [class_Lattices_Oboolean__algebra(_1440060), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1440060), _1440062), _1440064) = c_Orderings_Obot__class_Obot(_1440060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1440060), _1440062), _1440064) = c_Orderings_Otop__class_Otop(_1440060), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1440060), _1440062) = _1440064)], (35414 ^ _779448) ^ [_1440295, _1440297, _1440299, _1440301, _1440303] : [class_Groups_Ocomm__monoid__add(_1440295), class_Groups_Ocomm__monoid__mult(_1440295), _1440297 = _1440299, c_Nat__Transfer_Onat__set(_1440299), 35432 ^ _779448 : [(35433 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35431 ^ [_1440295, _1440297, _1440299, _1440301, _1440303])))], (35435 ^ _779448) ^ [] : [hAPP(_1440301, 35431 ^ [_1440295, _1440297, _1440299, _1440301, _1440303]) = hAPP(_1440303, 35431 ^ [_1440295, _1440297, _1440299, _1440301, _1440303])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1440295), _1440301), _1440297) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1440295), _1440303), _1440299))], (35439 ^ _779448) ^ [_1440776, _1440778, _1440780] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1440776, hAPP(hAPP(c_COMBC(_1440776, tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_fun(_1440776, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440776, tc_fun(tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_fun(_1440776, tc_HOL_Obool)), _1440776), c_COMBC(_1440776, tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1440776, tc_prod(_1440776, _1440776)), tc_fun(_1440776, tc_fun(tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_HOL_Obool)), _1440776), hAPP(c_COMBB(tc_prod(_1440776, _1440776), tc_fun(tc_fun(tc_prod(_1440776, _1440776), tc_HOL_Obool), tc_HOL_Obool), _1440776), c_member(tc_prod(_1440776, _1440776)))), c_Product__Type_OPair(_1440776, _1440776)))), _1440778)), _1440780)), -(hBOOL(hAPP(hAPP(c_member(_1440776), _1440780), c_Wellfounded_Oacc(_1440776, _1440778))))], (35445 ^ _779448) ^ [_1441117, _1441119, _1441121] : [hBOOL(hAPP(hAPP(c_member(_1441117), _1441121), c_Wellfounded_Oacc(_1441117, _1441119))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1441117, hAPP(hAPP(c_COMBC(_1441117, tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_fun(_1441117, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441117, tc_fun(tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_fun(_1441117, tc_HOL_Obool)), _1441117), c_COMBC(_1441117, tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441117, tc_prod(_1441117, _1441117)), tc_fun(_1441117, tc_fun(tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_HOL_Obool)), _1441117), hAPP(c_COMBB(tc_prod(_1441117, _1441117), tc_fun(tc_fun(tc_prod(_1441117, _1441117), tc_HOL_Obool), tc_HOL_Obool), _1441117), c_member(tc_prod(_1441117, _1441117)))), c_Product__Type_OPair(_1441117, _1441117)))), _1441119)), _1441121)))], (35451 ^ _779448) ^ [_1441464, _1441466] : [-(hBOOL(hAPP(hAPP(c_member(_1441464), _1441466), c_Orderings_Otop__class_Otop(tc_fun(_1441464, tc_HOL_Obool)))))], (35453 ^ _779448) ^ [_1441501, _1441503] : [class_Lattices_Obounded__lattice__top(_1441501), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441501), _1441503), c_Orderings_Otop__class_Otop(_1441501)) = c_Orderings_Otop__class_Otop(_1441501))], (35459 ^ _779448) ^ [_1441600, _1441602] : [class_Lattices_Obounded__lattice__top(_1441600), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1441600), c_Orderings_Otop__class_Otop(_1441600)), _1441602) = c_Orderings_Otop__class_Otop(_1441600))], (35465 ^ _779448) ^ [_1441699, _1441701, _1441703] : [class_Lattices_Obounded__lattice__top(_1441699), 35468 ^ _779448 : [(35469 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441699), _1441701), _1441703) = c_Orderings_Otop__class_Otop(_1441699), 35472 ^ _779448 : [(35473 ^ _779448) ^ [] : [-(_1441701 = c_Orderings_Otop__class_Otop(_1441699))], (35475 ^ _779448) ^ [] : [-(_1441703 = c_Orderings_Otop__class_Otop(_1441699))]]], (35477 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1441699), _1441701), _1441703) = c_Orderings_Otop__class_Otop(_1441699)), _1441701 = c_Orderings_Otop__class_Otop(_1441699), _1441703 = c_Orderings_Otop__class_Otop(_1441699)]]], (35487 ^ _779448) ^ [_1442026, _1442028] : [class_Lattices_Obounded__lattice__top(_1442026), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442026), _1442028), c_Orderings_Otop__class_Otop(_1442026)) = _1442028)], (35493 ^ _779448) ^ [_1442121, _1442123] : [class_Lattices_Obounded__lattice__top(_1442121), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1442121), c_Orderings_Otop__class_Otop(_1442121)), _1442123) = _1442123)], (35499 ^ _779448) ^ [_1442216, _1442218] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442216, tc_HOL_Obool)), _1442218), c_Orderings_Otop__class_Otop(tc_fun(_1442216, tc_HOL_Obool))) = _1442218)], (35501 ^ _779448) ^ [_1442257, _1442259] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442257, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1442257, tc_HOL_Obool))), _1442259) = _1442259)], (35503 ^ _779448) ^ [] : [-(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))], (35505 ^ _779448) ^ [_1442316] : [-(hAPP(c_Set_OPow(_1442316), c_Orderings_Otop__class_Otop(tc_fun(_1442316, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1442316, tc_HOL_Obool), tc_HOL_Obool)))], (35507 ^ _779448) ^ [_1442357, _1442359, _1442361] : [class_Orderings_Otop(_1442357), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1442359, _1442357)), _1442361) = c_Orderings_Otop__class_Otop(_1442357))], (35513 ^ _779448) ^ [_1442454, _1442456] : [-(c_Sum__Type_OPlus(_1442454, _1442456, c_Orderings_Otop__class_Otop(tc_fun(_1442454, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1442456, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1442454, _1442456), tc_HOL_Obool)))], (35515 ^ _779448) ^ [_1442502] : [class_Finite__Set_Ofinite(_1442502), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1442502), c_Orderings_Otop__class_Otop(tc_fun(_1442502, tc_HOL_Obool)))))], (35521 ^ _779448) ^ [_1442593, _1442595] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1442593), c_Orderings_Otop__class_Otop(tc_fun(_1442593, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442595), c_Orderings_Otop__class_Otop(tc_fun(_1442595, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1442593, _1442595)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1442593, _1442595), tc_HOL_Obool)))))], (35531 ^ _779448) ^ [_1442800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1442800)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1442800), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1442800), c_Orderings_Otop__class_Otop(tc_fun(_1442800, tc_HOL_Obool)))))], (35537 ^ _779448) ^ [_1442915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1442915), c_Orderings_Otop__class_Otop(tc_fun(_1442915, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1442915)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1442915), tc_HOL_Obool)))))], (35543 ^ _779448) ^ [_1443036, _1443038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1443036, _1443038)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1443036, _1443038), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1443038), c_Orderings_Otop__class_Otop(tc_fun(_1443038, tc_HOL_Obool)))))], (35549 ^ _779448) ^ [_1443176, _1443178] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1443176, _1443178)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1443176, _1443178), tc_HOL_Obool)))), 35552 ^ _779448 : [(35553 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1443176), c_Orderings_Otop__class_Otop(tc_fun(_1443176, tc_HOL_Obool)))))], (35555 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1443178), c_Orderings_Otop__class_Otop(tc_fun(_1443178, tc_HOL_Obool)))))]]], (35557 ^ _779448) ^ [_1443341, _1443343] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1443341, _1443343)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1443341, _1443343), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443341), c_Orderings_Otop__class_Otop(tc_fun(_1443341, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443343), c_Orderings_Otop__class_Otop(tc_fun(_1443343, tc_HOL_Obool))))], (35567 ^ _779448) ^ [_1443538, _1443540] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443538, tc_HOL_Obool)), _1443540), c_Orderings_Otop__class_Otop(tc_fun(_1443538, tc_HOL_Obool)))))], (35569 ^ _779448) ^ [_1443587] : [c_Orderings_Otop__class_Otop(tc_fun(_1443587, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1443587, tc_HOL_Obool))], (35571 ^ _779448) ^ [_1443620, _1443622] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443620, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1443620, tc_HOL_Obool))), _1443622) = c_Orderings_Otop__class_Otop(tc_fun(_1443620, tc_HOL_Obool)))], (35573 ^ _779448) ^ [_1443666, _1443668] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443666, tc_HOL_Obool)), _1443668), c_Orderings_Otop__class_Otop(tc_fun(_1443666, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1443666, tc_HOL_Obool)))], (35575 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (35577 ^ _779448) ^ [] : [-(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))], (35579 ^ _779448) ^ [] : [-(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))))], (35581 ^ _779448) ^ [_1443772, _1443774, _1443776, _1443778, _1443780] : [c_Fun_Oinj__on(_1443772, _1443774, _1443776, c_Orderings_Otop__class_Otop(tc_fun(_1443772, tc_HOL_Obool))), hAPP(_1443776, _1443778) = hAPP(_1443776, _1443780), -(_1443778 = _1443780)], (35591 ^ _779448) ^ [_1443939, _1443941, _1443943, _1443945, _1443947] : [c_Fun_Oinj__on(_1443939, _1443941, _1443943, c_Orderings_Otop__class_Otop(tc_fun(_1443939, tc_HOL_Obool))), 35594 ^ _779448 : [(35595 ^ _779448) ^ [] : [hAPP(_1443943, _1443945) = hAPP(_1443943, _1443947), -(_1443945 = _1443947)], (35601 ^ _779448) ^ [] : [_1443945 = _1443947, -(hAPP(_1443943, _1443945) = hAPP(_1443943, _1443947))]]], (35607 ^ _779448) ^ [_1444196, _1444198] : [class_Orderings_Otop(_1444196), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444196), _1444198), c_Orderings_Otop__class_Otop(_1444196))))], (35613 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (35615 ^ _779448) ^ [_1444313, _1444315, _1444317, _1444319, _1444321] : [-(hAPP(c_Set_Oimage(_1444313, _1444315, hAPP(hAPP(c_COMBB(_1444317, _1444315, _1444313), _1444319), _1444321)), c_Orderings_Otop__class_Otop(tc_fun(_1444313, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1444317, _1444315, _1444319), hAPP(c_Set_Oimage(_1444313, _1444317, _1444321), c_Orderings_Otop__class_Otop(tc_fun(_1444313, tc_HOL_Obool)))))], (35617 ^ _779448) ^ [] : [-(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)))], (35619 ^ _779448) ^ [] : [-(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)))], (35621 ^ _779448) ^ [_1444421, _1444423, _1444425, _1444427] : [-(hBOOL(hAPP(hAPP(c_member(_1444421), hAPP(_1444423, _1444425)), hAPP(c_Set_Oimage(_1444427, _1444421, _1444423), c_Orderings_Otop__class_Otop(tc_fun(_1444427, tc_HOL_Obool))))))], (35623 ^ _779448) ^ [_1444472, _1444474, _1444476, _1444478, _1444480] : [_1444472 = hAPP(_1444474, _1444476), -(hBOOL(hAPP(hAPP(c_member(_1444478), _1444472), hAPP(c_Set_Oimage(_1444480, _1444478, _1444474), c_Orderings_Otop__class_Otop(tc_fun(_1444480, tc_HOL_Obool))))))], (35629 ^ _779448) ^ [] : [-(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)))], (35631 ^ _779448) ^ [_1444617, _1444619] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1444617, tc_HOL_Obool)), _1444619), c_Orderings_Otop__class_Otop(tc_fun(_1444617, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1444617, tc_HOL_Obool)))], (35633 ^ _779448) ^ [_1444663, _1444665, _1444667, _1444669, _1444671] : [hAPP(c_Set_Oimage(_1444663, _1444665, _1444667), c_Orderings_Otop__class_Otop(tc_fun(_1444663, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1444665, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1444665, _1444669, _1444671), c_Orderings_Otop__class_Otop(tc_fun(_1444665, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1444669, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1444663, _1444669, hAPP(c_Fun_Ocomp(_1444665, _1444669, _1444663, _1444671), _1444667)), c_Orderings_Otop__class_Otop(tc_fun(_1444663, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1444669, tc_HOL_Obool)))], (35643 ^ _779448) ^ [_1444922, _1444924] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1444922), c_Orderings_Otop__class_Otop(tc_fun(_1444922, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1444922), _1444924) = hAPP(c_Finite__Set_Ocard(_1444922), c_Orderings_Otop__class_Otop(tc_fun(_1444922, tc_HOL_Obool))), -(_1444924 = c_Orderings_Otop__class_Otop(tc_fun(_1444922, tc_HOL_Obool)))], (35653 ^ _779448) ^ [_1445109, _1445111, _1445113, _1445115, _1445117] : [c_Fun_Oinj__on(_1445109, _1445111, _1445113, c_Orderings_Otop__class_Otop(tc_fun(_1445109, tc_HOL_Obool))), 35656 ^ _779448 : [(35657 ^ _779448) ^ [] : [hAPP(c_Set_Oimage(_1445109, _1445111, _1445113), _1445115) = hAPP(c_Set_Oimage(_1445109, _1445111, _1445113), _1445117), -(_1445115 = _1445117)], (35663 ^ _779448) ^ [] : [_1445115 = _1445117, -(hAPP(c_Set_Oimage(_1445109, _1445111, _1445113), _1445115) = hAPP(c_Set_Oimage(_1445109, _1445111, _1445113), _1445117))]]], (35669 ^ _779448) ^ [_1445390, _1445392, _1445394, _1445396, _1445398] : [c_Fun_Oinj__on(_1445390, _1445392, _1445394, c_Orderings_Otop__class_Otop(tc_fun(_1445390, tc_HOL_Obool))), c_Fun_Oinj__on(_1445396, _1445390, _1445398, c_Orderings_Otop__class_Otop(tc_fun(_1445396, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1445396, _1445392, hAPP(c_Fun_Ocomp(_1445390, _1445392, _1445396, _1445394), _1445398), c_Orderings_Otop__class_Otop(tc_fun(_1445396, tc_HOL_Obool))))], (35679 ^ _779448) ^ [_1445589] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445589, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1445589, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1445589, tc_HOL_Obool)))], (35681 ^ _779448) ^ [_1445630] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445630, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1445630, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1445630, tc_HOL_Obool)))], (35683 ^ _779448) ^ [_1445671, _1445673] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445671), _1445673)), 35686 ^ _779448 : [(35687 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445671), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445671, tc_HOL_Obool)), _1445673))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1445671), c_Orderings_Otop__class_Otop(tc_fun(_1445671, tc_HOL_Obool)))))], (35693 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445671), c_Orderings_Otop__class_Otop(tc_fun(_1445671, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1445671), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445671, tc_HOL_Obool)), _1445673))))]]], (35699 ^ _779448) ^ [_1445949, _1445951] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445949, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445949, tc_HOL_Obool)), _1445951)), _1445951) = c_Orderings_Otop__class_Otop(tc_fun(_1445949, tc_HOL_Obool)))], (35701 ^ _779448) ^ [_1445998, _1446000] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445998, tc_HOL_Obool)), _1446000), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1445998, tc_HOL_Obool)), _1446000)) = c_Orderings_Otop__class_Otop(tc_fun(_1445998, tc_HOL_Obool)))], (35703 ^ _779448) ^ [_1446047, _1446049] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1446047, tc_HOL_Obool)), _1446049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1446047, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1446047, tc_HOL_Obool))), _1446049))], (35705 ^ _779448) ^ [_1446117, _1446119, _1446121, _1446123] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446117, tc_fun(_1446119, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1446117, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446119, tc_HOL_Obool), tc_fun(_1446119, tc_HOL_Obool), _1446117), hAPP(c_COMBC(_1446119, tc_fun(_1446119, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446119))), _1446121)), _1446123)), -(hBOOL(hAPP(hAPP(c_member(_1446119), _1446123), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446117, tc_fun(_1446119, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1446117, tc_HOL_Obool))), _1446121))))], (35711 ^ _779448) ^ [_1446336, _1446338, _1446340, _1446342] : [hBOOL(hAPP(hAPP(c_member(_1446338), _1446342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446336, tc_fun(_1446338, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1446336, tc_HOL_Obool))), _1446340))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446336, tc_fun(_1446338, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1446336, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446338, tc_HOL_Obool), tc_fun(_1446338, tc_HOL_Obool), _1446336), hAPP(c_COMBC(_1446338, tc_fun(_1446338, tc_HOL_Obool), tc_HOL_Obool), c_member(_1446338))), _1446340)), _1446342)))], (35717 ^ _779448) ^ [_1446561, _1446563, _1446565, _1446567, _1446569] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1446561), hAPP(c_Set_Oimage(_1446563, _1446561, _1446565), c_Orderings_Otop__class_Otop(tc_fun(_1446563, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1446567), hAPP(c_Set_Oimage(_1446563, _1446567, hAPP(hAPP(c_COMBB(_1446561, _1446567, _1446563), _1446569), _1446565)), c_Orderings_Otop__class_Otop(tc_fun(_1446563, tc_HOL_Obool))))))], (35723 ^ _779448) ^ [_1446728, _1446730, _1446732, _1446734] : [c_Fun_Oinj__on(_1446728, _1446730, _1446732, c_Orderings_Otop__class_Otop(tc_fun(_1446728, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1446728, _1446730, c_Orderings_Otop__class_Otop(tc_fun(_1446728, tc_HOL_Obool)), _1446732), hAPP(_1446732, _1446734)) = _1446734)], (35729 ^ _779448) ^ [_1446855, _1446857] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1446855, _1446857)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1446855, _1446857), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1446857), c_Orderings_Otop__class_Otop(tc_fun(_1446857, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1446855), c_Orderings_Otop__class_Otop(tc_fun(_1446855, tc_HOL_Obool)))))], (35739 ^ _779448) ^ [_1447015] : [class_Nat_Osemiring__char__0(_1447015), -(c_Fun_Oinj__on(tc_Nat_Onat, _1447015, c_Nat_Osemiring__1__class_Oof__nat(_1447015), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (35745 ^ _779448) ^ [] : [-(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)))], (35747 ^ _779448) ^ [_1447114, _1447116, _1447118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447114, _1447114), tc_HOL_Obool)), _1447116), _1447118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447114, tc_HOL_Obool)), c_Wellfounded_Oacc(_1447114, _1447118)), c_Wellfounded_Oacc(_1447114, _1447116))))], (35753 ^ _779448) ^ [_1447251, _1447253, _1447255, _1447257] : [c_Fun_Oinj__on(_1447251, _1447253, _1447255, c_Orderings_Otop__class_Otop(tc_fun(_1447251, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1447251, tc_fun(_1447257, _1447253), hAPP(hAPP(c_COMBB(_1447253, tc_fun(_1447257, _1447253), _1447251), c_COMBK(_1447253, _1447257)), _1447255), c_Orderings_Otop__class_Otop(tc_fun(_1447251, tc_HOL_Obool))))], (35759 ^ _779448) ^ [_1447398] : [class_Lattices_Oboolean__algebra(_1447398), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1447398), c_Orderings_Obot__class_Obot(_1447398)) = c_Orderings_Otop__class_Otop(_1447398))], (35765 ^ _779448) ^ [_1447489] : [class_Lattices_Oboolean__algebra(_1447489), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1447489), c_Orderings_Otop__class_Otop(_1447489)) = c_Orderings_Obot__class_Obot(_1447489))], (35771 ^ _779448) ^ [_1447580, _1447582] : [class_Lattices_Oboolean__algebra(_1447580), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447580), hAPP(c_Groups_Ouminus__class_Ouminus(_1447580), _1447582)), _1447582) = c_Orderings_Otop__class_Otop(_1447580))], (35777 ^ _779448) ^ [_1447685, _1447687] : [class_Lattices_Oboolean__algebra(_1447685), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1447685), _1447687), hAPP(c_Groups_Ouminus__class_Ouminus(_1447685), _1447687)) = c_Orderings_Otop__class_Otop(_1447685))], (35783 ^ _779448) ^ [_1447790, _1447792, _1447794, _1447796] : [c_Fun_Oinj__on(_1447790, _1447792, _1447794, c_Orderings_Otop__class_Otop(tc_fun(_1447790, tc_HOL_Obool))), 35786 ^ _779448 : [(35787 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1447792), _1447796), hAPP(c_Set_Oimage(_1447790, _1447792, _1447794), c_Orderings_Otop__class_Otop(tc_fun(_1447790, tc_HOL_Obool))))), 35791 ^ _779448 : [(35792 ^ _779448) ^ [] : [-(_1447796 = hAPP(_1447794, 35790 ^ [_1447790, _1447792, _1447794, _1447796]))], (35794 ^ _779448) ^ [_1448055] : [_1447796 = hAPP(_1447794, _1448055), -(_1448055 = 35790 ^ [_1447790, _1447792, _1447794, _1447796])]]], (35800 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447792), _1447796), hAPP(c_Set_Oimage(_1447790, _1447792, _1447794), c_Orderings_Otop__class_Otop(tc_fun(_1447790, tc_HOL_Obool)))))), 35801 ^ _779448 : [(35802 ^ _779448) ^ [_1448193] : [_1447796 = hAPP(_1447794, _1448193), 35806 ^ _779448 : [(35807 ^ _779448) ^ [] : [-(_1447796 = hAPP(_1447794, 35805 ^ [_1447790, _1447792, _1447794, _1447796, _1448193]))], (35809 ^ _779448) ^ [] : [35805 ^ [_1447790, _1447792, _1447794, _1447796, _1448193] = _1448193]]]]]]], (35813 ^ _779448) ^ [_1448421, _1448423, _1448425, _1448427, _1448429] : [c_Fun_Oinj__on(_1448421, _1448423, _1448425, c_Orderings_Otop__class_Otop(tc_fun(_1448421, tc_HOL_Obool))), 35816 ^ _779448 : [(35817 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1448423), hAPP(_1448425, _1448427)), hAPP(c_Set_Oimage(_1448421, _1448423, _1448425), _1448429))), -(hBOOL(hAPP(hAPP(c_member(_1448421), _1448427), _1448429)))], (35823 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1448421), _1448427), _1448429)), -(hBOOL(hAPP(hAPP(c_member(_1448423), hAPP(_1448425, _1448427)), hAPP(c_Set_Oimage(_1448421, _1448423, _1448425), _1448429))))]]], (35829 ^ _779448) ^ [_1448732, _1448734] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448732), c_Orderings_Otop__class_Otop(tc_fun(_1448732, tc_HOL_Obool)))), c_Fun_Oinj__on(_1448732, _1448732, _1448734, c_Orderings_Otop__class_Otop(tc_fun(_1448732, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1448732, _1448732, _1448734), c_Orderings_Otop__class_Otop(tc_fun(_1448732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448732, tc_HOL_Obool)))], (35839 ^ _779448) ^ [_1448927, _1448929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448927), c_Orderings_Otop__class_Otop(tc_fun(_1448927, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1448927, _1448927, _1448929), c_Orderings_Otop__class_Otop(tc_fun(_1448927, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448927, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1448927, _1448927, _1448929, c_Orderings_Otop__class_Otop(tc_fun(_1448927, tc_HOL_Obool))))], (35849 ^ _779448) ^ [_1449122, _1449124, _1449126, _1449128, _1449130] : [c_Fun_Oinj__on(_1449122, _1449124, _1449126, c_Orderings_Otop__class_Otop(tc_fun(_1449122, tc_HOL_Obool))), 35852 ^ _779448 : [(35853 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449124, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449122, _1449124, _1449126), _1449128)), hAPP(c_Set_Oimage(_1449122, _1449124, _1449126), _1449130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449122, tc_HOL_Obool)), _1449128), _1449130)))], (35859 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449122, tc_HOL_Obool)), _1449128), _1449130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449124, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449122, _1449124, _1449126), _1449128)), hAPP(c_Set_Oimage(_1449122, _1449124, _1449126), _1449130))))]]], (35865 ^ _779448) ^ [_1449463, _1449465, _1449467, _1449469, _1449471] : [c_Fun_Oinj__on(_1449463, _1449465, _1449467, c_Orderings_Otop__class_Otop(tc_fun(_1449463, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1449463, _1449465, _1449467), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449463, tc_HOL_Obool)), _1449469), _1449471)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449465, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449463, _1449465, _1449467), _1449469)), hAPP(c_Set_Oimage(_1449463, _1449465, _1449467), _1449471)))], (35871 ^ _779448) ^ [_1449646, _1449648, _1449650, _1449652, _1449654] : [c_Fun_Oinj__on(_1449646, _1449648, _1449650, c_Orderings_Otop__class_Otop(tc_fun(_1449646, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1449646, _1449648, _1449650), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1449646, tc_HOL_Obool)), _1449652), _1449654)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1449648, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449646, _1449648, _1449650), _1449652)), hAPP(c_Set_Oimage(_1449646, _1449648, _1449650), _1449654)))], (35877 ^ _779448) ^ [_1449829, _1449831, _1449833, _1449835] : [hAPP(c_Set_Oimage(_1449829, _1449831, _1449833), c_Orderings_Otop__class_Otop(tc_fun(_1449829, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1449831, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1449831, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449831, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449829, _1449831, _1449833), _1449835))), hAPP(c_Set_Oimage(_1449829, _1449831, _1449833), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1449829, tc_HOL_Obool)), _1449835)))))], (35893 ^ _779448) ^ [_1450295, _1450297, _1450299] : [35895 ^ _779448 : [(35896 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450295, _1450295)), hAPP(hAPP(c_Product__Type_OPair(_1450295, _1450295), 35894 ^ [_1450295, _1450297, _1450299]), _1450297)), _1450299)))], (35898 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1450295), 35894 ^ [_1450295, _1450297, _1450299]), c_Wellfounded_Oacc(_1450295, _1450299)))]], -(hBOOL(hAPP(hAPP(c_member(_1450295), _1450297), c_Wellfounded_Oacc(_1450295, _1450299))))], (35883 ^ _779448) ^ [_1450042, _1450044, _1450046] : [hBOOL(hAPP(hAPP(c_member(_1450042), _1450044), c_Wellfounded_Oacc(_1450042, _1450046))), 35886 ^ _779448 : [(35887 ^ _779448) ^ [_1450156] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450042, _1450042)), hAPP(hAPP(c_Product__Type_OPair(_1450042, _1450042), _1450156), _1450044)), _1450046)), -(hBOOL(hAPP(hAPP(c_member(_1450042), _1450156), c_Wellfounded_Oacc(_1450042, _1450046))))]]], (35902 ^ _779448) ^ [_1450535, _1450537, _1450539, _1450541] : [hBOOL(hAPP(hAPP(c_member(_1450535), _1450537), c_Wellfounded_Oacc(_1450535, _1450539))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1450535, _1450535)), hAPP(hAPP(c_Product__Type_OPair(_1450535, _1450535), _1450541), _1450537)), _1450539)), -(hBOOL(hAPP(hAPP(c_member(_1450535), _1450541), c_Wellfounded_Oacc(_1450535, _1450539))))], (35912 ^ _779448) ^ [_1450750, _1450752] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1450750, 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(_1450750, tc_HOL_Obool)), tc_fun(_1450750, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1450750, tc_HOL_Obool)), tc_fun(_1450750, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1450750, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1450752)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1450750, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1450752))], (35914 ^ _779448) ^ [_1450846] : [-(c_Fun_Oinj__on(_1450846, tc_fun(_1450846, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1450846, tc_fun(_1450846, tc_HOL_Obool), tc_fun(_1450846, tc_HOL_Obool)), c_Set_Oinsert(_1450846)), c_Orderings_Obot__class_Obot(tc_fun(_1450846, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1450846, tc_HOL_Obool))))], (35916 ^ _779448) ^ [_1450902] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450902), c_Orderings_Otop__class_Otop(tc_fun(_1450902, 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(_1450902), c_Orderings_Otop__class_Otop(tc_fun(_1450902, tc_HOL_Obool))))))], (35922 ^ _779448) ^ [] : [-(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))))], (35924 ^ _779448) ^ [_1451037, _1451039, _1451041, _1451043] : [c_Fun_Oinj__on(_1451037, _1451039, _1451041, c_Orderings_Otop__class_Otop(tc_fun(_1451037, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451039, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1451037, _1451039, _1451041), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451037, tc_HOL_Obool)), _1451043))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1451039, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1451037, _1451039, _1451041), _1451043)))))], (35930 ^ _779448) ^ [] : [-(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))))], (35932 ^ _779448) ^ [_1451257, _1451259, _1451261, _1451263, _1451265, _1451267] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451257, tc_fun(_1451259, tc_fun(_1451261, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1451257, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_fun(_1451259, tc_fun(_1451261, tc_HOL_Obool)), _1451257), hAPP(c_COMBC(_1451259, tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_fun(_1451261, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451261, tc_fun(tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_fun(_1451261, tc_HOL_Obool)), _1451259), c_COMBC(_1451261, tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451261, tc_prod(_1451259, _1451261)), tc_fun(_1451261, tc_fun(tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_HOL_Obool)), _1451259), hAPP(c_COMBB(tc_prod(_1451259, _1451261), tc_fun(tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool), tc_HOL_Obool), _1451261), c_member(tc_prod(_1451259, _1451261)))), c_Product__Type_OPair(_1451259, _1451261))))), _1451263)), _1451265), _1451267)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451259, _1451261)), hAPP(hAPP(c_Product__Type_OPair(_1451259, _1451261), _1451265), _1451267)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451257, tc_fun(tc_prod(_1451259, _1451261), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451257, tc_HOL_Obool))), _1451263))))], (35938 ^ _779448) ^ [_1451740, _1451742, _1451744, _1451746, _1451748, _1451750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451742, _1451744)), hAPP(hAPP(c_Product__Type_OPair(_1451742, _1451744), _1451748), _1451750)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451740, tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1451740, tc_HOL_Obool))), _1451746))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1451740, tc_fun(_1451742, tc_fun(_1451744, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1451740, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_fun(_1451742, tc_fun(_1451744, tc_HOL_Obool)), _1451740), hAPP(c_COMBC(_1451742, tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_fun(_1451744, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451744, tc_fun(tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_fun(_1451744, tc_HOL_Obool)), _1451742), c_COMBC(_1451744, tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451744, tc_prod(_1451742, _1451744)), tc_fun(_1451744, tc_fun(tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_HOL_Obool)), _1451742), hAPP(c_COMBB(tc_prod(_1451742, _1451744), tc_fun(tc_fun(tc_prod(_1451742, _1451744), tc_HOL_Obool), tc_HOL_Obool), _1451744), c_member(tc_prod(_1451742, _1451744)))), c_Product__Type_OPair(_1451742, _1451744))))), _1451746)), _1451748), _1451750)))], (35944 ^ _779448) ^ [_1452229, _1452231, _1452233, _1452235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452229, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452229, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35945 ^ [_1452229, _1452231, _1452233, _1452235])), _1452231)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452229, 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), 35945 ^ [_1452229, _1452231, _1452233, _1452235]), _1452233))), _1452235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452229, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452229, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452231)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452229, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452235))))], (35951 ^ _779448) ^ [_1452559, _1452561, _1452563, _1452565] : [class_Complete__Lattice_Ocomplete__lattice(_1452559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452561), _1452563)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1452561, _1452559), _1452563), _1452565) = hAPP(hAPP(c_Finite__Set_Ofold(_1452561, _1452559, hAPP(hAPP(c_COMBB(_1452559, tc_fun(_1452559, _1452559), _1452561), c_Lattices_Osemilattice__inf__class_Oinf(_1452559)), _1452565)), c_Orderings_Otop__class_Otop(_1452559)), _1452563))], (35961 ^ _779448) ^ [_1452774, _1452776, _1452778, _1452780] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452774, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35962 ^ [_1452774, _1452776, _1452778, _1452780])), _1452776) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452774, 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), 35962 ^ [_1452774, _1452776, _1452778, _1452780]), _1452778))), _1452780), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452774, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452776) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1452774, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1452780))], (35968 ^ _779448) ^ [_1453054, _1453056] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1453054, tc_HOL_Obool)), _1453056)))], (35970 ^ _779448) ^ [_1453086, _1453088, _1453090, _1453092, _1453094, _1453096] : [hBOOL(hAPP(hAPP(c_member(_1453086), _1453088), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1453090, tc_fun(_1453086, tc_HOL_Obool)), _1453092), _1453094))), hBOOL(hAPP(hAPP(c_member(_1453090), _1453096), _1453092)), -(hBOOL(hAPP(hAPP(c_member(_1453086), _1453088), hAPP(_1453094, _1453096))))], (35980 ^ _779448) ^ [_1453303, _1453305, _1453307, _1453309, _1453311, _1453313] : [hBOOL(hAPP(hAPP(c_member(_1453303), _1453305), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1453307, tc_fun(_1453303, tc_HOL_Obool)), _1453309), _1453311))), -(hBOOL(hAPP(hAPP(c_member(_1453303), _1453305), hAPP(_1453311, _1453313)))), hBOOL(hAPP(hAPP(c_member(_1453307), _1453313), _1453309))], (35990 ^ _779448) ^ [_1453524, _1453526, _1453528, _1453530, _1453532, _1453534] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1453524, tc_fun(_1453526, tc_HOL_Obool)), _1453528), _1453530), _1453532)), hBOOL(hAPP(hAPP(c_member(_1453524), _1453534), _1453528)), -(hBOOL(hAPP(hAPP(_1453530, _1453534), _1453532)))], (36000 ^ _779448) ^ [_1453721, _1453723, _1453725, _1453727, _1453729, _1453731] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1453721, tc_fun(_1453723, tc_HOL_Obool)), _1453725), _1453727), _1453729)), -(hBOOL(hAPP(hAPP(_1453727, _1453731), _1453729))), hBOOL(hAPP(hAPP(c_member(_1453721), _1453731), _1453725))], (36010 ^ _779448) ^ [_1453922, _1453924, _1453926, _1453928, _1453930, _1453932, _1453934, _1453936] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1453922, tc_fun(_1453924, tc_fun(_1453926, tc_HOL_Obool))), _1453928), _1453930), _1453932), _1453934)), -(hBOOL(hAPP(hAPP(hAPP(_1453930, _1453936), _1453932), _1453934))), hBOOL(hAPP(hAPP(c_member(_1453922), _1453936), _1453928))], (36020 ^ _779448) ^ [_1454149, _1454151, _1454153, _1454155, _1454157, _1454159, _1454161, _1454163] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1454149, tc_fun(_1454151, tc_fun(_1454153, tc_HOL_Obool))), _1454155), _1454157), _1454159), _1454161)), hBOOL(hAPP(hAPP(c_member(_1454149), _1454163), _1454155)), -(hBOOL(hAPP(hAPP(hAPP(_1454157, _1454163), _1454159), _1454161)))], (36030 ^ _779448) ^ [_1454372, _1454374, _1454376, _1454378] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1454376), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1454372, tc_fun(_1454376, tc_HOL_Obool)), _1454374), _1454378)))), 36031 ^ _779448 : [(36032 ^ _779448) ^ [_1454446] : [hBOOL(hAPP(hAPP(c_member(_1454372), _1454446), _1454374)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454376), hAPP(_1454378, _1454446)))]]], (36050 ^ _779448) ^ [_1454850, _1454852, _1454854, _1454856] : [36052 ^ _779448 : [(36053 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1454850), 36051 ^ [_1454850, _1454852, _1454854, _1454856]), _1454854)))], (36055 ^ _779448) ^ [] : [hAPP(_1454856, 36051 ^ [_1454850, _1454852, _1454854, _1454856]) = c_Orderings_Otop__class_Otop(tc_fun(_1454852, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1454850, tc_fun(_1454852, tc_HOL_Obool)), _1454854), _1454856) = c_Orderings_Otop__class_Otop(tc_fun(_1454852, tc_HOL_Obool)))], (36040 ^ _779448) ^ [_1454621, _1454623, _1454625, _1454627] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1454621, tc_fun(_1454623, tc_HOL_Obool)), _1454625), _1454627) = c_Orderings_Otop__class_Otop(tc_fun(_1454623, tc_HOL_Obool)), 36043 ^ _779448 : [(36044 ^ _779448) ^ [_1454737] : [hBOOL(hAPP(hAPP(c_member(_1454621), _1454737), _1454625)), -(hAPP(_1454627, _1454737) = c_Orderings_Otop__class_Otop(tc_fun(_1454623, tc_HOL_Obool)))]]], (36069 ^ _779448) ^ [_1455330, _1455332, _1455334, _1455336] : [36071 ^ _779448 : [(36072 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1455332), 36070 ^ [_1455330, _1455332, _1455334, _1455336]), _1455334)))], (36074 ^ _779448) ^ [] : [hAPP(_1455336, 36070 ^ [_1455330, _1455332, _1455334, _1455336]) = c_Orderings_Otop__class_Otop(tc_fun(_1455330, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1455330, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455332, tc_fun(_1455330, tc_HOL_Obool)), _1455334), _1455336))], (36059 ^ _779448) ^ [_1455101, _1455103, _1455105, _1455107] : [c_Orderings_Otop__class_Otop(tc_fun(_1455101, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455103, tc_fun(_1455101, tc_HOL_Obool)), _1455105), _1455107), 36062 ^ _779448 : [(36063 ^ _779448) ^ [_1455217] : [hBOOL(hAPP(hAPP(c_member(_1455103), _1455217), _1455105)), -(hAPP(_1455107, _1455217) = c_Orderings_Otop__class_Otop(tc_fun(_1455101, tc_HOL_Obool)))]]], (36078 ^ _779448) ^ [_1455560, _1455562, _1455564] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455560, tc_fun(_1455562, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1455560, tc_HOL_Obool))), _1455564) = c_Orderings_Otop__class_Otop(tc_fun(_1455562, tc_HOL_Obool)))], (36080 ^ _779448) ^ [_1455624, _1455626, _1455628, _1455630] : [_1455624 = c_Orderings_Obot__class_Obot(tc_fun(_1455626, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455626, tc_fun(_1455628, tc_HOL_Obool)), _1455624), hAPP(c_COMBK(tc_fun(_1455628, tc_HOL_Obool), _1455626), _1455630)) = c_Orderings_Otop__class_Otop(tc_fun(_1455628, tc_HOL_Obool)))], (36086 ^ _779448) ^ [_1455761, _1455763, _1455765, _1455767] : [-(_1455761 = c_Orderings_Obot__class_Obot(tc_fun(_1455763, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455763, tc_fun(_1455765, tc_HOL_Obool)), _1455761), hAPP(c_COMBK(tc_fun(_1455765, tc_HOL_Obool), _1455763), _1455767)) = _1455767)], (36092 ^ _779448) ^ [_1455856, _1455858, _1455860, _1455862, _1455864, _1455866] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455856, tc_fun(_1455858, tc_fun(_1455860, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1455856, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_fun(_1455858, tc_fun(_1455860, tc_HOL_Obool)), _1455856), hAPP(c_COMBC(_1455858, tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_fun(_1455860, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455860, tc_fun(tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_fun(_1455860, tc_HOL_Obool)), _1455858), c_COMBC(_1455860, tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455860, tc_prod(_1455858, _1455860)), tc_fun(_1455860, tc_fun(tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_HOL_Obool)), _1455858), hAPP(c_COMBB(tc_prod(_1455858, _1455860), tc_fun(tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool), tc_HOL_Obool), _1455860), c_member(tc_prod(_1455858, _1455860)))), c_Product__Type_OPair(_1455858, _1455860))))), _1455862)), _1455864), _1455866)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455858, _1455860)), hAPP(hAPP(c_Product__Type_OPair(_1455858, _1455860), _1455864), _1455866)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1455856, tc_fun(tc_prod(_1455858, _1455860), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1455856, tc_HOL_Obool))), _1455862))))], (36098 ^ _779448) ^ [_1456339, _1456341, _1456343, _1456345, _1456347, _1456349] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456341, _1456343)), hAPP(hAPP(c_Product__Type_OPair(_1456341, _1456343), _1456347), _1456349)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1456339, tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1456339, tc_HOL_Obool))), _1456345))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1456339, tc_fun(_1456341, tc_fun(_1456343, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1456339, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_fun(_1456341, tc_fun(_1456343, tc_HOL_Obool)), _1456339), hAPP(c_COMBC(_1456341, tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_fun(_1456343, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456343, tc_fun(tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_fun(_1456343, tc_HOL_Obool)), _1456341), c_COMBC(_1456343, tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1456343, tc_prod(_1456341, _1456343)), tc_fun(_1456343, tc_fun(tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_HOL_Obool)), _1456341), hAPP(c_COMBB(tc_prod(_1456341, _1456343), tc_fun(tc_fun(tc_prod(_1456341, _1456343), tc_HOL_Obool), tc_HOL_Obool), _1456343), c_member(tc_prod(_1456341, _1456343)))), c_Product__Type_OPair(_1456341, _1456343))))), _1456345)), _1456347), _1456349)))], (36104 ^ _779448) ^ [_1456849, _1456851, _1456853, _1456855] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1456849, tc_fun(_1456851, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1456849, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1456851, tc_HOL_Obool), tc_fun(_1456851, tc_HOL_Obool), _1456849), hAPP(c_COMBC(_1456851, tc_fun(_1456851, tc_HOL_Obool), tc_HOL_Obool), c_member(_1456851))), _1456853)), _1456855)), -(hBOOL(hAPP(hAPP(c_member(_1456851), _1456855), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1456849, tc_fun(_1456851, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1456849, tc_HOL_Obool))), _1456853))))], (36110 ^ _779448) ^ [_1457068, _1457070, _1457072, _1457074] : [hBOOL(hAPP(hAPP(c_member(_1457070), _1457074), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457068, tc_fun(_1457070, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1457068, tc_HOL_Obool))), _1457072))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457068, tc_fun(_1457070, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1457068, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1457070, tc_HOL_Obool), tc_fun(_1457070, tc_HOL_Obool), _1457068), hAPP(c_COMBC(_1457070, tc_fun(_1457070, tc_HOL_Obool), tc_HOL_Obool), c_member(_1457070))), _1457072)), _1457074)))], (36116 ^ _779448) ^ [_1457293, _1457295, _1457297, _1457299, _1457301, _1457303] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457293, tc_fun(_1457295, tc_HOL_Obool)), _1457297), hAPP(hAPP(c_COMBC(_1457293, tc_fun(_1457299, tc_fun(_1457295, tc_HOL_Obool)), tc_fun(_1457295, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1457299, tc_HOL_Obool), tc_fun(tc_fun(_1457299, tc_fun(_1457295, tc_HOL_Obool)), tc_fun(_1457295, tc_HOL_Obool)), _1457293), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457299, tc_fun(_1457295, tc_HOL_Obool))), _1457301)), _1457303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457299, tc_fun(_1457295, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457293, tc_fun(_1457299, tc_HOL_Obool)), _1457297), _1457301)), _1457303))], (36118 ^ _779448) ^ [_1457412, _1457414, _1457416, _1457418, _1457420, _1457422] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457412, tc_fun(_1457414, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457416, tc_fun(_1457412, tc_HOL_Obool)), _1457418), _1457420)), _1457422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457416, tc_fun(_1457414, tc_HOL_Obool)), _1457418), hAPP(hAPP(c_COMBC(_1457416, tc_fun(_1457412, tc_fun(_1457414, tc_HOL_Obool)), tc_fun(_1457414, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1457412, tc_HOL_Obool), tc_fun(tc_fun(_1457412, tc_fun(_1457414, tc_HOL_Obool)), tc_fun(_1457414, tc_HOL_Obool)), _1457416), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457412, tc_fun(_1457414, tc_HOL_Obool))), _1457420)), _1457422)))], (36130 ^ _779448) ^ [_1457798, _1457800, _1457802, _1457804, _1457806] : [36132 ^ _779448 : [(36133 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457802), 36131 ^ [_1457798, _1457800, _1457802, _1457804, _1457806]), _1457804)))], (36135 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1457798), _1457800), hAPP(_1457806, 36131 ^ [_1457798, _1457800, _1457802, _1457804, _1457806])))]], -(hBOOL(hAPP(hAPP(c_member(_1457798), _1457800), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457802, tc_fun(_1457798, tc_HOL_Obool)), _1457804), _1457806))))], (36120 ^ _779448) ^ [_1457555, _1457557, _1457559, _1457561, _1457563] : [hBOOL(hAPP(hAPP(c_member(_1457555), _1457557), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1457559, tc_fun(_1457555, tc_HOL_Obool)), _1457561), _1457563))), 36123 ^ _779448 : [(36124 ^ _779448) ^ [_1457679] : [hBOOL(hAPP(hAPP(c_member(_1457559), _1457679), _1457561)), -(hBOOL(hAPP(hAPP(c_member(_1457555), _1457557), hAPP(_1457563, _1457679))))]]], (36149 ^ _779448) ^ [_1458328, _1458330, _1458332, _1458334, _1458336] : [36151 ^ _779448 : [(36152 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458332), 36150 ^ [_1458328, _1458330, _1458332, _1458334, _1458336]), _1458334)))], (36154 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458328, tc_HOL_Obool)), _1458330), hAPP(_1458336, 36150 ^ [_1458328, _1458330, _1458332, _1458334, _1458336])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458328, tc_HOL_Obool)), _1458330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458332, tc_fun(_1458328, tc_HOL_Obool)), _1458334), _1458336))))], (36139 ^ _779448) ^ [_1458070, _1458072, _1458074, _1458076, _1458078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458070, tc_HOL_Obool)), _1458072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458074, tc_fun(_1458070, tc_HOL_Obool)), _1458076), _1458078))), 36142 ^ _779448 : [(36143 ^ _779448) ^ [_1458203] : [hBOOL(hAPP(hAPP(c_member(_1458074), _1458203), _1458076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1458070, tc_HOL_Obool)), _1458072), hAPP(_1458078, _1458203))))]]], (36158 ^ _779448) ^ [_1458591, _1458593, _1458595, _1458597, _1458599] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458591, tc_fun(_1458593, tc_HOL_Obool)), _1458595), hAPP(hAPP(c_COMBB(tc_fun(_1458593, tc_HOL_Obool), tc_fun(_1458593, tc_HOL_Obool), _1458591), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458593, tc_HOL_Obool)), _1458597)), _1458599)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458593, tc_HOL_Obool)), _1458597), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458591, tc_fun(_1458593, tc_HOL_Obool)), _1458595), _1458599)))], (36160 ^ _779448) ^ [_1458681, _1458683, _1458685, _1458687, _1458689] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458681, tc_fun(_1458683, tc_HOL_Obool)), _1458685), hAPP(hAPP(c_COMBC(_1458681, tc_fun(_1458683, tc_HOL_Obool), tc_fun(_1458683, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458683, tc_HOL_Obool), tc_fun(tc_fun(_1458683, tc_HOL_Obool), tc_fun(_1458683, tc_HOL_Obool)), _1458681), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458683, tc_HOL_Obool))), _1458687)), _1458689)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458683, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458681, tc_fun(_1458683, tc_HOL_Obool)), _1458685), _1458687)), _1458689))], (36162 ^ _779448) ^ [_1458790, _1458792, _1458794, _1458796, _1458798] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458790, tc_HOL_Obool)), _1458792), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458794, tc_fun(_1458790, tc_HOL_Obool)), _1458796), _1458798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458794, tc_fun(_1458790, tc_HOL_Obool)), _1458796), hAPP(hAPP(c_COMBB(tc_fun(_1458790, tc_HOL_Obool), tc_fun(_1458790, tc_HOL_Obool), _1458794), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458790, tc_HOL_Obool)), _1458792)), _1458798)))], (36164 ^ _779448) ^ [_1458880, _1458882, _1458884, _1458886, _1458888] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458880, tc_HOL_Obool)), _1458882), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458884, tc_fun(_1458880, tc_HOL_Obool)), _1458886), _1458888)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458884, tc_fun(_1458880, tc_HOL_Obool)), _1458886), hAPP(hAPP(c_COMBB(tc_fun(_1458880, tc_HOL_Obool), tc_fun(_1458880, tc_HOL_Obool), _1458884), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458880, tc_HOL_Obool)), _1458882)), _1458888)))], (36166 ^ _779448) ^ [_1458970, _1458972, _1458974, _1458976, _1458978] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458970, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458972, tc_fun(_1458970, tc_HOL_Obool)), _1458974), _1458976)), _1458978) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458972, tc_fun(_1458970, tc_HOL_Obool)), _1458974), hAPP(hAPP(c_COMBC(_1458972, tc_fun(_1458970, tc_HOL_Obool), tc_fun(_1458970, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458970, tc_HOL_Obool), tc_fun(tc_fun(_1458970, tc_HOL_Obool), tc_fun(_1458970, tc_HOL_Obool)), _1458972), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458970, tc_HOL_Obool))), _1458976)), _1458978)))], (36168 ^ _779448) ^ [_1459079, _1459081, _1459083, _1459085, _1459087, _1459089, _1459091] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459079, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459081, tc_fun(_1459079, tc_HOL_Obool)), _1459083), _1459085)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459087, tc_fun(_1459079, tc_HOL_Obool)), _1459089), _1459091)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459081, tc_fun(_1459079, tc_HOL_Obool)), _1459083), hAPP(hAPP(c_COMBB(tc_fun(_1459087, tc_fun(_1459079, tc_HOL_Obool)), tc_fun(_1459079, tc_HOL_Obool), _1459081), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459087, tc_fun(_1459079, tc_HOL_Obool)), _1459089)), hAPP(hAPP(c_COMBC(_1459081, tc_fun(_1459087, tc_fun(_1459079, tc_HOL_Obool)), tc_fun(_1459087, tc_fun(_1459079, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1459079, tc_HOL_Obool), tc_fun(_1459079, tc_HOL_Obool)), tc_fun(tc_fun(_1459087, tc_fun(_1459079, tc_HOL_Obool)), tc_fun(_1459087, tc_fun(_1459079, tc_HOL_Obool))), _1459081), c_COMBB(tc_fun(_1459079, tc_HOL_Obool), tc_fun(_1459079, tc_HOL_Obool), _1459087)), hAPP(hAPP(c_COMBB(tc_fun(_1459079, tc_HOL_Obool), tc_fun(tc_fun(_1459079, tc_HOL_Obool), tc_fun(_1459079, tc_HOL_Obool)), _1459081), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459079, tc_HOL_Obool))), _1459085))), _1459091))))], (36170 ^ _779448) ^ [_1459282, _1459284, _1459286, _1459288, _1459290, _1459292] : [class_Complete__Lattice_Ocomplete__lattice(_1459282), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459284, _1459282), _1459286), hAPP(hAPP(c_COMBB(tc_fun(_1459288, _1459282), _1459282, _1459284), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459288, _1459282), _1459290)), _1459292)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459288, _1459282), _1459290), hAPP(hAPP(c_COMBB(tc_fun(_1459284, _1459282), _1459282, _1459288), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459284, _1459282), _1459286)), hAPP(c_COMBC(_1459284, _1459288, _1459282), _1459292))))], (36176 ^ _779448) ^ [_1459491, _1459493, _1459495, _1459497, _1459499, _1459501] : [class_Complete__Lattice_Ocomplete__lattice(_1459491), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459493, tc_fun(_1459495, _1459491)), _1459497), _1459499), _1459501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459493, _1459491), _1459497), hAPP(hAPP(c_COMBC(_1459493, _1459495, _1459491), _1459499), _1459501)))], (36182 ^ _779448) ^ [_1459642, _1459644, _1459646, _1459648] : [-(hAPP(c_Set_OPow(_1459642), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459644, tc_fun(_1459642, tc_HOL_Obool)), _1459646), _1459648)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459644, tc_fun(tc_fun(_1459642, tc_HOL_Obool), tc_HOL_Obool)), _1459646), hAPP(hAPP(c_COMBB(tc_fun(_1459642, tc_HOL_Obool), tc_fun(tc_fun(_1459642, tc_HOL_Obool), tc_HOL_Obool), _1459644), c_Set_OPow(_1459642)), _1459648)))], (36184 ^ _779448) ^ [_1459724, _1459726, _1459728, _1459730, _1459732, _1459734] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459724, tc_fun(_1459726, tc_HOL_Obool)), _1459728), hAPP(hAPP(c_COMBB(_1459730, tc_fun(_1459726, tc_HOL_Obool), _1459724), _1459732), _1459734)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459730, tc_fun(_1459726, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459724, _1459730, _1459734), _1459728)), _1459732))], (36186 ^ _779448) ^ [_1459801, _1459803, _1459805, _1459807, _1459809, _1459811] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459801, tc_fun(_1459803, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1459805, _1459801, _1459807), _1459809)), _1459811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459805, tc_fun(_1459803, tc_HOL_Obool)), _1459809), hAPP(hAPP(c_COMBB(_1459801, tc_fun(_1459803, tc_HOL_Obool), _1459805), _1459811), _1459807)))], (36188 ^ _779448) ^ [_1459878, _1459880, _1459882, _1459884, _1459886] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459878, tc_fun(_1459880, tc_HOL_Obool)), _1459882), hAPP(hAPP(c_COMBB(tc_fun(_1459880, tc_HOL_Obool), tc_fun(_1459880, tc_HOL_Obool), _1459878), hAPP(c_Set_Oinsert(_1459880), _1459884)), _1459886)) = hAPP(hAPP(c_Set_Oinsert(_1459880), _1459884), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459878, tc_fun(_1459880, tc_HOL_Obool)), _1459882), _1459886)))], (36190 ^ _779448) ^ [_1459962, _1459964, _1459966, _1459968, _1459970] : [-(hAPP(hAPP(c_Set_Oinsert(_1459962), _1459964), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459966, tc_fun(_1459962, tc_HOL_Obool)), _1459968), _1459970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1459966, tc_fun(_1459962, tc_HOL_Obool)), _1459968), hAPP(hAPP(c_COMBB(tc_fun(_1459962, tc_HOL_Obool), tc_fun(_1459962, tc_HOL_Obool), _1459966), hAPP(c_Set_Oinsert(_1459962), _1459964)), _1459970)))], (36192 ^ _779448) ^ [_1460046, _1460048, _1460050, _1460052, _1460054] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460046, tc_fun(_1460048, tc_HOL_Obool)), _1460050), hAPP(hAPP(c_COMBS(_1460046, tc_fun(_1460048, tc_HOL_Obool), tc_fun(_1460048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1460048, tc_HOL_Obool), tc_fun(tc_fun(_1460048, tc_HOL_Obool), tc_fun(_1460048, tc_HOL_Obool)), _1460046), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460048, tc_HOL_Obool))), _1460052)), _1460054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460048, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460046, tc_fun(_1460048, tc_HOL_Obool)), _1460050), _1460052)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460046, tc_fun(_1460048, tc_HOL_Obool)), _1460050), _1460054)))], (36194 ^ _779448) ^ [_1460167, _1460169, _1460171, _1460173, _1460175] : [class_Complete__Lattice_Ocomplete__lattice(_1460167), 36197 ^ _779448 : [(36208 ^ _779448) ^ [] : [36210 ^ _779448 : [(36211 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460171), 36209 ^ [_1460167, _1460169, _1460171, _1460173, _1460175]), _1460173)))], (36213 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460167), _1460169), hAPP(_1460175, 36209 ^ [_1460167, _1460169, _1460171, _1460173, _1460175])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460167), _1460169), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460171, _1460167), _1460173), _1460175))))], (36198 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460167), _1460169), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460171, _1460167), _1460173), _1460175))), 36201 ^ _779448 : [(36202 ^ _779448) ^ [_1460348] : [hBOOL(hAPP(hAPP(c_member(_1460171), _1460348), _1460173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460167), _1460169), hAPP(_1460175, _1460348))))]]]]], (36217 ^ _779448) ^ [_1460661, _1460663, _1460665, _1460667, _1460669] : [class_Complete__Lattice_Ocomplete__lattice(_1460661), class_Orderings_Olinorder(_1460661), 36224 ^ _779448 : [(36225 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460661), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460663, _1460661), _1460665), _1460667)), _1460669)), 36229 ^ _779448 : [(36230 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460663), 36228 ^ [_1460661, _1460663, _1460665, _1460667, _1460669]), _1460665)))], (36232 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460661), hAPP(_1460667, 36228 ^ [_1460661, _1460663, _1460665, _1460667, _1460669])), _1460669)))]]], (36234 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460661), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1460663, _1460661), _1460665), _1460667)), _1460669))), 36235 ^ _779448 : [(36236 ^ _779448) ^ [_1461009] : [hBOOL(hAPP(hAPP(c_member(_1460663), _1461009), _1460665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460661), hAPP(_1460667, _1461009)), _1460669))]]]]], (36244 ^ _779448) ^ [_1461179, _1461181, _1461183, _1461185, _1461187, _1461189] : [hBOOL(hAPP(hAPP(c_member(_1461179), _1461181), _1461183)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461179, tc_fun(_1461185, tc_HOL_Obool)), _1461183), hAPP(hAPP(c_COMBB(tc_fun(_1461185, tc_HOL_Obool), tc_fun(_1461185, tc_HOL_Obool), _1461179), hAPP(c_Set_Oinsert(_1461185), _1461187)), _1461189)) = hAPP(hAPP(c_Set_Oinsert(_1461185), _1461187), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461179, tc_fun(_1461185, tc_HOL_Obool)), _1461183), _1461189)))], (36250 ^ _779448) ^ [_1461384, _1461386, _1461388, _1461390, _1461392] : [hBOOL(hAPP(hAPP(c_member(_1461384), _1461386), _1461388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461390, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461384, tc_fun(_1461390, tc_HOL_Obool)), _1461388), _1461392)), hAPP(_1461392, _1461386))))], (36256 ^ _779448) ^ [_1461531, _1461533, _1461535, _1461537, _1461539] : [hBOOL(hAPP(hAPP(c_member(_1461531), _1461533), _1461535)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461537, tc_HOL_Obool)), hAPP(_1461539, _1461533)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461531, tc_fun(_1461537, tc_HOL_Obool)), _1461535), _1461539)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461531, tc_fun(_1461537, tc_HOL_Obool)), _1461535), _1461539))], (36262 ^ _779448) ^ [_1461704, _1461706, _1461708, _1461710] : [class_Complete__Lattice_Ocomplete__lattice(_1461704), -(_1461706 = c_Orderings_Obot__class_Obot(tc_fun(_1461708, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461708, _1461704), _1461706), hAPP(c_COMBK(_1461704, _1461708), _1461710)) = _1461710)], (36272 ^ _779448) ^ [_1461856, _1461858, _1461860, _1461862, _1461864] : [_1461856 = c_Orderings_Obot__class_Obot(tc_fun(_1461858, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461860, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461858, tc_fun(_1461860, tc_HOL_Obool)), _1461856), _1461862)), _1461864) = _1461864)], (36278 ^ _779448) ^ [_1461989, _1461991, _1461993, _1461995, _1461997] : [-(_1461989 = c_Orderings_Obot__class_Obot(tc_fun(_1461991, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461993, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461991, tc_fun(_1461993, tc_HOL_Obool)), _1461989), _1461995)), _1461997) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1461991, tc_fun(_1461993, tc_HOL_Obool)), _1461989), hAPP(hAPP(c_COMBC(_1461991, tc_fun(_1461993, tc_HOL_Obool), tc_fun(_1461993, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1461993, tc_HOL_Obool), tc_fun(tc_fun(_1461993, tc_HOL_Obool), tc_fun(_1461993, tc_HOL_Obool)), _1461991), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1461993, tc_HOL_Obool))), _1461995)), _1461997)))], (36284 ^ _779448) ^ [_1462134, _1462136, _1462138, _1462140, _1462142] : [_1462134 = c_Orderings_Obot__class_Obot(tc_fun(_1462136, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462138, tc_HOL_Obool)), _1462140), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462136, tc_fun(_1462138, tc_HOL_Obool)), _1462134), _1462142)) = _1462140)], (36290 ^ _779448) ^ [_1462267, _1462269, _1462271, _1462273, _1462275] : [-(_1462267 = c_Orderings_Obot__class_Obot(tc_fun(_1462269, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462271, tc_HOL_Obool)), _1462273), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462269, tc_fun(_1462271, tc_HOL_Obool)), _1462267), _1462275)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462269, tc_fun(_1462271, tc_HOL_Obool)), _1462267), hAPP(hAPP(c_COMBB(tc_fun(_1462271, tc_HOL_Obool), tc_fun(_1462271, tc_HOL_Obool), _1462269), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462271, tc_HOL_Obool)), _1462273)), _1462275)))], (36296 ^ _779448) ^ [_1462393, _1462395, _1462397, _1462399, _1462401] : [_1462393 = c_Orderings_Obot__class_Obot(tc_fun(_1462395, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462395, tc_fun(_1462397, tc_HOL_Obool)), _1462393), hAPP(hAPP(c_COMBB(tc_fun(_1462397, tc_HOL_Obool), tc_fun(_1462397, tc_HOL_Obool), _1462395), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462397, tc_HOL_Obool)), _1462399)), _1462401)) = c_Orderings_Otop__class_Otop(tc_fun(_1462397, tc_HOL_Obool)))], (36302 ^ _779448) ^ [_1462562, _1462564, _1462566, _1462568, _1462570] : [-(_1462562 = c_Orderings_Obot__class_Obot(tc_fun(_1462564, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462564, tc_fun(_1462566, tc_HOL_Obool)), _1462562), hAPP(hAPP(c_COMBB(tc_fun(_1462566, tc_HOL_Obool), tc_fun(_1462566, tc_HOL_Obool), _1462564), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462566, tc_HOL_Obool)), _1462568)), _1462570)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462566, tc_HOL_Obool)), _1462568), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462564, tc_fun(_1462566, tc_HOL_Obool)), _1462562), _1462570)))], (36308 ^ _779448) ^ [_1462688, _1462690, _1462692, _1462694, _1462696] : [_1462688 = c_Orderings_Obot__class_Obot(tc_fun(_1462690, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462690, tc_fun(_1462692, tc_HOL_Obool)), _1462688), hAPP(hAPP(c_COMBC(_1462690, tc_fun(_1462692, tc_HOL_Obool), tc_fun(_1462692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462692, tc_HOL_Obool), tc_fun(tc_fun(_1462692, tc_HOL_Obool), tc_fun(_1462692, tc_HOL_Obool)), _1462690), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462692, tc_HOL_Obool))), _1462694)), _1462696)) = c_Orderings_Otop__class_Otop(tc_fun(_1462692, tc_HOL_Obool)))], (36314 ^ _779448) ^ [_1462895, _1462897, _1462899, _1462901, _1462903] : [-(_1462895 = c_Orderings_Obot__class_Obot(tc_fun(_1462897, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462897, tc_fun(_1462899, tc_HOL_Obool)), _1462895), hAPP(hAPP(c_COMBC(_1462897, tc_fun(_1462899, tc_HOL_Obool), tc_fun(_1462899, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462899, tc_HOL_Obool), tc_fun(tc_fun(_1462899, tc_HOL_Obool), tc_fun(_1462899, tc_HOL_Obool)), _1462897), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462899, tc_HOL_Obool))), _1462901)), _1462903)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462899, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1462897, tc_fun(_1462899, tc_HOL_Obool)), _1462895), _1462901)), _1462903))], (36320 ^ _779448) ^ [_1463022, _1463024, _1463026, _1463028, _1463030] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463022, tc_fun(_1463024, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1463022), _1463026), _1463028)), _1463030) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463024, tc_HOL_Obool)), hAPP(_1463030, _1463026)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463022, tc_fun(_1463024, tc_HOL_Obool)), _1463028), _1463030)))], (36322 ^ _779448) ^ [_1463117, _1463119, _1463121, _1463123, _1463125] : [_1463117 = c_Orderings_Obot__class_Obot(tc_fun(_1463119, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463121, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463119, tc_fun(_1463121, tc_HOL_Obool)), _1463117), _1463123)), _1463125) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463121, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1463121, tc_HOL_Obool))), _1463125))], (36328 ^ _779448) ^ [_1463282, _1463284, _1463286, _1463288, _1463290] : [-(_1463282 = c_Orderings_Obot__class_Obot(tc_fun(_1463284, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463286, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463284, tc_fun(_1463286, tc_HOL_Obool)), _1463282), _1463288)), _1463290) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463284, tc_fun(_1463286, tc_HOL_Obool)), _1463282), hAPP(hAPP(c_COMBC(_1463284, tc_fun(_1463286, tc_HOL_Obool), tc_fun(_1463286, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463286, tc_HOL_Obool), tc_fun(tc_fun(_1463286, tc_HOL_Obool), tc_fun(_1463286, tc_HOL_Obool)), _1463284), c_Groups_Ominus__class_Ominus(tc_fun(_1463286, tc_HOL_Obool))), _1463288)), _1463290)))], (36334 ^ _779448) ^ [_1463427, _1463429, _1463431, _1463433, _1463435] : [_1463427 = c_Orderings_Obot__class_Obot(tc_fun(_1463429, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463429, tc_fun(_1463431, tc_HOL_Obool)), _1463427), hAPP(hAPP(c_COMBC(_1463429, tc_fun(_1463431, tc_HOL_Obool), tc_fun(_1463431, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463431, tc_HOL_Obool), tc_fun(tc_fun(_1463431, tc_HOL_Obool), tc_fun(_1463431, tc_HOL_Obool)), _1463429), c_Groups_Ominus__class_Ominus(tc_fun(_1463431, tc_HOL_Obool))), _1463433)), _1463435)) = c_Orderings_Otop__class_Otop(tc_fun(_1463431, tc_HOL_Obool)))], (36340 ^ _779448) ^ [_1463634, _1463636, _1463638, _1463640, _1463642] : [-(_1463634 = c_Orderings_Obot__class_Obot(tc_fun(_1463636, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463636, tc_fun(_1463638, tc_HOL_Obool)), _1463634), hAPP(hAPP(c_COMBC(_1463636, tc_fun(_1463638, tc_HOL_Obool), tc_fun(_1463638, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1463638, tc_HOL_Obool), tc_fun(tc_fun(_1463638, tc_HOL_Obool), tc_fun(_1463638, tc_HOL_Obool)), _1463636), c_Groups_Ominus__class_Ominus(tc_fun(_1463638, tc_HOL_Obool))), _1463640)), _1463642)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463638, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463636, tc_fun(_1463638, tc_HOL_Obool)), _1463634), _1463640)), _1463642))], (36346 ^ _779448) ^ [_1463761, _1463763, _1463765, _1463767, _1463769] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463761, tc_fun(_1463763, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463761, tc_HOL_Obool)), _1463765), _1463767)), _1463769) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463763, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463761, tc_fun(_1463763, tc_HOL_Obool)), _1463765), _1463769)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463761, tc_fun(_1463763, tc_HOL_Obool)), _1463767), _1463769)))], (36348 ^ _779448) ^ [_1463850, _1463852, _1463854, _1463856, _1463858] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1463850, tc_fun(_1463852, tc_HOL_Obool)), _1463854), hAPP(hAPP(c_COMBB(tc_fun(_1463852, tc_HOL_Obool), tc_fun(_1463852, tc_HOL_Obool), _1463850), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463852, tc_HOL_Obool)), _1463856)), _1463858)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463852, tc_HOL_Obool)), _1463856), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463850, tc_fun(_1463852, tc_HOL_Obool)), _1463854), _1463858)))], (36350 ^ _779448) ^ [_1463940, _1463942, _1463944, _1463946, _1463948] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463940, tc_HOL_Obool)), _1463942), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1463944, tc_fun(_1463940, tc_HOL_Obool)), _1463946), _1463948)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1463944, tc_fun(_1463940, tc_HOL_Obool)), _1463946), hAPP(hAPP(c_COMBB(tc_fun(_1463940, tc_HOL_Obool), tc_fun(_1463940, tc_HOL_Obool), _1463944), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1463940, tc_HOL_Obool)), _1463942)), _1463948)))], (36352 ^ _779448) ^ [_1464030, _1464032, _1464034, _1464036, _1464038, _1464040] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464030, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1464032, _1464030, _1464034), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464036, tc_fun(_1464032, tc_HOL_Obool)), _1464038), _1464040))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464036, tc_fun(_1464030, tc_HOL_Obool)), _1464038), hAPP(hAPP(c_COMBB(tc_fun(_1464032, tc_HOL_Obool), tc_fun(_1464030, tc_HOL_Obool), _1464036), c_Relation_OImage(_1464032, _1464030, _1464034)), _1464040)))))], (36354 ^ _779448) ^ [_1464124, _1464126, _1464128, _1464130] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464124, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464126, tc_fun(_1464124, tc_HOL_Obool)), _1464128), _1464130)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464126, tc_fun(_1464124, tc_HOL_Obool)), _1464128), hAPP(hAPP(c_COMBB(tc_fun(_1464124, tc_HOL_Obool), tc_fun(_1464124, tc_HOL_Obool), _1464126), c_Groups_Ouminus__class_Ouminus(tc_fun(_1464124, tc_HOL_Obool))), _1464130)))], (36356 ^ _779448) ^ [_1464206, _1464208, _1464210, _1464212] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1464206, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464208, tc_fun(_1464206, tc_HOL_Obool)), _1464210), _1464212)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464208, tc_fun(_1464206, tc_HOL_Obool)), _1464210), hAPP(hAPP(c_COMBB(tc_fun(_1464206, tc_HOL_Obool), tc_fun(_1464206, tc_HOL_Obool), _1464208), c_Groups_Ouminus__class_Ouminus(tc_fun(_1464206, tc_HOL_Obool))), _1464212)))], (36358 ^ _779448) ^ [] : [-(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)))], (36360 ^ _779448) ^ [_1464306, _1464308, _1464310, _1464312, _1464314] : [class_Complete__Lattice_Ocomplete__lattice(_1464306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1464308, tc_HOL_Obool)), _1464310), _1464312)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1464306), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464308, _1464306), _1464312), _1464314)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464308, _1464306), _1464310), _1464314))))], (36370 ^ _779448) ^ [_1464533, _1464535, _1464537, _1464539, _1464541] : [_1464533 = c_Orderings_Obot__class_Obot(tc_fun(_1464535, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464537, tc_HOL_Obool)), _1464539), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464535, tc_fun(_1464537, tc_HOL_Obool)), _1464533), _1464541)) = _1464539)], (36376 ^ _779448) ^ [_1464666, _1464668, _1464670, _1464672, _1464674] : [-(_1464666 = c_Orderings_Obot__class_Obot(tc_fun(_1464668, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464670, tc_HOL_Obool)), _1464672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464668, tc_fun(_1464670, tc_HOL_Obool)), _1464666), _1464674)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464668, tc_fun(_1464670, tc_HOL_Obool)), _1464666), hAPP(hAPP(c_COMBB(tc_fun(_1464670, tc_HOL_Obool), tc_fun(_1464670, tc_HOL_Obool), _1464668), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464670, tc_HOL_Obool)), _1464672)), _1464674)))], (36382 ^ _779448) ^ [_1464792, _1464794, _1464796, _1464798, _1464800] : [_1464792 = c_Orderings_Obot__class_Obot(tc_fun(_1464794, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464794, tc_fun(_1464796, tc_HOL_Obool)), _1464792), hAPP(hAPP(c_COMBB(tc_fun(_1464796, tc_HOL_Obool), tc_fun(_1464796, tc_HOL_Obool), _1464794), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464796, tc_HOL_Obool)), _1464798)), _1464800)) = c_Orderings_Otop__class_Otop(tc_fun(_1464796, tc_HOL_Obool)))], (36388 ^ _779448) ^ [_1464961, _1464963, _1464965, _1464967, _1464969] : [-(_1464961 = c_Orderings_Obot__class_Obot(tc_fun(_1464963, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1464963, tc_fun(_1464965, tc_HOL_Obool)), _1464961), hAPP(hAPP(c_COMBB(tc_fun(_1464965, tc_HOL_Obool), tc_fun(_1464965, tc_HOL_Obool), _1464963), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464965, tc_HOL_Obool)), _1464967)), _1464969)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464965, tc_HOL_Obool)), _1464967), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1464963, tc_fun(_1464965, tc_HOL_Obool)), _1464961), _1464969)))], (36394 ^ _779448) ^ [_1465069, _1465071, _1465073, _1465075, _1465077] : [class_Complete__Lattice_Ocomplete__lattice(_1465069), hBOOL(hAPP(hAPP(c_member(_1465071), _1465073), _1465075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1465069), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1465071, _1465069), _1465075), _1465077)), hAPP(_1465077, _1465073))))], (36404 ^ _779448) ^ [_1465260, _1465262, _1465264, _1465266, _1465268] : [class_Complete__Lattice_Ocomplete__lattice(_1465260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465262), _1465264)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1465260), _1465266), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1465262, _1465260), _1465264), _1465268)) = hAPP(hAPP(c_Finite__Set_Ofold(_1465262, _1465260, hAPP(hAPP(c_COMBB(_1465260, tc_fun(_1465260, _1465260), _1465262), c_Lattices_Osemilattice__inf__class_Oinf(_1465260)), _1465268)), _1465266), _1465264))], (36414 ^ _779448) ^ [] : [-(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))], (36416 ^ _779448) ^ [_1465509, _1465511, _1465513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465509, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1465509, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36417 ^ [_1465509, _1465511, _1465513])), _1465511)), _1465513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465509, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1465509, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1465511)), _1465513)))], (36423 ^ _779448) ^ [_1465735, _1465737] : [-(hBOOL(hAPP(hAPP(c_member(_1465735), _1465737), c_Orderings_Otop__class_Otop(tc_fun(_1465735, tc_HOL_Obool)))))], (36435 ^ _779448) ^ [_1466014, _1466016, _1466018, _1466020, _1466022] : [36437 ^ _779448 : [(36438 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466014), 36436 ^ [_1466014, _1466016, _1466018, _1466020, _1466022]), _1466018)))], (36440 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1466020, 36436 ^ [_1466014, _1466016, _1466018, _1466020, _1466022]), _1466022))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1466014, tc_fun(_1466016, tc_HOL_Obool)), _1466018), _1466020), _1466022)))], (36425 ^ _779448) ^ [_1465796, _1465798, _1465800, _1465802, _1465804] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1465796, tc_fun(_1465798, tc_HOL_Obool)), _1465800), _1465802), _1465804)), 36428 ^ _779448 : [(36429 ^ _779448) ^ [_1465905] : [hBOOL(hAPP(hAPP(c_member(_1465796), _1465905), _1465800)), -(hBOOL(hAPP(hAPP(_1465802, _1465905), _1465804)))]]], (36454 ^ _779448) ^ [_1466514, _1466516, _1466518, _1466520, _1466522, _1466524, _1466526] : [36456 ^ _779448 : [(36457 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466514), 36455 ^ [_1466514, _1466516, _1466518, _1466520, _1466522, _1466524, _1466526]), _1466520)))], (36459 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1466522, 36455 ^ [_1466514, _1466516, _1466518, _1466520, _1466522, _1466524, _1466526]), _1466524), _1466526))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1466514, tc_fun(_1466516, tc_fun(_1466518, tc_HOL_Obool))), _1466520), _1466522), _1466524), _1466526)))], (36444 ^ _779448) ^ [_1466267, _1466269, _1466271, _1466273, _1466275, _1466277, _1466279] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1466267, tc_fun(_1466269, tc_fun(_1466271, tc_HOL_Obool))), _1466273), _1466275), _1466277), _1466279)), 36447 ^ _779448 : [(36448 ^ _779448) ^ [_1466395] : [hBOOL(hAPP(hAPP(c_member(_1466267), _1466395), _1466273)), -(hBOOL(hAPP(hAPP(hAPP(_1466275, _1466395), _1466277), _1466279)))]]], (36463 ^ _779448) ^ [_1466774] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1466774)), c_Int_OInteg)))], (36465 ^ _779448) ^ [_1466805, _1466807, _1466809, _1466811, _1466813, _1466815, _1466817] : [hAPP(c_Fun_Ocomp(_1466805, _1466807, _1466809, _1466811), _1466813) = _1466815, -(hAPP(_1466811, hAPP(_1466813, _1466817)) = hAPP(_1466815, _1466817))], (36471 ^ _779448) ^ [_1466926, _1466928, _1466930, _1466932, _1466934, _1466936] : [-(hAPP(hAPP(c_Fun_Ocomp(_1466926, _1466928, _1466930, hAPP(c_COMBK(_1466928, _1466926), _1466932)), _1466934), _1466936) = _1466932)], (36473 ^ _779448) ^ [_1466976, _1466978, _1466980, _1466982, _1466984, _1466986, _1466988, _1466990] : [c_Fun_Oinj__on(_1466976, _1466978, _1466980, _1466982), 36479 ^ _779448 : [(36480 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466984), 36478 ^ [_1466976, _1466978, _1466980, _1466982, _1466984, _1466986, _1466988, _1466990]), _1466986)))], (36482 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466976, tc_HOL_Obool)), hAPP(_1466988, 36478 ^ [_1466976, _1466978, _1466980, _1466982, _1466984, _1466986, _1466988, _1466990])), _1466982))]], hBOOL(hAPP(hAPP(c_member(_1466984), _1466990), _1466986)), -(hAPP(c_Set_Oimage(_1466976, _1466978, _1466980), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1466984, tc_fun(_1466976, tc_HOL_Obool)), _1466986), _1466988)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1466984, tc_fun(_1466978, tc_HOL_Obool)), _1466986), hAPP(hAPP(c_COMBB(tc_fun(_1466976, tc_HOL_Obool), tc_fun(_1466978, tc_HOL_Obool), _1466984), c_Set_Oimage(_1466976, _1466978, _1466980)), _1466988)))], (36490 ^ _779448) ^ [_1467480, _1467482] : [c_Equiv__Relations_Oequiv(_1467480, c_Orderings_Otop__class_Otop(tc_fun(_1467480, tc_HOL_Obool)), _1467482), -(c_Equiv__Relations_Oequivp(_1467480, hAPP(hAPP(c_COMBC(_1467480, tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_fun(_1467480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467480, tc_fun(tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_fun(_1467480, tc_HOL_Obool)), _1467480), c_COMBC(_1467480, tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467480, tc_prod(_1467480, _1467480)), tc_fun(_1467480, tc_fun(tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_HOL_Obool)), _1467480), hAPP(c_COMBB(tc_prod(_1467480, _1467480), tc_fun(tc_fun(tc_prod(_1467480, _1467480), tc_HOL_Obool), tc_HOL_Obool), _1467480), c_member(tc_prod(_1467480, _1467480)))), c_Product__Type_OPair(_1467480, _1467480)))), _1467482)))], (36496 ^ _779448) ^ [_1467801, _1467803] : [c_Equiv__Relations_Oequivp(_1467801, hAPP(hAPP(c_COMBC(_1467801, tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_fun(_1467801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467801, tc_fun(tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_fun(_1467801, tc_HOL_Obool)), _1467801), c_COMBC(_1467801, tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467801, tc_prod(_1467801, _1467801)), tc_fun(_1467801, tc_fun(tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_HOL_Obool)), _1467801), hAPP(c_COMBB(tc_prod(_1467801, _1467801), tc_fun(tc_fun(tc_prod(_1467801, _1467801), tc_HOL_Obool), tc_HOL_Obool), _1467801), c_member(tc_prod(_1467801, _1467801)))), c_Product__Type_OPair(_1467801, _1467801)))), _1467803)), -(c_Equiv__Relations_Oequiv(_1467801, c_Orderings_Otop__class_Otop(tc_fun(_1467801, tc_HOL_Obool)), _1467803))], (36502 ^ _779448) ^ [] : [-(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))], (36504 ^ _779448) ^ [_1468146, _1468148, _1468150, _1468152, _1468154] : [c_Equiv__Relations_Oequivp(_1468146, _1468148), hBOOL(hAPP(hAPP(_1468148, _1468150), _1468152)), hBOOL(hAPP(hAPP(_1468148, _1468152), _1468154)), -(hBOOL(hAPP(hAPP(_1468148, _1468150), _1468154)))], (36518 ^ _779448) ^ [_1468375, _1468377, _1468379, _1468381] : [c_Equiv__Relations_Oequivp(_1468375, _1468377), hBOOL(hAPP(hAPP(_1468377, _1468379), _1468381)), -(hBOOL(hAPP(hAPP(_1468377, _1468381), _1468379)))], (36528 ^ _779448) ^ [_1468532, _1468534, _1468536] : [c_Equiv__Relations_Oequivp(_1468532, _1468534), -(hBOOL(hAPP(hAPP(_1468534, _1468536), _1468536)))], (36550 ^ _779448) ^ [_1468934, _1468936] : [-(c_Equiv__Relations_Oequivp(_1468934, _1468936)), 36555 ^ _779448 : [(36556 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1468936, 36551 ^ [_1468934, _1468936]), 36552 ^ [_1468934, _1468936])))], (36558 ^ _779448) ^ [] : [hAPP(_1468936, 36551 ^ [_1468934, _1468936]) = hAPP(_1468936, 36552 ^ [_1468934, _1468936])]], 36559 ^ _779448 : [(36560 ^ _779448) ^ [] : [-(hAPP(_1468936, 36551 ^ [_1468934, _1468936]) = hAPP(_1468936, 36552 ^ [_1468934, _1468936]))], (36562 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1468936, 36551 ^ [_1468934, _1468936]), 36552 ^ [_1468934, _1468936]))]]], (36534 ^ _779448) ^ [_1468636, _1468638] : [c_Equiv__Relations_Oequivp(_1468636, _1468638), 36537 ^ _779448 : [(36538 ^ _779448) ^ [_1468730, _1468732] : [hBOOL(hAPP(hAPP(_1468638, _1468732), _1468730)), -(hAPP(_1468638, _1468732) = hAPP(_1468638, _1468730))], (36544 ^ _779448) ^ [_1468829, _1468831] : [hAPP(_1468638, _1468831) = hAPP(_1468638, _1468829), -(hBOOL(hAPP(hAPP(_1468638, _1468831), _1468829)))]]], (36566 ^ _779448) ^ [_1469263] : [-(c_Equiv__Relations_Oequivp(_1469263, c_fequal))], (36568 ^ _779448) ^ [_1469286, _1469288, _1469290, _1469292, _1469294] : [c_Typedef_Otype__definition(_1469286, _1469288, _1469290, _1469292, _1469294), -(hAPP(c_Set_Oimage(_1469288, _1469286, _1469292), _1469294) = c_Orderings_Otop__class_Otop(tc_fun(_1469286, tc_HOL_Obool)))], (36574 ^ _779448) ^ [_1469399, _1469401, _1469403, _1469405, _1469407] : [c_Typedef_Otype__definition(_1469399, _1469401, _1469403, _1469405, _1469407), -(hAPP(c_Set_Oimage(_1469399, _1469401, _1469403), c_Orderings_Otop__class_Otop(tc_fun(_1469399, tc_HOL_Obool))) = _1469407)], (36580 ^ _779448) ^ [_1469512, _1469514, _1469516, _1469518, _1469520, _1469522, _1469524] : [c_Typedef_Otype__definition(_1469512, _1469514, _1469516, _1469518, _1469520), hBOOL(hAPP(hAPP(c_member(_1469514), _1469522), _1469520)), hBOOL(hAPP(hAPP(c_member(_1469514), _1469524), _1469520)), 36591 ^ _779448 : [(36592 ^ _779448) ^ [] : [hAPP(_1469518, _1469522) = hAPP(_1469518, _1469524), -(_1469522 = _1469524)], (36598 ^ _779448) ^ [] : [_1469522 = _1469524, -(hAPP(_1469518, _1469522) = hAPP(_1469518, _1469524))]]], (36604 ^ _779448) ^ [_1469925, _1469927, _1469929, _1469931, _1469933, _1469935, _1469937] : [c_Typedef_Otype__definition(_1469925, _1469927, _1469929, _1469931, _1469933), 36607 ^ _779448 : [(36608 ^ _779448) ^ [] : [hAPP(_1469929, _1469935) = hAPP(_1469929, _1469937), -(_1469935 = _1469937)], (36614 ^ _779448) ^ [] : [_1469935 = _1469937, -(hAPP(_1469929, _1469935) = hAPP(_1469929, _1469937))]]], (36620 ^ _779448) ^ [_1470186, _1470188, _1470190, _1470192, _1470194, _1470196] : [c_Typedef_Otype__definition(_1470186, _1470188, _1470190, _1470192, _1470194), -(hAPP(_1470192, hAPP(_1470190, _1470196)) = _1470196)], (36626 ^ _779448) ^ [_1470289, _1470291, _1470293, _1470295, _1470297, _1470299] : [c_Typedef_Otype__definition(_1470289, _1470291, _1470293, _1470295, _1470297), -(hBOOL(hAPP(hAPP(c_member(_1470291), hAPP(_1470293, _1470299)), _1470297)))], (36632 ^ _779448) ^ [_1470400, _1470402, _1470404, _1470406, _1470408, _1470410] : [c_Typedef_Otype__definition(_1470400, _1470402, _1470404, _1470406, _1470408), hBOOL(hAPP(hAPP(c_member(_1470402), _1470410), _1470408)), -(hAPP(_1470404, hAPP(_1470406, _1470410)) = _1470410)], (36642 ^ _779448) ^ [_1470577, _1470579, _1470581, _1470583] : [c_Fun_Oinj__on(_1470577, _1470579, _1470581, c_Orderings_Otop__class_Otop(tc_fun(_1470577, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470577, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1470577, _1470579, _1470581), hAPP(hAPP(c_Set_Oinsert(_1470579), _1470583), c_Orderings_Obot__class_Obot(tc_fun(_1470579, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1470577), c_HOL_OThe(_1470577, hAPP(hAPP(c_COMBC(_1470577, _1470579, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1470579, tc_fun(_1470579, tc_HOL_Obool), _1470577), c_fequal), _1470581)), _1470583))), c_Orderings_Obot__class_Obot(tc_fun(_1470577, tc_HOL_Obool))))))], (36648 ^ _779448) ^ [_1470810, _1470812] : [class_Complete__Lattice_Ocomplete__lattice(_1470810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470810), _1470812)), -(c_Complete__Lattice_OInf__class_OInf(_1470810, _1470812) = hAPP(hAPP(c_Finite__Set_Ofold(_1470810, _1470810, c_Lattices_Osemilattice__inf__class_Oinf(_1470810)), c_Orderings_Otop__class_Otop(_1470810)), _1470812))], (36658 ^ _779448) ^ [_1471000, _1471002, _1471004, _1471006] : [c_Wellfounded_Omax__extp(_1471000, _1471002, _1471004, _1471006), 36661 ^ _779448 : [(36662 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1471000), _1471004)))], (36664 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1471000), _1471006)))], (36666 ^ _779448) ^ [] : [_1471006 = c_Orderings_Obot__class_Obot(tc_fun(_1471000, tc_HOL_Obool))], (36668 ^ _779448) ^ [_1471216] : [hBOOL(hAPP(hAPP(c_member(_1471000), _1471216), _1471004)), 36672 ^ _779448 : [(36673 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471000), 36671 ^ [_1471000, _1471002, _1471004, _1471006, _1471216]), _1471006)))], (36675 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1471002, _1471216), 36671 ^ [_1471000, _1471002, _1471004, _1471006, _1471216])))]]]]], (36677 ^ _779448) ^ [_1471400, _1471402, _1471404, _1471406] : [-(c_Wellfounded_Omax__extp(_1471400, _1471402, _1471404, _1471406)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471400), _1471404)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471400), _1471406)), -(_1471406 = c_Orderings_Obot__class_Obot(tc_fun(_1471400, tc_HOL_Obool))), 36691 ^ _779448 : [(36692 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471400), 36690 ^ [_1471400, _1471402, _1471404, _1471406]), _1471404)))], (36694 ^ _779448) ^ [_1471745] : [hBOOL(hAPP(hAPP(c_member(_1471400), _1471745), _1471406)), hBOOL(hAPP(hAPP(_1471402, 36690 ^ [_1471400, _1471402, _1471404, _1471406]), _1471745))]]], (36702 ^ _779448) ^ [_1471913, _1471915] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1471913), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1471913, tc_HOL_Obool), _1471915)))), 36703 ^ _779448 : [(36704 ^ _779448) ^ [_1471977] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1471913, tc_HOL_Obool)), _1471977), _1471915)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471913), _1471977))]]], (36712 ^ _779448) ^ [_1472121, _1472123, _1472125, _1472127] : [hBOOL(hAPP(hAPP(c_member(_1472121), _1472123), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1472121, tc_HOL_Obool), _1472125))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1472121, tc_HOL_Obool)), _1472127), _1472125)), -(hBOOL(hAPP(hAPP(c_member(_1472121), _1472123), _1472127)))], (36722 ^ _779448) ^ [_1472318, _1472320, _1472322, _1472324] : [hBOOL(hAPP(hAPP(c_member(_1472318), _1472320), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1472318, tc_HOL_Obool), _1472322))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1472318, tc_HOL_Obool)), _1472324), _1472322)), -(hBOOL(hAPP(hAPP(c_member(_1472318), _1472320), _1472324)))], (36732 ^ _779448) ^ [_1472515, _1472517, _1472519, _1472521, _1472523, _1472525] : [hAPP(_1472515, _1472517) = _1472519, hBOOL(hAPP(hAPP(c_member(_1472521), _1472519), _1472523)), -(hBOOL(hAPP(hAPP(c_member(_1472525), _1472517), hAPP(c_Set_Ovimage(_1472525, _1472521, _1472515), _1472523))))], (36742 ^ _779448) ^ [_1472708, _1472710, _1472712] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472708, tc_HOL_Obool)), _1472710), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1472708, tc_HOL_Obool), _1472712)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1472708, tc_HOL_Obool), tc_fun(_1472708, tc_HOL_Obool)), _1472712), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472708, tc_HOL_Obool)), _1472710)))], (36744 ^ _779448) ^ [_1472775, _1472777, _1472779, _1472781, _1472783, _1472785] : [-(hAPP(c_Set_Ovimage(_1472775, _1472777, _1472779), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1472781, tc_fun(_1472777, tc_HOL_Obool)), _1472783), _1472785)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1472781, tc_fun(_1472775, tc_HOL_Obool)), _1472783), hAPP(hAPP(c_COMBB(tc_fun(_1472777, tc_HOL_Obool), tc_fun(_1472775, tc_HOL_Obool), _1472781), c_Set_Ovimage(_1472775, _1472777, _1472779)), _1472785)))], (36746 ^ _779448) ^ [_1472859, _1472861, _1472863, _1472865, _1472867] : [-(hAPP(c_Set_Ovimage(_1472859, _1472861, _1472863), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472861, tc_HOL_Obool)), _1472865), _1472867)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1472859, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1472859, _1472861, _1472863), _1472865)), hAPP(c_Set_Ovimage(_1472859, _1472861, _1472863), _1472867)))], (36748 ^ _779448) ^ [_1472933, _1472935, _1472937] : [class_Complete__Lattice_Ocomplete__lattice(_1472933), 36751 ^ _779448 : [(36762 ^ _779448) ^ [] : [36764 ^ _779448 : [(36765 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472933), 36763 ^ [_1472933, _1472935, _1472937]), _1472937)))], (36767 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472933), _1472935), 36763 ^ [_1472933, _1472935, _1472937]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472933), _1472935), c_Complete__Lattice_OInf__class_OInf(_1472933, _1472937))))], (36752 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472933), _1472935), c_Complete__Lattice_OInf__class_OInf(_1472933, _1472937))), 36755 ^ _779448 : [(36756 ^ _779448) ^ [_1473091] : [hBOOL(hAPP(hAPP(c_member(_1472933), _1473091), _1472937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1472933), _1472935), _1473091)))]]]]], (36771 ^ _779448) ^ [_1473367, _1473369, _1473371] : [class_Complete__Lattice_Ocomplete__lattice(_1473367), class_Orderings_Olinorder(_1473367), 36778 ^ _779448 : [(36779 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473367), c_Complete__Lattice_OInf__class_OInf(_1473367, _1473369)), _1473371)), 36783 ^ _779448 : [(36784 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473367), 36782 ^ [_1473367, _1473369, _1473371]), _1473369)))], (36786 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473367), 36782 ^ [_1473367, _1473369, _1473371]), _1473371)))]]], (36788 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473367), c_Complete__Lattice_OInf__class_OInf(_1473367, _1473369)), _1473371))), 36789 ^ _779448 : [(36790 ^ _779448) ^ [_1473673] : [hBOOL(hAPP(hAPP(c_member(_1473367), _1473673), _1473369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1473367), _1473673), _1473371))]]]]], (36798 ^ _779448) ^ [_1473827, _1473829, _1473831, _1473833, _1473835] : [-(hAPP(c_Set_Ovimage(_1473827, _1473829, _1473831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473829, tc_HOL_Obool)), _1473833), _1473835)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473827, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473827, _1473829, _1473831), _1473833)), hAPP(c_Set_Ovimage(_1473827, _1473829, _1473831), _1473835)))], (36800 ^ _779448) ^ [_1473901, _1473903, _1473905] : [-(hAPP(c_Set_Ovimage(_1473901, _1473903, _1473905), c_Orderings_Obot__class_Obot(tc_fun(_1473903, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1473901, tc_HOL_Obool)))], (36802 ^ _779448) ^ [_1473945, _1473947, _1473949, _1473951, _1473953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473945, tc_HOL_Obool)), _1473947), _1473949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1473951, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1473951, _1473945, _1473953), _1473947)), hAPP(c_Set_Ovimage(_1473951, _1473945, _1473953), _1473949))))], (36808 ^ _779448) ^ [_1474096, _1474098, _1474100, _1474102, _1474104, _1474106] : [-(hAPP(c_Set_Ovimage(_1474096, _1474098, hAPP(c_Fun_Ocomp(_1474100, _1474098, _1474096, _1474102), _1474104)), _1474106) = hAPP(c_Set_Ovimage(_1474096, _1474100, _1474104), hAPP(c_Set_Ovimage(_1474100, _1474098, _1474102), _1474106)))], (36810 ^ _779448) ^ [_1474158, _1474160] : [-(hAPP(c_Set_Ovimage(_1474158, _1474158, c_COMBI(_1474158)), _1474160) = _1474160)], (36812 ^ _779448) ^ [_1474216, _1474218, _1474220, _1474222, _1474224] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1474216, _1474218, _1474220), _1474222), _1474224)), -(hBOOL(hAPP(_1474222, hAPP(_1474220, _1474224))))], (36818 ^ _779448) ^ [_1474323, _1474325, _1474327, _1474329, _1474331] : [hBOOL(hAPP(_1474329, hAPP(_1474327, _1474331))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1474323, _1474325, _1474327), _1474329), _1474331)))], (36824 ^ _779448) ^ [_1474436, _1474438, _1474440, _1474442] : [-(hAPP(c_Set_Ovimage(_1474436, _1474438, _1474440), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1474438, tc_HOL_Obool)), _1474442)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1474436, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1474436, _1474438, _1474440), _1474442)))], (36826 ^ _779448) ^ [_1474495, _1474497, _1474499, _1474501, _1474503] : [-(hAPP(c_Set_Ovimage(_1474495, _1474497, _1474499), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474497, tc_HOL_Obool)), _1474501), _1474503)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1474495, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1474495, _1474497, _1474499), _1474501)), hAPP(c_Set_Ovimage(_1474495, _1474497, _1474499), _1474503)))], (36828 ^ _779448) ^ [_1474569, _1474571, _1474573, _1474575, _1474577, _1474579] : [-(hAPP(c_Set_Ovimage(_1474569, _1474571, _1474573), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474575, tc_fun(_1474571, tc_HOL_Obool)), _1474577), _1474579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474575, tc_fun(_1474569, tc_HOL_Obool)), _1474577), hAPP(hAPP(c_COMBB(tc_fun(_1474571, tc_HOL_Obool), tc_fun(_1474569, tc_HOL_Obool), _1474575), c_Set_Ovimage(_1474569, _1474571, _1474573)), _1474579)))], (36830 ^ _779448) ^ [_1474653, _1474655, _1474657] : [-(hAPP(c_Set_Ovimage(_1474653, _1474655, _1474657), c_Orderings_Otop__class_Otop(tc_fun(_1474655, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1474653, tc_HOL_Obool)))], (36832 ^ _779448) ^ [_1474721, _1474723, _1474725, _1474727, _1474729] : [hBOOL(hAPP(hAPP(c_member(_1474721), _1474723), hAPP(c_Set_Ovimage(_1474721, _1474725, _1474727), _1474729))), -(hBOOL(hAPP(hAPP(c_member(_1474725), hAPP(_1474727, _1474723)), _1474729)))], (36838 ^ _779448) ^ [_1474848, _1474850, _1474852, _1474854, _1474856] : [hBOOL(hAPP(hAPP(c_member(_1474852), hAPP(_1474854, _1474850)), _1474856)), -(hBOOL(hAPP(hAPP(c_member(_1474848), _1474850), hAPP(c_Set_Ovimage(_1474848, _1474852, _1474854), _1474856))))], (36844 ^ _779448) ^ [_1474981, _1474983, _1474985, _1474987, _1474989] : [hBOOL(hAPP(hAPP(c_member(_1474981), _1474983), hAPP(c_Set_Ovimage(_1474981, _1474985, _1474987), _1474989))), -(hBOOL(hAPP(hAPP(c_member(_1474985), hAPP(_1474987, _1474983)), _1474989)))], (36850 ^ _779448) ^ [_1475112, _1475114, _1475116, _1475118, _1475120] : [hBOOL(hAPP(hAPP(c_member(_1475112), hAPP(_1475114, _1475116)), _1475118)), -(hBOOL(hAPP(hAPP(c_member(_1475120), _1475116), hAPP(c_Set_Ovimage(_1475120, _1475112, _1475114), _1475118))))], (36856 ^ _779448) ^ [_1475243, _1475245, _1475247, _1475249] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475243, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1475245, _1475243, _1475247), hAPP(c_Set_Ovimage(_1475245, _1475243, _1475247), _1475249))), _1475249)))], (36858 ^ _779448) ^ [_1475296, _1475298, _1475300, _1475302] : [hAPP(c_Set_Oimage(_1475296, _1475298, _1475300), c_Orderings_Otop__class_Otop(tc_fun(_1475296, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1475298, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1475296, _1475298, _1475300), hAPP(c_Set_Ovimage(_1475296, _1475298, _1475300), _1475302)) = _1475302)], (36864 ^ _779448) ^ [_1475439, _1475441, _1475443] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1475439, tc_HOL_Obool)), _1475441), _1475443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475439, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475439, tc_HOL_Obool), _1475443)), _1475441)))], (36870 ^ _779448) ^ [_1475570, _1475572, _1475574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1475570, tc_HOL_Obool), tc_HOL_Obool)), _1475572), _1475574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1475570, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475570, tc_HOL_Obool), _1475574)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475570, tc_HOL_Obool), _1475572))))], (36876 ^ _779448) ^ [_1475719] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475719, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1475719, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1475719, tc_HOL_Obool)))], (36878 ^ _779448) ^ [_1475761, _1475763, _1475765] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475761, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1475761, tc_HOL_Obool)), _1475763), _1475765)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475761, tc_HOL_Obool)), _1475763), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475761, tc_HOL_Obool), _1475765)))], (36880 ^ _779448) ^ [_1475822] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1475822, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1475822, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1475822, tc_HOL_Obool)))], (36882 ^ _779448) ^ [_1475864, _1475866, _1475868] : [class_Complete__Lattice_Ocomplete__lattice(_1475864), hBOOL(hAPP(hAPP(c_member(_1475864), _1475866), _1475868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1475864), c_Complete__Lattice_OInf__class_OInf(_1475864, _1475868)), _1475866)))], (36892 ^ _779448) ^ [_1476029, _1476031, _1476033] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1476029, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1476029, tc_HOL_Obool), tc_HOL_Obool)), _1476031), _1476033)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476029, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1476029, tc_HOL_Obool), _1476031)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1476029, tc_HOL_Obool), _1476033)))], (36894 ^ _779448) ^ [_1476123, _1476125, _1476127, _1476129, _1476131] : [hBOOL(hAPP(hAPP(c_member(_1476123), _1476125), hAPP(c_Set_Ovimage(_1476123, _1476127, _1476129), hAPP(hAPP(c_Set_Oinsert(_1476127), _1476131), c_Orderings_Obot__class_Obot(tc_fun(_1476127, tc_HOL_Obool)))))), -(hAPP(_1476129, _1476125) = _1476131)], (36900 ^ _779448) ^ [_1476262, _1476264, _1476266, _1476268, _1476270] : [hAPP(_1476268, _1476264) = _1476270, -(hBOOL(hAPP(hAPP(c_member(_1476262), _1476264), hAPP(c_Set_Ovimage(_1476262, _1476266, _1476268), hAPP(hAPP(c_Set_Oinsert(_1476266), _1476270), c_Orderings_Obot__class_Obot(tc_fun(_1476266, tc_HOL_Obool)))))))], (36906 ^ _779448) ^ [_1476407, _1476409] : [class_Complete__Lattice_Ocomplete__lattice(_1476407), -(c_Complete__Lattice_OInf__class_OInf(_1476407, hAPP(hAPP(c_Set_Oinsert(_1476407), _1476409), c_Orderings_Obot__class_Obot(tc_fun(_1476407, tc_HOL_Obool)))) = _1476409)], (36912 ^ _779448) ^ [_1476514] : [class_Complete__Lattice_Ocomplete__lattice(_1476514), -(c_Complete__Lattice_OInf__class_OInf(_1476514, c_Orderings_Obot__class_Obot(tc_fun(_1476514, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1476514))], (36918 ^ _779448) ^ [_1476607] : [class_Complete__Lattice_Ocomplete__lattice(_1476607), -(c_Complete__Lattice_OInf__class_OInf(_1476607, c_Orderings_Otop__class_Otop(tc_fun(_1476607, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1476607))], (36924 ^ _779448) ^ [_1476700, _1476702, _1476704] : [class_Complete__Lattice_Ocomplete__lattice(_1476700), -(c_Complete__Lattice_OInf__class_OInf(_1476700, hAPP(hAPP(c_Set_Oinsert(_1476700), _1476702), _1476704)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1476700), _1476702), c_Complete__Lattice_OInf__class_OInf(_1476700, _1476704)))], (36930 ^ _779448) ^ [_1476821, _1476823, _1476825, _1476827, _1476829] : [-(hAPP(c_Set_Ovimage(_1476821, _1476823, _1476825), hAPP(hAPP(c_Set_Oinsert(_1476823), _1476827), _1476829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476821, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1476821, _1476823, _1476825), hAPP(hAPP(c_Set_Oinsert(_1476823), _1476827), c_Orderings_Obot__class_Obot(tc_fun(_1476823, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1476821, _1476823, _1476825), _1476829)))], (36932 ^ _779448) ^ [_1476905, _1476907, _1476909, _1476911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476905), hAPP(c_Set_Ovimage(_1476905, _1476907, _1476909), _1476911))), hAPP(c_Set_Oimage(_1476905, _1476907, _1476909), c_Orderings_Otop__class_Otop(tc_fun(_1476905, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1476907, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476907), _1476911)))], (36942 ^ _779448) ^ [_1477106, _1477108, _1477110, _1477112] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1477106, tc_HOL_Obool), hAPP(c_Set_Oimage(_1477108, tc_fun(_1477106, tc_HOL_Obool), _1477110), _1477112)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477108, tc_fun(_1477106, tc_HOL_Obool)), _1477112), _1477110))], (36944 ^ _779448) ^ [_1477163, _1477165, _1477167, _1477169] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477163, tc_fun(_1477165, tc_HOL_Obool)), _1477167), _1477169) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1477165, tc_HOL_Obool), hAPP(c_Set_Oimage(_1477163, tc_fun(_1477165, tc_HOL_Obool), _1477169), _1477167)))], (36946 ^ _779448) ^ [_1477220, _1477222, _1477224, _1477226, _1477228] : [hAPP(c_Set_Oimage(_1477220, _1477222, _1477224), c_Orderings_Otop__class_Otop(tc_fun(_1477220, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1477222, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477220, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1477220, _1477222, _1477224), _1477226)), _1477228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477222, tc_HOL_Obool)), _1477226), hAPP(c_Set_Oimage(_1477220, _1477222, _1477224), _1477228))))], (36956 ^ _779448) ^ [_1477463, _1477465, _1477467, _1477469] : [-(hAPP(c_Set_Oimage(_1477463, _1477465, _1477467), hAPP(c_Set_Ovimage(_1477463, _1477465, _1477467), _1477469)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1477465, tc_HOL_Obool)), _1477469), hAPP(c_Set_Oimage(_1477463, _1477465, _1477467), c_Orderings_Otop__class_Otop(tc_fun(_1477463, tc_HOL_Obool)))))], (36958 ^ _779448) ^ [_1477529, _1477531, _1477533, _1477535] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477529), _1477531)), c_Fun_Oinj__on(_1477533, _1477529, _1477535, c_Orderings_Otop__class_Otop(tc_fun(_1477533, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1477533), hAPP(c_Set_Ovimage(_1477533, _1477529, _1477535), _1477531))))], (36968 ^ _779448) ^ [_1477710, _1477712, _1477714, _1477716] : [c_Fun_Oinj__on(_1477710, _1477712, _1477714, c_Orderings_Otop__class_Otop(tc_fun(_1477710, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1477710, _1477712, _1477714), hAPP(c_Set_Oimage(_1477710, _1477712, _1477714), _1477716)) = _1477716)], (36974 ^ _779448) ^ [_1477848, _1477850, _1477852, _1477854] : [hBOOL(hAPP(hAPP(c_member(_1477848), _1477850), _1477852)), -(hAPP(c_Set_Ovimage(_1477854, _1477848, hAPP(c_COMBK(_1477848, _1477854), _1477850)), _1477852) = c_Orderings_Otop__class_Otop(tc_fun(_1477854, tc_HOL_Obool)))], (36980 ^ _779448) ^ [_1477973, _1477975, _1477977, _1477979] : [-(hBOOL(hAPP(hAPP(c_member(_1477973), _1477975), _1477977))), -(hAPP(c_Set_Ovimage(_1477979, _1477973, hAPP(c_COMBK(_1477973, _1477979), _1477975)), _1477977) = c_Orderings_Obot__class_Obot(tc_fun(_1477979, tc_HOL_Obool)))], (36986 ^ _779448) ^ [_1478040, _1478042, _1478044, _1478046] : [-(hAPP(c_Set_Ovimage(_1478040, _1478042, _1478044), _1478046) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478042, tc_fun(_1478040, tc_HOL_Obool)), _1478046), hAPP(hAPP(c_COMBB(tc_fun(_1478042, tc_HOL_Obool), tc_fun(_1478040, tc_HOL_Obool), _1478042), c_Set_Ovimage(_1478040, _1478042, _1478044)), hAPP(hAPP(c_COMBC(_1478042, tc_fun(_1478042, tc_HOL_Obool), tc_fun(_1478042, tc_HOL_Obool)), c_Set_Oinsert(_1478042)), c_Orderings_Obot__class_Obot(tc_fun(_1478042, tc_HOL_Obool))))))], (36988 ^ _779448) ^ [_1478131, _1478133, _1478135] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478131, tc_HOL_Obool)), _1478133), _1478135) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478131, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1478131, tc_HOL_Obool)), _1478133), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1478131, tc_HOL_Obool)), _1478135), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1478131, tc_HOL_Obool), tc_HOL_Obool))))))], (36990 ^ _779448) ^ [_1478205, _1478207, _1478209, _1478211, _1478213] : [c_Fun_Oinj__on(_1478205, _1478207, _1478209, c_Orderings_Otop__class_Otop(tc_fun(_1478205, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478207, tc_HOL_Obool)), _1478211), hAPP(c_Set_Oimage(_1478205, _1478207, _1478209), _1478213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478205, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1478205, _1478207, _1478209), _1478211)), _1478213)))], (37000 ^ _779448) ^ [_1478428, _1478430, _1478432, _1478434, _1478436] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1478428, tc_fun(_1478430, tc_HOL_Obool)), _1478432), hAPP(hAPP(c_COMBS(_1478428, tc_fun(_1478430, tc_HOL_Obool), tc_fun(_1478430, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478430, tc_HOL_Obool), tc_fun(tc_fun(_1478430, tc_HOL_Obool), tc_fun(_1478430, tc_HOL_Obool)), _1478428), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478430, tc_HOL_Obool))), _1478434)), _1478436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478430, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478430, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478428, tc_fun(_1478430, tc_HOL_Obool), _1478434), _1478432))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478430, tc_HOL_Obool), hAPP(c_Set_Oimage(_1478428, tc_fun(_1478430, tc_HOL_Obool), _1478436), _1478432))))], (37002 ^ _779448) ^ [_1478557, _1478559, _1478561] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1478557, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478557, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478557, tc_HOL_Obool), _1478559)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478557, tc_HOL_Obool), _1478561))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478557, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1478557, tc_HOL_Obool), tc_HOL_Obool)), _1478559), _1478561)))))], (37004 ^ _779448) ^ [_1478637, _1478639, _1478641] : [class_Complete__Lattice_Ocomplete__lattice(_1478637), -(c_Complete__Lattice_OInf__class_OInf(_1478637, hAPP(hAPP(c_Set_Oinsert(_1478637), _1478639), hAPP(hAPP(c_Set_Oinsert(_1478637), _1478641), c_Orderings_Obot__class_Obot(tc_fun(_1478637, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1478637), _1478639), _1478641))], (37010 ^ _779448) ^ [_1478799, _1478801, _1478803, _1478805, _1478807, _1478809] : [hBOOL(hAPP(hAPP(c_member(_1478799), _1478801), _1478803)), 37013 ^ _779448 : [(37014 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1478799), _1478805), _1478803)), -(hAPP(c_Set_Ovimage(_1478807, _1478799, hAPP(hAPP(c_COMBC(_1478807, _1478799, _1478799), hAPP(hAPP(c_COMBC(_1478807, _1478799, tc_fun(_1478799, _1478799)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1478799, tc_fun(_1478799, _1478799)), _1478807), c_If(_1478799)), hAPP(hAPP(c_COMBC(_1478807, tc_fun(_1478807, tc_HOL_Obool), tc_HOL_Obool), c_member(_1478807)), _1478809))), _1478801)), _1478805)), _1478803) = c_Orderings_Otop__class_Otop(tc_fun(_1478807, tc_HOL_Obool)))], (37020 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478799), _1478805), _1478803))), -(hAPP(c_Set_Ovimage(_1478807, _1478799, hAPP(hAPP(c_COMBC(_1478807, _1478799, _1478799), hAPP(hAPP(c_COMBC(_1478807, _1478799, tc_fun(_1478799, _1478799)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1478799, tc_fun(_1478799, _1478799)), _1478807), c_If(_1478799)), hAPP(hAPP(c_COMBC(_1478807, tc_fun(_1478807, tc_HOL_Obool), tc_HOL_Obool), c_member(_1478807)), _1478809))), _1478801)), _1478805)), _1478803) = _1478809)]]], (37026 ^ _779448) ^ [_1479290, _1479292, _1479294, _1479296, _1479298, _1479300] : [-(hBOOL(hAPP(hAPP(c_member(_1479290), _1479292), _1479294))), 37029 ^ _779448 : [(37030 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1479290), _1479296), _1479294)), -(hAPP(c_Set_Ovimage(_1479298, _1479290, hAPP(hAPP(c_COMBC(_1479298, _1479290, _1479290), hAPP(hAPP(c_COMBC(_1479298, _1479290, tc_fun(_1479290, _1479290)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1479290, tc_fun(_1479290, _1479290)), _1479298), c_If(_1479290)), hAPP(hAPP(c_COMBC(_1479298, tc_fun(_1479298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479298)), _1479300))), _1479292)), _1479296)), _1479294) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1479298, tc_HOL_Obool)), _1479300))], (37036 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1479290), _1479296), _1479294))), -(hAPP(c_Set_Ovimage(_1479298, _1479290, hAPP(hAPP(c_COMBC(_1479298, _1479290, _1479290), hAPP(hAPP(c_COMBC(_1479298, _1479290, tc_fun(_1479290, _1479290)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1479290, tc_fun(_1479290, _1479290)), _1479298), c_If(_1479290)), hAPP(hAPP(c_COMBC(_1479298, tc_fun(_1479298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479298)), _1479300))), _1479292)), _1479296)), _1479294) = c_Orderings_Obot__class_Obot(tc_fun(_1479298, tc_HOL_Obool)))]]], (37042 ^ _779448) ^ [_1479795, _1479797, _1479799] : [class_Complete__Lattice_Ocomplete__lattice(_1479795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479795), _1479797)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1479795), _1479799), c_Complete__Lattice_OInf__class_OInf(_1479795, _1479797)) = hAPP(hAPP(c_Finite__Set_Ofold(_1479795, _1479795, c_Lattices_Osemilattice__inf__class_Oinf(_1479795)), _1479799), _1479797))], (37052 ^ _779448) ^ [_1479980, _1479982] : [class_Complete__Lattice_Ocomplete__lattice(_1479980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1479980), _1479982)), -(_1479982 = c_Orderings_Obot__class_Obot(tc_fun(_1479980, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1479980, _1479982) = c_Complete__Lattice_OInf__class_OInf(_1479980, _1479982))], (37066 ^ _779448) ^ [_1480152, _1480154] : [class_Complete__Lattice_Ocomplete__lattice(_1480152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480152), _1480154)), -(c_Complete__Lattice_OSup__class_OSup(_1480152, _1480154) = hAPP(hAPP(c_Finite__Set_Ofold(_1480152, _1480152, c_Lattices_Osemilattice__sup__class_Osup(_1480152)), c_Orderings_Obot__class_Obot(_1480152)), _1480154))], (37076 ^ _779448) ^ [_1480321, _1480323, _1480325, _1480327] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1480321), _1480323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1480321), _1480325)), -(_1480325 = c_Orderings_Obot__class_Obot(tc_fun(_1480321, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480321, tc_HOL_Obool), tc_fun(_1480321, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480321, tc_HOL_Obool), tc_fun(_1480321, tc_HOL_Obool)), _1480323), _1480325)), c_Wellfounded_Omax__ext(_1480321, _1480327)))), 37090 ^ _779448 : [(37091 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480321), 37089 ^ [_1480321, _1480323, _1480325, _1480327]), _1480323)))], (37093 ^ _779448) ^ [_1480726] : [hBOOL(hAPP(hAPP(c_member(_1480321), _1480726), _1480325)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1480321, _1480321)), hAPP(hAPP(c_Product__Type_OPair(_1480321, _1480321), 37089 ^ [_1480321, _1480323, _1480325, _1480327]), _1480726)), _1480327))]]], (37101 ^ _779448) ^ [_1480952] : [-(c_Nitpick_Ozero__frac(_1480952) = c_Nitpick_OAbs__Frac(_1480952, 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))))], (37103 ^ _779448) ^ [_1480980, _1480982, _1480984, _1480986] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1480980, tc_HOL_Obool)), _1480982), _1480984)), hBOOL(hAPP(hAPP(c_member(_1480980), _1480986), _1480982)), -(hBOOL(hAPP(hAPP(c_member(_1480980), _1480986), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1480980, tc_HOL_Obool), _1480984))))], (37113 ^ _779448) ^ [_1481177, _1481179] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1481177, tc_HOL_Obool), _1481179) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1481177, tc_HOL_Obool), tc_fun(_1481177, tc_HOL_Obool)), _1481179), c_COMBI(tc_fun(_1481177, tc_HOL_Obool))))], (37115 ^ _779448) ^ [_1481228, _1481230, _1481232, _1481234] : [-(hAPP(c_Set_Ovimage(_1481228, _1481230, _1481232), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481230, tc_HOL_Obool), _1481234)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481230, tc_HOL_Obool), tc_fun(_1481228, tc_HOL_Obool)), _1481234), c_Set_Ovimage(_1481228, _1481230, _1481232)))], (37117 ^ _779448) ^ [_1481289, _1481291, _1481293, _1481295] : [-(hAPP(c_Set_Oimage(_1481289, _1481291, _1481293), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481289, tc_HOL_Obool), _1481295)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481289, tc_HOL_Obool), tc_fun(_1481291, tc_HOL_Obool)), _1481295), c_Set_Oimage(_1481289, _1481291, _1481293)))], (37119 ^ _779448) ^ [_1481350, _1481352, _1481354, _1481356] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481350, tc_HOL_Obool), tc_fun(_1481352, tc_HOL_Obool)), _1481354), hAPP(hAPP(c_COMBC(tc_fun(_1481350, tc_HOL_Obool), tc_fun(_1481350, tc_fun(_1481352, tc_HOL_Obool)), tc_fun(_1481352, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481350, tc_fun(_1481352, tc_HOL_Obool))), _1481356)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481350, tc_fun(_1481352, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481350, tc_HOL_Obool), _1481354)), _1481356))], (37121 ^ _779448) ^ [_1481440, _1481442, _1481444, _1481446] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481440, tc_fun(_1481442, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481440, tc_HOL_Obool), _1481444)), _1481446) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481440, tc_HOL_Obool), tc_fun(_1481442, tc_HOL_Obool)), _1481444), hAPP(hAPP(c_COMBC(tc_fun(_1481440, tc_HOL_Obool), tc_fun(_1481440, tc_fun(_1481442, tc_HOL_Obool)), tc_fun(_1481442, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481440, tc_fun(_1481442, tc_HOL_Obool))), _1481446)))], (37123 ^ _779448) ^ [_1481530, _1481532, _1481534] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481530, tc_HOL_Obool)), _1481532), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481530, tc_HOL_Obool), _1481534)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481530, tc_HOL_Obool), tc_fun(_1481530, tc_HOL_Obool)), _1481534), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481530, tc_HOL_Obool)), _1481532)))], (37125 ^ _779448) ^ [_1481597, _1481599, _1481601] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481597, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481597, tc_HOL_Obool), _1481599)), _1481601) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1481597, tc_HOL_Obool), tc_fun(_1481597, tc_HOL_Obool)), _1481599), hAPP(hAPP(c_COMBC(tc_fun(_1481597, tc_HOL_Obool), tc_fun(_1481597, tc_HOL_Obool), tc_fun(_1481597, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481597, tc_HOL_Obool))), _1481601)))], (37127 ^ _779448) ^ [_1481680, _1481682] : [-(hAPP(c_Relation_OField(_1481680), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1481680, _1481680), tc_HOL_Obool), _1481682)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481680, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1481680, _1481680), tc_HOL_Obool), tc_fun(_1481680, tc_HOL_Obool), c_Relation_OField(_1481680)), _1481682)))], (37129 ^ _779448) ^ [_1481743, _1481745] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1481743, tc_HOL_Obool), hAPP(c_Set_OPow(_1481743), _1481745)) = _1481745)], (37131 ^ _779448) ^ [_1481779, _1481781, _1481783] : [class_Complete__Lattice_Ocomplete__lattice(_1481779), class_Orderings_Olinorder(_1481779), 37138 ^ _779448 : [(37139 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1481779), _1481781), c_Complete__Lattice_OSup__class_OSup(_1481779, _1481783))), 37143 ^ _779448 : [(37144 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481779), 37142 ^ [_1481779, _1481781, _1481783]), _1481783)))], (37146 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1481779), _1481781), 37142 ^ [_1481779, _1481781, _1481783])))]]], (37148 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1481779), _1481781), c_Complete__Lattice_OSup__class_OSup(_1481779, _1481783)))), 37149 ^ _779448 : [(37150 ^ _779448) ^ [_1482085] : [hBOOL(hAPP(hAPP(c_member(_1481779), _1482085), _1481783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1481779), _1481781), _1482085))]]]]], (37158 ^ _779448) ^ [_1482239, _1482241, _1482243] : [class_Complete__Lattice_Ocomplete__lattice(_1482239), 37161 ^ _779448 : [(37172 ^ _779448) ^ [] : [37174 ^ _779448 : [(37175 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482239), 37173 ^ [_1482239, _1482241, _1482243]), _1482241)))], (37177 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482239), 37173 ^ [_1482239, _1482241, _1482243]), _1482243))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482239), c_Complete__Lattice_OSup__class_OSup(_1482239, _1482241)), _1482243)))], (37162 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482239), c_Complete__Lattice_OSup__class_OSup(_1482239, _1482241)), _1482243)), 37165 ^ _779448 : [(37166 ^ _779448) ^ [_1482397] : [hBOOL(hAPP(hAPP(c_member(_1482239), _1482397), _1482241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482239), _1482397), _1482243)))]]]]], (37181 ^ _779448) ^ [_1482673, _1482675, _1482677, _1482679] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482673, tc_fun(_1482675, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482673, tc_HOL_Obool), _1482677)), _1482679) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1482673, tc_HOL_Obool), tc_fun(_1482675, tc_HOL_Obool)), _1482677), hAPP(hAPP(c_COMBC(tc_fun(_1482673, tc_HOL_Obool), tc_fun(_1482673, tc_fun(_1482675, tc_HOL_Obool)), tc_fun(_1482675, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482673, tc_fun(_1482675, tc_HOL_Obool))), _1482679)))], (37183 ^ _779448) ^ [_1482763, _1482765, _1482767, _1482769] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1482763, tc_HOL_Obool), tc_fun(_1482765, tc_HOL_Obool)), _1482767), hAPP(hAPP(c_COMBC(tc_fun(_1482763, tc_HOL_Obool), tc_fun(_1482763, tc_fun(_1482765, tc_HOL_Obool)), tc_fun(_1482765, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482763, tc_fun(_1482765, tc_HOL_Obool))), _1482769)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1482763, tc_fun(_1482765, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482763, tc_HOL_Obool), _1482767)), _1482769))], (37195 ^ _779448) ^ [_1483139, _1483141, _1483143] : [37197 ^ _779448 : [(37198 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1483139, tc_HOL_Obool)), 37196 ^ [_1483139, _1483141, _1483143]), _1483141)))], (37200 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483139, tc_HOL_Obool)), 37196 ^ [_1483139, _1483141, _1483143]), _1483143) = c_Orderings_Obot__class_Obot(tc_fun(_1483139, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483139, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483139, tc_HOL_Obool), _1483141)), _1483143) = c_Orderings_Obot__class_Obot(tc_fun(_1483139, tc_HOL_Obool)))], (37185 ^ _779448) ^ [_1482871, _1482873, _1482875] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482871, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482871, tc_HOL_Obool), _1482873)), _1482875) = c_Orderings_Obot__class_Obot(tc_fun(_1482871, tc_HOL_Obool)), 37188 ^ _779448 : [(37189 ^ _779448) ^ [_1483006] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1482871, tc_HOL_Obool)), _1483006), _1482873)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482871, tc_HOL_Obool)), _1483006), _1482875) = c_Orderings_Obot__class_Obot(tc_fun(_1482871, tc_HOL_Obool)))]]], (37204 ^ _779448) ^ [_1483402, _1483404, _1483406] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1483402, tc_HOL_Obool)), _1483404), _1483406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483402, tc_HOL_Obool)), _1483404), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483402, tc_HOL_Obool), _1483406))))], (37210 ^ _779448) ^ [_1483533] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483533, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1483533, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1483533, tc_HOL_Obool)))], (37212 ^ _779448) ^ [_1483575, _1483577, _1483579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1483575, tc_HOL_Obool), tc_HOL_Obool)), _1483577), _1483579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483575, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483575, tc_HOL_Obool), _1483577)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483575, tc_HOL_Obool), _1483579))))], (37218 ^ _779448) ^ [_1483724, _1483726, _1483728] : [c_Equiv__Relations_Oequiv(_1483724, _1483726, _1483728), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483724, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1483724), _1483726), _1483728)) = _1483726)], (37224 ^ _779448) ^ [_1483833, _1483835, _1483837] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483833, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1483833, tc_HOL_Obool)), _1483835), _1483837)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483833, tc_HOL_Obool)), _1483835), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483833, tc_HOL_Obool), _1483837)))], (37226 ^ _779448) ^ [_1483894, _1483896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483894), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1483894, tc_HOL_Obool), _1483896))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1483894, tc_HOL_Obool)), _1483896)))], (37232 ^ _779448) ^ [_1484005, _1484007] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1484005, tc_HOL_Obool), tc_HOL_Obool)), _1484007), hAPP(c_Set_OPow(_1484005), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484005, tc_HOL_Obool), _1484007)))))], (37234 ^ _779448) ^ [_1484054] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484054, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1484054, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1484054, tc_HOL_Obool)))], (37236 ^ _779448) ^ [_1484096, _1484098, _1484100] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484096, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1484096, tc_HOL_Obool), tc_HOL_Obool)), _1484098), _1484100)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484096, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484096, tc_HOL_Obool), _1484098)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484096, tc_HOL_Obool), _1484100)))], (37238 ^ _779448) ^ [_1484166, _1484168, _1484170, _1484172] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484166, tc_fun(_1484168, tc_HOL_Obool)), _1484170), _1484172) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484168, tc_HOL_Obool), hAPP(c_Set_Oimage(_1484166, tc_fun(_1484168, tc_HOL_Obool), _1484172), _1484170)))], (37240 ^ _779448) ^ [_1484223, _1484225, _1484227, _1484229] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484223, tc_HOL_Obool), hAPP(c_Set_Oimage(_1484225, tc_fun(_1484223, tc_HOL_Obool), _1484227), _1484229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484225, tc_fun(_1484223, tc_HOL_Obool)), _1484229), _1484227))], (37242 ^ _779448) ^ [_1484280, _1484282, _1484284] : [class_Complete__Lattice_Ocomplete__lattice(_1484280), hBOOL(hAPP(hAPP(c_member(_1484280), _1484282), _1484284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484280), _1484282), c_Complete__Lattice_OSup__class_OSup(_1484280, _1484284))))], (37252 ^ _779448) ^ [_1484445] : [class_Complete__Lattice_Ocomplete__lattice(_1484445), -(c_Complete__Lattice_OSup__class_OSup(_1484445, c_Orderings_Obot__class_Obot(tc_fun(_1484445, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1484445))], (37258 ^ _779448) ^ [_1484538, _1484540] : [class_Complete__Lattice_Ocomplete__lattice(_1484538), -(c_Complete__Lattice_OSup__class_OSup(_1484538, hAPP(hAPP(c_Set_Oinsert(_1484538), _1484540), c_Orderings_Obot__class_Obot(tc_fun(_1484538, tc_HOL_Obool)))) = _1484540)], (37264 ^ _779448) ^ [_1484645, _1484647, _1484649] : [class_Complete__Lattice_Ocomplete__lattice(_1484645), -(c_Complete__Lattice_OSup__class_OSup(_1484645, hAPP(hAPP(c_Set_Oinsert(_1484645), _1484647), _1484649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1484645), _1484647), c_Complete__Lattice_OSup__class_OSup(_1484645, _1484649)))], (37270 ^ _779448) ^ [_1484766] : [class_Complete__Lattice_Ocomplete__lattice(_1484766), -(c_Complete__Lattice_OSup__class_OSup(_1484766, c_Orderings_Otop__class_Otop(tc_fun(_1484766, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1484766))], (37276 ^ _779448) ^ [_1484859, _1484861, _1484863] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484859, tc_HOL_Obool)), _1484861), _1484863) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484859, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1484859, tc_HOL_Obool)), _1484861), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1484859, tc_HOL_Obool)), _1484863), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1484859, tc_HOL_Obool), tc_HOL_Obool))))))], (37278 ^ _779448) ^ [_1484933, _1484935, _1484937, _1484939, _1484941] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484933, tc_fun(_1484935, tc_HOL_Obool)), _1484937), hAPP(hAPP(c_COMBS(_1484933, tc_fun(_1484935, tc_HOL_Obool), tc_fun(_1484935, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484935, tc_HOL_Obool), tc_fun(tc_fun(_1484935, tc_HOL_Obool), tc_fun(_1484935, tc_HOL_Obool)), _1484933), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484935, tc_HOL_Obool))), _1484939)), _1484941)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484935, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484935, tc_HOL_Obool), hAPP(c_Set_Oimage(_1484933, tc_fun(_1484935, tc_HOL_Obool), _1484939), _1484937))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1484935, tc_HOL_Obool), hAPP(c_Set_Oimage(_1484933, tc_fun(_1484935, tc_HOL_Obool), _1484941), _1484937))))], (37280 ^ _779448) ^ [_1485062, _1485064, _1485066] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485062, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1485062, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1485062, tc_HOL_Obool), tc_HOL_Obool)), _1485064), _1485066))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485062, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1485062, tc_HOL_Obool), _1485064)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1485062, tc_HOL_Obool), _1485066)))))], (37282 ^ _779448) ^ [_1485142, _1485144, _1485146] : [class_Complete__Lattice_Ocomplete__lattice(_1485142), -(c_Complete__Lattice_OSup__class_OSup(_1485142, hAPP(hAPP(c_Set_Oinsert(_1485142), _1485144), hAPP(hAPP(c_Set_Oinsert(_1485142), _1485146), c_Orderings_Obot__class_Obot(tc_fun(_1485142, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1485142), _1485144), _1485146))], (37288 ^ _779448) ^ [_1485283, _1485285, _1485287] : [class_Complete__Lattice_Ocomplete__lattice(_1485283), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485283), _1485285)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1485283), _1485287), c_Complete__Lattice_OSup__class_OSup(_1485283, _1485285)) = hAPP(hAPP(c_Finite__Set_Ofold(_1485283, _1485283, c_Lattices_Osemilattice__sup__class_Osup(_1485283)), _1485287), _1485285))], (37298 ^ _779448) ^ [_1485468, _1485470] : [class_Complete__Lattice_Ocomplete__lattice(_1485468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485468), _1485470)), -(_1485470 = c_Orderings_Obot__class_Obot(tc_fun(_1485468, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1485468, _1485470) = c_Complete__Lattice_OSup__class_OSup(_1485468, _1485470))], (37312 ^ _779448) ^ [_1485640] : [-(c_Nitpick_Oone__frac(_1485640) = c_Nitpick_OAbs__Frac(_1485640, 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))))], (37314 ^ _779448) ^ [_1485668, _1485670] : [-(c_Nitpick_Onumber__of__frac(_1485668, _1485670) = c_Nitpick_OAbs__Frac(_1485668, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1485670), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37316 ^ _779448) ^ [_1485705, _1485707, _1485709] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1485705), _1485707), _1485709) = c_Nitpick_OAbs__Frac(_1485705, c_Nitpick_Onorm__frac(_1485707, _1485709)))], (37318 ^ _779448) ^ [_1485746, _1485748] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1485746, tc_HOL_Obool), _1485748) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1485746, tc_HOL_Obool), tc_fun(_1485746, tc_HOL_Obool)), _1485748), c_COMBI(tc_fun(_1485746, tc_HOL_Obool))))], (37320 ^ _779448) ^ [_1485797, _1485799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1485797, tc_HOL_Obool)), _1485799)), 37326 ^ _779448 : [(37327 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1485797, tc_HOL_Obool)), 37325 ^ [_1485797, _1485799]), _1485799)))], (37329 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1485797), 37325 ^ [_1485797, _1485799]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1485797), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1485797, tc_HOL_Obool), _1485799))))], (37333 ^ _779448) ^ [_1486055, _1486057, _1486059] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486055, tc_HOL_Obool)), _1486057), _1486059))), 37339 ^ _779448 : [(37340 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486055, tc_HOL_Obool)), 37338 ^ [_1486055, _1486057, _1486059]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1486055, tc_HOL_Obool)), _1486057), _1486059))))], (37343 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486055, tc_HOL_Obool)), 37341 ^ [_1486055, _1486057, _1486059]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1486055, tc_HOL_Obool)), _1486057), _1486059))))], (37345 ^ _779448) ^ [] : [37338 ^ [_1486055, _1486057, _1486059] = 37341 ^ [_1486055, _1486057, _1486059]], (37347 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486055, tc_HOL_Obool)), 37338 ^ [_1486055, _1486057, _1486059]), 37341 ^ [_1486055, _1486057, _1486059]) = c_Orderings_Obot__class_Obot(tc_fun(_1486055, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486055, tc_HOL_Obool)), _1486057), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1486055, tc_HOL_Obool), _1486059)) = c_Orderings_Obot__class_Obot(tc_fun(_1486055, tc_HOL_Obool)))], (37351 ^ _779448) ^ [_1486649, _1486651, _1486653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1486649, tc_HOL_Obool)), _1486651)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486649), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1486649, tc_HOL_Obool), _1486651))), 37361 ^ _779448 : [(37362 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486649, tc_HOL_Obool)), 37360 ^ [_1486649, _1486651, _1486653]), _1486651)))], (37364 ^ _779448) ^ [] : [hAPP(c_Finite__Set_Ocard(_1486649), 37360 ^ [_1486649, _1486651, _1486653]) = _1486653]], 37368 ^ _779448 : [(37369 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486649, tc_HOL_Obool)), 37367 ^ [_1486649, _1486651, _1486653]), _1486651)))], (37372 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486649, tc_HOL_Obool)), 37370 ^ [_1486649, _1486651, _1486653]), _1486651)))], (37374 ^ _779448) ^ [] : [37367 ^ [_1486649, _1486651, _1486653] = 37370 ^ [_1486649, _1486651, _1486653]], (37376 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1486649, tc_HOL_Obool)), 37367 ^ [_1486649, _1486651, _1486653]), 37370 ^ [_1486649, _1486651, _1486653]) = c_Orderings_Obot__class_Obot(tc_fun(_1486649, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1486653), hAPP(c_Finite__Set_Ocard(tc_fun(_1486649, tc_HOL_Obool)), _1486651)) = hAPP(c_Finite__Set_Ocard(_1486649), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1486649, tc_HOL_Obool), _1486651)))], (37380 ^ _779448) ^ [_1487430, _1487432, _1487434, _1487436] : [-(_1487430 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1487432, tc_HOL_Obool), tc_HOL_Obool))), 37386 ^ _779448 : [(37387 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1487432, tc_HOL_Obool)), 37385 ^ [_1487430, _1487432, _1487434, _1487436]), _1487430)))], (37389 ^ _779448) ^ [] : [c_Fun_Oinj__on(_1487432, _1487434, _1487436, 37385 ^ [_1487430, _1487432, _1487434, _1487436])]], -(c_Fun_Oinj__on(_1487432, _1487434, _1487436, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1487432, tc_HOL_Obool), _1487430)))], (37393 ^ _779448) ^ [_1487691, _1487693, _1487695] : [37395 ^ _779448 : [(37396 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1487691, tc_HOL_Obool)), 37394 ^ [_1487691, _1487693, _1487695]), _1487693)))], (37398 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487691, tc_HOL_Obool)), 37394 ^ [_1487691, _1487693, _1487695]), _1487695))]], -(_1487693 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1487691, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1487691, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1487691, tc_HOL_Obool), _1487693)), _1487695)))], (37406 ^ _779448) ^ [_1487953, _1487955, _1487957, _1487959, _1487961, _1487963] : [-(hAPP(c_Set_Oimage(_1487953, tc_prod(_1487955, _1487957), hAPP(hAPP(c_COMBS(_1487953, _1487957, tc_prod(_1487955, _1487957)), hAPP(hAPP(c_COMBB(_1487955, tc_fun(_1487957, tc_prod(_1487955, _1487957)), _1487953), c_Product__Type_OPair(_1487955, _1487957)), _1487959)), _1487961)), _1487963) = hAPP(hAPP(c_Product__Type_OSigma(_1487955, _1487957), hAPP(c_Set_Oimage(_1487953, _1487955, _1487959), _1487963)), hAPP(hAPP(c_COMBB(tc_fun(_1487953, tc_HOL_Obool), tc_fun(_1487957, tc_HOL_Obool), _1487955), c_Set_Oimage(_1487953, _1487957, _1487961)), hAPP(hAPP(c_COMBC(_1487955, tc_fun(_1487953, tc_HOL_Obool), tc_fun(_1487953, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1487953, tc_HOL_Obool), tc_fun(tc_fun(_1487953, tc_HOL_Obool), tc_fun(_1487953, tc_HOL_Obool)), _1487955), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487953, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1487955, tc_HOL_Obool), tc_fun(_1487953, tc_HOL_Obool), _1487955), c_Set_Ovimage(_1487953, _1487955, _1487959)), hAPP(hAPP(c_COMBC(_1487955, tc_fun(_1487955, tc_HOL_Obool), tc_fun(_1487955, tc_HOL_Obool)), c_Set_Oinsert(_1487955)), c_Orderings_Obot__class_Obot(tc_fun(_1487955, tc_HOL_Obool)))))), _1487963))))], (37408 ^ _779448) ^ [_1488150, _1488152, _1488154, _1488156, _1488158, _1488160] : [hBOOL(hAPP(hAPP(c_member(_1488150), _1488152), _1488154)), hBOOL(hAPP(hAPP(c_member(_1488156), _1488158), hAPP(_1488160, _1488152))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1488150, _1488156)), hAPP(hAPP(c_Product__Type_OPair(_1488150, _1488156), _1488152), _1488158)), hAPP(hAPP(c_Product__Type_OSigma(_1488150, _1488156), _1488154), _1488160))))], (37418 ^ _779448) ^ [_1488385, _1488387, _1488389, _1488391, _1488393] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1488385, _1488387), _1488389), hAPP(hAPP(c_COMBS(_1488385, tc_fun(_1488387, tc_HOL_Obool), tc_fun(_1488387, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1488387, tc_HOL_Obool), tc_fun(tc_fun(_1488387, tc_HOL_Obool), tc_fun(_1488387, tc_HOL_Obool)), _1488385), c_Groups_Ominus__class_Ominus(tc_fun(_1488387, tc_HOL_Obool))), _1488391)), _1488393)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1488385, _1488387), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488385, _1488387), _1488389), _1488391)), hAPP(hAPP(c_Product__Type_OSigma(_1488385, _1488387), _1488389), _1488393)))], (37420 ^ _779448) ^ [_1488500, _1488502, _1488504, _1488506, _1488508] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1488500, _1488502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1488500, tc_HOL_Obool)), _1488504), _1488506)), hAPP(c_COMBK(tc_fun(_1488502, tc_HOL_Obool), _1488500), _1488508)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1488500, _1488502), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488500, _1488502), _1488504), hAPP(c_COMBK(tc_fun(_1488502, tc_HOL_Obool), _1488500), _1488508))), hAPP(hAPP(c_Product__Type_OSigma(_1488500, _1488502), _1488506), hAPP(c_COMBK(tc_fun(_1488502, tc_HOL_Obool), _1488500), _1488508))))], (37422 ^ _779448) ^ [_1488610, _1488612, _1488614, _1488616, _1488618] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1488610, _1488612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1488610, tc_HOL_Obool)), _1488614), _1488616)), _1488618) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1488610, _1488612), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1488610, _1488612), _1488614), _1488618)), hAPP(hAPP(c_Product__Type_OSigma(_1488610, _1488612), _1488616), _1488618)))], (37424 ^ _779448) ^ [_1488693, _1488695, _1488697, _1488699, _1488701, _1488703] : [hBOOL(hAPP(hAPP(c_member(_1488693), _1488695), _1488697)), 37427 ^ _779448 : [(37428 ^ _779448) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1488699, _1488693), _1488701), hAPP(c_COMBK(tc_fun(_1488693, tc_HOL_Obool), _1488699), _1488697)) = hAPP(hAPP(c_Product__Type_OSigma(_1488699, _1488693), _1488703), hAPP(c_COMBK(tc_fun(_1488693, tc_HOL_Obool), _1488699), _1488697)), -(_1488701 = _1488703)], (37434 ^ _779448) ^ [] : [_1488701 = _1488703, -(hAPP(hAPP(c_Product__Type_OSigma(_1488699, _1488693), _1488701), hAPP(c_COMBK(tc_fun(_1488693, tc_HOL_Obool), _1488699), _1488697)) = hAPP(hAPP(c_Product__Type_OSigma(_1488699, _1488693), _1488703), hAPP(c_COMBK(tc_fun(_1488693, tc_HOL_Obool), _1488699), _1488697)))]]], (37440 ^ _779448) ^ [_1489046, _1489048, _1489050] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489046, _1489048), c_Orderings_Obot__class_Obot(tc_fun(_1489046, tc_HOL_Obool))), _1489050) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489046, _1489048), tc_HOL_Obool)))], (37442 ^ _779448) ^ [_1489095, _1489097, _1489099, _1489101] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489095, _1489097), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1489095, tc_HOL_Obool), _1489099)), _1489101) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1489095, tc_HOL_Obool), tc_fun(tc_prod(_1489095, _1489097), tc_HOL_Obool)), _1489099), hAPP(hAPP(c_COMBC(tc_fun(_1489095, tc_HOL_Obool), tc_fun(_1489095, tc_fun(_1489097, tc_HOL_Obool)), tc_fun(tc_prod(_1489095, _1489097), tc_HOL_Obool)), c_Product__Type_OSigma(_1489095, _1489097)), _1489101)))], (37444 ^ _779448) ^ [_1489185, _1489187, _1489189, _1489191] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1489185, _1489187)), hAPP(hAPP(c_Product__Type_OSigma(_1489185, _1489187), _1489189), hAPP(c_COMBK(tc_fun(_1489187, tc_HOL_Obool), _1489185), _1489191))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1489185), _1489189)), hAPP(c_Finite__Set_Ocard(_1489187), _1489191)))], (37446 ^ _779448) ^ [_1489256, _1489258, _1489260, _1489262, _1489264, _1489266] : [class_Groups_Ocomm__monoid__add(_1489256), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489258, _1489256), hAPP(hAPP(c_COMBC(_1489258, tc_fun(_1489260, tc_HOL_Obool), _1489256), hAPP(hAPP(c_COMBB(tc_fun(_1489260, _1489256), tc_fun(tc_fun(_1489260, tc_HOL_Obool), _1489256), _1489258), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489260, _1489256)), _1489262)), _1489264)), _1489266) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1489258, _1489260), _1489256), hAPP(c_Product__Type_Oprod_Oprod__case(_1489258, _1489260, _1489256), _1489262)), hAPP(hAPP(c_Product__Type_OSigma(_1489258, _1489260), _1489266), hAPP(c_COMBK(tc_fun(_1489260, tc_HOL_Obool), _1489258), _1489264))))], (37452 ^ _779448) ^ [_1489501, _1489503, _1489505] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489501, _1489503), _1489505), hAPP(c_COMBK(tc_fun(_1489503, tc_HOL_Obool), _1489501), c_Orderings_Obot__class_Obot(tc_fun(_1489503, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489501, _1489503), tc_HOL_Obool)))], (37464 ^ _779448) ^ [_1489742, _1489744, _1489746, _1489748] : [37465 ^ _779448 : [(37466 ^ _779448) ^ [] : [_1489746 = c_Orderings_Obot__class_Obot(tc_fun(_1489742, tc_HOL_Obool))], (37468 ^ _779448) ^ [] : [_1489748 = c_Orderings_Obot__class_Obot(tc_fun(_1489744, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1489742, _1489744), _1489746), hAPP(c_COMBK(tc_fun(_1489744, tc_HOL_Obool), _1489742), _1489748)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489742, _1489744), tc_HOL_Obool)))], (37454 ^ _779448) ^ [_1489580, _1489582, _1489584, _1489586] : [hAPP(hAPP(c_Product__Type_OSigma(_1489580, _1489582), _1489584), hAPP(c_COMBK(tc_fun(_1489582, tc_HOL_Obool), _1489580), _1489586)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489580, _1489582), tc_HOL_Obool)), -(_1489584 = c_Orderings_Obot__class_Obot(tc_fun(_1489580, tc_HOL_Obool))), -(_1489586 = c_Orderings_Obot__class_Obot(tc_fun(_1489582, tc_HOL_Obool)))], (37472 ^ _779448) ^ [_1489935, _1489937, _1489939] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1489935, _1489937), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1489935, _1489937), c_Orderings_Otop__class_Otop(tc_fun(_1489935, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1489937, tc_HOL_Obool), _1489935), _1489939))) = hAPP(hAPP(c_Product__Type_OSigma(_1489935, _1489937), c_Orderings_Otop__class_Otop(tc_fun(_1489935, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1489937, tc_HOL_Obool), _1489935), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1489937, tc_HOL_Obool)), _1489939))))], (37474 ^ _779448) ^ [_1490027, _1490029, _1490031] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1490027, _1490029), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490027, _1490029), _1490031), hAPP(c_COMBK(tc_fun(_1490029, tc_HOL_Obool), _1490027), c_Orderings_Otop__class_Otop(tc_fun(_1490029, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1490027, _1490029), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1490027, tc_HOL_Obool)), _1490031)), hAPP(c_COMBK(tc_fun(_1490029, tc_HOL_Obool), _1490027), c_Orderings_Otop__class_Otop(tc_fun(_1490029, tc_HOL_Obool)))))], (37476 ^ _779448) ^ [_1490119, _1490121, _1490123, _1490125, _1490127, _1490129] : [class_Groups_Ocomm__monoid__mult(_1490119), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490121, _1490119), hAPP(hAPP(c_COMBC(_1490121, tc_fun(_1490123, tc_HOL_Obool), _1490119), hAPP(hAPP(c_COMBB(tc_fun(_1490123, _1490119), tc_fun(tc_fun(_1490123, tc_HOL_Obool), _1490119), _1490121), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490123, _1490119)), _1490125)), _1490127)), _1490129) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1490121, _1490123), _1490119), hAPP(c_Product__Type_Oprod_Oprod__case(_1490121, _1490123, _1490119), _1490125)), hAPP(hAPP(c_Product__Type_OSigma(_1490121, _1490123), _1490129), hAPP(c_COMBK(tc_fun(_1490123, tc_HOL_Obool), _1490121), _1490127))))], (37482 ^ _779448) ^ [_1490364, _1490366, _1490368, _1490370, _1490372] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1490364, _1490366), _1490368), hAPP(hAPP(c_COMBS(_1490364, tc_fun(_1490366, tc_HOL_Obool), tc_fun(_1490366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490366, tc_HOL_Obool), tc_fun(tc_fun(_1490366, tc_HOL_Obool), tc_fun(_1490366, tc_HOL_Obool)), _1490364), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490366, tc_HOL_Obool))), _1490370)), _1490372)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490364, _1490366), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490364, _1490366), _1490368), _1490370)), hAPP(hAPP(c_Product__Type_OSigma(_1490364, _1490366), _1490368), _1490372)))], (37484 ^ _779448) ^ [_1490479, _1490481, _1490483, _1490485, _1490487] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1490479, _1490481), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490479, tc_HOL_Obool)), _1490483), _1490485)), hAPP(c_COMBK(tc_fun(_1490481, tc_HOL_Obool), _1490479), _1490487)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490479, _1490481), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490479, _1490481), _1490483), hAPP(c_COMBK(tc_fun(_1490481, tc_HOL_Obool), _1490479), _1490487))), hAPP(hAPP(c_Product__Type_OSigma(_1490479, _1490481), _1490485), hAPP(c_COMBK(tc_fun(_1490481, tc_HOL_Obool), _1490479), _1490487))))], (37486 ^ _779448) ^ [_1490589, _1490591, _1490593, _1490595, _1490597] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1490589, _1490591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490589, tc_HOL_Obool)), _1490593), _1490595)), _1490597) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490589, _1490591), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490589, _1490591), _1490593), _1490597)), hAPP(hAPP(c_Product__Type_OSigma(_1490589, _1490591), _1490595), _1490597)))], (37488 ^ _779448) ^ [_1490672, _1490674, _1490676, _1490678] : [-(hAPP(c_Set_Oimage(tc_prod(_1490672, _1490674), tc_prod(_1490674, _1490672), hAPP(c_Product__Type_Oprod_Oprod__case(_1490672, _1490674, tc_prod(_1490674, _1490672)), hAPP(c_COMBC(_1490674, _1490672, tc_prod(_1490674, _1490672)), c_Product__Type_OPair(_1490674, _1490672)))), hAPP(hAPP(c_Product__Type_OSigma(_1490672, _1490674), _1490676), hAPP(c_COMBK(tc_fun(_1490674, tc_HOL_Obool), _1490672), _1490678))) = hAPP(hAPP(c_Product__Type_OSigma(_1490674, _1490672), _1490678), hAPP(c_COMBK(tc_fun(_1490672, tc_HOL_Obool), _1490674), _1490676)))], (37490 ^ _779448) ^ [_1490773, _1490775, _1490777, _1490779] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1490773), _1490775)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1490777), _1490779)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1490773, _1490777)), hAPP(hAPP(c_Product__Type_OSigma(_1490773, _1490777), _1490775), hAPP(c_COMBK(tc_fun(_1490777, tc_HOL_Obool), _1490773), _1490779)))))], (37500 ^ _779448) ^ [_1490976, _1490978, _1490980] : [c_Equiv__Relations_Oequiv(_1490976, _1490978, _1490980), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490976, _1490976), tc_HOL_Obool)), _1490980), hAPP(hAPP(c_Product__Type_OSigma(_1490976, _1490976), _1490978), hAPP(c_COMBK(tc_fun(_1490976, tc_HOL_Obool), _1490976), _1490978)))))], (37506 ^ _779448) ^ [_1491119, _1491121, _1491123, _1491125, _1491127] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491119, _1491121), _1491123), hAPP(hAPP(c_COMBS(_1491119, tc_fun(_1491121, tc_HOL_Obool), tc_fun(_1491121, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491121, tc_HOL_Obool), tc_fun(tc_fun(_1491121, tc_HOL_Obool), tc_fun(_1491121, tc_HOL_Obool)), _1491119), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491121, tc_HOL_Obool))), _1491125)), _1491127)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1491119, _1491121), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491119, _1491121), _1491123), _1491125)), hAPP(hAPP(c_Product__Type_OSigma(_1491119, _1491121), _1491123), _1491127)))], (37508 ^ _779448) ^ [_1491234, _1491236, _1491238, _1491240, _1491242] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491234, _1491236), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491234, tc_HOL_Obool)), _1491238), _1491240)), hAPP(c_COMBK(tc_fun(_1491236, tc_HOL_Obool), _1491234), _1491242)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1491234, _1491236), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491234, _1491236), _1491238), hAPP(c_COMBK(tc_fun(_1491236, tc_HOL_Obool), _1491234), _1491242))), hAPP(hAPP(c_Product__Type_OSigma(_1491234, _1491236), _1491240), hAPP(c_COMBK(tc_fun(_1491236, tc_HOL_Obool), _1491234), _1491242))))], (37510 ^ _779448) ^ [_1491344, _1491346, _1491348, _1491350, _1491352] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491344, _1491346), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491344, tc_HOL_Obool)), _1491348), _1491350)), _1491352) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1491344, _1491346), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491344, _1491346), _1491348), _1491352)), hAPP(hAPP(c_Product__Type_OSigma(_1491344, _1491346), _1491350), _1491352)))], (37512 ^ _779448) ^ [_1491427, _1491429] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491427, _1491427), tc_HOL_Obool)), c_Relation_OId__on(_1491427, _1491429)), hAPP(hAPP(c_Product__Type_OSigma(_1491427, _1491427), _1491429), hAPP(c_COMBK(tc_fun(_1491427, tc_HOL_Obool), _1491427), _1491429)))))], (37514 ^ _779448) ^ [_1491486, _1491488] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491486, _1491488), c_Orderings_Otop__class_Otop(tc_fun(_1491486, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1491488, tc_HOL_Obool), _1491486), c_Orderings_Otop__class_Otop(tc_fun(_1491488, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1491486, _1491488), tc_HOL_Obool)))], (37516 ^ _779448) ^ [_1491574, _1491576, _1491578, _1491580, _1491582, _1491584] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491574, _1491576)), hAPP(hAPP(c_Product__Type_OPair(_1491574, _1491576), _1491578), _1491580)), hAPP(hAPP(c_Product__Type_OSigma(_1491574, _1491576), _1491582), _1491584))), 37519 ^ _779448 : [(37520 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491574), _1491578), _1491582)))], (37522 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491576), _1491580), hAPP(_1491584, _1491578))))]]], (37524 ^ _779448) ^ [_1491771, _1491773, _1491775, _1491777, _1491779, _1491781] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491771, _1491773)), hAPP(hAPP(c_Product__Type_OPair(_1491771, _1491773), _1491775), _1491777)), hAPP(hAPP(c_Product__Type_OSigma(_1491771, _1491773), _1491779), _1491781)))), hBOOL(hAPP(hAPP(c_member(_1491771), _1491775), _1491779)), hBOOL(hAPP(hAPP(c_member(_1491773), _1491777), hAPP(_1491781, _1491775)))], (37534 ^ _779448) ^ [_1492008, _1492010, _1492012, _1492014, _1492016, _1492018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492008, _1492010)), hAPP(hAPP(c_Product__Type_OPair(_1492008, _1492010), _1492012), _1492014)), hAPP(hAPP(c_Product__Type_OSigma(_1492008, _1492010), _1492016), _1492018))), -(hBOOL(hAPP(hAPP(c_member(_1492008), _1492012), _1492016)))], (37540 ^ _779448) ^ [_1492163, _1492165, _1492167, _1492169, _1492171, _1492173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492163, _1492165)), hAPP(hAPP(c_Product__Type_OPair(_1492163, _1492165), _1492167), _1492169)), hAPP(hAPP(c_Product__Type_OSigma(_1492163, _1492165), _1492171), _1492173))), -(hBOOL(hAPP(hAPP(c_member(_1492165), _1492169), hAPP(_1492173, _1492167))))], (37546 ^ _779448) ^ [_1492324, _1492326, _1492328, _1492330, _1492332, _1492334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492324, _1492326)), hAPP(hAPP(c_Product__Type_OPair(_1492324, _1492326), _1492328), _1492330)), hAPP(hAPP(c_Product__Type_OSigma(_1492324, _1492326), _1492332), _1492334))), 37549 ^ _779448 : [(37550 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492324), _1492328), _1492332)))], (37552 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492326), _1492330), hAPP(_1492334, _1492328))))]]], (37554 ^ _779448) ^ [_1492529, _1492531, _1492533, _1492535] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1492529, _1492531)), hAPP(hAPP(c_Product__Type_OSigma(_1492529, _1492531), hAPP(hAPP(c_Set_Oinsert(_1492529), _1492533), c_Orderings_Obot__class_Obot(tc_fun(_1492529, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1492531, tc_HOL_Obool), _1492529), _1492535))) = hAPP(c_Finite__Set_Ocard(_1492531), _1492535))], (37556 ^ _779448) ^ [_1492602, _1492604, _1492606, _1492608, _1492610, _1492612] : [hBOOL(hAPP(hAPP(c_member(_1492602), _1492604), _1492606)), 37559 ^ _779448 : [(37560 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492608, _1492602), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1492608, _1492602), _1492610), hAPP(c_COMBK(tc_fun(_1492602, tc_HOL_Obool), _1492608), _1492606))), hAPP(hAPP(c_Product__Type_OSigma(_1492608, _1492602), _1492612), hAPP(c_COMBK(tc_fun(_1492602, tc_HOL_Obool), _1492608), _1492606)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492608, tc_HOL_Obool)), _1492610), _1492612)))], (37566 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492608, tc_HOL_Obool)), _1492610), _1492612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492608, _1492602), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1492608, _1492602), _1492610), hAPP(c_COMBK(tc_fun(_1492602, tc_HOL_Obool), _1492608), _1492606))), hAPP(hAPP(c_Product__Type_OSigma(_1492608, _1492602), _1492612), hAPP(c_COMBK(tc_fun(_1492602, tc_HOL_Obool), _1492608), _1492606)))))]]], (37572 ^ _779448) ^ [_1493024, _1493026, _1493028, _1493030, _1493032, _1493034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493024, _1493026), tc_HOL_Obool)), _1493028), hAPP(hAPP(c_Product__Type_OSigma(_1493024, _1493026), _1493030), hAPP(c_COMBK(tc_fun(_1493026, tc_HOL_Obool), _1493024), _1493032)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493026, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1493024, _1493026, _1493028), _1493034)), _1493032)))], (37578 ^ _779448) ^ [_1493205, _1493207, _1493209, _1493211] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1493205, _1493207)), hAPP(hAPP(c_Product__Type_OSigma(_1493205, _1493207), _1493209), hAPP(c_COMBK(tc_fun(_1493207, tc_HOL_Obool), _1493205), _1493211)))), -(_1493211 = c_Orderings_Obot__class_Obot(tc_fun(_1493207, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493205), _1493209)))], (37588 ^ _779448) ^ [_1493369, _1493371, _1493373, _1493375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1493369, _1493371)), hAPP(hAPP(c_Product__Type_OSigma(_1493369, _1493371), _1493373), hAPP(c_COMBK(tc_fun(_1493371, tc_HOL_Obool), _1493369), _1493375)))), -(_1493373 = c_Orderings_Obot__class_Obot(tc_fun(_1493369, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493371), _1493375)))], (37598 ^ _779448) ^ [_1493548, _1493550, _1493552, _1493554] : [_1493548 = c_Orderings_Obot__class_Obot(tc_fun(_1493550, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1493552, _1493550), _1493552, c_Product__Type_Ofst(_1493552, _1493550)), hAPP(hAPP(c_Product__Type_OSigma(_1493552, _1493550), _1493554), hAPP(c_COMBK(tc_fun(_1493550, tc_HOL_Obool), _1493552), _1493548))) = c_Orderings_Obot__class_Obot(tc_fun(_1493552, tc_HOL_Obool)))], (37604 ^ _779448) ^ [_1493705, _1493707, _1493709, _1493711] : [-(_1493705 = c_Orderings_Obot__class_Obot(tc_fun(_1493707, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1493709, _1493707), _1493709, c_Product__Type_Ofst(_1493709, _1493707)), hAPP(hAPP(c_Product__Type_OSigma(_1493709, _1493707), _1493711), hAPP(c_COMBK(tc_fun(_1493707, tc_HOL_Obool), _1493709), _1493705))) = _1493711)], (37610 ^ _779448) ^ [_1493798, _1493800, _1493802, _1493804] : [_1493798 = c_Orderings_Obot__class_Obot(tc_fun(_1493800, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1493800, _1493802), _1493802, c_Product__Type_Osnd(_1493800, _1493802)), hAPP(hAPP(c_Product__Type_OSigma(_1493800, _1493802), _1493798), hAPP(c_COMBK(tc_fun(_1493802, tc_HOL_Obool), _1493800), _1493804))) = c_Orderings_Obot__class_Obot(tc_fun(_1493802, tc_HOL_Obool)))], (37616 ^ _779448) ^ [_1493955, _1493957, _1493959, _1493961] : [-(_1493955 = c_Orderings_Obot__class_Obot(tc_fun(_1493957, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1493957, _1493959), _1493959, c_Product__Type_Osnd(_1493957, _1493959)), hAPP(hAPP(c_Product__Type_OSigma(_1493957, _1493959), _1493955), hAPP(c_COMBK(tc_fun(_1493959, tc_HOL_Obool), _1493957), _1493961))) = _1493961)], (37622 ^ _779448) ^ [_1494033, _1494035, _1494037, _1494039, _1494041, _1494043] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494033, _1494035), hAPP(hAPP(c_Set_Oinsert(_1494033), _1494037), _1494039)), hAPP(c_COMBK(tc_fun(_1494035, tc_HOL_Obool), _1494033), hAPP(hAPP(c_Set_Oinsert(_1494035), _1494041), _1494043))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1494033, _1494035)), hAPP(hAPP(c_Product__Type_OPair(_1494033, _1494035), _1494037), _1494041)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1494033, _1494035), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494033, _1494035), _1494039), hAPP(c_COMBK(tc_fun(_1494035, tc_HOL_Obool), _1494033), hAPP(hAPP(c_Set_Oinsert(_1494035), _1494041), _1494043)))), hAPP(hAPP(c_Product__Type_OSigma(_1494033, _1494035), hAPP(hAPP(c_Set_Oinsert(_1494033), _1494037), _1494039)), hAPP(c_COMBK(tc_fun(_1494035, tc_HOL_Obool), _1494033), _1494043)))))], (37624 ^ _779448) ^ [_1494186, _1494188, _1494190, _1494192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1494186), _1494188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494186, _1494186), tc_HOL_Obool)), _1494190), hAPP(hAPP(c_Product__Type_OSigma(_1494186, _1494186), _1494188), hAPP(c_COMBK(tc_fun(_1494186, tc_HOL_Obool), _1494186), _1494188)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1494186, tc_HOL_Obool)), _1494192), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494186), _1494188), _1494190))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1494186), _1494192)))], (37638 ^ _779448) ^ [_1494493, _1494495, _1494497, _1494499, _1494501, _1494503] : [-(hAPP(c_Set_Ovimage(_1494493, tc_prod(_1494495, _1494497), _1494499), hAPP(hAPP(c_Product__Type_OSigma(_1494495, _1494497), _1494501), hAPP(c_COMBK(tc_fun(_1494497, tc_HOL_Obool), _1494495), _1494503))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1494493, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1494493, _1494495, hAPP(c_Fun_Ocomp(tc_prod(_1494495, _1494497), _1494495, _1494493, c_Product__Type_Ofst(_1494495, _1494497)), _1494499)), _1494501)), hAPP(c_Set_Ovimage(_1494493, _1494497, hAPP(c_Fun_Ocomp(tc_prod(_1494495, _1494497), _1494497, _1494493, c_Product__Type_Osnd(_1494495, _1494497)), _1494499)), _1494503)))], (37640 ^ _779448) ^ [_1494607, _1494609, _1494611, _1494613, _1494615, _1494617, _1494619, _1494621] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1494607, _1494609), tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494607, _1494609), _1494615), hAPP(c_COMBK(tc_fun(_1494609, tc_HOL_Obool), _1494607), _1494617))), hAPP(c_Product__Type_Oprod_Oprod__case(_1494607, _1494609, tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1494607, tc_fun(_1494609, tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool))), tc_fun(_1494609, tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool)), tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool)), tc_fun(tc_fun(_1494609, tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool))), tc_fun(_1494609, tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool))), _1494607), c_COMBB(tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool)), tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool), _1494609)), hAPP(hAPP(c_COMBB(tc_fun(_1494611, tc_HOL_Obool), tc_fun(tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool)), tc_fun(tc_prod(_1494611, _1494613), tc_HOL_Obool)), _1494607), c_Product__Type_OSigma(_1494611, _1494613)), _1494619))), hAPP(hAPP(c_COMBB(tc_fun(_1494613, tc_HOL_Obool), tc_fun(_1494611, tc_fun(_1494613, tc_HOL_Obool)), _1494609), c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494611)), _1494621)))) = hAPP(hAPP(c_Product__Type_OSigma(_1494611, _1494613), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1494607, tc_fun(_1494611, tc_HOL_Obool)), _1494615), _1494619)), hAPP(c_COMBK(tc_fun(_1494613, tc_HOL_Obool), _1494611), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1494609, tc_fun(_1494613, tc_HOL_Obool)), _1494617), _1494621))))], (37642 ^ _779448) ^ [_1494881, _1494883, _1494885, _1494887] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1494881, _1494883), _1494885), _1494887) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1494881, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), _1494885), hAPP(hAPP(c_COMBS(_1494881, tc_fun(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1494883, tc_HOL_Obool), tc_fun(tc_fun(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), _1494881), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), _1494887)), hAPP(hAPP(c_COMBC(_1494881, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1494883, tc_fun(tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), _1494881), c_COMBC(_1494883, tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1494883, tc_prod(_1494881, _1494883)), tc_fun(_1494883, tc_fun(tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))), _1494881), hAPP(c_COMBB(tc_prod(_1494881, _1494883), tc_fun(tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool), tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool)), _1494883), c_Set_Oinsert(tc_prod(_1494881, _1494883)))), c_Product__Type_OPair(_1494881, _1494883)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1494881, _1494883), tc_HOL_Obool))))))], (37644 ^ _779448) ^ [_1495161, _1495163, _1495165] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495161), _1495163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495161, _1495161), tc_HOL_Obool)), _1495165), hAPP(hAPP(c_Product__Type_OSigma(_1495161, _1495161), _1495163), hAPP(c_COMBK(tc_fun(_1495161, tc_HOL_Obool), _1495161), _1495163)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1495161, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1495161), _1495163), _1495165))))], (37655 ^ _779448) ^ [_1495392, _1495394, _1495396, _1495398] : [-(c_Fun_Oinj__on(_1495392, tc_prod(_1495394, _1495392), 37653 ^ [_1495392, _1495394, _1495396, _1495398], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1495394, tc_fun(_1495392, tc_HOL_Obool)), _1495396), _1495398)))], (37657 ^ _779448) ^ [_1495446, _1495448, _1495450, _1495452] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495448, _1495446), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1495446, tc_prod(_1495448, _1495446), 37653 ^ [_1495446, _1495448, _1495450, _1495452]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1495448, tc_fun(_1495446, tc_HOL_Obool)), _1495450), _1495452))), hAPP(hAPP(c_Product__Type_OSigma(_1495448, _1495446), _1495450), _1495452))))], (37659 ^ _779448) ^ [_1495532, _1495534, _1495536, _1495538, _1495540, _1495542] : [class_Groups_Ocomm__monoid__mult(_1495532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495534), _1495536)), 37669 ^ _779448 : [(37670 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1495534), 37668 ^ [_1495532, _1495534, _1495536, _1495538, _1495540, _1495542]), _1495536)))], (37672 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1495538), hAPP(_1495540, 37668 ^ [_1495532, _1495534, _1495536, _1495538, _1495540, _1495542])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1495532, _1495534, c_Groups_Otimes__class_Otimes(_1495532)), hAPP(hAPP(c_COMBS(_1495534, tc_fun(_1495538, tc_HOL_Obool), _1495532), hAPP(hAPP(c_COMBC(_1495534, _1495532, tc_fun(tc_fun(_1495538, tc_HOL_Obool), _1495532)), hAPP(hAPP(c_COMBB(tc_fun(_1495538, _1495532), tc_fun(_1495532, tc_fun(tc_fun(_1495538, tc_HOL_Obool), _1495532)), _1495534), c_Finite__Set_Ofold__image(_1495532, _1495538, c_Groups_Otimes__class_Otimes(_1495532))), _1495542)), c_Groups_Oone__class_Oone(_1495532))), _1495540)), c_Groups_Oone__class_Oone(_1495532)), _1495536) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1495532, tc_prod(_1495534, _1495538), c_Groups_Otimes__class_Otimes(_1495532)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495534, _1495538, _1495532), _1495542)), c_Groups_Oone__class_Oone(_1495532)), hAPP(hAPP(c_Product__Type_OSigma(_1495534, _1495538), _1495536), _1495540)))], (37676 ^ _779448) ^ [_1496089, _1496091, _1496093, _1496095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496089), _1496091)), 37682 ^ _779448 : [(37683 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496089), 37681 ^ [_1496089, _1496091, _1496093, _1496095]), _1496091)))], (37685 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496093), hAPP(_1496095, 37681 ^ [_1496089, _1496091, _1496093, _1496095])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1496089, _1496093)), hAPP(hAPP(c_Product__Type_OSigma(_1496089, _1496093), _1496091), _1496095))))], (37689 ^ _779448) ^ [_1496376, _1496378, _1496380, _1496382, _1496384, _1496386] : [class_Groups_Ocomm__monoid__mult(_1496376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496378), _1496380)), 37699 ^ _779448 : [(37700 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496378), 37698 ^ [_1496376, _1496378, _1496380, _1496382, _1496384, _1496386]), _1496380)))], (37702 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496382), hAPP(_1496384, 37698 ^ [_1496376, _1496378, _1496380, _1496382, _1496384, _1496386])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1496378, _1496376), hAPP(hAPP(c_COMBS(_1496378, tc_fun(_1496382, tc_HOL_Obool), _1496376), hAPP(hAPP(c_COMBB(tc_fun(_1496382, _1496376), tc_fun(tc_fun(_1496382, tc_HOL_Obool), _1496376), _1496378), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1496382, _1496376)), _1496386)), _1496384)), _1496380) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1496378, _1496382), _1496376), hAPP(c_Product__Type_Oprod_Oprod__case(_1496378, _1496382, _1496376), _1496386)), hAPP(hAPP(c_Product__Type_OSigma(_1496378, _1496382), _1496380), _1496384)))], (37706 ^ _779448) ^ [_1496853, _1496855, _1496857, _1496859, _1496861, _1496863] : [class_Groups_Ocomm__monoid__add(_1496853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496855), _1496857)), 37716 ^ _779448 : [(37717 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1496855), 37715 ^ [_1496853, _1496855, _1496857, _1496859, _1496861, _1496863]), _1496857)))], (37719 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1496859), hAPP(_1496861, 37715 ^ [_1496853, _1496855, _1496857, _1496859, _1496861, _1496863])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1496855, _1496853), hAPP(hAPP(c_COMBS(_1496855, tc_fun(_1496859, tc_HOL_Obool), _1496853), hAPP(hAPP(c_COMBB(tc_fun(_1496859, _1496853), tc_fun(tc_fun(_1496859, tc_HOL_Obool), _1496853), _1496855), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1496859, _1496853)), _1496863)), _1496861)), _1496857) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1496855, _1496859), _1496853), hAPP(c_Product__Type_Oprod_Oprod__case(_1496855, _1496859, _1496853), _1496863)), hAPP(hAPP(c_Product__Type_OSigma(_1496855, _1496859), _1496857), _1496861)))], (37723 ^ _779448) ^ [_1497330, _1497332, _1497334, _1497336] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497330), _1497332)), 37729 ^ _779448 : [(37730 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497330), 37728 ^ [_1497330, _1497332, _1497334, _1497336]), _1497332)))], (37732 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1497334), hAPP(_1497336, 37728 ^ [_1497330, _1497332, _1497334, _1497336])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1497330, _1497334)), hAPP(hAPP(c_Product__Type_OSigma(_1497330, _1497334), _1497332), _1497336)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497330, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1497334, tc_HOL_Obool), tc_Nat_Onat, _1497330), c_Finite__Set_Ocard(_1497334)), _1497336)), _1497332))], (37736 ^ _779448) ^ [_1497667, _1497669, _1497671, _1497673, _1497675] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497667, _1497669)), _1497671), hAPP(hAPP(c_Product__Type_OSigma(_1497667, _1497669), _1497673), _1497675))), 37740 ^ _779448 : [(37741 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497667), 37739 ^ [_1497667, _1497669, _1497671, _1497673, _1497675]), _1497673)))], (37744 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497669), 37742 ^ [_1497667, _1497669, _1497671, _1497673, _1497675]), hAPP(_1497675, 37739 ^ [_1497667, _1497669, _1497671, _1497673, _1497675]))))], (37746 ^ _779448) ^ [] : [-(_1497671 = hAPP(hAPP(c_Product__Type_OPair(_1497667, _1497669), 37739 ^ [_1497667, _1497669, _1497671, _1497673, _1497675]), 37742 ^ [_1497667, _1497669, _1497671, _1497673, _1497675]))]]], (37748 ^ _779448) ^ [_1497969, _1497971, _1497973, _1497975, _1497977, _1497979] : [hAPP(c_Set_Oimage(_1497969, _1497971, _1497973), c_Orderings_Otop__class_Otop(tc_fun(_1497969, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1497971, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1497975, _1497977, _1497979), c_Orderings_Otop__class_Otop(tc_fun(_1497975, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1497977, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1497969, _1497975), tc_prod(_1497971, _1497977), c_Product__Type_Omap__pair(_1497969, _1497971, _1497975, _1497977, _1497973, _1497979)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1497969, _1497975), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1497971, _1497977), tc_HOL_Obool)))], (37758 ^ _779448) ^ [_1498254, _1498256, _1498258, _1498260, _1498262, _1498264, _1498266, _1498268] : [c_Fun_Oinj__on(_1498254, _1498256, _1498258, _1498260), c_Fun_Oinj__on(_1498262, _1498264, _1498266, _1498268), -(c_Fun_Oinj__on(tc_prod(_1498254, _1498262), tc_prod(_1498256, _1498264), c_Product__Type_Omap__pair(_1498254, _1498256, _1498262, _1498264, _1498258, _1498266), hAPP(hAPP(c_Product__Type_OSigma(_1498254, _1498262), _1498260), hAPP(c_COMBK(tc_fun(_1498262, tc_HOL_Obool), _1498254), _1498268))))], (37768 ^ _779448) ^ [_1498481, _1498483, _1498485, _1498487, _1498489, _1498491, _1498493, _1498495, _1498497] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498481, _1498483)), hAPP(hAPP(c_Product__Type_OPair(_1498481, _1498483), _1498485), _1498487)), _1498489)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498491, _1498493)), hAPP(hAPP(c_Product__Type_OPair(_1498491, _1498493), hAPP(_1498495, _1498485)), hAPP(_1498497, _1498487))), hAPP(c_Set_Oimage(tc_prod(_1498481, _1498483), tc_prod(_1498491, _1498493), c_Product__Type_Omap__pair(_1498481, _1498491, _1498483, _1498493, _1498495, _1498497)), _1498489))))], (37774 ^ _779448) ^ [_1498700, _1498702, _1498704, _1498706, _1498708, _1498710, _1498712, _1498714] : [-(hAPP(c_Product__Type_Omap__pair(_1498700, _1498702, _1498704, _1498706, _1498708, _1498710), hAPP(hAPP(c_Product__Type_OPair(_1498700, _1498704), _1498712), _1498714)) = hAPP(hAPP(c_Product__Type_OPair(_1498702, _1498706), hAPP(_1498708, _1498712)), hAPP(_1498710, _1498714)))], (37776 ^ _779448) ^ [_1498771, _1498773, _1498775] : [-(hAPP(c_Product__Type_Omap__pair(_1498771, _1498771, _1498773, _1498773, c_COMBI(_1498771), c_COMBI(_1498773)), _1498775) = _1498775)], (37778 ^ _779448) ^ [_1498812, _1498814, _1498816, _1498818, _1498820, _1498822, _1498824] : [-(hAPP(c_Product__Type_Osnd(_1498812, _1498814), hAPP(c_Product__Type_Omap__pair(_1498816, _1498812, _1498818, _1498814, _1498820, _1498822), _1498824)) = hAPP(_1498822, hAPP(c_Product__Type_Osnd(_1498816, _1498818), _1498824)))], (37780 ^ _779448) ^ [_1498872, _1498874, _1498876, _1498878, _1498880, _1498882, _1498884] : [-(hAPP(c_Product__Type_Ofst(_1498872, _1498874), hAPP(c_Product__Type_Omap__pair(_1498876, _1498872, _1498878, _1498874, _1498880, _1498882), _1498884)) = hAPP(_1498880, hAPP(c_Product__Type_Ofst(_1498876, _1498878), _1498884)))], (37782 ^ _779448) ^ [_1498932, _1498934, _1498936, _1498938, _1498940, _1498942] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1498932, _1498934), _1498932, tc_prod(_1498936, _1498938), c_Product__Type_Ofst(_1498932, _1498934)), c_Product__Type_Omap__pair(_1498936, _1498932, _1498938, _1498934, _1498940, _1498942)) = hAPP(c_Fun_Ocomp(_1498936, _1498932, tc_prod(_1498936, _1498938), _1498940), c_Product__Type_Ofst(_1498936, _1498938)))], (37784 ^ _779448) ^ [_1499003, _1499005, _1499007, _1499009, _1499011, _1499013] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1499003, _1499005), _1499005, tc_prod(_1499007, _1499009), c_Product__Type_Osnd(_1499003, _1499005)), c_Product__Type_Omap__pair(_1499007, _1499003, _1499009, _1499005, _1499011, _1499013)) = hAPP(c_Fun_Ocomp(_1499009, _1499005, tc_prod(_1499007, _1499009), _1499013), c_Product__Type_Osnd(_1499007, _1499009)))], (37786 ^ _779448) ^ [_1499074, _1499076, _1499078, _1499080, _1499082, _1499084, _1499086, _1499088, _1499090, _1499092] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1499074, _1499076), tc_prod(_1499078, _1499080), tc_prod(_1499082, _1499084), c_Product__Type_Omap__pair(_1499074, _1499078, _1499076, _1499080, _1499086, _1499088)), c_Product__Type_Omap__pair(_1499082, _1499074, _1499084, _1499076, _1499090, _1499092)) = c_Product__Type_Omap__pair(_1499082, _1499078, _1499084, _1499080, hAPP(c_Fun_Ocomp(_1499074, _1499078, _1499082, _1499086), _1499090), hAPP(c_Fun_Ocomp(_1499076, _1499080, _1499084, _1499088), _1499092)))], (37788 ^ _779448) ^ [_1499169, _1499171, _1499173, _1499175, _1499177, _1499179, _1499181, _1499183, _1499185, _1499187] : [-(c_Product__Type_Omap__pair(_1499169, _1499171, _1499173, _1499175, hAPP(c_Fun_Ocomp(_1499177, _1499171, _1499169, _1499179), _1499181), hAPP(c_Fun_Ocomp(_1499183, _1499175, _1499173, _1499185), _1499187)) = hAPP(c_Fun_Ocomp(tc_prod(_1499177, _1499183), tc_prod(_1499171, _1499175), tc_prod(_1499169, _1499173), c_Product__Type_Omap__pair(_1499177, _1499171, _1499183, _1499175, _1499179, _1499185)), c_Product__Type_Omap__pair(_1499169, _1499177, _1499173, _1499183, _1499181, _1499187)))], (37790 ^ _779448) ^ [_1499264, _1499266, _1499268, _1499270, _1499272, _1499274, _1499276, _1499278, _1499280, _1499282, _1499284] : [-(hAPP(c_Product__Type_Omap__pair(_1499264, _1499266, _1499268, _1499270, _1499272, _1499274), hAPP(c_Product__Type_Omap__pair(_1499276, _1499264, _1499278, _1499268, _1499280, _1499282), _1499284)) = hAPP(c_Product__Type_Omap__pair(_1499276, _1499266, _1499278, _1499270, hAPP(c_Fun_Ocomp(_1499264, _1499266, _1499276, _1499272), _1499280), hAPP(c_Fun_Ocomp(_1499268, _1499270, _1499278, _1499274), _1499282)), _1499284))], (37792 ^ _779448) ^ [_1499353, _1499355, _1499357, _1499359, _1499361, _1499363] : [-(c_Product__Type_Omap__pair(_1499353, _1499355, _1499357, _1499359, _1499361, _1499363) = hAPP(c_Product__Type_Oprod_Oprod__case(_1499353, _1499357, tc_prod(_1499355, _1499359)), hAPP(hAPP(c_COMBC(_1499353, tc_fun(_1499357, _1499359), tc_fun(_1499357, tc_prod(_1499355, _1499359))), hAPP(hAPP(c_COMBB(tc_fun(_1499359, tc_prod(_1499355, _1499359)), tc_fun(tc_fun(_1499357, _1499359), tc_fun(_1499357, tc_prod(_1499355, _1499359))), _1499353), c_COMBB(_1499359, tc_prod(_1499355, _1499359), _1499357)), hAPP(hAPP(c_COMBB(_1499355, tc_fun(_1499359, tc_prod(_1499355, _1499359)), _1499353), c_Product__Type_OPair(_1499355, _1499359)), _1499361))), _1499363)))], (37794 ^ _779448) ^ [_1499476, _1499478, _1499480, _1499482, _1499484, _1499486, _1499488, _1499490, _1499492, _1499494] : [hAPP(c_Set_Oimage(_1499476, _1499478, _1499480), _1499482) = _1499484, hAPP(c_Set_Oimage(_1499486, _1499488, _1499490), _1499492) = _1499494, -(hAPP(c_Set_Oimage(tc_prod(_1499476, _1499486), tc_prod(_1499478, _1499488), c_Product__Type_Omap__pair(_1499476, _1499478, _1499486, _1499488, _1499480, _1499490)), hAPP(hAPP(c_Product__Type_OSigma(_1499476, _1499486), _1499482), hAPP(c_COMBK(tc_fun(_1499486, tc_HOL_Obool), _1499476), _1499492))) = hAPP(hAPP(c_Product__Type_OSigma(_1499478, _1499488), _1499484), hAPP(c_COMBK(tc_fun(_1499488, tc_HOL_Obool), _1499478), _1499494)))], (37804 ^ _779448) ^ [_1499777, _1499779, _1499781, _1499783, _1499785, _1499787, _1499789, _1499791] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499777, _1499779)), _1499781), hAPP(c_Set_Oimage(tc_prod(_1499783, _1499785), tc_prod(_1499777, _1499779), c_Product__Type_Omap__pair(_1499783, _1499777, _1499785, _1499779, _1499787, _1499789)), _1499791))), 37809 ^ _779448 : [(37810 ^ _779448) ^ [] : [-(_1499781 = hAPP(hAPP(c_Product__Type_OPair(_1499777, _1499779), hAPP(_1499787, 37807 ^ [_1499777, _1499779, _1499781, _1499783, _1499785, _1499787, _1499789, _1499791])), hAPP(_1499789, 37808 ^ [_1499777, _1499779, _1499781, _1499783, _1499785, _1499787, _1499789, _1499791])))], (37812 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499783, _1499785)), hAPP(hAPP(c_Product__Type_OPair(_1499783, _1499785), 37807 ^ [_1499777, _1499779, _1499781, _1499783, _1499785, _1499787, _1499789, _1499791]), 37808 ^ [_1499777, _1499779, _1499781, _1499783, _1499785, _1499787, _1499789, _1499791])), _1499791)))]]], (37814 ^ _779448) ^ [_1500128, _1500130, _1500132] : [c_Relation_Orefl__on(_1500128, _1500130, _1500132), 37817 ^ _779448 : [(37818 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500128, _1500128), tc_HOL_Obool)), _1500132), hAPP(hAPP(c_Product__Type_OSigma(_1500128, _1500128), _1500130), hAPP(c_COMBK(tc_fun(_1500128, tc_HOL_Obool), _1500128), _1500130)))))], (37820 ^ _779448) ^ [_1500310] : [hBOOL(hAPP(hAPP(c_member(_1500128), _1500310), _1500130)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500128, _1500128)), hAPP(hAPP(c_Product__Type_OPair(_1500128, _1500128), _1500310), _1500310)), _1500132)))]]], (37826 ^ _779448) ^ [_1500445, _1500447, _1500449] : [-(c_Relation_Orefl__on(_1500445, _1500447, _1500449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500445, _1500445), tc_HOL_Obool)), _1500449), hAPP(hAPP(c_Product__Type_OSigma(_1500445, _1500445), _1500447), hAPP(c_COMBK(tc_fun(_1500445, tc_HOL_Obool), _1500445), _1500447)))), 37832 ^ _779448 : [(37833 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500445), 37831 ^ [_1500445, _1500447, _1500449]), _1500447)))], (37835 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500445, _1500445)), hAPP(hAPP(c_Product__Type_OPair(_1500445, _1500445), 37831 ^ [_1500445, _1500447, _1500449]), 37831 ^ [_1500445, _1500447, _1500449])), _1500449))]]], (37839 ^ _779448) ^ [_1500794, _1500796, _1500798] : [37841 ^ _779448 : [(37842 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 37840 ^ [_1500794, _1500796, _1500798]), _1500794)))], (37844 ^ _779448) ^ [] : [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(_1500796, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 37840 ^ [_1500794, _1500796, _1500798]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1500796, 37840 ^ [_1500794, _1500796, _1500798])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1500796, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1500798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1500798), hAPP(_1500796, _1500794))), 37854 ^ _779448 : [(37855 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 37853 ^ [_1500794, _1500796, _1500798]), _1500794)))], (37857 ^ _779448) ^ [] : [-(hAPP(_1500796, 37853 ^ [_1500794, _1500796, _1500798]) = _1500798)]]], (37859 ^ _779448) ^ [_1501244, _1501246] : [-(c_Relation_Orefl__on(_1501244, _1501246, c_Relation_OId__on(_1501244, _1501246)))], (37861 ^ _779448) ^ [_1501273] : [-(c_Relation_Orefl__on(_1501273, c_Orderings_Obot__class_Obot(tc_fun(_1501273, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501273, _1501273), tc_HOL_Obool))))], (37863 ^ _779448) ^ [_1501310, _1501312, _1501314, _1501316, _1501318] : [c_Relation_Orefl__on(_1501310, _1501312, _1501314), c_Relation_Orefl__on(_1501310, _1501316, _1501318), -(c_Relation_Orefl__on(_1501310, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501310, tc_HOL_Obool)), _1501312), _1501316), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1501310, _1501310), tc_HOL_Obool)), _1501314), _1501318)))], (37873 ^ _779448) ^ [_1501507, _1501509, _1501511, _1501513, _1501515] : [c_Relation_Orefl__on(_1501507, _1501509, _1501511), c_Relation_Orefl__on(_1501507, _1501513, _1501515), -(c_Relation_Orefl__on(_1501507, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501507, tc_HOL_Obool)), _1501509), _1501513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1501507, _1501507), tc_HOL_Obool)), _1501511), _1501515)))], (37883 ^ _779448) ^ [_1501704, _1501706, _1501708, _1501710] : [c_Relation_Orefl__on(_1501704, _1501706, _1501708), hBOOL(hAPP(hAPP(c_member(_1501704), _1501710), _1501706)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501704, _1501704)), hAPP(hAPP(c_Product__Type_OPair(_1501704, _1501704), _1501710), _1501710)), _1501708)))], (37893 ^ _779448) ^ [_1501895, _1501897, _1501899, _1501901, _1501903] : [c_Relation_Orefl__on(_1501895, _1501897, _1501899), hBOOL(hAPP(hAPP(c_member(tc_prod(_1501895, _1501895)), hAPP(hAPP(c_Product__Type_OPair(_1501895, _1501895), _1501901), _1501903)), _1501899)), -(hBOOL(hAPP(hAPP(c_member(_1501895), _1501901), _1501897)))], (37903 ^ _779448) ^ [_1502090, _1502092, _1502094, _1502096, _1502098] : [c_Relation_Orefl__on(_1502090, _1502092, _1502094), hBOOL(hAPP(hAPP(c_member(tc_prod(_1502090, _1502090)), hAPP(hAPP(c_Product__Type_OPair(_1502090, _1502090), _1502096), _1502098)), _1502094)), -(hBOOL(hAPP(hAPP(c_member(_1502090), _1502098), _1502092)))], (37913 ^ _779448) ^ [_1502285, _1502287, _1502289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1502285, _1502285), tc_HOL_Obool)), _1502287), hAPP(hAPP(c_Product__Type_OSigma(_1502285, _1502285), _1502289), hAPP(c_COMBK(tc_fun(_1502285, tc_HOL_Obool), _1502285), _1502289)))), 37919 ^ _779448 : [(37920 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502285), 37918 ^ [_1502285, _1502287, _1502289]), _1502289)))], (37922 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1502285, _1502285)), hAPP(hAPP(c_Product__Type_OPair(_1502285, _1502285), 37918 ^ [_1502285, _1502287, _1502289]), 37918 ^ [_1502285, _1502287, _1502289])), _1502287))]], -(c_Relation_Orefl__on(_1502285, _1502289, _1502287))], (37926 ^ _779448) ^ [_1502632, _1502634, _1502636] : [37928 ^ _779448 : [(37929 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 37927 ^ [_1502632, _1502634, _1502636]), _1502632)))], (37931 ^ _779448) ^ [] : [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(_1502634, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 37927 ^ [_1502632, _1502634, _1502636]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1502634, 37927 ^ [_1502632, _1502634, _1502636])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1502634, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1502636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1502636), hAPP(_1502634, _1502632))), 37941 ^ _779448 : [(37942 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 37940 ^ [_1502632, _1502634, _1502636]), _1502632)))], (37944 ^ _779448) ^ [] : [-(hAPP(_1502634, 37940 ^ [_1502632, _1502634, _1502636]) = _1502636)]]], (37946 ^ _779448) ^ [_1503082, _1503084, _1503086] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503082), _1503084)), 37952 ^ _779448 : [(37953 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503082), 37951 ^ [_1503082, _1503084, _1503086]), _1503084)))], (37955 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1503086, 37951 ^ [_1503082, _1503084, _1503086])))]], -(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(_1503082, tc_Nat_Onat), _1503086), _1503084))))], (37959 ^ _779448) ^ [_1503343, _1503345] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1503343), c_Int_OInteg)), hBOOL(hAPP(_1503345, hAPP(c_Int_ORep__Integ, 37964 ^ [_1503343, _1503345]))), -(hBOOL(hAPP(_1503345, _1503343)))], (37970 ^ _779448) ^ [_1503525] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1503525), c_Int_OInteg)), -(_1503525 = hAPP(c_Int_ORep__Integ, 37973 ^ [_1503525]))], (37977 ^ _779448) ^ [_1503630, _1503632, _1503634, _1503636, _1503638, _1503640, _1503642, _1503644] : [c_Finite__Set_Ofolding__image__simple(_1503630, _1503632, _1503634, _1503636, _1503638, _1503640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503632), _1503642)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503632), _1503644)), 37991 ^ _779448 : [(37992 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503632), 37990 ^ [_1503630, _1503632, _1503634, _1503636, _1503638, _1503640, _1503642, _1503644]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1503632, tc_HOL_Obool)), _1503642), _1503644))))], (37994 ^ _779448) ^ [] : [hAPP(_1503638, 37990 ^ [_1503630, _1503632, _1503634, _1503636, _1503638, _1503640, _1503642, _1503644]) = _1503636]], -(hAPP(_1503640, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1503632, tc_HOL_Obool)), _1503642), _1503644)) = hAPP(hAPP(_1503634, hAPP(_1503640, _1503642)), hAPP(_1503640, _1503644)))], (37998 ^ _779448) ^ [_1504130, _1504132, _1504134, _1504136, _1504138, _1504140] : [-(_1504130 = c_Orderings_Obot__class_Obot(tc_fun(_1504132, tc_HOL_Obool))), 38004 ^ _779448 : [(38005 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504132), 38003 ^ [_1504130, _1504132, _1504134, _1504136, _1504138, _1504140]), _1504130)))], (38007 ^ _779448) ^ [] : [c_Fun_Oinj__on(_1504134, _1504136, _1504138, hAPP(_1504140, 38003 ^ [_1504130, _1504132, _1504134, _1504136, _1504138, _1504140]))]], -(c_Fun_Oinj__on(_1504134, _1504136, _1504138, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1504132, tc_fun(_1504134, tc_HOL_Obool)), _1504130), _1504140)))], (38011 ^ _779448) ^ [_1504422, _1504424] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1504422)), -(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)), _1504422))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1504424))))) = 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)), _1504422))), 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, _1504424))))))], (38017 ^ _779448) ^ [_1504599, _1504601] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1504599)), 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)), _1504599))), 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, _1504601))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38023 ^ _779448) ^ [_1504729, _1504731, _1504733] : [hBOOL(hAPP(_1504729, _1504731)), -(hBOOL(hAPP(hAPP(c_member(_1504733), _1504731), hAPP(c_Set_OCollect(_1504733), _1504729))))], (38029 ^ _779448) ^ [_1504836, _1504838, _1504840] : [38030 ^ _779448 : [(38031 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504836), hAPP(c_Set_OCollect(_1504836), _1504838)))], (38033 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504836), hAPP(c_Set_OCollect(_1504836), _1504840)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1504836), hAPP(c_Set_OCollect(_1504836), hAPP(hAPP(c_COMBS(_1504836, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504836), c_fconj), _1504838)), _1504840)))))], (38037 ^ _779448) ^ [_1505047] : [-(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)), _1505047)))))], (38039 ^ _779448) ^ [_1505078] : [-(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)), _1505078)))))], (38041 ^ _779448) ^ [_1505109, _1505111, _1505113] : [hBOOL(hAPP(hAPP(c_member(_1505109), _1505111), hAPP(c_Set_OCollect(_1505109), _1505113))), -(hBOOL(hAPP(_1505113, _1505111)))], (38047 ^ _779448) ^ [_1505216, _1505218, _1505220] : [hBOOL(hAPP(hAPP(c_member(_1505216), _1505218), hAPP(c_Set_OCollect(_1505216), _1505220))), -(hBOOL(hAPP(_1505220, _1505218)))], (38053 ^ _779448) ^ [_1505341, _1505343, _1505345] : [hBOOL(hAPP(hAPP(c_member(_1505341), _1505343), hAPP(c_Set_OCollect(_1505341), _1505345))), -(hBOOL(hAPP(_1505345, _1505343)))], (38059 ^ _779448) ^ [_1505444, _1505446, _1505448] : [hBOOL(hAPP(_1505448, _1505446)), -(hBOOL(hAPP(hAPP(c_member(_1505444), _1505446), hAPP(c_Set_OCollect(_1505444), _1505448))))], (38065 ^ _779448) ^ [_1505553, _1505555] : [-(hAPP(c_Set_OCollect(_1505553), hAPP(hAPP(c_COMBC(_1505553, tc_fun(_1505553, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505553)), _1505555)) = _1505555)], (38067 ^ _779448) ^ [_1505598] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1505598, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1505598), hAPP(c_COMBK(tc_HOL_Obool, _1505598), c_fTrue)))], (38069 ^ _779448) ^ [_1505655, _1505657, _1505659] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1505655), hAPP(c_Set_OCollect(_1505655), hAPP(hAPP(c_COMBS(_1505655, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505655), c_fdisj), _1505657)), _1505659)))), 38072 ^ _779448 : [(38073 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505655), hAPP(c_Set_OCollect(_1505655), _1505657))))], (38075 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505655), hAPP(c_Set_OCollect(_1505655), _1505659))))]]], (38077 ^ _779448) ^ [_1505850, _1505852, _1505854] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1505850), hAPP(c_Set_OCollect(_1505850), hAPP(hAPP(c_COMBS(_1505850, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505850), c_fdisj), _1505852)), _1505854))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505850), hAPP(c_Set_OCollect(_1505850), _1505852))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505850), hAPP(c_Set_OCollect(_1505850), _1505854)))], (38087 ^ _779448) ^ [_1506079, _1506081, _1506083] : [-(hAPP(c_Set_OCollect(_1506079), hAPP(hAPP(c_COMBS(_1506079, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506079), c_fconj), _1506081)), _1506083)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506079, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1506079), _1506081)), hAPP(c_Set_OCollect(_1506079), _1506083)))], (38089 ^ _779448) ^ [_1506152, _1506154, _1506156] : [-(hAPP(hAPP(c_Set_Oinsert(_1506152), _1506154), hAPP(c_Set_OCollect(_1506152), _1506156)) = hAPP(c_Set_OCollect(_1506152), hAPP(hAPP(c_COMBS(_1506152, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506152), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506152), c_fNot), hAPP(hAPP(c_COMBC(_1506152, _1506152, tc_HOL_Obool), c_fequal), _1506154)))), _1506156)))], (38091 ^ _779448) ^ [_1506237, _1506239, _1506241] : [-(hAPP(c_Set_OCollect(_1506237), hAPP(hAPP(c_COMBS(_1506237, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506237), c_fdisj), _1506239)), _1506241)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506237, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1506237), _1506239)), hAPP(c_Set_OCollect(_1506237), _1506241)))], (38093 ^ _779448) ^ [_1506310, _1506312] : [-(hAPP(c_Set_OCollect(_1506310), _1506312) = _1506312)], (38095 ^ _779448) ^ [_1506340] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1506340, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1506340), hAPP(c_COMBK(tc_HOL_Obool, _1506340), c_fFalse)))], (38097 ^ _779448) ^ [_1506394, _1506396] : [hAPP(c_Set_OCollect(_1506394), _1506396) = c_Orderings_Obot__class_Obot(tc_fun(_1506394, tc_HOL_Obool)), 38100 ^ _779448 : [(38101 ^ _779448) ^ [_1506479] : [hBOOL(hAPP(_1506396, _1506479))]]], (38103 ^ _779448) ^ [_1506502, _1506504] : [-(hBOOL(hAPP(_1506504, 38104 ^ [_1506502, _1506504]))), -(hAPP(c_Set_OCollect(_1506502), _1506504) = c_Orderings_Obot__class_Obot(tc_fun(_1506502, tc_HOL_Obool)))], (38110 ^ _779448) ^ [_1506574, _1506576] : [c_Orderings_Obot__class_Obot(tc_fun(_1506574, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1506574), _1506576), 38113 ^ _779448 : [(38114 ^ _779448) ^ [_1506659] : [hBOOL(hAPP(_1506576, _1506659))]]], (38116 ^ _779448) ^ [_1506682, _1506684] : [-(hBOOL(hAPP(_1506684, 38117 ^ [_1506682, _1506684]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1506682, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1506682), _1506684))], (38123 ^ _779448) ^ [_1506739, _1506741] : [-(hAPP(c_Set_OCollect(_1506739), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506739), c_fNot), _1506741)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1506739, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1506739), _1506741)))], (38125 ^ _779448) ^ [_1506792, _1506794, _1506796, _1506798] : [-(hAPP(c_Set_Ovimage(_1506792, _1506794, _1506796), hAPP(c_Set_OCollect(_1506794), _1506798)) = hAPP(c_Set_OCollect(_1506792), hAPP(hAPP(c_COMBB(_1506794, tc_HOL_Obool, _1506792), _1506798), _1506796)))], (38127 ^ _779448) ^ [_1506848, _1506850, _1506852, _1506854] : [-(hAPP(c_Set_OCollect(tc_prod(_1506848, _1506850)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506848, _1506850, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1506848, tc_fun(_1506850, tc_HOL_Obool), tc_fun(_1506850, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1506850, tc_HOL_Obool), tc_fun(_1506850, tc_HOL_Obool)), _1506848), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506850)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506848), c_fconj), _1506852))), _1506854))) = hAPP(hAPP(c_Product__Type_OSigma(_1506848, _1506850), hAPP(c_Set_OCollect(_1506848), _1506852)), hAPP(c_COMBK(tc_fun(_1506850, tc_HOL_Obool), _1506848), hAPP(c_Set_OCollect(_1506850), _1506854))))], (38129 ^ _779448) ^ [_1506969, _1506971, _1506973, _1506975] : [-(hAPP(c_Set_OCollect(tc_prod(_1506969, _1506971)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506969, _1506971, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1506969, tc_fun(_1506971, tc_HOL_Obool), tc_fun(_1506971, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1506971, tc_HOL_Obool), tc_fun(_1506971, tc_HOL_Obool)), _1506969), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1506971)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506969), c_fconj), _1506973))), _1506975))) = hAPP(hAPP(c_Product__Type_OSigma(_1506969, _1506971), hAPP(c_Set_OCollect(_1506969), _1506973)), hAPP(hAPP(c_COMBB(tc_fun(_1506971, tc_HOL_Obool), tc_fun(_1506971, tc_HOL_Obool), _1506969), c_Set_OCollect(_1506971)), _1506975)))], (38131 ^ _779448) ^ [_1507094, _1507096, _1507098] : [-(hAPP(hAPP(c_Set_Oinsert(_1507094), _1507096), _1507098) = hAPP(c_Set_OCollect(_1507094), hAPP(hAPP(c_COMBS(_1507094, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507094), c_fdisj), hAPP(hAPP(c_COMBC(_1507094, _1507094, tc_HOL_Obool), c_fequal), _1507096))), hAPP(hAPP(c_COMBC(_1507094, tc_fun(_1507094, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507094)), _1507098))))], (38133 ^ _779448) ^ [_1507179, _1507181, _1507183] : [-(hAPP(hAPP(c_Set_Oinsert(_1507179), _1507181), _1507183) = hAPP(c_Set_OCollect(_1507179), hAPP(hAPP(c_COMBS(_1507179, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507179), c_fdisj), hAPP(hAPP(c_COMBC(_1507179, _1507179, tc_HOL_Obool), c_fequal), _1507181))), hAPP(hAPP(c_COMBC(_1507179, tc_fun(_1507179, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507179)), _1507183))))], (38135 ^ _779448) ^ [_1507264, _1507266, _1507268] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507264, tc_HOL_Obool)), _1507266), _1507268) = hAPP(c_Set_OCollect(_1507264), hAPP(hAPP(c_COMBS(_1507264, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507264), c_fdisj), hAPP(hAPP(c_COMBC(_1507264, tc_fun(_1507264, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507264)), _1507266))), hAPP(hAPP(c_COMBC(_1507264, tc_fun(_1507264, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507264)), _1507268))))], (38137 ^ _779448) ^ [_1507378, _1507380, _1507382, _1507384] : [hBOOL(hAPP(hAPP(c_member(_1507378), _1507380), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507378, tc_HOL_Obool)), _1507382), hAPP(c_Set_OCollect(_1507378), _1507384)))), 38140 ^ _779448 : [(38141 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507378), _1507380), _1507382)))], (38143 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1507384, _1507380)))]]], (38145 ^ _779448) ^ [_1507545, _1507547, _1507549, _1507551] : [-(hBOOL(hAPP(hAPP(c_member(_1507545), _1507547), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507545, tc_HOL_Obool)), _1507549), hAPP(c_Set_OCollect(_1507545), _1507551))))), hBOOL(hAPP(hAPP(c_member(_1507545), _1507547), _1507549)), hBOOL(hAPP(_1507551, _1507547))], (38155 ^ _779448) ^ [_1507748, _1507750, _1507752] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1507748, tc_HOL_Obool)), _1507750), _1507752) = hAPP(c_Set_OCollect(_1507748), hAPP(hAPP(c_COMBS(_1507748, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507748), c_fconj), hAPP(hAPP(c_COMBC(_1507748, tc_fun(_1507748, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507748)), _1507750))), hAPP(hAPP(c_COMBC(_1507748, tc_fun(_1507748, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507748)), _1507752))))], (38157 ^ _779448) ^ [_1507841, _1507843] : [-(hAPP(c_Set_OCollect(_1507841), hAPP(c_fequal, _1507843)) = hAPP(hAPP(c_Set_Oinsert(_1507841), _1507843), c_Orderings_Obot__class_Obot(tc_fun(_1507841, tc_HOL_Obool))))], (38159 ^ _779448) ^ [_1507887, _1507889] : [-(hAPP(c_Set_OCollect(_1507887), hAPP(hAPP(c_COMBC(_1507887, _1507887, tc_HOL_Obool), c_fequal), _1507889)) = hAPP(hAPP(c_Set_Oinsert(_1507887), _1507889), c_Orderings_Obot__class_Obot(tc_fun(_1507887, tc_HOL_Obool))))], (38161 ^ _779448) ^ [_1507952, _1507954, _1507956] : [hBOOL(hAPP(_1507952, _1507954)), -(hAPP(c_Set_OCollect(_1507956), hAPP(hAPP(c_COMBS(_1507956, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507956), c_fconj), hAPP(c_fequal, _1507954))), _1507952)) = hAPP(hAPP(c_Set_Oinsert(_1507956), _1507954), c_Orderings_Obot__class_Obot(tc_fun(_1507956, tc_HOL_Obool))))], (38167 ^ _779448) ^ [_1508111, _1508113, _1508115] : [-(hBOOL(hAPP(_1508111, _1508113))), -(hAPP(c_Set_OCollect(_1508115), hAPP(hAPP(c_COMBS(_1508115, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508115), c_fconj), hAPP(c_fequal, _1508113))), _1508111)) = c_Orderings_Obot__class_Obot(tc_fun(_1508115, tc_HOL_Obool)))], (38173 ^ _779448) ^ [_1508198, _1508200, _1508202] : [hBOOL(hAPP(_1508198, _1508200)), -(hAPP(c_Set_OCollect(_1508202), hAPP(hAPP(c_COMBS(_1508202, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508202), c_fconj), hAPP(hAPP(c_COMBC(_1508202, _1508202, tc_HOL_Obool), c_fequal), _1508200))), _1508198)) = hAPP(hAPP(c_Set_Oinsert(_1508202), _1508200), c_Orderings_Obot__class_Obot(tc_fun(_1508202, tc_HOL_Obool))))], (38179 ^ _779448) ^ [_1508371, _1508373, _1508375] : [-(hBOOL(hAPP(_1508371, _1508373))), -(hAPP(c_Set_OCollect(_1508375), hAPP(hAPP(c_COMBS(_1508375, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508375), c_fconj), hAPP(hAPP(c_COMBC(_1508375, _1508375, tc_HOL_Obool), c_fequal), _1508373))), _1508371)) = c_Orderings_Obot__class_Obot(tc_fun(_1508375, tc_HOL_Obool)))], (38185 ^ _779448) ^ [_1508453, _1508455, _1508457] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508453, tc_HOL_Obool)), _1508455), _1508457) = hAPP(c_Set_OCollect(_1508453), hAPP(hAPP(c_COMBS(_1508453, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508453), c_fconj), hAPP(hAPP(c_COMBC(_1508453, tc_fun(_1508453, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508453)), _1508455))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508453), c_fNot), hAPP(hAPP(c_COMBC(_1508453, tc_fun(_1508453, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508453)), _1508457)))))], (38187 ^ _779448) ^ [_1508556, _1508558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508556), hAPP(c_Set_OCollect(_1508556), _1508558))), 38190 ^ _779448 : [(38191 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508556), hAPP(c_Set_OCollect(_1508556), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508556), c_fNot), _1508558)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1508556), c_Orderings_Otop__class_Otop(tc_fun(_1508556, tc_HOL_Obool)))))], (38197 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1508556), c_Orderings_Otop__class_Otop(tc_fun(_1508556, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1508556), hAPP(c_Set_OCollect(_1508556), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508556), c_fNot), _1508558)))))]]], (38203 ^ _779448) ^ [_1508865, _1508867, _1508869] : [-(hAPP(hAPP(c_Set_Oinsert(_1508865), _1508867), _1508869) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1508865, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1508865), hAPP(hAPP(c_COMBC(_1508865, _1508865, tc_HOL_Obool), c_fequal), _1508867))), _1508869))], (38205 ^ _779448) ^ [_1508926, _1508928] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1508926, tc_HOL_Obool)), _1508928) = hAPP(c_Set_OCollect(_1508926), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508926), c_fNot), hAPP(hAPP(c_COMBC(_1508926, tc_fun(_1508926, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508926)), _1508928))))], (38207 ^ _779448) ^ [_1508989, _1508991, _1508993, _1508995] : [-(hAPP(c_Set_Ovimage(_1508989, _1508991, _1508993), _1508995) = hAPP(c_Set_OCollect(_1508989), hAPP(hAPP(c_COMBC(_1508989, tc_fun(_1508991, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1508991, tc_fun(tc_fun(_1508991, tc_HOL_Obool), tc_HOL_Obool), _1508989), c_member(_1508991)), _1508993)), _1508995)))], (38209 ^ _779448) ^ [_1509061, _1509063, _1509065] : [-(hAPP(c_Set_OCollect(_1509061), hAPP(hAPP(c_COMBS(_1509061, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509061), c_fimplies), _1509063)), _1509065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509061, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1509061, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1509061), _1509063))), hAPP(c_Set_OCollect(_1509061), _1509065)))], (38211 ^ _779448) ^ [_1509142, _1509144] : [-(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), _1509142)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1509144))))))], (38213 ^ _779448) ^ [_1509184, _1509186, _1509188, _1509190, _1509192, _1509194, _1509196] : [class_Groups_Ocomm__monoid__add(_1509184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509186), _1509188)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509190), _1509192)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509186, _1509184), hAPP(hAPP(c_COMBS(_1509186, tc_fun(_1509190, tc_HOL_Obool), _1509184), hAPP(hAPP(c_COMBB(tc_fun(_1509190, _1509184), tc_fun(tc_fun(_1509190, tc_HOL_Obool), _1509184), _1509186), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509190, _1509184)), _1509194)), hAPP(hAPP(c_COMBB(tc_fun(_1509190, tc_HOL_Obool), tc_fun(_1509190, tc_HOL_Obool), _1509186), c_Set_OCollect(_1509190)), hAPP(hAPP(c_COMBB(tc_fun(_1509190, tc_HOL_Obool), tc_fun(_1509190, tc_HOL_Obool), _1509186), hAPP(c_COMBS(_1509190, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509190), c_fconj), hAPP(hAPP(c_COMBC(_1509190, tc_fun(_1509190, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509190)), _1509192)))), _1509196)))), _1509188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509190, _1509184), hAPP(hAPP(c_COMBS(_1509190, tc_fun(_1509186, tc_HOL_Obool), _1509184), hAPP(hAPP(c_COMBB(tc_fun(_1509186, _1509184), tc_fun(tc_fun(_1509186, tc_HOL_Obool), _1509184), _1509190), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1509186, _1509184)), hAPP(c_COMBC(_1509186, _1509190, _1509184), _1509194))), hAPP(hAPP(c_COMBB(tc_fun(_1509186, tc_HOL_Obool), tc_fun(_1509186, tc_HOL_Obool), _1509190), c_Set_OCollect(_1509186)), hAPP(hAPP(c_COMBB(tc_fun(_1509186, tc_HOL_Obool), tc_fun(_1509186, tc_HOL_Obool), _1509190), hAPP(c_COMBS(_1509186, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509186), c_fconj), hAPP(hAPP(c_COMBC(_1509186, tc_fun(_1509186, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509186)), _1509188)))), hAPP(c_COMBC(_1509186, _1509190, tc_HOL_Obool), _1509196))))), _1509192))], (38227 ^ _779448) ^ [_1509877, _1509879, _1509881, _1509883, _1509885, _1509887] : [-(hAPP(c_Set_Oimage(_1509877, _1509879, hAPP(hAPP(c_COMBS(_1509877, _1509879, _1509879), hAPP(hAPP(c_COMBS(_1509877, _1509879, tc_fun(_1509879, _1509879)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1509879, tc_fun(_1509879, _1509879)), _1509877), c_If(_1509879)), _1509881)), _1509883)), _1509885)), _1509887) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509879, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509877, _1509879, _1509883), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509877, tc_HOL_Obool)), _1509887), hAPP(c_Set_OCollect(_1509877), _1509881)))), hAPP(c_Set_Oimage(_1509877, _1509879, _1509885), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509877, tc_HOL_Obool)), _1509887), hAPP(c_Set_OCollect(_1509877), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1509877), c_fNot), _1509881))))))], (38229 ^ _779448) ^ [_1510025, _1510027, _1510029, _1510031] : [_1510025 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1510027, _1510029), 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)), _1510031))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1510027), _1510025)))], (38235 ^ _779448) ^ [_1510140, _1510142, _1510144, _1510146, _1510148] : [class_Groups_Ocomm__monoid__add(_1510140), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510142), _1510144)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510142, _1510140), _1510146), hAPP(c_Set_OCollect(_1510142), hAPP(hAPP(c_COMBS(_1510142, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510142), c_fconj), hAPP(hAPP(c_COMBC(_1510142, tc_fun(_1510142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510142)), _1510144))), hAPP(hAPP(c_COMBC(_1510142, tc_fun(_1510142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510142)), _1510148)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510142, _1510140), hAPP(hAPP(c_COMBC(_1510142, _1510140, _1510140), hAPP(hAPP(c_COMBS(_1510142, _1510140, tc_fun(_1510140, _1510140)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1510140, tc_fun(_1510140, _1510140)), _1510142), c_If(_1510140)), hAPP(hAPP(c_COMBC(_1510142, tc_fun(_1510142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510142)), _1510148))), _1510146)), c_Groups_Ozero__class_Ozero(_1510140))), _1510144))], (38245 ^ _779448) ^ [_1510549, _1510551, _1510553, _1510555, _1510557, _1510559] : [class_Groups_Ocomm__monoid__add(_1510549), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510551), _1510553)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510551, _1510549), _1510555), _1510553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510557, _1510549), hAPP(hAPP(c_COMBB(tc_fun(_1510551, tc_HOL_Obool), _1510549, _1510557), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510551, _1510549), _1510555)), hAPP(hAPP(c_COMBB(tc_fun(_1510551, tc_HOL_Obool), tc_fun(_1510551, tc_HOL_Obool), _1510557), c_Set_OCollect(_1510551)), hAPP(hAPP(c_COMBB(tc_fun(_1510551, tc_HOL_Obool), tc_fun(_1510551, tc_HOL_Obool), _1510557), hAPP(c_COMBS(_1510551, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510551), c_fconj), hAPP(hAPP(c_COMBC(_1510551, tc_fun(_1510551, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510551)), _1510553)))), hAPP(c_COMBC(_1510551, _1510557, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1510557, tc_fun(_1510557, tc_HOL_Obool), _1510551), c_fequal), _1510559)))))), hAPP(c_Set_Oimage(_1510551, _1510557, _1510559), _1510553)))], (38255 ^ _779448) ^ [_1510960, _1510962, _1510964, _1510966] : [-(hAPP(c_Relation_OImage(_1510960, _1510962, _1510964), hAPP(hAPP(c_Set_Oinsert(_1510960), _1510966), c_Orderings_Obot__class_Obot(tc_fun(_1510960, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1510962), hAPP(hAPP(c_COMBC(_1510962, tc_fun(tc_prod(_1510960, _1510962), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1510960, _1510962), tc_fun(tc_fun(tc_prod(_1510960, _1510962), tc_HOL_Obool), tc_HOL_Obool), _1510962), c_member(tc_prod(_1510960, _1510962))), hAPP(c_Product__Type_OPair(_1510960, _1510962), _1510966))), _1510964)))], (38257 ^ _779448) ^ [_1511063, _1511065, _1511067, _1511069, _1511071, _1511073] : [class_Groups_Ocomm__monoid__add(_1511063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511065), _1511067)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511065, _1511063), hAPP(hAPP(c_COMBS(_1511065, _1511063, _1511063), hAPP(hAPP(c_COMBS(_1511065, _1511063, tc_fun(_1511063, _1511063)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1511063, tc_fun(_1511063, _1511063)), _1511065), c_If(_1511063)), _1511069)), _1511071)), _1511073)), _1511067) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1511063), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511065, _1511063), _1511071), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511065, tc_HOL_Obool)), _1511067), hAPP(c_Set_OCollect(_1511065), _1511069)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511065, _1511063), _1511073), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511065, tc_HOL_Obool)), _1511067), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1511065, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1511065), _1511069))))))], (38267 ^ _779448) ^ [_1511442, _1511444] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1511442))), -(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)), _1511442))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1511444)))) = 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)), _1511442))), 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, _1511444))))))], (38273 ^ _779448) ^ [_1511525, _1511527, _1511529, _1511531, _1511533, _1511535] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511525), _1511527)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511529), _1511531)), 38283 ^ _779448 : [(38284 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1511529), 38282 ^ [_1511525, _1511527, _1511529, _1511531, _1511533, _1511535]), _1511531)))], (38286 ^ _779448) ^ [] : [hAPP(c_Finite__Set_Ocard(_1511525), hAPP(c_Set_OCollect(_1511525), hAPP(hAPP(c_COMBS(_1511525, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511525), c_fconj), hAPP(hAPP(c_COMBC(_1511525, tc_fun(_1511525, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511525)), _1511527))), hAPP(hAPP(c_COMBC(_1511525, _1511529, tc_HOL_Obool), _1511533), 38282 ^ [_1511525, _1511527, _1511529, _1511531, _1511533, _1511535])))) = _1511535]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1511525, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1511529, tc_HOL_Obool), tc_Nat_Onat, _1511525), c_Finite__Set_Ocard(_1511529)), hAPP(hAPP(c_COMBB(tc_fun(_1511529, tc_HOL_Obool), tc_fun(_1511529, tc_HOL_Obool), _1511525), c_Set_OCollect(_1511529)), hAPP(hAPP(c_COMBB(tc_fun(_1511529, tc_HOL_Obool), tc_fun(_1511529, tc_HOL_Obool), _1511525), hAPP(c_COMBS(_1511529, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511529), c_fconj), hAPP(hAPP(c_COMBC(_1511529, tc_fun(_1511529, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511529)), _1511531)))), _1511533)))), _1511527) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1511535), hAPP(c_Finite__Set_Ocard(_1511529), _1511531)))], (38290 ^ _779448) ^ [_1512215, _1512217, _1512219] : [class_Orderings_Olinorder(_1512215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512215), _1512217)), -(_1512217 = c_Orderings_Obot__class_Obot(tc_fun(_1512215, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512215), _1512219)), -(_1512219 = c_Orderings_Obot__class_Obot(tc_fun(_1512215, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1512215), c_Big__Operators_Olattice_OInf__fin(_1512215, c_Orderings_Oord__class_Omin(_1512215), _1512217)), c_Big__Operators_Olattice_OInf__fin(_1512215, c_Orderings_Oord__class_Omin(_1512215), _1512219)) = c_Big__Operators_Olattice_OInf__fin(_1512215, c_Orderings_Oord__class_Omin(_1512215), hAPP(c_Set_OCollect(_1512215), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_HOL_Obool), tc_HOL_Obool, _1512215), c_HOL_OEx(_1512215)), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool)), tc_fun(_1512215, tc_HOL_Obool), _1512215), hAPP(c_COMBB(tc_fun(_1512215, tc_HOL_Obool), tc_HOL_Obool, _1512215), c_HOL_OEx(_1512215))), hAPP(hAPP(c_COMBC(_1512215, tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool)), tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_fun(tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool))), tc_fun(tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool)), tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool))), _1512215), c_COMBS(_1512215, tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_fun(_1512215, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1512215, tc_fun(tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool))), _1512215), hAPP(c_COMBB(tc_fun(_1512215, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool)), _1512215), c_COMBS(_1512215, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool)), tc_fun(_1512215, tc_fun(_1512215, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1512215), hAPP(c_COMBB(tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512215), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512215), c_fconj))), hAPP(hAPP(c_COMBC(_1512215, tc_fun(_1512215, tc_fun(_1512215, _1512215)), tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1512215, _1512215), tc_fun(_1512215, tc_HOL_Obool)), tc_fun(tc_fun(_1512215, tc_fun(_1512215, _1512215)), tc_fun(_1512215, tc_fun(_1512215, tc_HOL_Obool))), _1512215), c_COMBB(tc_fun(_1512215, _1512215), tc_fun(_1512215, tc_HOL_Obool), _1512215)), hAPP(hAPP(c_COMBB(tc_fun(_1512215, tc_HOL_Obool), tc_fun(tc_fun(_1512215, _1512215), tc_fun(_1512215, tc_HOL_Obool)), _1512215), c_COMBB(_1512215, tc_HOL_Obool, _1512215)), c_fequal))), c_Orderings_Oord__class_Omax(_1512215)))))), hAPP(hAPP(c_COMBC(_1512215, tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1512215, tc_HOL_Obool), tc_fun(_1512215, tc_HOL_Obool)), _1512215), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512215)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512215), c_fconj), hAPP(hAPP(c_COMBC(_1512215, tc_fun(_1512215, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512215)), _1512217)))), hAPP(hAPP(c_COMBC(_1512215, tc_fun(_1512215, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512215)), _1512219))))))))], (38312 ^ _779448) ^ [_1513332, _1513334, _1513336] : [class_Orderings_Olinorder(_1513332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513332), _1513334)), -(_1513334 = c_Orderings_Obot__class_Obot(tc_fun(_1513332, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1513332), _1513336), c_Big__Operators_Olattice_OInf__fin(_1513332, c_Orderings_Oord__class_Omin(_1513332), _1513334)) = c_Big__Operators_Olattice_OInf__fin(_1513332, c_Orderings_Oord__class_Omin(_1513332), hAPP(c_Set_OCollect(_1513332), hAPP(hAPP(c_COMBB(tc_fun(_1513332, tc_HOL_Obool), tc_HOL_Obool, _1513332), c_HOL_OEx(_1513332)), hAPP(hAPP(c_COMBC(_1513332, tc_fun(_1513332, tc_HOL_Obool), tc_fun(_1513332, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513332, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1513332, tc_HOL_Obool), tc_fun(_1513332, tc_HOL_Obool)), _1513332), c_COMBS(_1513332, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513332, tc_HOL_Obool), tc_fun(_1513332, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1513332), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513332), c_fconj)), hAPP(hAPP(c_COMBC(_1513332, tc_fun(_1513332, _1513332), tc_fun(_1513332, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1513332, tc_HOL_Obool), tc_fun(tc_fun(_1513332, _1513332), tc_fun(_1513332, tc_HOL_Obool)), _1513332), c_COMBB(_1513332, tc_HOL_Obool, _1513332)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1513332), _1513336))))), hAPP(hAPP(c_COMBC(_1513332, tc_fun(_1513332, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513332)), _1513334))))))], (38326 ^ _779448) ^ [_1513830, _1513832] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513830), _1513832)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1513830, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1513830, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1513830, tc_HOL_Obool), tc_fun(_1513830, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1513830, tc_HOL_Obool))), _1513832)))))], (38332 ^ _779448) ^ [_1513987, _1513989] : [-(hAPP(c_Set_OPow(_1513987), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513987, tc_HOL_Obool)), _1513989)) = hAPP(c_Set_OCollect(tc_fun(_1513987, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1513987, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1513987, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1513987, tc_HOL_Obool), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1513987, tc_HOL_Obool)), c_COMBS(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1513987, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1513987, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1513987, tc_HOL_Obool), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_fun(_1513987, tc_HOL_Obool)), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_fun(_1513987, tc_HOL_Obool)), tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1513987, tc_HOL_Obool)), c_COMBB(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1513987, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1513987, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513987, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1513987, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1513987, tc_HOL_Obool)), _1513989)), c_Set_OPow(_1513987))))))], (38334 ^ _779448) ^ [_1514267, _1514269] : [-(hAPP(c_Set_OPow(_1514267), _1514269) = hAPP(c_Set_OCollect(tc_fun(_1514267, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1514267, tc_HOL_Obool), tc_fun(_1514267, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1514267, tc_HOL_Obool))), _1514269)))], (38336 ^ _779448) ^ [_1514326, _1514328, _1514330, _1514332] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514326), hAPP(c_Set_OCollect(_1514326), _1514328))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514330), hAPP(c_Set_OCollect(_1514330), hAPP(hAPP(c_COMBB(tc_fun(_1514326, tc_HOL_Obool), tc_HOL_Obool, _1514330), c_HOL_OEx(_1514326)), hAPP(hAPP(c_COMBC(_1514330, tc_fun(_1514326, tc_HOL_Obool), tc_fun(_1514326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514326, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1514326, tc_HOL_Obool), tc_fun(_1514326, tc_HOL_Obool)), _1514330), c_COMBS(_1514326, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514326, tc_HOL_Obool), tc_fun(_1514326, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1514330), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514326), c_fconj)), hAPP(hAPP(c_COMBC(_1514330, tc_fun(_1514326, _1514330), tc_fun(_1514326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1514330, tc_HOL_Obool), tc_fun(tc_fun(_1514326, _1514330), tc_fun(_1514326, tc_HOL_Obool)), _1514330), c_COMBB(_1514330, tc_HOL_Obool, _1514326)), c_fequal)), _1514332)))), _1514328))))))], (38342 ^ _779448) ^ [_1514687, _1514689, _1514691, _1514693] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514687), hAPP(c_Set_OCollect(_1514687), _1514689))), 38345 ^ _779448 : [(38356 ^ _779448) ^ [] : [38358 ^ _779448 : [(38359 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1514689, 38357 ^ [_1514687, _1514689, _1514691, _1514693])))], (38361 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514691), hAPP(c_Set_OCollect(_1514691), hAPP(hAPP(c_COMBC(_1514691, _1514687, tc_HOL_Obool), _1514693), 38357 ^ [_1514687, _1514689, _1514691, _1514693]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514691), hAPP(c_Set_OCollect(_1514691), hAPP(hAPP(c_COMBB(tc_fun(_1514687, tc_HOL_Obool), tc_HOL_Obool, _1514691), c_HOL_OEx(_1514687)), hAPP(hAPP(c_COMBB(tc_fun(_1514687, tc_HOL_Obool), tc_fun(_1514687, tc_HOL_Obool), _1514691), hAPP(c_COMBS(_1514687, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514687), c_fconj), _1514689))), _1514693))))))], (38346 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514691), hAPP(c_Set_OCollect(_1514691), hAPP(hAPP(c_COMBB(tc_fun(_1514687, tc_HOL_Obool), tc_HOL_Obool, _1514691), c_HOL_OEx(_1514687)), hAPP(hAPP(c_COMBB(tc_fun(_1514687, tc_HOL_Obool), tc_fun(_1514687, tc_HOL_Obool), _1514691), hAPP(c_COMBS(_1514687, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1514687), c_fconj), _1514689))), _1514693))))), 38349 ^ _779448 : [(38350 ^ _779448) ^ [_1514970] : [hBOOL(hAPP(_1514689, _1514970)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1514691), hAPP(c_Set_OCollect(_1514691), hAPP(hAPP(c_COMBC(_1514691, _1514687, tc_HOL_Obool), _1514693), _1514970)))))]]]]], (38365 ^ _779448) ^ [_1515335, _1515337] : [-(c_Fun_Oinj__on(tc_fun(_1515335, _1515337), tc_fun(tc_prod(_1515335, _1515337), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1515335, _1515337), tc_HOL_Obool), tc_fun(tc_prod(_1515335, _1515337), tc_HOL_Obool), tc_fun(_1515335, _1515337)), c_Set_OCollect(tc_prod(_1515335, _1515337))), hAPP(hAPP(c_COMBB(tc_fun(_1515335, tc_fun(_1515337, tc_HOL_Obool)), tc_fun(tc_prod(_1515335, _1515337), tc_HOL_Obool), tc_fun(_1515335, _1515337)), c_Product__Type_Oprod_Oprod__case(_1515335, _1515337, tc_HOL_Obool)), hAPP(c_COMBB(_1515337, tc_fun(_1515337, tc_HOL_Obool), _1515335), hAPP(c_COMBC(_1515337, _1515337, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1515335, _1515337), tc_HOL_Obool))))], (38367 ^ _779448) ^ [_1515455] : [-(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)))), _1515455))))], (38369 ^ _779448) ^ [_1515483] : [-(c_Wellfounded_Ofinite__psubset(_1515483) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1515483, tc_HOL_Obool), tc_fun(_1515483, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1515483, tc_HOL_Obool), tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1515483, tc_HOL_Obool), tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1515483, tc_HOL_Obool)), c_COMBS(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1515483, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1515483, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1515483, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1515483, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1515483)))))], (38371 ^ _779448) ^ [_1515643, _1515645, _1515647, _1515649] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1515643, _1515645), _1515647), _1515649) = hAPP(c_Set_OCollect(tc_prod(_1515645, _1515645)), hAPP(c_Product__Type_Oprod_Oprod__case(_1515645, _1515645, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1515645, tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_fun(_1515645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515645, tc_fun(tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_fun(_1515645, tc_HOL_Obool)), _1515645), c_COMBC(_1515645, tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515645, tc_prod(_1515643, _1515643)), tc_fun(_1515645, tc_fun(tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_HOL_Obool)), _1515645), hAPP(c_COMBB(tc_prod(_1515643, _1515643), tc_fun(tc_fun(tc_prod(_1515643, _1515643), tc_HOL_Obool), tc_HOL_Obool), _1515645), c_member(tc_prod(_1515643, _1515643)))), hAPP(hAPP(c_COMBC(_1515645, tc_fun(_1515645, _1515643), tc_fun(_1515645, tc_prod(_1515643, _1515643))), hAPP(hAPP(c_COMBB(tc_fun(_1515643, tc_prod(_1515643, _1515643)), tc_fun(tc_fun(_1515645, _1515643), tc_fun(_1515645, tc_prod(_1515643, _1515643))), _1515645), c_COMBB(_1515643, tc_prod(_1515643, _1515643), _1515645)), hAPP(hAPP(c_COMBB(_1515643, tc_fun(_1515643, tc_prod(_1515643, _1515643)), _1515645), c_Product__Type_OPair(_1515643, _1515643)), _1515649))), _1515649)))), _1515647))))], (38373 ^ _779448) ^ [_1515884] : [-(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)))), _1515884)) = 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), _1515884), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (38375 ^ _779448) ^ [_1515925] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1515925) = 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), _1515925), c_Int_Onat)))))], (38377 ^ _779448) ^ [_1515966, _1515968, _1515970] : [class_Groups_Olinordered__ab__semigroup__add(_1515966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1515966), _1515968)), -(_1515968 = c_Orderings_Obot__class_Obot(tc_fun(_1515966, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1515966), _1515970), c_Big__Operators_Olinorder__class_OMax(_1515966, _1515968)) = c_Big__Operators_Olinorder__class_OMax(_1515966, hAPP(c_Set_OCollect(_1515966), hAPP(hAPP(c_COMBB(tc_fun(_1515966, tc_HOL_Obool), tc_HOL_Obool, _1515966), c_HOL_OEx(_1515966)), hAPP(hAPP(c_COMBC(_1515966, tc_fun(_1515966, tc_HOL_Obool), tc_fun(_1515966, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515966, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1515966, tc_HOL_Obool), tc_fun(_1515966, tc_HOL_Obool)), _1515966), c_COMBS(_1515966, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515966, tc_HOL_Obool), tc_fun(_1515966, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1515966), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1515966), c_fconj)), hAPP(hAPP(c_COMBC(_1515966, tc_fun(_1515966, _1515966), tc_fun(_1515966, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515966, tc_HOL_Obool), tc_fun(tc_fun(_1515966, _1515966), tc_fun(_1515966, tc_HOL_Obool)), _1515966), c_COMBB(_1515966, tc_HOL_Obool, _1515966)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1515966), _1515970))))), hAPP(hAPP(c_COMBC(_1515966, tc_fun(_1515966, tc_HOL_Obool), tc_HOL_Obool), c_member(_1515966)), _1515968))))))], (38391 ^ _779448) ^ [_1516452, _1516454, _1516456] : [class_Groups_Olinordered__ab__semigroup__add(_1516452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516452), _1516454)), -(_1516454 = c_Orderings_Obot__class_Obot(tc_fun(_1516452, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1516452), _1516456), c_Big__Operators_Olinorder__class_OMin(_1516452, _1516454)) = c_Big__Operators_Olinorder__class_OMin(_1516452, hAPP(c_Set_OCollect(_1516452), hAPP(hAPP(c_COMBB(tc_fun(_1516452, tc_HOL_Obool), tc_HOL_Obool, _1516452), c_HOL_OEx(_1516452)), hAPP(hAPP(c_COMBC(_1516452, tc_fun(_1516452, tc_HOL_Obool), tc_fun(_1516452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516452, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1516452, tc_HOL_Obool), tc_fun(_1516452, tc_HOL_Obool)), _1516452), c_COMBS(_1516452, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516452, tc_HOL_Obool), tc_fun(_1516452, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1516452), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1516452), c_fconj)), hAPP(hAPP(c_COMBC(_1516452, tc_fun(_1516452, _1516452), tc_fun(_1516452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516452, tc_HOL_Obool), tc_fun(tc_fun(_1516452, _1516452), tc_fun(_1516452, tc_HOL_Obool)), _1516452), c_COMBB(_1516452, tc_HOL_Obool, _1516452)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1516452), _1516456))))), hAPP(hAPP(c_COMBC(_1516452, tc_fun(_1516452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1516452)), _1516454))))))], (38405 ^ _779448) ^ [_1516938, _1516940, _1516942] : [class_Lattices_Odistrib__lattice(_1516938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516938), _1516940)), -(_1516940 = c_Orderings_Obot__class_Obot(tc_fun(_1516938, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1516938), _1516942), c_Big__Operators_Olattice__class_OInf__fin(_1516938, _1516940)) = c_Big__Operators_Olattice__class_OInf__fin(_1516938, hAPP(c_Set_OCollect(_1516938), hAPP(hAPP(c_COMBB(tc_fun(_1516938, tc_HOL_Obool), tc_HOL_Obool, _1516938), c_HOL_OEx(_1516938)), hAPP(hAPP(c_COMBC(_1516938, tc_fun(_1516938, tc_HOL_Obool), tc_fun(_1516938, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516938, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1516938, tc_HOL_Obool), tc_fun(_1516938, tc_HOL_Obool)), _1516938), c_COMBS(_1516938, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516938, tc_HOL_Obool), tc_fun(_1516938, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1516938), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1516938), c_fconj)), hAPP(hAPP(c_COMBC(_1516938, tc_fun(_1516938, _1516938), tc_fun(_1516938, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1516938, tc_HOL_Obool), tc_fun(tc_fun(_1516938, _1516938), tc_fun(_1516938, tc_HOL_Obool)), _1516938), c_COMBB(_1516938, tc_HOL_Obool, _1516938)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1516938), _1516942))))), hAPP(hAPP(c_COMBC(_1516938, tc_fun(_1516938, tc_HOL_Obool), tc_HOL_Obool), c_member(_1516938)), _1516940))))))], (38419 ^ _779448) ^ [_1517424, _1517426, _1517428] : [class_Lattices_Odistrib__lattice(_1517424), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517424), _1517426)), -(_1517426 = c_Orderings_Obot__class_Obot(tc_fun(_1517424, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517424), _1517428)), -(_1517428 = c_Orderings_Obot__class_Obot(tc_fun(_1517424, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1517424), c_Big__Operators_Olattice__class_OInf__fin(_1517424, _1517426)), c_Big__Operators_Olattice__class_OInf__fin(_1517424, _1517428)) = c_Big__Operators_Olattice__class_OInf__fin(_1517424, hAPP(c_Set_OCollect(_1517424), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_HOL_Obool), tc_HOL_Obool, _1517424), c_HOL_OEx(_1517424)), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool)), tc_fun(_1517424, tc_HOL_Obool), _1517424), hAPP(c_COMBB(tc_fun(_1517424, tc_HOL_Obool), tc_HOL_Obool, _1517424), c_HOL_OEx(_1517424))), hAPP(hAPP(c_COMBC(_1517424, tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool)), tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_fun(tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool))), tc_fun(tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool)), tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool))), _1517424), c_COMBS(_1517424, tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_fun(_1517424, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1517424, tc_fun(tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool))), _1517424), hAPP(c_COMBB(tc_fun(_1517424, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool)), _1517424), c_COMBS(_1517424, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool)), tc_fun(_1517424, tc_fun(_1517424, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1517424), hAPP(c_COMBB(tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517424), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517424), c_fconj))), hAPP(hAPP(c_COMBC(_1517424, tc_fun(_1517424, tc_fun(_1517424, _1517424)), tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517424, _1517424), tc_fun(_1517424, tc_HOL_Obool)), tc_fun(tc_fun(_1517424, tc_fun(_1517424, _1517424)), tc_fun(_1517424, tc_fun(_1517424, tc_HOL_Obool))), _1517424), c_COMBB(tc_fun(_1517424, _1517424), tc_fun(_1517424, tc_HOL_Obool), _1517424)), hAPP(hAPP(c_COMBB(tc_fun(_1517424, tc_HOL_Obool), tc_fun(tc_fun(_1517424, _1517424), tc_fun(_1517424, tc_HOL_Obool)), _1517424), c_COMBB(_1517424, tc_HOL_Obool, _1517424)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1517424)))))), hAPP(hAPP(c_COMBC(_1517424, tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1517424, tc_HOL_Obool), tc_fun(_1517424, tc_HOL_Obool)), _1517424), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1517424)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517424), c_fconj), hAPP(hAPP(c_COMBC(_1517424, tc_fun(_1517424, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517424)), _1517426)))), hAPP(hAPP(c_COMBC(_1517424, tc_fun(_1517424, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517424)), _1517428))))))))], (38441 ^ _779448) ^ [_1518523, _1518525, _1518527] : [class_Lattices_Odistrib__lattice(_1518523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518523), _1518525)), -(_1518525 = c_Orderings_Obot__class_Obot(tc_fun(_1518523, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1518523), _1518527), c_Big__Operators_Olattice__class_OSup__fin(_1518523, _1518525)) = c_Big__Operators_Olattice__class_OSup__fin(_1518523, hAPP(c_Set_OCollect(_1518523), hAPP(hAPP(c_COMBB(tc_fun(_1518523, tc_HOL_Obool), tc_HOL_Obool, _1518523), c_HOL_OEx(_1518523)), hAPP(hAPP(c_COMBC(_1518523, tc_fun(_1518523, tc_HOL_Obool), tc_fun(_1518523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518523, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1518523, tc_HOL_Obool), tc_fun(_1518523, tc_HOL_Obool)), _1518523), c_COMBS(_1518523, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518523, tc_HOL_Obool), tc_fun(_1518523, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1518523), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1518523), c_fconj)), hAPP(hAPP(c_COMBC(_1518523, tc_fun(_1518523, _1518523), tc_fun(_1518523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518523, tc_HOL_Obool), tc_fun(tc_fun(_1518523, _1518523), tc_fun(_1518523, tc_HOL_Obool)), _1518523), c_COMBB(_1518523, tc_HOL_Obool, _1518523)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1518523), _1518527))))), hAPP(hAPP(c_COMBC(_1518523, tc_fun(_1518523, tc_HOL_Obool), tc_HOL_Obool), c_member(_1518523)), _1518525))))))], (38455 ^ _779448) ^ [_1519009, _1519011, _1519013] : [class_Lattices_Odistrib__lattice(_1519009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519009), _1519011)), -(_1519011 = c_Orderings_Obot__class_Obot(tc_fun(_1519009, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519009), _1519013)), -(_1519013 = c_Orderings_Obot__class_Obot(tc_fun(_1519009, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1519009), c_Big__Operators_Olattice__class_OSup__fin(_1519009, _1519011)), c_Big__Operators_Olattice__class_OSup__fin(_1519009, _1519013)) = c_Big__Operators_Olattice__class_OSup__fin(_1519009, hAPP(c_Set_OCollect(_1519009), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_HOL_Obool), tc_HOL_Obool, _1519009), c_HOL_OEx(_1519009)), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool)), tc_fun(_1519009, tc_HOL_Obool), _1519009), hAPP(c_COMBB(tc_fun(_1519009, tc_HOL_Obool), tc_HOL_Obool, _1519009), c_HOL_OEx(_1519009))), hAPP(hAPP(c_COMBC(_1519009, tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool)), tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_fun(tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool))), tc_fun(tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool)), tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool))), _1519009), c_COMBS(_1519009, tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_fun(_1519009, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1519009, tc_fun(tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool))), _1519009), hAPP(c_COMBB(tc_fun(_1519009, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool)), _1519009), c_COMBS(_1519009, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool)), tc_fun(_1519009, tc_fun(_1519009, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1519009), hAPP(c_COMBB(tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1519009), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519009), c_fconj))), hAPP(hAPP(c_COMBC(_1519009, tc_fun(_1519009, tc_fun(_1519009, _1519009)), tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1519009, _1519009), tc_fun(_1519009, tc_HOL_Obool)), tc_fun(tc_fun(_1519009, tc_fun(_1519009, _1519009)), tc_fun(_1519009, tc_fun(_1519009, tc_HOL_Obool))), _1519009), c_COMBB(tc_fun(_1519009, _1519009), tc_fun(_1519009, tc_HOL_Obool), _1519009)), hAPP(hAPP(c_COMBB(tc_fun(_1519009, tc_HOL_Obool), tc_fun(tc_fun(_1519009, _1519009), tc_fun(_1519009, tc_HOL_Obool)), _1519009), c_COMBB(_1519009, tc_HOL_Obool, _1519009)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1519009)))))), hAPP(hAPP(c_COMBC(_1519009, tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1519009, tc_HOL_Obool), tc_fun(_1519009, tc_HOL_Obool)), _1519009), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1519009)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519009), c_fconj), hAPP(hAPP(c_COMBC(_1519009, tc_fun(_1519009, tc_HOL_Obool), tc_HOL_Obool), c_member(_1519009)), _1519011)))), hAPP(hAPP(c_COMBC(_1519009, tc_fun(_1519009, tc_HOL_Obool), tc_HOL_Obool), c_member(_1519009)), _1519013))))))))], (38477 ^ _779448) ^ [_1520108, _1520110, _1520112] : [class_Orderings_Olinorder(_1520108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520108), _1520110)), -(_1520110 = c_Orderings_Obot__class_Obot(tc_fun(_1520108, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1520108), _1520112), c_Big__Operators_Olattice_OSup__fin(_1520108, c_Orderings_Oord__class_Omax(_1520108), _1520110)) = c_Big__Operators_Olattice_OSup__fin(_1520108, c_Orderings_Oord__class_Omax(_1520108), hAPP(c_Set_OCollect(_1520108), hAPP(hAPP(c_COMBB(tc_fun(_1520108, tc_HOL_Obool), tc_HOL_Obool, _1520108), c_HOL_OEx(_1520108)), hAPP(hAPP(c_COMBC(_1520108, tc_fun(_1520108, tc_HOL_Obool), tc_fun(_1520108, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520108, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1520108, tc_HOL_Obool), tc_fun(_1520108, tc_HOL_Obool)), _1520108), c_COMBS(_1520108, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520108, tc_HOL_Obool), tc_fun(_1520108, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1520108), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520108), c_fconj)), hAPP(hAPP(c_COMBC(_1520108, tc_fun(_1520108, _1520108), tc_fun(_1520108, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1520108, tc_HOL_Obool), tc_fun(tc_fun(_1520108, _1520108), tc_fun(_1520108, tc_HOL_Obool)), _1520108), c_COMBB(_1520108, tc_HOL_Obool, _1520108)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1520108), _1520112))))), hAPP(hAPP(c_COMBC(_1520108, tc_fun(_1520108, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520108)), _1520110))))))], (38491 ^ _779448) ^ [_1520606, _1520608, _1520610] : [class_Orderings_Olinorder(_1520606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520606), _1520608)), -(_1520608 = c_Orderings_Obot__class_Obot(tc_fun(_1520606, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1520606), _1520610)), -(_1520610 = c_Orderings_Obot__class_Obot(tc_fun(_1520606, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1520606), c_Big__Operators_Olattice_OSup__fin(_1520606, c_Orderings_Oord__class_Omax(_1520606), _1520608)), c_Big__Operators_Olattice_OSup__fin(_1520606, c_Orderings_Oord__class_Omax(_1520606), _1520610)) = c_Big__Operators_Olattice_OSup__fin(_1520606, c_Orderings_Oord__class_Omax(_1520606), hAPP(c_Set_OCollect(_1520606), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_HOL_Obool), tc_HOL_Obool, _1520606), c_HOL_OEx(_1520606)), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool)), tc_fun(_1520606, tc_HOL_Obool), _1520606), hAPP(c_COMBB(tc_fun(_1520606, tc_HOL_Obool), tc_HOL_Obool, _1520606), c_HOL_OEx(_1520606))), hAPP(hAPP(c_COMBC(_1520606, tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool)), tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_fun(tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool))), tc_fun(tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool)), tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool))), _1520606), c_COMBS(_1520606, tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_fun(_1520606, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1520606, tc_fun(tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool))), _1520606), hAPP(c_COMBB(tc_fun(_1520606, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool)), _1520606), c_COMBS(_1520606, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool)), tc_fun(_1520606, tc_fun(_1520606, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1520606), hAPP(c_COMBB(tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1520606), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520606), c_fconj))), hAPP(hAPP(c_COMBC(_1520606, tc_fun(_1520606, tc_fun(_1520606, _1520606)), tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1520606, _1520606), tc_fun(_1520606, tc_HOL_Obool)), tc_fun(tc_fun(_1520606, tc_fun(_1520606, _1520606)), tc_fun(_1520606, tc_fun(_1520606, tc_HOL_Obool))), _1520606), c_COMBB(tc_fun(_1520606, _1520606), tc_fun(_1520606, tc_HOL_Obool), _1520606)), hAPP(hAPP(c_COMBB(tc_fun(_1520606, tc_HOL_Obool), tc_fun(tc_fun(_1520606, _1520606), tc_fun(_1520606, tc_HOL_Obool)), _1520606), c_COMBB(_1520606, tc_HOL_Obool, _1520606)), c_fequal))), c_Orderings_Oord__class_Omin(_1520606)))))), hAPP(hAPP(c_COMBC(_1520606, tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1520606, tc_HOL_Obool), tc_fun(_1520606, tc_HOL_Obool)), _1520606), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520606)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520606), c_fconj), hAPP(hAPP(c_COMBC(_1520606, tc_fun(_1520606, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520606)), _1520608)))), hAPP(hAPP(c_COMBC(_1520606, tc_fun(_1520606, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520606)), _1520610))))))))], (38513 ^ _779448) ^ [_1521723, _1521725, _1521727, _1521729] : [-(c_Nitpick_Oprod(_1521723, _1521725, _1521727, _1521729) = hAPP(c_Set_OCollect(tc_prod(_1521723, _1521725)), hAPP(c_Product__Type_Oprod_Oprod__case(_1521723, _1521725, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1521723, tc_fun(_1521725, tc_HOL_Obool), tc_fun(_1521725, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1521725, tc_HOL_Obool), tc_fun(_1521725, tc_HOL_Obool)), _1521723), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1521725)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521723), c_fconj), hAPP(hAPP(c_COMBC(_1521723, tc_fun(_1521723, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521723)), _1521727)))), hAPP(hAPP(c_COMBC(_1521725, tc_fun(_1521725, tc_HOL_Obool), tc_HOL_Obool), c_member(_1521725)), _1521729)))))], (38515 ^ _779448) ^ [_1521851] : [-(c_Int_Oint__ge__less__than(_1521851) = 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), _1521851)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38517 ^ _779448) ^ [_1521897] : [-(c_Int_Oint__ge__less__than2(_1521897) = 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), _1521897)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (38519 ^ _779448) ^ [_1521958, _1521960] : [c_Predicate_Oreflp(_1521958, _1521960), -(c_Relation_Orefl__on(_1521958, c_Orderings_Otop__class_Otop(tc_fun(_1521958, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1521958, _1521958)), hAPP(c_Product__Type_Oprod_Oprod__case(_1521958, _1521958, tc_HOL_Obool), _1521960))))], (38525 ^ _779448) ^ [_1522073, _1522075] : [c_Relation_Orefl__on(_1522073, c_Orderings_Otop__class_Otop(tc_fun(_1522073, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1522073, _1522073)), hAPP(c_Product__Type_Oprod_Oprod__case(_1522073, _1522073, tc_HOL_Obool), _1522075))), -(c_Predicate_Oreflp(_1522073, _1522075))], (38531 ^ _779448) ^ [_1522194, _1522196, _1522198, _1522200, _1522202, _1522204, _1522206] : [class_Rings_Osemiring__0(_1522194), c_Fun_Oinj__on(tc_prod(_1522196, _1522198), _1522194, hAPP(c_Product__Type_Oprod_Oprod__case(_1522196, _1522198, _1522194), hAPP(hAPP(c_COMBC(_1522196, tc_fun(_1522198, _1522194), tc_fun(_1522198, _1522194)), hAPP(hAPP(c_COMBB(tc_fun(_1522194, _1522194), tc_fun(tc_fun(_1522198, _1522194), tc_fun(_1522198, _1522194)), _1522196), c_COMBB(_1522194, _1522194, _1522198)), hAPP(hAPP(c_COMBB(_1522194, tc_fun(_1522194, _1522194), _1522196), c_Groups_Otimes__class_Otimes(_1522194)), _1522200))), _1522202)), hAPP(hAPP(c_Product__Type_OSigma(_1522196, _1522198), _1522204), hAPP(c_COMBK(tc_fun(_1522198, tc_HOL_Obool), _1522196), _1522206))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1522194), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522196, _1522194), _1522200), _1522204)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522198, _1522194), _1522202), _1522206)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1522194, _1522194), c_Fun_Oid(_1522194)), hAPP(c_Set_OCollect(_1522194), hAPP(hAPP(c_COMBB(tc_fun(_1522196, tc_HOL_Obool), tc_HOL_Obool, _1522194), c_HOL_OEx(_1522196)), hAPP(hAPP(c_COMBB(tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool)), tc_fun(_1522196, tc_HOL_Obool), _1522194), hAPP(c_COMBB(tc_fun(_1522198, tc_HOL_Obool), tc_HOL_Obool, _1522196), c_HOL_OEx(_1522198))), hAPP(hAPP(c_COMBC(_1522194, tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool)), tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522196, tc_fun(tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool))), tc_fun(tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool)), tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool))), _1522194), c_COMBS(_1522196, tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522196, tc_fun(_1522198, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1522196, tc_fun(tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool))), _1522194), hAPP(c_COMBB(tc_fun(_1522198, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool)), _1522196), c_COMBS(_1522198, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool)), tc_fun(_1522196, tc_fun(_1522198, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1522194), hAPP(c_COMBB(tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1522196), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522198), c_fconj))), hAPP(hAPP(c_COMBC(_1522194, tc_fun(_1522196, tc_fun(_1522198, _1522194)), tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1522198, _1522194), tc_fun(_1522198, tc_HOL_Obool)), tc_fun(tc_fun(_1522196, tc_fun(_1522198, _1522194)), tc_fun(_1522196, tc_fun(_1522198, tc_HOL_Obool))), _1522194), c_COMBB(tc_fun(_1522198, _1522194), tc_fun(_1522198, tc_HOL_Obool), _1522196)), hAPP(hAPP(c_COMBB(tc_fun(_1522194, tc_HOL_Obool), tc_fun(tc_fun(_1522198, _1522194), tc_fun(_1522198, tc_HOL_Obool)), _1522194), c_COMBB(_1522194, tc_HOL_Obool, _1522198)), c_fequal))), hAPP(hAPP(c_COMBC(_1522196, tc_fun(_1522198, _1522194), tc_fun(_1522198, _1522194)), hAPP(hAPP(c_COMBB(tc_fun(_1522194, _1522194), tc_fun(tc_fun(_1522198, _1522194), tc_fun(_1522198, _1522194)), _1522196), c_COMBB(_1522194, _1522194, _1522198)), hAPP(hAPP(c_COMBB(_1522194, tc_fun(_1522194, _1522194), _1522196), c_Groups_Otimes__class_Otimes(_1522194)), _1522200))), _1522202)))))), hAPP(hAPP(c_COMBC(_1522196, tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1522198, tc_HOL_Obool), tc_fun(_1522198, tc_HOL_Obool)), _1522196), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1522198)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522196), c_fconj), hAPP(hAPP(c_COMBC(_1522196, tc_fun(_1522196, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522196)), _1522204)))), hAPP(hAPP(c_COMBC(_1522198, tc_fun(_1522198, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522198)), _1522206))))))))], (38541 ^ _779448) ^ [_1523471, _1523473, _1523475, _1523477, _1523479, _1523481] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523471), _1523473)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1523475), _1523477)), 38551 ^ _779448 : [(38552 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1523475), 38550 ^ [_1523471, _1523473, _1523475, _1523477, _1523479, _1523481]), _1523477)))], (38554 ^ _779448) ^ [] : [hAPP(c_Finite__Set_Ocard(_1523471), hAPP(c_Set_OCollect(_1523471), hAPP(hAPP(c_COMBS(_1523471, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523471), c_fconj), hAPP(hAPP(c_COMBC(_1523471, tc_fun(_1523471, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523471)), _1523473))), hAPP(hAPP(c_COMBC(_1523471, _1523475, tc_HOL_Obool), _1523479), 38550 ^ [_1523471, _1523473, _1523475, _1523477, _1523479, _1523481])))) = hAPP(_1523481, 38550 ^ [_1523471, _1523473, _1523475, _1523477, _1523479, _1523481])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523471, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1523475, tc_HOL_Obool), tc_Nat_Onat, _1523471), c_Finite__Set_Ocard(_1523475)), hAPP(hAPP(c_COMBB(tc_fun(_1523475, tc_HOL_Obool), tc_fun(_1523475, tc_HOL_Obool), _1523471), c_Set_OCollect(_1523475)), hAPP(hAPP(c_COMBB(tc_fun(_1523475, tc_HOL_Obool), tc_fun(_1523475, tc_HOL_Obool), _1523471), hAPP(c_COMBS(_1523475, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523475), c_fconj), hAPP(hAPP(c_COMBC(_1523475, tc_fun(_1523475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523475)), _1523477)))), _1523479)))), _1523473) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1523475, tc_Nat_Onat), _1523481), _1523477))], (38558 ^ _779448) ^ [_1524181, _1524183] : [-(c_Fun_Oinj__on(_1524181, _1524181, c_Fun_Oid(_1524181), _1524183))], (38560 ^ _779448) ^ [_1524210, _1524212] : [-(c_Product__Type_Omap__pair(_1524210, _1524210, _1524212, _1524212, c_Fun_Oid(_1524210), c_Fun_Oid(_1524212)) = c_Fun_Oid(tc_prod(_1524210, _1524212)))], (38562 ^ _779448) ^ [_1524251, _1524253] : [-(c_Product__Type_Omap__pair(_1524251, _1524251, _1524253, _1524253, c_COMBI(_1524251), c_COMBI(_1524253)) = c_Fun_Oid(tc_prod(_1524251, _1524253)))], (38564 ^ _779448) ^ [_1524292, _1524294] : [-(hAPP(c_Set_Ovimage(_1524292, _1524292, c_Fun_Oid(_1524292)), _1524294) = _1524294)], (38566 ^ _779448) ^ [_1524326, _1524328] : [-(c_Product__Type_Oapsnd(_1524326, _1524326, _1524328, c_Fun_Oid(_1524326)) = c_Fun_Oid(tc_prod(_1524328, _1524326)))], (38568 ^ _779448) ^ [_1524363, _1524365] : [-(hAPP(c_Fun_Oid(_1524363), _1524365) = _1524365)], (38570 ^ _779448) ^ [_1524393, _1524395] : [-(hAPP(c_Fun_Oid(_1524393), _1524395) = _1524395)], (38572 ^ _779448) ^ [_1524423, _1524425, _1524427] : [c_Predicate_Oreflp(_1524423, _1524425), -(hBOOL(hAPP(hAPP(_1524425, _1524427), _1524427)))], (38578 ^ _779448) ^ [_1524512, _1524514] : [-(c_Product__Type_Oapfst(_1524512, _1524512, _1524514, c_Fun_Oid(_1524512)) = c_Fun_Oid(tc_prod(_1524512, _1524514)))], (38580 ^ _779448) ^ [_1524549, _1524551, _1524553, _1524555, _1524557, _1524559, _1524561] : [hAPP(c_Fun_Ocomp(_1524549, _1524551, _1524553, _1524555), _1524557) = hAPP(c_Fun_Ocomp(_1524551, _1524551, _1524553, c_Fun_Oid(_1524551)), _1524559), -(hAPP(_1524555, hAPP(_1524557, _1524561)) = hAPP(_1524559, _1524561))], (38586 ^ _779448) ^ [_1524690, _1524692, _1524694] : [-(hAPP(c_Fun_Ocomp(_1524690, _1524692, _1524690, _1524694), c_Fun_Oid(_1524690)) = _1524694)], (38588 ^ _779448) ^ [_1524727, _1524729, _1524731] : [-(hAPP(c_Fun_Ocomp(_1524727, _1524727, _1524729, c_Fun_Oid(_1524727)), _1524731) = _1524731)], (38590 ^ _779448) ^ [_1524764, _1524766] : [-(hAPP(c_Set_Oimage(_1524764, _1524764, c_Fun_Oid(_1524764)), _1524766) = _1524766)], (38592 ^ _779448) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (38594 ^ _779448) ^ [_1524816] : [-(hAPP(c_Set_Oimage(_1524816, _1524816, c_Fun_Oid(_1524816)), c_Orderings_Otop__class_Otop(tc_fun(_1524816, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1524816, tc_HOL_Obool)))], (38596 ^ _779448) ^ [_1524858, _1524860, _1524862, _1524864] : [c_Finite__Set_Ofolding(_1524858, _1524860, _1524862, _1524864), -(hAPP(_1524864, c_Orderings_Obot__class_Obot(tc_fun(_1524858, tc_HOL_Obool))) = c_Fun_Oid(_1524860))], (38602 ^ _779448) ^ [_1524963, _1524965, _1524967, _1524969] : [-(c_Product__Type_Oapsnd(_1524963, _1524965, _1524967, _1524969) = c_Product__Type_Omap__pair(_1524967, _1524967, _1524963, _1524965, c_Fun_Oid(_1524967), _1524969))], (38604 ^ _779448) ^ [_1525006, _1525008, _1525010, _1525012] : [-(c_Product__Type_Oapfst(_1525006, _1525008, _1525010, _1525012) = c_Product__Type_Omap__pair(_1525006, _1525008, _1525010, _1525010, _1525012, c_Fun_Oid(_1525010)))], (38606 ^ _779448) ^ [_1525049, _1525051] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1525049, _1525051, tc_prod(_1525049, _1525051)), c_Product__Type_OPair(_1525049, _1525051)) = c_Fun_Oid(tc_prod(_1525049, _1525051)))], (38608 ^ _779448) ^ [_1525092, _1525094, _1525096, _1525098] : [class_Groups_Ocomm__monoid__add(_1525092), c_Fun_Oinj__on(_1525094, _1525092, _1525096, _1525098), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525094, _1525092), _1525096), _1525098) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525092, _1525092), c_Fun_Oid(_1525092)), hAPP(c_Set_Oimage(_1525094, _1525092, _1525096), _1525098)))], (38618 ^ _779448) ^ [_1525285, _1525287, _1525289, _1525291] : [class_Groups_Ocomm__monoid__mult(_1525285), c_Fun_Oinj__on(_1525287, _1525285, _1525289, _1525291), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1525287, _1525285), _1525289), _1525291) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1525285, _1525285), c_Fun_Oid(_1525285)), hAPP(c_Set_Oimage(_1525287, _1525285, _1525289), _1525291)))], (38628 ^ _779448) ^ [_1525493, _1525495] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1525493), _1525495)), -(_1525495 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1525493, 38632 ^ [_1525493, _1525495]), 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)), 38631 ^ [_1525493, _1525495]))))], (38636 ^ _779448) ^ [_1525624, _1525626] : [38637 ^ _779448 : [(38638 ^ _779448) ^ [_1525688, _1525690] : [_1525626 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1525624, _1525688), 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)), _1525690)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525624), _1525626)))], (38642 ^ _779448) ^ [_1525760, _1525762, _1525764, _1525766, _1525768] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1525760, _1525762, _1525764), _1525766), _1525768) = hAPP(c_Set_OCollect(tc_prod(_1525760, _1525764)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525760, _1525764, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1525764, tc_fun(_1525762, tc_HOL_Obool)), tc_fun(_1525764, tc_HOL_Obool), _1525760), hAPP(c_COMBB(tc_fun(_1525762, tc_HOL_Obool), tc_HOL_Obool, _1525764), c_HOL_OEx(_1525762))), hAPP(hAPP(c_COMBC(_1525760, tc_fun(_1525764, tc_fun(_1525762, tc_HOL_Obool)), tc_fun(_1525764, tc_fun(_1525762, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1525762, tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), tc_fun(tc_fun(_1525764, tc_fun(_1525762, tc_HOL_Obool)), tc_fun(_1525764, tc_fun(_1525762, tc_HOL_Obool))), _1525760), c_COMBB(tc_fun(_1525762, tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool), _1525764)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1525762, tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), _1525760), c_COMBS(_1525762, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_HOL_Obool), tc_fun(_1525762, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1525760), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525762), c_fconj)), hAPP(hAPP(c_COMBC(_1525760, tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_fun(tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), _1525760), c_COMBC(_1525762, tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_prod(_1525760, _1525762)), tc_fun(_1525762, tc_fun(tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_HOL_Obool)), _1525760), hAPP(c_COMBB(tc_prod(_1525760, _1525762), tc_fun(tc_fun(tc_prod(_1525760, _1525762), tc_HOL_Obool), tc_HOL_Obool), _1525762), c_member(tc_prod(_1525760, _1525762)))), c_Product__Type_OPair(_1525760, _1525762)))), _1525766))))), hAPP(hAPP(c_COMBC(_1525764, tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_fun(tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_fun(_1525762, tc_HOL_Obool)), _1525764), c_COMBC(_1525762, tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525762, tc_prod(_1525762, _1525764)), tc_fun(_1525762, tc_fun(tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_HOL_Obool)), _1525764), hAPP(c_COMBB(tc_prod(_1525762, _1525764), tc_fun(tc_fun(tc_prod(_1525762, _1525764), tc_HOL_Obool), tc_HOL_Obool), _1525762), c_member(tc_prod(_1525762, _1525764)))), hAPP(c_COMBC(_1525762, _1525764, tc_prod(_1525762, _1525764)), c_Product__Type_OPair(_1525762, _1525764))))), _1525768))))))], (38644 ^ _779448) ^ [_1526208, _1526210, _1526212] : [-(hAPP(c_Relation_ORange(_1526208, _1526210), hAPP(c_Set_OCollect(tc_prod(_1526208, _1526210)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526208, _1526210, tc_HOL_Obool), _1526212))) = hAPP(c_Set_OCollect(_1526210), hAPP(hAPP(c_COMBB(tc_fun(_1526208, tc_HOL_Obool), tc_HOL_Obool, _1526210), c_HOL_OEx(_1526208)), hAPP(c_COMBC(_1526208, _1526210, tc_HOL_Obool), _1526212))))], (38646 ^ _779448) ^ [_1526283, _1526285, _1526287, _1526289, _1526291, _1526293, _1526295, _1526297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526283, _1526285)), hAPP(hAPP(c_Product__Type_OPair(_1526283, _1526285), _1526287), _1526289)), _1526291)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1526285, _1526293)), hAPP(hAPP(c_Product__Type_OPair(_1526285, _1526293), _1526289), _1526295)), _1526297)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526283, _1526293)), hAPP(hAPP(c_Product__Type_OPair(_1526283, _1526293), _1526287), _1526295)), hAPP(hAPP(c_Relation_Orel__comp(_1526283, _1526285, _1526293), _1526291), _1526297))))], (38656 ^ _779448) ^ [_1526570, _1526572, _1526574, _1526576, _1526578] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526570, _1526572)), hAPP(hAPP(c_Product__Type_OPair(_1526570, _1526572), _1526574), _1526576)), _1526578)), -(hBOOL(hAPP(hAPP(c_member(_1526572), _1526576), hAPP(c_Relation_ORange(_1526570, _1526572), _1526578))))], (38662 ^ _779448) ^ [_1526717, _1526719] : [-(hAPP(c_Relation_ORange(_1526717, _1526717), c_Relation_OId__on(_1526717, _1526719)) = _1526719)], (38664 ^ _779448) ^ [_1526751, _1526753, _1526755, _1526757, _1526759, _1526761, _1526763] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1526751, _1526753, _1526755), hAPP(hAPP(c_Relation_Orel__comp(_1526751, _1526757, _1526753), _1526759), _1526761)), _1526763) = hAPP(hAPP(c_Relation_Orel__comp(_1526751, _1526757, _1526755), _1526759), hAPP(hAPP(c_Relation_Orel__comp(_1526757, _1526753, _1526755), _1526761), _1526763)))], (38666 ^ _779448) ^ [_1526826, _1526828, _1526830, _1526832] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1526826, _1526828, _1526830), _1526832), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526828, _1526830), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526826, _1526830), tc_HOL_Obool)))], (38668 ^ _779448) ^ [_1526881, _1526883, _1526885, _1526887] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1526881, _1526883, _1526885), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526881, _1526883), tc_HOL_Obool))), _1526887) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526881, _1526885), tc_HOL_Obool)))], (38670 ^ _779448) ^ [_1526936, _1526938, _1526940, _1526942, _1526944, _1526946, _1526948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526936, _1526938), tc_HOL_Obool)), _1526940), _1526942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526938, _1526944), tc_HOL_Obool)), _1526946), _1526948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526936, _1526944), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1526936, _1526938, _1526944), _1526940), _1526946)), hAPP(hAPP(c_Relation_Orel__comp(_1526936, _1526938, _1526944), _1526942), _1526948))))], (38680 ^ _779448) ^ [_1527203, _1527205, _1527207, _1527209, _1527211, _1527213] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527203, _1527205, _1527207), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527203, _1527205), tc_HOL_Obool)), _1527209), _1527211)), _1527213) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527203, _1527207), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527203, _1527205, _1527207), _1527209), _1527213)), hAPP(hAPP(c_Relation_Orel__comp(_1527203, _1527205, _1527207), _1527211), _1527213)))], (38682 ^ _779448) ^ [_1527294, _1527296, _1527298, _1527300, _1527302, _1527304] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527294, _1527296, _1527298), _1527300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527296, _1527298), tc_HOL_Obool)), _1527302), _1527304)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527294, _1527298), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527294, _1527296, _1527298), _1527300), _1527302)), hAPP(hAPP(c_Relation_Orel__comp(_1527294, _1527296, _1527298), _1527300), _1527304)))], (38684 ^ _779448) ^ [_1527385, _1527387, _1527389, _1527391, _1527393, _1527395, _1527397] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527385, _1527387, _1527389), _1527391), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527393, tc_fun(tc_prod(_1527387, _1527389), tc_HOL_Obool)), _1527395), _1527397)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527393, tc_fun(tc_prod(_1527385, _1527389), tc_HOL_Obool)), _1527395), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527387, _1527389), tc_HOL_Obool), tc_fun(tc_prod(_1527385, _1527389), tc_HOL_Obool), _1527393), hAPP(c_Relation_Orel__comp(_1527385, _1527387, _1527389), _1527391)), _1527397)))], (38686 ^ _779448) ^ [_1527489, _1527491, _1527493, _1527495, _1527497, _1527499, _1527501] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527489, _1527491, _1527493), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527495, tc_fun(tc_prod(_1527489, _1527491), tc_HOL_Obool)), _1527497), _1527499)), _1527501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1527495, tc_fun(tc_prod(_1527489, _1527493), tc_HOL_Obool)), _1527497), hAPP(hAPP(c_COMBC(_1527495, tc_fun(tc_prod(_1527491, _1527493), tc_HOL_Obool), tc_fun(tc_prod(_1527489, _1527493), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1527489, _1527491), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1527491, _1527493), tc_HOL_Obool), tc_fun(tc_prod(_1527489, _1527493), tc_HOL_Obool)), _1527495), c_Relation_Orel__comp(_1527489, _1527491, _1527493)), _1527499)), _1527501)))], (38688 ^ _779448) ^ [_1527621, _1527623, _1527625, _1527627] : [hAPP(hAPP(c_Relation_Orel__comp(_1527621, _1527621, _1527621), _1527623), _1527625) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527621, _1527621), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527621, _1527621, _1527621), _1527627), _1527625) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527621, _1527621), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1527621, _1527621, _1527621), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527621, _1527621), tc_HOL_Obool)), _1527623), _1527627)), _1527625) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527621, _1527621), tc_HOL_Obool)))], (38698 ^ _779448) ^ [_1527894, _1527896, _1527898, _1527900] : [hAPP(hAPP(c_Relation_Orel__comp(_1527894, _1527894, _1527894), _1527896), _1527898) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527894, _1527894), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1527894, _1527894, _1527894), _1527896), _1527900) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527894, _1527894), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1527894, _1527894, _1527894), _1527896), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1527894, _1527894), tc_HOL_Obool)), _1527898), _1527900)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527894, _1527894), tc_HOL_Obool)))], (38708 ^ _779448) ^ [_1528167, _1528169, _1528171] : [-(hAPP(c_Relation_ORange(_1528167, _1528169), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1528167, _1528169), tc_HOL_Obool), _1528171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1528167, _1528169), tc_HOL_Obool), tc_fun(_1528169, tc_HOL_Obool)), _1528171), c_Relation_ORange(_1528167, _1528169)))], (38710 ^ _779448) ^ [_1528230, _1528232] : [-(hAPP(c_Relation_ORange(_1528230, _1528232), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528230, _1528232), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1528232, tc_HOL_Obool)))], (38712 ^ _779448) ^ [_1528292, _1528294, _1528296] : [hAPP(c_Relation_ORange(_1528292, _1528294), _1528296) = c_Orderings_Obot__class_Obot(tc_fun(_1528294, tc_HOL_Obool)), -(_1528296 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528292, _1528294), tc_HOL_Obool)))], (38718 ^ _779448) ^ [_1528405, _1528407, _1528409] : [_1528409 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528405, _1528407), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1528405, _1528407), _1528409) = c_Orderings_Obot__class_Obot(tc_fun(_1528407, tc_HOL_Obool)))], (38724 ^ _779448) ^ [_1528524, _1528526, _1528528, _1528530, _1528532, _1528534, _1528536, _1528538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528524, _1528526), tc_HOL_Obool)), _1528528), hAPP(hAPP(c_Product__Type_OSigma(_1528524, _1528526), _1528530), hAPP(c_COMBK(tc_fun(_1528526, tc_HOL_Obool), _1528524), _1528532)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528526, _1528534), tc_HOL_Obool)), _1528536), hAPP(hAPP(c_Product__Type_OSigma(_1528526, _1528534), _1528532), hAPP(c_COMBK(tc_fun(_1528534, tc_HOL_Obool), _1528526), _1528538)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528524, _1528534), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528524, _1528526, _1528534), _1528528), _1528536)), hAPP(hAPP(c_Product__Type_OSigma(_1528524, _1528534), _1528530), hAPP(c_COMBK(tc_fun(_1528534, tc_HOL_Obool), _1528524), _1528538)))))], (38734 ^ _779448) ^ [_1528883, _1528885, _1528887, _1528889] : [-(hAPP(c_Relation_ORange(_1528883, _1528885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528883, _1528885), tc_HOL_Obool)), _1528887), _1528889)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528885, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1528883, _1528885), _1528887)), hAPP(c_Relation_ORange(_1528883, _1528885), _1528889)))], (38736 ^ _779448) ^ [_1528955, _1528957, _1528959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1528955, _1528957)), _1528959)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1528957), hAPP(c_Relation_ORange(_1528955, _1528957), _1528959))))], (38742 ^ _779448) ^ [_1529068, _1529070, _1529072] : [-(hAPP(c_Set_Oimage(tc_prod(_1529068, _1529070), _1529070, c_Product__Type_Osnd(_1529068, _1529070)), _1529072) = hAPP(c_Relation_ORange(_1529068, _1529070), _1529072))], (38744 ^ _779448) ^ [_1529135, _1529137, _1529139, _1529141] : [hBOOL(hAPP(hAPP(c_member(_1529135), _1529137), hAPP(c_Relation_ORange(_1529139, _1529135), _1529141))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529139, _1529135)), hAPP(hAPP(c_Product__Type_OPair(_1529139, _1529135), 38747 ^ [_1529135, _1529137, _1529139, _1529141]), _1529137)), _1529141)))], (38751 ^ _779448) ^ [_1529292, _1529294, _1529296, _1529298] : [38752 ^ _779448 : [(38753 ^ _779448) ^ [_1529367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529296, _1529292)), hAPP(hAPP(c_Product__Type_OPair(_1529296, _1529292), _1529367), _1529294)), _1529298))]], -(hBOOL(hAPP(hAPP(c_member(_1529292), _1529294), hAPP(c_Relation_ORange(_1529296, _1529292), _1529298))))], (38757 ^ _779448) ^ [_1529452, _1529454, _1529456, _1529458, _1529460] : [-(hAPP(c_Relation_ORange(_1529452, _1529454), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1529452, _1529454)), hAPP(hAPP(c_Product__Type_OPair(_1529452, _1529454), _1529456), _1529458)), _1529460)) = hAPP(hAPP(c_Set_Oinsert(_1529454), _1529458), hAPP(c_Relation_ORange(_1529452, _1529454), _1529460)))], (38759 ^ _779448) ^ [_1529523, _1529525, _1529527, _1529529] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1529523, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1529525, _1529523), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529525, _1529523), tc_HOL_Obool)), _1529527), _1529529))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529523, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1529525, _1529523), _1529527)), hAPP(c_Relation_ORange(_1529525, _1529523), _1529529)))))], (38761 ^ _779448) ^ [_1529605, _1529607, _1529609, _1529611] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1529605, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529605, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1529607, _1529605), _1529609)), hAPP(c_Relation_ORange(_1529607, _1529605), _1529611))), hAPP(c_Relation_ORange(_1529607, _1529605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529607, _1529605), tc_HOL_Obool)), _1529609), _1529611)))))], (38763 ^ _779448) ^ [_1529687, _1529689, _1529691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529687, _1529687), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529687, _1529687, _1529687), _1529689), _1529691)), _1529689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1529687, _1529689)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1529687, _1529691)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1529687, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1529687, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1529687, tc_HOL_Obool), tc_fun(_1529687, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1529687, _1529689))))], (38769 ^ _779448) ^ [_1530058, _1530060, _1530062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530058, _1530058), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530058, _1530058, _1530058), _1530060), _1530062)), _1530060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1530058, _1530060)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1530058, _1530062)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1530058, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1530058, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1530058, tc_HOL_Obool), tc_fun(_1530058, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1530058, _1530060))))], (38775 ^ _779448) ^ [_1530450, _1530452, _1530454, _1530456] : [hBOOL(hAPP(c_Predicate_ORangeP(_1530450, _1530452, hAPP(hAPP(c_COMBC(_1530450, tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_fun(_1530452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530452, tc_fun(tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_fun(_1530452, tc_HOL_Obool)), _1530450), c_COMBC(_1530452, tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530452, tc_prod(_1530450, _1530452)), tc_fun(_1530452, tc_fun(tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_HOL_Obool)), _1530450), hAPP(c_COMBB(tc_prod(_1530450, _1530452), tc_fun(tc_fun(tc_prod(_1530450, _1530452), tc_HOL_Obool), tc_HOL_Obool), _1530452), c_member(tc_prod(_1530450, _1530452)))), c_Product__Type_OPair(_1530450, _1530452)))), _1530454)), _1530456)), -(hBOOL(hAPP(hAPP(c_member(_1530452), _1530456), hAPP(c_Relation_ORange(_1530450, _1530452), _1530454))))], (38781 ^ _779448) ^ [_1530801, _1530803, _1530805, _1530807] : [hBOOL(hAPP(hAPP(c_member(_1530803), _1530807), hAPP(c_Relation_ORange(_1530801, _1530803), _1530805))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1530801, _1530803, hAPP(hAPP(c_COMBC(_1530801, tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_fun(_1530803, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530803, tc_fun(tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_fun(_1530803, tc_HOL_Obool)), _1530801), c_COMBC(_1530803, tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530803, tc_prod(_1530801, _1530803)), tc_fun(_1530803, tc_fun(tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_HOL_Obool)), _1530801), hAPP(c_COMBB(tc_prod(_1530801, _1530803), tc_fun(tc_fun(tc_prod(_1530801, _1530803), tc_HOL_Obool), tc_HOL_Obool), _1530803), c_member(tc_prod(_1530801, _1530803)))), c_Product__Type_OPair(_1530801, _1530803)))), _1530805)), _1530807)))], (38787 ^ _779448) ^ [_1531158, _1531160, _1531162, _1531164] : [hBOOL(hAPP(hAPP(c_member(_1531158), _1531160), hAPP(c_Relation_ORange(_1531162, _1531158), _1531164))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531162, _1531158)), hAPP(hAPP(c_Product__Type_OPair(_1531162, _1531158), 38790 ^ [_1531158, _1531160, _1531162, _1531164]), _1531160)), _1531164)))], (38794 ^ _779448) ^ [_1531353, _1531355, _1531357, _1531359, _1531361, _1531363, _1531365] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1531353, _1531355, _1531357, hAPP(hAPP(c_COMBC(_1531353, tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_fun(_1531355, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531355, tc_fun(tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_fun(_1531355, tc_HOL_Obool)), _1531353), c_COMBC(_1531355, tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531355, tc_prod(_1531353, _1531355)), tc_fun(_1531355, tc_fun(tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_HOL_Obool)), _1531353), hAPP(c_COMBB(tc_prod(_1531353, _1531355), tc_fun(tc_fun(tc_prod(_1531353, _1531355), tc_HOL_Obool), tc_HOL_Obool), _1531355), c_member(tc_prod(_1531353, _1531355)))), c_Product__Type_OPair(_1531353, _1531355)))), _1531359), hAPP(hAPP(c_COMBC(_1531355, tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_fun(_1531357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531357, tc_fun(tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_fun(_1531357, tc_HOL_Obool)), _1531355), c_COMBC(_1531357, tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531357, tc_prod(_1531355, _1531357)), tc_fun(_1531357, tc_fun(tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_HOL_Obool)), _1531355), hAPP(c_COMBB(tc_prod(_1531355, _1531357), tc_fun(tc_fun(tc_prod(_1531355, _1531357), tc_HOL_Obool), tc_HOL_Obool), _1531357), c_member(tc_prod(_1531355, _1531357)))), c_Product__Type_OPair(_1531355, _1531357)))), _1531361)), _1531363), _1531365)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531353, _1531357)), hAPP(hAPP(c_Product__Type_OPair(_1531353, _1531357), _1531363), _1531365)), hAPP(hAPP(c_Relation_Orel__comp(_1531353, _1531355, _1531357), _1531359), _1531361))))], (38800 ^ _779448) ^ [_1531988, _1531990, _1531992, _1531994, _1531996, _1531998, _1532000] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531988, _1531992)), hAPP(hAPP(c_Product__Type_OPair(_1531988, _1531992), _1531998), _1532000)), hAPP(hAPP(c_Relation_Orel__comp(_1531988, _1531990, _1531992), _1531994), _1531996))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1531988, _1531990, _1531992, hAPP(hAPP(c_COMBC(_1531988, tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_fun(_1531990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531990, tc_fun(tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_fun(_1531990, tc_HOL_Obool)), _1531988), c_COMBC(_1531990, tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531990, tc_prod(_1531988, _1531990)), tc_fun(_1531990, tc_fun(tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_HOL_Obool)), _1531988), hAPP(c_COMBB(tc_prod(_1531988, _1531990), tc_fun(tc_fun(tc_prod(_1531988, _1531990), tc_HOL_Obool), tc_HOL_Obool), _1531990), c_member(tc_prod(_1531988, _1531990)))), c_Product__Type_OPair(_1531988, _1531990)))), _1531994), hAPP(hAPP(c_COMBC(_1531990, tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_fun(_1531992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_fun(tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_fun(_1531992, tc_HOL_Obool)), _1531990), c_COMBC(_1531992, tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531992, tc_prod(_1531990, _1531992)), tc_fun(_1531992, tc_fun(tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_HOL_Obool)), _1531990), hAPP(c_COMBB(tc_prod(_1531990, _1531992), tc_fun(tc_fun(tc_prod(_1531990, _1531992), tc_HOL_Obool), tc_HOL_Obool), _1531992), c_member(tc_prod(_1531990, _1531992)))), c_Product__Type_OPair(_1531990, _1531992)))), _1531996)), _1531998), _1532000)))], (38806 ^ _779448) ^ [_1532629, _1532631, _1532633, _1532635, _1532637, _1532639, _1532641, _1532643] : [hBOOL(hAPP(hAPP(_1532629, _1532631), _1532633)), hBOOL(hAPP(hAPP(_1532635, _1532633), _1532637)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1532639, _1532641, _1532643, _1532629, _1532635), _1532631), _1532637)))], (38816 ^ _779448) ^ [_1532824, _1532826, _1532828, _1532830, _1532832] : [hBOOL(hAPP(hAPP(_1532824, _1532826), _1532828)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1532830, _1532832, _1532824), _1532828)))], (38822 ^ _779448) ^ [_1532959, _1532961, _1532963, _1532965, _1532967, _1532969, _1532971] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1532959, _1532961, _1532963, _1532965, _1532967), _1532969), _1532971)), 38826 ^ _779448 : [(38827 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1532965, _1532969), 38825 ^ [_1532959, _1532961, _1532963, _1532965, _1532967, _1532969, _1532971])))], (38829 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1532967, 38825 ^ [_1532959, _1532961, _1532963, _1532965, _1532967, _1532969, _1532971]), _1532971)))]]], (38831 ^ _779448) ^ [_1533149, _1533151, _1533153, _1533155, _1533157, _1533159, _1533161] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1533149, _1533151, _1533153, _1533155, _1533157), _1533159), _1533161))), 38832 ^ _779448 : [(38833 ^ _779448) ^ [_1533220] : [hBOOL(hAPP(hAPP(_1533155, _1533159), _1533220)), hBOOL(hAPP(hAPP(_1533157, _1533220), _1533161))]]], (38841 ^ _779448) ^ [_1533390, _1533392, _1533394, _1533396] : [hBOOL(hAPP(c_Predicate_ORangeP(_1533390, _1533392, _1533394), _1533396)), -(hBOOL(hAPP(hAPP(_1533394, 38844 ^ [_1533390, _1533392, _1533394, _1533396]), _1533396)))], (38848 ^ _779448) ^ [_1533505, _1533507, _1533509, _1533511] : [38849 ^ _779448 : [(38850 ^ _779448) ^ [_1533559] : [hBOOL(hAPP(hAPP(_1533509, _1533559), _1533511))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1533505, _1533507, _1533509), _1533511)))], (38854 ^ _779448) ^ [_1533623, _1533625, _1533627] : [c_Wellfounded_Owf(_1533623, _1533625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533623, _1533623), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1533623, _1533623, _1533623), _1533625), _1533627)), _1533625)), -(c_FunDef_Oreduction__pair(_1533623, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1533623, _1533623), tc_HOL_Obool), tc_fun(tc_prod(_1533623, _1533623), tc_HOL_Obool)), _1533625), _1533627)))], (38864 ^ _779448) ^ [_1533844, _1533846, _1533848] : [-(hAPP(c_Relation_ODomain(_1533844, _1533846), hAPP(c_Set_OCollect(tc_prod(_1533844, _1533846)), hAPP(c_Product__Type_Oprod_Oprod__case(_1533844, _1533846, tc_HOL_Obool), _1533848))) = hAPP(c_Set_OCollect(_1533844), hAPP(hAPP(c_COMBB(tc_fun(_1533846, tc_HOL_Obool), tc_HOL_Obool, _1533844), c_HOL_OEx(_1533846)), _1533848)))], (38866 ^ _779448) ^ [_1533911, _1533913, _1533915, _1533917] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533911), _1533913))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533915), hAPP(c_Set_Oimage(_1533911, _1533915, _1533917), _1533913))), 38874 ^ _779448 : [(38875 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1533911), 38873 ^ [_1533911, _1533913, _1533915, _1533917]), _1533913)))], (38877 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533911), hAPP(c_Set_OCollect(_1533911), hAPP(hAPP(c_COMBS(_1533911, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533911), c_fconj), hAPP(hAPP(c_COMBC(_1533911, tc_fun(_1533911, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533911)), _1533913))), hAPP(hAPP(c_COMBC(_1533911, _1533915, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1533915, tc_fun(_1533915, tc_HOL_Obool), _1533911), c_fequal), _1533917)), hAPP(_1533917, 38873 ^ [_1533911, _1533913, _1533915, _1533917]))))))]]], (38879 ^ _779448) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (38881 ^ _779448) ^ [_1534394] : [-(c_Wellfounded_Owf(_1534394, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1534394, _1534394), tc_HOL_Obool))))], (38883 ^ _779448) ^ [_1534425, _1534427, _1534429, _1534431] : [c_Wellfounded_Owf(_1534425, _1534427), -(c_Wellfounded_Owf(_1534429, hAPP(hAPP(c_Relation_Oinv__image(_1534425, _1534429), _1534427), _1534431)))], (38889 ^ _779448) ^ [_1534524, _1534526, _1534528, _1534530] : [c_Wellfounded_Owf(_1534524, _1534526), c_Wellfounded_Owf(_1534528, _1534530), -(c_Wellfounded_Owf(tc_prod(_1534524, _1534528), c_Wellfounded_Olex__prod(_1534524, _1534528, _1534526, _1534530)))], (38899 ^ _779448) ^ [_1534677, _1534679] : [-(c_Wellfounded_Owf(_1534677, hAPP(c_Wellfounded_Omeasure(_1534677), _1534679)))], (38901 ^ _779448) ^ [_1534707, _1534709, _1534711, _1534713, _1534715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534707, _1534709)), hAPP(hAPP(c_Product__Type_OPair(_1534707, _1534709), _1534711), _1534713)), _1534715)), -(hBOOL(hAPP(hAPP(c_member(_1534707), _1534711), hAPP(c_Relation_ODomain(_1534707, _1534709), _1534715))))], (38907 ^ _779448) ^ [_1534869, _1534871] : [c_Wellfounded_Owf(_1534869, _1534871), -(c_Wellfounded_Owf(_1534869, hAPP(hAPP(c_Relation_Orel__comp(_1534869, _1534869, _1534869), _1534871), _1534871)))], (38913 ^ _779448) ^ [_1534962, _1534964] : [c_Wellfounded_Owf(_1534962, hAPP(hAPP(c_Relation_Orel__comp(_1534962, _1534962, _1534962), _1534964), _1534964)), -(c_Wellfounded_Owf(_1534962, _1534964))], (38919 ^ _779448) ^ [_1535061, _1535063, _1535065] : [c_Wellfounded_Owf(_1535061, _1535063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535061, _1535061), tc_HOL_Obool)), _1535065), _1535063)), -(c_Wellfounded_Owf(_1535061, _1535065))], (38929 ^ _779448) ^ [_1535220, _1535222] : [c_Wellfounded_Owf(_1535220, _1535222), -(c_Wellfounded_Owf(tc_fun(_1535220, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1535220, _1535222)))], (38935 ^ _779448) ^ [_1535309] : [-(c_Wellfounded_Owf(tc_fun(_1535309, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1535309)))], (38937 ^ _779448) ^ [_1535337, _1535339, _1535341] : [c_Wellfounded_Owf(_1535337, _1535339), -(c_Wellfounded_Owf(_1535337, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535337, _1535337), tc_HOL_Obool)), _1535341), _1535339)))], (38943 ^ _779448) ^ [_1535444, _1535446, _1535448] : [c_Wellfounded_Owf(_1535444, _1535446), -(c_Wellfounded_Owf(_1535444, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1535444, _1535444), tc_HOL_Obool)), _1535446), _1535448)))], (38949 ^ _779448) ^ [_1535551, _1535553] : [c_Wellfounded_Owf(_1535551, _1535553), -(c_Wellfounded_Owf(tc_fun(_1535551, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1535551, _1535553)))], (38955 ^ _779448) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38957 ^ _779448) ^ [_1535658, _1535660] : [-(hAPP(c_Relation_ODomain(_1535658, _1535658), c_Relation_OId__on(_1535658, _1535660)) = _1535660)], (38959 ^ _779448) ^ [_1535692, _1535694, _1535696] : [c_Wellfounded_Owf(_1535692, _1535694), -(c_Wellfounded_Owf(_1535692, c_Wellfounded_Omlex__prod(_1535692, _1535696, _1535694)))], (38965 ^ _779448) ^ [] : [-(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)))))], (38967 ^ _779448) ^ [_1535797, _1535799, _1535801] : [c_Wellfounded_Owf(_1535797, _1535799), hBOOL(hAPP(hAPP(c_member(tc_prod(_1535797, _1535797)), hAPP(hAPP(c_Product__Type_OPair(_1535797, _1535797), _1535801), _1535801)), _1535799))], (38973 ^ _779448) ^ [_1535915, _1535917, _1535919, _1535921] : [c_Wellfounded_Owf(_1535915, _1535917), hBOOL(hAPP(hAPP(c_member(tc_prod(_1535915, _1535915)), hAPP(hAPP(c_Product__Type_OPair(_1535915, _1535915), _1535919), _1535921)), _1535917)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1535915, _1535915)), hAPP(hAPP(c_Product__Type_OPair(_1535915, _1535915), _1535921), _1535919)), _1535917))], (38983 ^ _779448) ^ [_1536129, _1536131, _1536133, _1536135] : [c_Wellfounded_Owf(_1536129, _1536131), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536129, _1536129)), hAPP(hAPP(c_Product__Type_OPair(_1536129, _1536129), _1536133), _1536135)), _1536131)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536129, _1536129)), hAPP(hAPP(c_Product__Type_OPair(_1536129, _1536129), _1536135), _1536133)), _1536131))], (38993 ^ _779448) ^ [_1536343, _1536345, _1536347] : [c_Wellfounded_Owf(_1536343, _1536345), hBOOL(hAPP(hAPP(c_member(tc_prod(_1536343, _1536343)), hAPP(hAPP(c_Product__Type_OPair(_1536343, _1536343), _1536347), _1536347)), _1536345))], (38999 ^ _779448) ^ [_1536461] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1536461)))], (39001 ^ _779448) ^ [_1536486] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1536486)))], (39003 ^ _779448) ^ [_1536511, _1536513, _1536515] : [c_Wellfounded_Owf(_1536511, _1536513), c_Wellfounded_Owf(_1536511, _1536515), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1536511, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1536511, _1536511), _1536513)), hAPP(c_Relation_ORange(_1536511, _1536511), _1536515)) = c_Orderings_Obot__class_Obot(tc_fun(_1536511, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1536511, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1536511, _1536511), tc_HOL_Obool)), _1536513), _1536515)))], (39017 ^ _779448) ^ [_1536782, _1536784, _1536786] : [c_Wellfounded_Owf(_1536782, _1536784), -(hBOOL(hAPP(hAPP(c_member(_1536782), _1536786), c_Wellfounded_Oacc(_1536782, _1536784))))], (39023 ^ _779448) ^ [_1536896, _1536898] : [c_Wellfounded_Owf(_1536896, _1536898), 39026 ^ _779448 : [(39027 ^ _779448) ^ [_1536965] : [-(hBOOL(hAPP(hAPP(c_member(_1536896), _1536965), c_Wellfounded_Oacc(_1536896, _1536898))))]]], (39029 ^ _779448) ^ [_1536998, _1537000] : [hBOOL(hAPP(hAPP(c_member(_1536998), 39030 ^ [_1536998, _1537000]), c_Wellfounded_Oacc(_1536998, _1537000))), -(c_Wellfounded_Owf(_1536998, _1537000))], (39036 ^ _779448) ^ [_1537131, _1537133] : [hAPP(hAPP(c_Relation_Orel__comp(_1537131, _1537131, _1537131), _1537133), _1537133) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537131, _1537131), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1537131, _1537133))], (39042 ^ _779448) ^ [_1537262, _1537264, _1537266] : [c_Wellfounded_Owf(_1537262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537262, _1537262), tc_HOL_Obool)), _1537264), _1537266)), -(c_Wellfounded_Owf(_1537262, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537262, _1537262), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537262, _1537262), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1537262, _1537262, _1537262), _1537264), _1537264)), hAPP(hAPP(c_Relation_Orel__comp(_1537262, _1537262, _1537262), _1537266), _1537264))), _1537266)))], (39048 ^ _779448) ^ [_1537461, _1537463, _1537465] : [c_Wellfounded_Owf(_1537461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537461, _1537461), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537461, _1537461), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1537461, _1537461, _1537461), _1537463), _1537463)), hAPP(hAPP(c_Relation_Orel__comp(_1537461, _1537461, _1537461), _1537465), _1537463))), _1537465)), -(c_Wellfounded_Owf(_1537461, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1537461, _1537461), tc_HOL_Obool)), _1537463), _1537465)))], (39054 ^ _779448) ^ [_1537666, _1537668] : [-(hAPP(c_Relation_ODomain(_1537666, _1537668), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537666, _1537668), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1537666, tc_HOL_Obool)))], (39056 ^ _779448) ^ [_1537728, _1537730, _1537732] : [hAPP(c_Relation_ODomain(_1537728, _1537730), _1537732) = c_Orderings_Obot__class_Obot(tc_fun(_1537728, tc_HOL_Obool)), -(_1537732 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537728, _1537730), tc_HOL_Obool)))], (39062 ^ _779448) ^ [_1537841, _1537843, _1537845] : [_1537845 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537841, _1537843), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1537841, _1537843), _1537845) = c_Orderings_Obot__class_Obot(tc_fun(_1537841, tc_HOL_Obool)))], (39068 ^ _779448) ^ [_1537960, _1537962, _1537964, _1537966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537960, _1537962), tc_HOL_Obool)), _1537964), _1537966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537960, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1537960, _1537962), _1537964)), hAPP(c_Relation_ODomain(_1537960, _1537962), _1537966))))], (39074 ^ _779448) ^ [_1538111, _1538113, _1538115, _1538117] : [-(hAPP(c_Relation_ODomain(_1538111, _1538113), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538111, _1538113), tc_HOL_Obool)), _1538115), _1538117)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1538111, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1538111, _1538113), _1538115)), hAPP(c_Relation_ODomain(_1538111, _1538113), _1538117)))], (39076 ^ _779448) ^ [_1538183, _1538185, _1538187] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538183, _1538185)), _1538187)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1538183), hAPP(c_Relation_ODomain(_1538183, _1538185), _1538187))))], (39082 ^ _779448) ^ [_1538296, _1538298, _1538300] : [-(hAPP(c_Set_Oimage(tc_prod(_1538296, _1538298), _1538296, c_Product__Type_Ofst(_1538296, _1538298)), _1538300) = hAPP(c_Relation_ODomain(_1538296, _1538298), _1538300))], (39084 ^ _779448) ^ [_1538357, _1538359] : [c_Wellfounded_Owf(_1538357, _1538359), 39088 ^ _779448 : [(39089 ^ _779448) ^ [_1538493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538357, _1538357)), hAPP(hAPP(c_Product__Type_OPair(_1538357, _1538357), hAPP(_1538493, hAPP(c_Nat_OSuc, 39087 ^ [_1538357, _1538359, _1538493]))), hAPP(_1538493, 39087 ^ [_1538357, _1538359, _1538493]))), _1538359))]]], (39091 ^ _779448) ^ [_1538560, _1538562] : [39093 ^ _779448 : [(39094 ^ _779448) ^ [_1538585] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538560, _1538560)), hAPP(hAPP(c_Product__Type_OPair(_1538560, _1538560), hAPP(39092 ^ [_1538560, _1538562], hAPP(c_Nat_OSuc, _1538585))), hAPP(39092 ^ [_1538560, _1538562], _1538585))), _1538562)))]], -(c_Wellfounded_Owf(_1538560, _1538562))], (39098 ^ _779448) ^ [_1538661, _1538663, _1538665] : [c_Wellfounded_Owf(_1538661, _1538663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538661, tc_HOL_Obool)), _1538665), hAPP(c_Relation_OImage(_1538661, _1538661, _1538663), _1538665))), -(_1538665 = c_Orderings_Obot__class_Obot(tc_fun(_1538661, tc_HOL_Obool)))], (39108 ^ _779448) ^ [_1538838, _1538840, _1538842] : [c_Wellfounded_Owf(_1538838, _1538840), c_Wellfounded_Owf(_1538838, _1538842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538838, _1538838), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1538838, _1538838, _1538838), _1538840), _1538842)), _1538840)), -(c_Wellfounded_Owf(_1538838, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1538838, _1538838), tc_HOL_Obool)), _1538840), _1538842)))], (39122 ^ _779448) ^ [_1539120, _1539122, _1539124, _1539126] : [hBOOL(hAPP(hAPP(c_member(_1539120), _1539122), hAPP(c_Relation_ODomain(_1539120, _1539124), _1539126))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539120, _1539124)), hAPP(hAPP(c_Product__Type_OPair(_1539120, _1539124), _1539122), 39125 ^ [_1539120, _1539122, _1539124, _1539126])), _1539126)))], (39129 ^ _779448) ^ [_1539277, _1539279, _1539281, _1539283] : [39130 ^ _779448 : [(39131 ^ _779448) ^ [_1539352] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539277, _1539281)), hAPP(hAPP(c_Product__Type_OPair(_1539277, _1539281), _1539279), _1539352)), _1539283))]], -(hBOOL(hAPP(hAPP(c_member(_1539277), _1539279), hAPP(c_Relation_ODomain(_1539277, _1539281), _1539283))))], (39135 ^ _779448) ^ [_1539437] : [class_Orderings_Owellorder(_1539437), -(c_Wellfounded_Owf(_1539437, hAPP(c_Set_OCollect(tc_prod(_1539437, _1539437)), hAPP(c_Product__Type_Oprod_Oprod__case(_1539437, _1539437, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1539437)))))], (39141 ^ _779448) ^ [_1539544, _1539546, _1539548, _1539550, _1539552] : [-(hAPP(c_Relation_ODomain(_1539544, _1539546), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1539544, _1539546)), hAPP(hAPP(c_Product__Type_OPair(_1539544, _1539546), _1539548), _1539550)), _1539552)) = hAPP(hAPP(c_Set_Oinsert(_1539544), _1539548), hAPP(c_Relation_ODomain(_1539544, _1539546), _1539552)))], (39143 ^ _779448) ^ [_1539630, _1539632] : [c_FunDef_Oreduction__pair(_1539630, _1539632), 39146 ^ _779448 : [(39147 ^ _779448) ^ [] : [-(c_Wellfounded_Owf(_1539630, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool), tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool)), _1539632)))], (39149 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1539630, _1539630, _1539630), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool), tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool)), _1539632)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool), tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool)), _1539632))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool), tc_fun(tc_prod(_1539630, _1539630), tc_HOL_Obool)), _1539632))))]]], (39151 ^ _779448) ^ [_1539919, _1539921] : [-(c_FunDef_Oreduction__pair(_1539919, _1539921)), c_Wellfounded_Owf(_1539919, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool), tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool)), _1539921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1539919, _1539919, _1539919), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool), tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool)), _1539921)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool), tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool)), _1539921))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool), tc_fun(tc_prod(_1539919, _1539919), tc_HOL_Obool)), _1539921)))], (39161 ^ _779448) ^ [_1540240, _1540242, _1540244, _1540246] : [c_FunDef_Oreduction__pair(_1540240, _1540242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool)), _1540244), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool), tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool)), _1540242))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool)), _1540246), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool), tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool)), _1540242))), c_Wellfounded_Owf(_1540240, _1540246), -(c_Wellfounded_Owf(_1540240, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540240, _1540240), tc_HOL_Obool)), _1540244), _1540246)))], (39179 ^ _779448) ^ [_1540641, _1540643, _1540645, _1540647] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540641, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1540641, _1540643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1540641, _1540643), tc_HOL_Obool)), _1540645), _1540647))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1540641, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1540641, _1540643), _1540645)), hAPP(c_Relation_ODomain(_1540641, _1540643), _1540647)))))], (39181 ^ _779448) ^ [_1540723, _1540725, _1540727, _1540729] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540723, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1540723, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1540723, _1540725), _1540727)), hAPP(c_Relation_ODomain(_1540723, _1540725), _1540729))), hAPP(c_Relation_ODomain(_1540723, _1540725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1540723, _1540725), tc_HOL_Obool)), _1540727), _1540729)))))], (39183 ^ _779448) ^ [_1540805, _1540807] : [-(hAPP(c_Relation_OField(_1540805), _1540807) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1540805, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1540805, _1540805), _1540807)), hAPP(c_Relation_ORange(_1540805, _1540805), _1540807)))], (39185 ^ _779448) ^ [_1540858, _1540860, _1540862, _1540864] : [c_Wellfounded_Owf(_1540858, _1540860), c_Fun_Oinj__on(_1540858, _1540862, _1540864, c_Orderings_Otop__class_Otop(tc_fun(_1540858, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1540862, hAPP(c_Set_Oimage(tc_prod(_1540858, _1540858), tc_prod(_1540862, _1540862), c_Product__Type_Omap__pair(_1540858, _1540862, _1540858, _1540862, _1540864, _1540864)), _1540860)))], (39195 ^ _779448) ^ [_1541049, _1541051, _1541053] : [-(hAPP(c_Relation_ODomain(_1541049, _1541051), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1541049, _1541051), tc_HOL_Obool), _1541053)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1541049, _1541051), tc_HOL_Obool), tc_fun(_1541049, tc_HOL_Obool)), _1541053), c_Relation_ODomain(_1541049, _1541051)))], (39197 ^ _779448) ^ [_1541133, _1541135, _1541137, _1541139] : [hBOOL(hAPP(c_Predicate_ODomainP(_1541133, _1541135, hAPP(hAPP(c_COMBC(_1541133, tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_fun(_1541135, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541135, tc_fun(tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_fun(_1541135, tc_HOL_Obool)), _1541133), c_COMBC(_1541135, tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541135, tc_prod(_1541133, _1541135)), tc_fun(_1541135, tc_fun(tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_HOL_Obool)), _1541133), hAPP(c_COMBB(tc_prod(_1541133, _1541135), tc_fun(tc_fun(tc_prod(_1541133, _1541135), tc_HOL_Obool), tc_HOL_Obool), _1541135), c_member(tc_prod(_1541133, _1541135)))), c_Product__Type_OPair(_1541133, _1541135)))), _1541137)), _1541139)), -(hBOOL(hAPP(hAPP(c_member(_1541133), _1541139), hAPP(c_Relation_ODomain(_1541133, _1541135), _1541137))))], (39203 ^ _779448) ^ [_1541484, _1541486, _1541488, _1541490] : [hBOOL(hAPP(hAPP(c_member(_1541484), _1541490), hAPP(c_Relation_ODomain(_1541484, _1541486), _1541488))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1541484, _1541486, hAPP(hAPP(c_COMBC(_1541484, tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_fun(_1541486, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541486, tc_fun(tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_fun(_1541486, tc_HOL_Obool)), _1541484), c_COMBC(_1541486, tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541486, tc_prod(_1541484, _1541486)), tc_fun(_1541486, tc_fun(tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_HOL_Obool)), _1541484), hAPP(c_COMBB(tc_prod(_1541484, _1541486), tc_fun(tc_fun(tc_prod(_1541484, _1541486), tc_HOL_Obool), tc_HOL_Obool), _1541486), c_member(tc_prod(_1541484, _1541486)))), c_Product__Type_OPair(_1541484, _1541486)))), _1541488)), _1541490)))], (39209 ^ _779448) ^ [_1541841, _1541843] : [c_Wellfounded_Owf(_1541841, _1541843), -(c_Wellfounded_Owf(tc_List_Olist(_1541841), c_List_Olenlex(_1541841, _1541843)))], (39215 ^ _779448) ^ [_1541928, _1541930, _1541932, _1541934] : [hBOOL(hAPP(hAPP(c_member(_1541928), _1541930), hAPP(c_Relation_ODomain(_1541928, _1541932), _1541934))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541928, _1541932)), hAPP(hAPP(c_Product__Type_OPair(_1541928, _1541932), _1541930), 39218 ^ [_1541928, _1541930, _1541932, _1541934])), _1541934)))], (39222 ^ _779448) ^ [_1542093, _1542095, _1542097, _1542099, _1542101] : [hBOOL(hAPP(hAPP(_1542093, _1542095), _1542097)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1542099, _1542101, _1542093), _1542095)))], (39228 ^ _779448) ^ [_1542219, _1542221, _1542223, _1542225] : [hBOOL(hAPP(c_Predicate_ODomainP(_1542219, _1542221, _1542223), _1542225)), -(hBOOL(hAPP(hAPP(_1542223, _1542225), 39231 ^ [_1542219, _1542221, _1542223, _1542225])))], (39235 ^ _779448) ^ [_1542334, _1542336, _1542338, _1542340] : [39236 ^ _779448 : [(39237 ^ _779448) ^ [_1542388] : [hBOOL(hAPP(hAPP(_1542338, _1542340), _1542388))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1542334, _1542336, _1542338), _1542340)))], (39241 ^ _779448) ^ [] : [-(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))))], (39243 ^ _779448) ^ [_1542470, _1542472] : [c_Wellfounded_Owf(_1542470, _1542472), -(c_Wellfounded_Owf(tc_List_Olist(_1542470), c_List_Olex(_1542470, _1542472)))], (39249 ^ _779448) ^ [_1542557, _1542559, _1542561] : [c_Wellfounded_Owf(_1542557, _1542559), -(c_Wellfounded_Owf(tc_List_Olist(_1542557), hAPP(c_List_Olexn(_1542557, _1542559), _1542561)))], (39255 ^ _779448) ^ [_1542652, _1542654] : [-(c_List_Olex(_1542652, _1542654) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1542652), tc_List_Olist(_1542652)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1542652, _1542654)))], (39257 ^ _779448) ^ [_1542702, _1542704] : [-(hAPP(c_List_Olexn(_1542702, _1542704), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1542702), tc_List_Olist(_1542702)), tc_HOL_Obool)))], (39259 ^ _779448) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39261 ^ _779448) ^ [_1542763, _1542765, _1542767, _1542769] : [39263 ^ _779448 : [(39264 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1542763, 39262 ^ [_1542763, _1542765, _1542767, _1542769])))], (39266 ^ _779448) ^ [] : [c_Wellfounded_Owf(_1542765, hAPP(_1542767, 39262 ^ [_1542763, _1542765, _1542767, _1542769]))]], -(c_Wellfounded_Owf(tc_prod(_1542769, _1542765), c_Recdef_Osame__fst(_1542769, _1542765, _1542763, _1542767)))], (39270 ^ _779448) ^ [_1542948, _1542950, _1542952, _1542954] : [39272 ^ _779448 : [(39273 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1542948, 39271 ^ [_1542948, _1542950, _1542952, _1542954])))], (39275 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1542950, hAPP(_1542952, 39271 ^ [_1542948, _1542950, _1542952, _1542954]))), hAPP(_1542950, 39271 ^ [_1542948, _1542950, _1542952, _1542954])))]], -(c_Wellfounded_Owf(_1542954, hAPP(c_Set_OCollect(tc_prod(_1542954, _1542954)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542954, _1542954, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1542954, tc_HOL_Obool), tc_fun(_1542954, tc_HOL_Obool), _1542954), hAPP(c_COMBS(_1542954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542954), c_fconj), _1542948))), hAPP(hAPP(c_COMBC(_1542954, tc_fun(_1542954, _1542954), tc_fun(_1542954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542954, tc_HOL_Obool), tc_fun(tc_fun(_1542954, _1542954), tc_fun(_1542954, tc_HOL_Obool)), _1542954), c_COMBB(_1542954, tc_HOL_Obool, _1542954)), c_fequal)), _1542952))))))], (39279 ^ _779448) ^ [_1543356, _1543358] : [c_Wellfounded_OwfP(_1543356, _1543358), -(c_Wellfounded_Owf(_1543356, hAPP(c_Set_OCollect(tc_prod(_1543356, _1543356)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543356, _1543356, tc_HOL_Obool), _1543358))))], (39285 ^ _779448) ^ [_1543459, _1543461] : [c_Wellfounded_Owf(_1543459, hAPP(c_Set_OCollect(tc_prod(_1543459, _1543459)), hAPP(c_Product__Type_Oprod_Oprod__case(_1543459, _1543459, tc_HOL_Obool), _1543461))), -(c_Wellfounded_OwfP(_1543459, _1543461))], (39291 ^ _779448) ^ [_1543568] : [-(c_Wellfounded_OwfP(_1543568, hAPP(c_COMBK(tc_fun(_1543568, tc_HOL_Obool), _1543568), hAPP(c_COMBK(tc_HOL_Obool, _1543568), c_fFalse))))], (39293 ^ _779448) ^ [_1543621, _1543623] : [c_Wellfounded_OwfP(_1543621, _1543623), 39296 ^ _779448 : [(39297 ^ _779448) ^ [_1543685] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1543621, _1543623), _1543685)))]]], (39299 ^ _779448) ^ [_1543713, _1543715] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1543713, _1543715), 39300 ^ [_1543713, _1543715])), -(c_Wellfounded_OwfP(_1543713, _1543715))], (39306 ^ _779448) ^ [_1543831, _1543833, _1543835] : [c_Wellfounded_OwfP(_1543831, _1543833), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1543831, _1543833), _1543835)))], (39312 ^ _779448) ^ [_1543920, _1543922, _1543924] : [c_Wellfounded_OwfP(_1543920, _1543922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1543920, tc_fun(_1543920, tc_HOL_Obool))), _1543924), _1543922)), -(c_Wellfounded_OwfP(_1543920, _1543924))], (39322 ^ _779448) ^ [_1544079, _1544081] : [c_Wellfounded_Owf(_1544079, _1544081), -(c_Wellfounded_OwfP(_1544079, c_FunDef_Oin__rel(_1544079, _1544079, _1544081)))], (39328 ^ _779448) ^ [_1544179, _1544181] : [c_Wellfounded_OwfP(_1544179, hAPP(hAPP(c_COMBC(_1544179, tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_fun(_1544179, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544179, tc_fun(tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_fun(_1544179, tc_HOL_Obool)), _1544179), c_COMBC(_1544179, tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544179, tc_prod(_1544179, _1544179)), tc_fun(_1544179, tc_fun(tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_HOL_Obool)), _1544179), hAPP(c_COMBB(tc_prod(_1544179, _1544179), tc_fun(tc_fun(tc_prod(_1544179, _1544179), tc_HOL_Obool), tc_HOL_Obool), _1544179), c_member(tc_prod(_1544179, _1544179)))), c_Product__Type_OPair(_1544179, _1544179)))), _1544181)), -(c_Wellfounded_Owf(_1544179, _1544181))], (39334 ^ _779448) ^ [_1544488, _1544490] : [c_Wellfounded_Owf(_1544488, _1544490), -(c_Wellfounded_OwfP(_1544488, hAPP(hAPP(c_COMBC(_1544488, tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_fun(_1544488, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544488, tc_fun(tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_fun(_1544488, tc_HOL_Obool)), _1544488), c_COMBC(_1544488, tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544488, tc_prod(_1544488, _1544488)), tc_fun(_1544488, tc_fun(tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_HOL_Obool)), _1544488), hAPP(c_COMBB(tc_prod(_1544488, _1544488), tc_fun(tc_fun(tc_prod(_1544488, _1544488), tc_HOL_Obool), tc_HOL_Obool), _1544488), c_member(tc_prod(_1544488, _1544488)))), c_Product__Type_OPair(_1544488, _1544488)))), _1544490)))], (39340 ^ _779448) ^ [_1544803, _1544805] : [c_Wellfounded_OwfP(_1544803, _1544805), -(c_Wellfounded_Oacyclic(_1544803, hAPP(c_Set_OCollect(tc_prod(_1544803, _1544803)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544803, _1544803, tc_HOL_Obool), _1544805))))], (39362 ^ _779448) ^ [_1545547, _1545549, _1545551] : [-(c_Relation_Orefl__on(_1545547, _1545549, _1545551)), 39366 ^ _779448 : [(39367 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545547, _1545547)), 39365 ^ [_1545547, _1545549, _1545551]), _1545551)))], (39369 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545547, _1545547, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1545547, tc_fun(_1545547, tc_HOL_Obool), tc_fun(_1545547, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1545547, tc_HOL_Obool), tc_fun(_1545547, tc_HOL_Obool)), _1545547), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1545547)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1545547), c_fconj), hAPP(hAPP(c_COMBC(_1545547, tc_fun(_1545547, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545547)), _1545549)))), hAPP(hAPP(c_COMBC(_1545547, tc_fun(_1545547, tc_HOL_Obool), tc_HOL_Obool), c_member(_1545547)), _1545549))), 39365 ^ [_1545547, _1545549, _1545551]))]], 39371 ^ _779448 : [(39372 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1545547), 39370 ^ [_1545547, _1545549, _1545551]), _1545549)))], (39374 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545547, _1545547)), hAPP(hAPP(c_Product__Type_OPair(_1545547, _1545547), 39370 ^ [_1545547, _1545549, _1545551]), 39370 ^ [_1545547, _1545549, _1545551])), _1545551))]]], (39346 ^ _779448) ^ [_1544928, _1544930, _1544932] : [c_Relation_Orefl__on(_1544928, _1544930, _1544932), 39349 ^ _779448 : [(39350 ^ _779448) ^ [_1545139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544928, _1544928)), _1545139), _1544932)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1544928, _1544928, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1544928, tc_fun(_1544928, tc_HOL_Obool), tc_fun(_1544928, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1544928, tc_HOL_Obool), tc_fun(_1544928, tc_HOL_Obool)), _1544928), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1544928)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1544928), c_fconj), hAPP(hAPP(c_COMBC(_1544928, tc_fun(_1544928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544928)), _1544930)))), hAPP(hAPP(c_COMBC(_1544928, tc_fun(_1544928, tc_HOL_Obool), tc_HOL_Obool), c_member(_1544928)), _1544930))), _1545139)))], (39356 ^ _779448) ^ [_1545412] : [hBOOL(hAPP(hAPP(c_member(_1544928), _1545412), _1544930)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544928, _1544928)), hAPP(hAPP(c_Product__Type_OPair(_1544928, _1544928), _1545412), _1545412)), _1544932)))]]], (39378 ^ _779448) ^ [_1546188, _1546190] : [39380 ^ _779448 : [(39381 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39379 ^ [_1546188, _1546190]), c_Int_OInteg)))], (39383 ^ _779448) ^ [] : [hBOOL(hAPP(_1546188, hAPP(c_Int_OAbs__Integ, 39379 ^ [_1546188, _1546190])))]], -(hBOOL(hAPP(_1546188, _1546190)))], (39387 ^ _779448) ^ [_1546357, _1546359, _1546361] : [hBOOL(hAPP(hAPP(c_member(_1546359), _1546357), c_Orderings_Obot__class_Obot(tc_fun(_1546359, tc_HOL_Obool)))), -(hBOOL(hAPP(_1546361, _1546357)))], (39393 ^ _779448) ^ [_1546464, _1546466] : [c_Wellfounded_Owf(_1546464, _1546466), -(c_Wellfounded_Oacyclic(_1546464, _1546466))], (39399 ^ _779448) ^ [_1546541, _1546543, _1546545] : [c_Wellfounded_Oacyclic(_1546541, _1546543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1546541, _1546541), tc_HOL_Obool)), _1546545), _1546543)), -(c_Wellfounded_Oacyclic(_1546541, _1546545))], (39419 ^ _779448) ^ [_1546901, _1546903, _1546905] : [39421 ^ _779448 : [(39422 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546901), 39420 ^ [_1546901, _1546903, _1546905]), _1546905)))], (39424 ^ _779448) ^ [] : [hBOOL(hAPP(_1546903, 39420 ^ [_1546901, _1546903, _1546905]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1546901, _1546903), _1546905)))], (39409 ^ _779448) ^ [_1546718, _1546720, _1546722] : [hBOOL(hAPP(c_Predicate_OPowp(_1546718, _1546720), _1546722)), 39412 ^ _779448 : [(39413 ^ _779448) ^ [_1546802] : [hBOOL(hAPP(hAPP(c_member(_1546718), _1546802), _1546722)), -(hBOOL(hAPP(_1546720, _1546802)))]]], (39428 ^ _779448) ^ [_1547081] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547081, tc_HOL_Obool) = c_Set_OBall(_1547081))], (39430 ^ _779448) ^ [_1547109, _1547111, _1547113, _1547115] : [-(hAPP(c_Set_OCollect(_1547109), hAPP(hAPP(c_COMBB(tc_fun(_1547111, tc_HOL_Obool), tc_HOL_Obool, _1547109), c_HOL_OAll(_1547111)), hAPP(hAPP(c_COMBB(tc_fun(_1547111, tc_HOL_Obool), tc_fun(_1547111, tc_HOL_Obool), _1547109), hAPP(c_COMBS(_1547111, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547111), c_fimplies), hAPP(hAPP(c_COMBC(_1547111, tc_fun(_1547111, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547111)), _1547113)))), _1547115))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1547111, tc_fun(_1547109, tc_HOL_Obool)), _1547113), hAPP(hAPP(c_COMBB(tc_fun(_1547109, tc_HOL_Obool), tc_fun(_1547109, tc_HOL_Obool), _1547111), c_Set_OCollect(_1547109)), hAPP(c_COMBC(_1547109, _1547111, tc_HOL_Obool), _1547115))))], (39442 ^ _779448) ^ [_1547640, _1547642, _1547644, _1547646] : [39444 ^ _779448 : [(39445 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547640, _1547640)), 39443 ^ [_1547640, _1547642, _1547644, _1547646]), _1547644)))], (39447 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1547640, _1547640, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1547640, tc_fun(_1547640, _1547642), tc_fun(_1547640, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547642, tc_HOL_Obool), tc_fun(tc_fun(_1547640, _1547642), tc_fun(_1547640, tc_HOL_Obool)), _1547640), c_COMBB(_1547642, tc_HOL_Obool, _1547640)), hAPP(hAPP(c_COMBB(_1547642, tc_fun(_1547642, tc_HOL_Obool), _1547640), c_fequal), _1547646))), _1547646)), 39443 ^ [_1547640, _1547642, _1547644, _1547646]))]], -(c_Equiv__Relations_Ocongruent(_1547640, _1547642, _1547644, _1547646))], (39432 ^ _779448) ^ [_1547264, _1547266, _1547268, _1547270] : [c_Equiv__Relations_Ocongruent(_1547264, _1547266, _1547268, _1547270), 39435 ^ _779448 : [(39436 ^ _779448) ^ [_1547409] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547264, _1547264)), _1547409), _1547268)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1547264, _1547264, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1547264, tc_fun(_1547264, _1547266), tc_fun(_1547264, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547266, tc_HOL_Obool), tc_fun(tc_fun(_1547264, _1547266), tc_fun(_1547264, tc_HOL_Obool)), _1547264), c_COMBB(_1547266, tc_HOL_Obool, _1547264)), hAPP(hAPP(c_COMBB(_1547266, tc_fun(_1547266, tc_HOL_Obool), _1547264), c_fequal), _1547270))), _1547270)), _1547409)))]]], (39451 ^ _779448) ^ [_1548015, _1548017, _1548019, _1548021] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548015, tc_fun(_1548017, tc_HOL_Obool)), _1548019), _1548021) = hAPP(c_Set_OCollect(_1548017), hAPP(hAPP(c_COMBB(tc_fun(_1548015, tc_HOL_Obool), tc_HOL_Obool, _1548017), c_HOL_OAll(_1548015)), hAPP(hAPP(c_COMBB(tc_fun(_1548015, tc_HOL_Obool), tc_fun(_1548015, tc_HOL_Obool), _1548017), hAPP(c_COMBS(_1548015, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548015), c_fimplies), hAPP(hAPP(c_COMBC(_1548015, tc_fun(_1548015, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548015)), _1548019)))), hAPP(hAPP(c_COMBC(_1548017, tc_fun(_1548015, tc_fun(_1548017, tc_HOL_Obool)), tc_fun(_1548015, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1548017, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1548015, tc_fun(_1548017, tc_HOL_Obool)), tc_fun(_1548015, tc_HOL_Obool)), _1548017), c_COMBB(tc_fun(_1548017, tc_HOL_Obool), tc_HOL_Obool, _1548015)), c_member(_1548017))), _1548021)))))], (39453 ^ _779448) ^ [_1548180, _1548182] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548180, _1548180)), _1548182)), 39456 ^ _779448 : [(39457 ^ _779448) ^ [] : [c_Wellfounded_Owf(_1548180, _1548182), -(c_Wellfounded_Oacyclic(_1548180, _1548182))], (39463 ^ _779448) ^ [] : [c_Wellfounded_Oacyclic(_1548180, _1548182), -(c_Wellfounded_Owf(_1548180, _1548182))]]], (39469 ^ _779448) ^ [_1548401, _1548403] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548401, _1548401)), _1548403)), c_Wellfounded_Oacyclic(_1548401, _1548403), -(c_Wellfounded_Owf(_1548401, _1548403))], (39479 ^ _779448) ^ [_1548544, _1548546] : [class_Complete__Lattice_Ocomplete__lattice(_1548544), -(c_Complete__Lattice_OSup__class_OSup(_1548544, _1548546) = c_Complete__Lattice_OInf__class_OInf(_1548544, hAPP(c_Set_OCollect(_1548544), hAPP(hAPP(c_COMBB(tc_fun(_1548544, tc_HOL_Obool), tc_HOL_Obool, _1548544), c_HOL_OAll(_1548544)), hAPP(hAPP(c_COMBB(tc_fun(_1548544, tc_HOL_Obool), tc_fun(_1548544, tc_HOL_Obool), _1548544), hAPP(c_COMBS(_1548544, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548544), c_fimplies), hAPP(hAPP(c_COMBC(_1548544, tc_fun(_1548544, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548544)), _1548546)))), hAPP(c_COMBC(_1548544, _1548544, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1548544)))))))], (39485 ^ _779448) ^ [_1548785, _1548787] : [class_Complete__Lattice_Ocomplete__lattice(_1548785), -(c_Complete__Lattice_OInf__class_OInf(_1548785, _1548787) = c_Complete__Lattice_OSup__class_OSup(_1548785, hAPP(c_Set_OCollect(_1548785), hAPP(hAPP(c_COMBB(tc_fun(_1548785, tc_HOL_Obool), tc_HOL_Obool, _1548785), c_HOL_OAll(_1548785)), hAPP(hAPP(c_COMBB(tc_fun(_1548785, tc_HOL_Obool), tc_fun(_1548785, tc_HOL_Obool), _1548785), hAPP(c_COMBS(_1548785, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548785), c_fimplies), hAPP(hAPP(c_COMBC(_1548785, tc_fun(_1548785, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548785)), _1548787)))), c_Orderings_Oord__class_Oless__eq(_1548785))))))], (39491 ^ _779448) ^ [_1549027, _1549029] : [c_Nitpick_Owf_H(_1549027, _1549029), 39494 ^ _779448 : [(39495 ^ _779448) ^ [] : [-(c_Wellfounded_Oacyclic(_1549027, _1549029))], (39497 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549027, _1549027)), _1549029))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (39503 ^ _779448) ^ [_1549147, _1549149] : [-(c_Nitpick_Owf_H(_1549147, _1549149)), c_Wellfounded_Oacyclic(_1549147, _1549149), 39508 ^ _779448 : [(39509 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549147, _1549147)), _1549149))], (39511 ^ _779448) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (39516 ^ _779448) ^ [_1549322] : [-(_1549322 = hAPP(c_Int_OAbs__Integ, 39514 ^ [_1549322]))], (39518 ^ _779448) ^ [_1549350] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39514 ^ [_1549350]), c_Int_OInteg)))], (39520 ^ _779448) ^ [_1549385, _1549387, _1549389, _1549391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549385), _1549387)), 39526 ^ _779448 : [(39527 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549385), 39525 ^ [_1549385, _1549387, _1549389, _1549391]), _1549387)))], (39529 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549389), hAPP(_1549391, 39525 ^ [_1549385, _1549387, _1549389, _1549391])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1549389), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549385, tc_fun(_1549389, tc_HOL_Obool)), _1549387), _1549391))))], (39533 ^ _779448) ^ [_1549672, _1549674] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1549672, tc_HOL_Obool), _1549674) = hAPP(c_Set_OCollect(_1549672), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549672, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1549672), c_HOL_OAll(tc_fun(_1549672, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549672, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549672, tc_HOL_Obool), tc_HOL_Obool), _1549672), hAPP(c_COMBS(tc_fun(_1549672, 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(_1549672, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1549672, tc_HOL_Obool), tc_fun(tc_fun(_1549672, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1549672, tc_HOL_Obool))), _1549674)))), c_member(_1549672)))))], (39535 ^ _779448) ^ [_1549800, _1549802, _1549804] : [c_Wellfounded_OwfP(_1549800, hAPP(_1549802, 39536 ^ [_1549800, _1549802, _1549804])), 39543 ^ _779448 : [(39544 ^ _779448) ^ [] : [hAPP(_1549802, 39541 ^ [_1549800, _1549802, _1549804]) = hAPP(_1549802, 39542 ^ [_1549800, _1549802, _1549804])], (39546 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549800, tc_HOL_Obool)), c_Predicate_ODomainP(_1549800, _1549800, hAPP(_1549802, 39541 ^ [_1549800, _1549802, _1549804]))), c_Predicate_ORangeP(_1549800, _1549800, hAPP(_1549802, 39542 ^ [_1549800, _1549802, _1549804]))) = c_Orderings_Obot__class_Obot(tc_fun(_1549800, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1549800, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1549804, tc_fun(_1549800, tc_fun(_1549800, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1549804, tc_HOL_Obool))), _1549802)))], (39550 ^ _779448) ^ [_1550240, _1550242, _1550244, _1550246, _1550248, _1550250] : [hBOOL(hAPP(hAPP(c_member(_1550240), _1550242), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550244, _1550246, tc_fun(_1550240, tc_HOL_Obool)), _1550248), _1550250))), 39555 ^ _779448 : [(39556 ^ _779448) ^ [] : [-(_1550250 = hAPP(hAPP(c_Product__Type_OPair(_1550244, _1550246), 39553 ^ [_1550240, _1550242, _1550244, _1550246, _1550248, _1550250]), 39554 ^ [_1550240, _1550242, _1550244, _1550246, _1550248, _1550250]))], (39558 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550240), _1550242), hAPP(hAPP(_1550248, 39553 ^ [_1550240, _1550242, _1550244, _1550246, _1550248, _1550250]), 39554 ^ [_1550240, _1550242, _1550244, _1550246, _1550248, _1550250]))))]]], (39560 ^ _779448) ^ [_1550509, _1550511, _1550513, _1550515, _1550517, _1550519] : [39563 ^ _779448 : [(39564 ^ _779448) ^ [] : [-(_1550509 = hAPP(hAPP(c_Product__Type_OPair(_1550511, _1550513), 39561 ^ [_1550509, _1550511, _1550513, _1550515, _1550517, _1550519]), 39562 ^ [_1550509, _1550511, _1550513, _1550515, _1550517, _1550519]))], (39566 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550515), _1550517), hAPP(hAPP(_1550519, 39561 ^ [_1550509, _1550511, _1550513, _1550515, _1550517, _1550519]), 39562 ^ [_1550509, _1550511, _1550513, _1550515, _1550517, _1550519])))]], -(hBOOL(hAPP(hAPP(c_member(_1550515), _1550517), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550511, _1550513, tc_fun(_1550515, tc_HOL_Obool)), _1550519), _1550509))))], (39570 ^ _779448) ^ [_1550834, _1550836, _1550838, _1550840] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550834, tc_Nat_Onat), _1550836), _1550838) = hAPP(c_Nat_OSuc, _1550840), 39574 ^ _779448 : [(39575 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550834), 39573 ^ [_1550834, _1550836, _1550838, _1550840]), _1550838)))], (39577 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1550836, 39573 ^ [_1550834, _1550836, _1550838, _1550840]))))]]], (39579 ^ _779448) ^ [_1551016, _1551018, _1551020] : [-(c_Hilbert__Choice_OEps(tc_prod(_1551016, _1551018), hAPP(c_Product__Type_Oprod_Oprod__case(_1551016, _1551018, tc_HOL_Obool), _1551020)) = c_Hilbert__Choice_OEps(tc_prod(_1551016, _1551018), hAPP(hAPP(c_COMBS(tc_prod(_1551016, _1551018), _1551018, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1551016, tc_fun(_1551018, tc_HOL_Obool), tc_prod(_1551016, _1551018)), _1551020), c_Product__Type_Ofst(_1551016, _1551018))), c_Product__Type_Osnd(_1551016, _1551018))))], (39581 ^ _779448) ^ [_1551097, _1551099, _1551101] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1551097, _1551099) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1551101, _1551099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1551101), _1551097)), -(_1551097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1551101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1551099), 39588 ^ [_1551097, _1551099, _1551101])))], (39592 ^ _779448) ^ [_1551294, _1551296, _1551298] : [39593 ^ _779448 : [(39594 ^ _779448) ^ [_1551348] : [hBOOL(hAPP(_1551294, _1551348))]], _1551296 = c_Hilbert__Choice_OEps(_1551298, _1551294), -(hBOOL(hAPP(_1551294, _1551296)))], (39602 ^ _779448) ^ [_1551454, _1551456] : [-(c_Hilbert__Choice_OEps(_1551454, hAPP(c_fequal, _1551456)) = _1551456)], (39604 ^ _779448) ^ [_1551485, _1551487] : [-(c_Hilbert__Choice_OEps(_1551485, hAPP(hAPP(c_COMBC(_1551485, _1551485, tc_HOL_Obool), c_fequal), _1551487)) = _1551487)], (39606 ^ _779448) ^ [_1551538, _1551540] : [hBOOL(hAPP(_1551538, c_Hilbert__Choice_OEps(_1551540, _1551538))), -(hBOOL(hAPP(_1551538, 39609 ^ [_1551538, _1551540])))], (39613 ^ _779448) ^ [_1551637, _1551639] : [39614 ^ _779448 : [(39615 ^ _779448) ^ [_1551683] : [hBOOL(hAPP(_1551637, _1551683))]], -(hBOOL(hAPP(_1551637, c_Hilbert__Choice_OEps(_1551639, _1551637))))], (39619 ^ _779448) ^ [_1551743, _1551745] : [39620 ^ _779448 : [(39621 ^ _779448) ^ [_1551789] : [hBOOL(hAPP(_1551743, _1551789))]], -(hBOOL(hAPP(_1551743, c_Hilbert__Choice_OEps(_1551745, _1551743))))], (39625 ^ _779448) ^ [_1551847, _1551849, _1551851] : [hBOOL(hAPP(_1551847, _1551849)), -(hBOOL(hAPP(_1551847, c_Hilbert__Choice_OEps(_1551851, _1551847))))], (39631 ^ _779448) ^ [_1551940, _1551942] : [39632 ^ _779448 : [(39633 ^ _779448) ^ [_1551986] : [hBOOL(hAPP(_1551940, _1551986))]], -(hBOOL(hAPP(_1551940, c_Hilbert__Choice_OEps(_1551942, _1551940))))], (39637 ^ _779448) ^ [_1552044, _1552046, _1552048, _1552050] : [-(c_Hilbert__Choice_OEps(tc_prod(_1552044, _1552046), hAPP(c_Product__Type_Oprod_Oprod__case(_1552044, _1552046, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1552044, tc_fun(_1552046, tc_HOL_Obool), tc_fun(_1552046, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1552046, tc_HOL_Obool), tc_fun(_1552046, tc_HOL_Obool)), _1552044), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1552046)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1552044), c_fconj), hAPP(c_fequal, _1552048)))), hAPP(c_fequal, _1552050)))) = hAPP(hAPP(c_Product__Type_OPair(_1552044, _1552046), _1552048), _1552050))], (39639 ^ _779448) ^ [_1552150, _1552152, _1552154] : [-(c_Hilbert__Choice_OEps(tc_prod(_1552150, _1552152), _1552154) = c_Hilbert__Choice_OEps(tc_prod(_1552150, _1552152), hAPP(c_Product__Type_Oprod_Oprod__case(_1552150, _1552152, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1552152, tc_prod(_1552150, _1552152)), tc_fun(_1552152, tc_HOL_Obool), _1552150), hAPP(c_COMBB(tc_prod(_1552150, _1552152), tc_HOL_Obool, _1552152), _1552154)), c_Product__Type_OPair(_1552150, _1552152)))))], (39641 ^ _779448) ^ [_1552228, _1552230] : [39643 ^ _779448 : [(39644 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552228, tc_HOL_Obool)), 39642 ^ [_1552228, _1552230]), hAPP(c_Relation_OImage(_1552228, _1552228, _1552230), 39642 ^ [_1552228, _1552230]))))], (39646 ^ _779448) ^ [] : [39642 ^ [_1552228, _1552230] = c_Orderings_Obot__class_Obot(tc_fun(_1552228, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1552228, _1552230))], (39650 ^ _779448) ^ [_1552425, _1552427, _1552429, _1552431, _1552433, _1552435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552425, tc_HOL_Obool)), _1552427), _1552429)), 39656 ^ _779448 : [(39657 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552425), 39655 ^ [_1552425, _1552427, _1552429, _1552431, _1552433, _1552435]), _1552427)))], (39659 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552431, tc_HOL_Obool)), hAPP(_1552433, 39655 ^ [_1552425, _1552427, _1552429, _1552431, _1552433, _1552435])), hAPP(_1552435, 39655 ^ [_1552425, _1552427, _1552429, _1552431, _1552433, _1552435])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552425, _1552431), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552425, _1552431), _1552427), _1552433)), hAPP(hAPP(c_Product__Type_OSigma(_1552425, _1552431), _1552429), _1552435))))], (39663 ^ _779448) ^ [_1552815, _1552817, _1552819] : [-(hBOOL(hAPP(hAPP(c_member(_1552815), _1552817), c_Wellfounded_Oacc(_1552815, _1552819)))), 39667 ^ _779448 : [(39668 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552815, _1552815)), hAPP(hAPP(c_Product__Type_OPair(_1552815, _1552815), 39666 ^ [_1552815, _1552817, _1552819]), _1552817)), _1552819)))], (39670 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1552815), 39666 ^ [_1552815, _1552817, _1552819]), c_Wellfounded_Oacc(_1552815, _1552819)))]]], (39672 ^ _779448) ^ [_1553042, _1553044, _1553046] : [39674 ^ _779448 : [(39675 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553042, _1553042)), hAPP(hAPP(c_Product__Type_OPair(_1553042, _1553042), 39673 ^ [_1553042, _1553044, _1553046]), _1553044)), _1553046)))], (39677 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1553042), 39673 ^ [_1553042, _1553044, _1553046]), c_Wellfounded_Oacc(_1553042, _1553046)))]], -(hBOOL(hAPP(hAPP(c_member(_1553042), _1553044), c_Wellfounded_Oacc(_1553042, _1553046))))], (39681 ^ _779448) ^ [_1553301, _1553303, _1553305, _1553307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1553301, tc_HOL_Obool), tc_fun(_1553301, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1553301, tc_HOL_Obool), tc_fun(_1553301, tc_HOL_Obool)), _1553303), _1553305)), c_Wellfounded_Omax__ext(_1553301, _1553307))), 39684 ^ _779448 : [(39685 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1553301), _1553303)))], (39687 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1553301), _1553305)))], (39689 ^ _779448) ^ [] : [_1553305 = c_Orderings_Obot__class_Obot(tc_fun(_1553301, tc_HOL_Obool))], (39691 ^ _779448) ^ [_1553595] : [hBOOL(hAPP(hAPP(c_member(_1553301), _1553595), _1553303)), 39695 ^ _779448 : [(39696 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553301), 39694 ^ [_1553301, _1553303, _1553305, _1553307, _1553595]), _1553305)))], (39698 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1553301, _1553301)), hAPP(hAPP(c_Product__Type_OPair(_1553301, _1553301), _1553595), 39694 ^ [_1553301, _1553303, _1553305, _1553307, _1553595])), _1553307)))]]]]], (39700 ^ _779448) ^ [_1553807, _1553809, _1553811, _1553813] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1553807, tc_HOL_Obool), tc_fun(_1553807, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1553807, tc_HOL_Obool), tc_fun(_1553807, tc_HOL_Obool)), _1553809), _1553811)), c_Wellfounded_Omax__ext(_1553807, _1553813)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553807), _1553809)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553807), _1553811)), -(_1553811 = c_Orderings_Obot__class_Obot(tc_fun(_1553807, tc_HOL_Obool))), 39714 ^ _779448 : [(39715 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553807), 39713 ^ [_1553807, _1553809, _1553811, _1553813]), _1553809)))], (39717 ^ _779448) ^ [_1554212] : [hBOOL(hAPP(hAPP(c_member(_1553807), _1554212), _1553811)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1553807, _1553807)), hAPP(hAPP(c_Product__Type_OPair(_1553807, _1553807), 39713 ^ [_1553807, _1553809, _1553811, _1553813]), _1554212)), _1553813))]]], (39725 ^ _779448) ^ [_1554440, _1554442, _1554444, _1554446] : [class_Orderings_Olinorder(_1554440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554440), _1554442)), 39735 ^ _779448 : [(39736 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554440), 39734 ^ [_1554440, _1554442, _1554444, _1554446]), _1554442)))], (39738 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554440), 39734 ^ [_1554440, _1554442, _1554444, _1554446]), _1554444))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554440), hAPP(hAPP(c_Finite__Set_Ofold(_1554440, _1554440, c_Orderings_Oord__class_Omax(_1554440)), _1554446), _1554442)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1554440), _1554444), _1554446))))], (39742 ^ _779448) ^ [_1554804, _1554806, _1554808, _1554810] : [class_Orderings_Olinorder(_1554804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554804), _1554806)), 39752 ^ _779448 : [(39753 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554804), 39751 ^ [_1554804, _1554806, _1554808, _1554810]), _1554806)))], (39755 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554804), _1554808), 39751 ^ [_1554804, _1554806, _1554808, _1554810]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1554804), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1554804), _1554808), _1554810)), hAPP(hAPP(c_Finite__Set_Ofold(_1554804, _1554804, c_Orderings_Oord__class_Omin(_1554804)), _1554810), _1554806))))], (39759 ^ _779448) ^ [_1555168, _1555170, _1555172] : [39761 ^ _779448 : [(39762 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39760 ^ [_1555168, _1555170, _1555172]), _1555168)))], (39764 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1555170, 39760 ^ [_1555168, _1555170, _1555172])))], (39766 ^ _779448) ^ [] : [hBOOL(hAPP(_1555170, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 39760 ^ [_1555168, _1555170, _1555172]), _1555168)))]], hBOOL(hAPP(_1555170, _1555172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1555172), _1555168)), -(hBOOL(hAPP(_1555170, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39778 ^ _779448) ^ [_1555530, _1555532, _1555534] : [39780 ^ _779448 : [(39781 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1555530, tc_HOL_Obool)), 39779 ^ [_1555530, _1555532, _1555534]), _1555532)))], (39783 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1555530), _1555534), 39779 ^ [_1555530, _1555532, _1555534]))]], -(hBOOL(hAPP(hAPP(c_member(_1555530), _1555534), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1555530, tc_HOL_Obool), _1555532))))], (39787 ^ _779448) ^ [_1555746, _1555748, _1555750] : [class_Orderings_Olinorder(_1555746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555746), _1555748)), 39797 ^ _779448 : [(39798 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555746), 39796 ^ [_1555746, _1555748, _1555750]), _1555748)))], (39800 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1555746), _1555750), 39796 ^ [_1555746, _1555748, _1555750]))]], hBOOL(hAPP(hAPP(c_member(_1555746), _1555750), _1555748)), -(c_Big__Operators_Olinorder__class_OMin(_1555746, _1555748) = _1555750)], (39808 ^ _779448) ^ [_1556118, _1556120, _1556122] : [class_Orderings_Olinorder(_1556118), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556118), _1556120)), 39818 ^ _779448 : [(39819 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556118), 39817 ^ [_1556118, _1556120, _1556122]), _1556120)))], (39821 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556118), 39817 ^ [_1556118, _1556120, _1556122]), _1556122))]], hBOOL(hAPP(hAPP(c_member(_1556118), _1556122), _1556120)), -(c_Big__Operators_Olinorder__class_OMax(_1556118, _1556120) = _1556122)], (39829 ^ _779448) ^ [_1556490, _1556492, _1556494, _1556496] : [class_Lattices_Osemilattice__inf(_1556490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556490), _1556492)), 39839 ^ _779448 : [(39840 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556490), 39838 ^ [_1556490, _1556492, _1556494, _1556496]), _1556492)))], (39842 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556490), _1556494), 39838 ^ [_1556490, _1556492, _1556494, _1556496]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556490), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1556490), _1556494), _1556496)), hAPP(hAPP(c_Finite__Set_Ofold(_1556490, _1556490, c_Lattices_Osemilattice__inf__class_Oinf(_1556490)), _1556496), _1556492))))], (39846 ^ _779448) ^ [_1556854, _1556856, _1556858, _1556860] : [class_Lattices_Osemilattice__sup(_1556854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556854), _1556856)), 39856 ^ _779448 : [(39857 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556854), 39855 ^ [_1556854, _1556856, _1556858, _1556860]), _1556856)))], (39859 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556854), 39855 ^ [_1556854, _1556856, _1556858, _1556860]), _1556858))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1556854), hAPP(hAPP(c_Finite__Set_Ofold(_1556854, _1556854, c_Lattices_Osemilattice__sup__class_Osup(_1556854)), _1556860), _1556856)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1556854), _1556858), _1556860))))], (39863 ^ _779448) ^ [_1557218, _1557220, _1557222] : [c_Wellfounded_Owf(_1557218, _1557220), hBOOL(hAPP(hAPP(c_member(tc_prod(_1557218, _1557218)), hAPP(hAPP(c_Product__Type_OPair(_1557218, _1557218), hAPP(_1557222, hAPP(c_Nat_OSuc, 39866 ^ [_1557218, _1557220, _1557222]))), hAPP(_1557222, 39866 ^ [_1557218, _1557220, _1557222]))), _1557220))], (39870 ^ _779448) ^ [_1557419, _1557421, _1557423, _1557425, _1557427, _1557429, _1557431, _1557433] : [class_Groups_Ocomm__monoid__add(_1557419), c_Fun_Oinj__on(_1557421, _1557423, _1557425, _1557427), _1557429 = hAPP(c_Set_Oimage(_1557421, _1557423, _1557425), _1557427), 39884 ^ _779448 : [(39885 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557421), 39883 ^ [_1557419, _1557421, _1557423, _1557425, _1557427, _1557429, _1557431, _1557433]), _1557427)))], (39887 ^ _779448) ^ [] : [hAPP(_1557431, 39883 ^ [_1557419, _1557421, _1557423, _1557425, _1557427, _1557429, _1557431, _1557433]) = hAPP(_1557433, hAPP(_1557425, 39883 ^ [_1557419, _1557421, _1557423, _1557425, _1557427, _1557429, _1557431, _1557433]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557423, _1557419), _1557433), _1557429) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557421, _1557419), _1557431), _1557427))], (39891 ^ _779448) ^ [_1557911, _1557913, _1557915, _1557917, _1557919, _1557921, _1557923] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1557911, _1557913, _1557915, _1557917), _1557919), _1557921), _1557923) = hAPP(hAPP(_1557921, hAPP(c_Product__Type_Ofst(_1557913, _1557915), hAPP(_1557919, _1557923))), hAPP(c_Product__Type_Osnd(_1557913, _1557915), hAPP(_1557919, _1557923))))], (39893 ^ _779448) ^ [_1557984, _1557986, _1557988, _1557990, _1557992, _1557994, _1557996, _1557998] : [class_Groups_Ocomm__monoid__add(_1557984), class_Orderings_Oord(_1557986), _1557988 = _1557990, _1557992 = _1557994, 39911 ^ _779448 : [(39912 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1557986), _1557990), 39910 ^ [_1557984, _1557986, _1557988, _1557990, _1557992, _1557994, _1557996, _1557998])))], (39914 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1557986), 39910 ^ [_1557984, _1557986, _1557988, _1557990, _1557992, _1557994, _1557996, _1557998]), _1557994)))], (39916 ^ _779448) ^ [] : [hAPP(_1557996, 39910 ^ [_1557984, _1557986, _1557988, _1557990, _1557992, _1557994, _1557996, _1557998]) = hAPP(_1557998, 39910 ^ [_1557984, _1557986, _1557988, _1557990, _1557992, _1557994, _1557996, _1557998])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557986, _1557984), _1557996), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1557986, _1557988), _1557992)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1557986, _1557984), _1557998), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1557986, _1557990), _1557994)))], (39920 ^ _779448) ^ [_1558628, _1558630] : [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), _1558628), _1558630)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558628), _1558630)))], (39926 ^ _779448) ^ [_1558733, _1558735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558733), _1558735)), -(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), _1558733), _1558735)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (39932 ^ _779448) ^ [_1558844, _1558846, _1558848, _1558850, _1558852, _1558854, _1558856, _1558858, _1558860] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1558844, _1558846, _1558848, _1558850), hAPP(hAPP(c_Product__Type_Oscomp(_1558844, _1558852, _1558854, tc_prod(_1558846, _1558848)), _1558856), _1558858)), _1558860) = hAPP(hAPP(c_Product__Type_Oscomp(_1558844, _1558852, _1558854, _1558850), _1558856), hAPP(hAPP(c_COMBC(_1558852, tc_fun(_1558846, tc_fun(_1558848, _1558850)), tc_fun(_1558854, _1558850)), hAPP(hAPP(c_COMBB(tc_fun(_1558854, tc_prod(_1558846, _1558848)), tc_fun(tc_fun(_1558846, tc_fun(_1558848, _1558850)), tc_fun(_1558854, _1558850)), _1558852), c_Product__Type_Oscomp(_1558854, _1558846, _1558848, _1558850)), _1558858)), _1558860)))], (39934 ^ _779448) ^ [_1558971, _1558973, _1558975, _1558977] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1558971, _1558973, _1558975, tc_prod(_1558973, _1558975)), _1558977), c_Product__Type_OPair(_1558973, _1558975)) = _1558977)], (39936 ^ _779448) ^ [_1559017, _1559019, _1559021, _1559023, _1559025] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1559017, _1559019, _1559017, _1559021), hAPP(c_Product__Type_OPair(_1559019, _1559017), _1559023)), _1559025) = hAPP(_1559025, _1559023))], (39938 ^ _779448) ^ [_1559068, _1559070, _1559072, _1559074, _1559076, _1559078, _1559080] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1559068, _1559070, _1559072, _1559074), _1559076), _1559078), _1559080) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559070, _1559072, _1559074), _1559078), hAPP(_1559076, _1559080)))], (39940 ^ _779448) ^ [_1559130, _1559132] : [c_Wellfounded_Owf(_1559130, _1559132), -(c_Wellfounded_Owf(_1559130, c_Transitive__Closure_Otrancl(_1559130, _1559132)))], (39946 ^ _779448) ^ [_1559213, _1559215, _1559217, _1559219, _1559221, _1559223, _1559225] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1559213, _1559215, _1559217, _1559219), _1559221), _1559223), _1559225) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559215, _1559217, _1559219), _1559223), hAPP(_1559221, _1559225)))], (39948 ^ _779448) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39950 ^ _779448) ^ [_1559308, _1559310] : [c_Wellfounded_Oacyclic(_1559308, _1559310), 39953 ^ _779448 : [(39954 ^ _779448) ^ [_1559393] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559308, _1559308)), hAPP(hAPP(c_Product__Type_OPair(_1559308, _1559308), _1559393), _1559393)), c_Transitive__Closure_Otrancl(_1559308, _1559310)))]]], (39956 ^ _779448) ^ [_1559436, _1559438] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559436, _1559436)), hAPP(hAPP(c_Product__Type_OPair(_1559436, _1559436), 39957 ^ [_1559436, _1559438]), 39957 ^ [_1559436, _1559438])), c_Transitive__Closure_Otrancl(_1559436, _1559438)))), -(c_Wellfounded_Oacyclic(_1559436, _1559438))], (39963 ^ _779448) ^ [_1559510, _1559512, _1559514, _1559516] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1559510, _1559510)), hAPP(hAPP(c_Product__Type_OPair(_1559510, _1559510), _1559512), _1559514)), _1559516)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559510, _1559510)), hAPP(hAPP(c_Product__Type_OPair(_1559510, _1559510), _1559512), _1559514)), c_Transitive__Closure_Otrancl(_1559510, _1559516))))], (39969 ^ _779448) ^ [_1559673, _1559675] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559673, _1559673), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559673, _1559675)), hAPP(hAPP(c_Product__Type_OSigma(_1559673, _1559673), hAPP(c_Relation_OField(_1559673), _1559675)), hAPP(c_COMBK(tc_fun(_1559673, tc_HOL_Obool), _1559673), hAPP(c_Relation_OField(_1559673), _1559675))))))], (39971 ^ _779448) ^ [_1559742, _1559744, _1559746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559742, _1559742), tc_HOL_Obool)), _1559744), _1559746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559742, _1559742), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1559742, _1559742, _1559742), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1559742, _1559742), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559742, _1559744)), _1559746)), _1559744)), _1559746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559742, _1559742), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1559742, _1559744)), _1559746)))], (39981 ^ _779448) ^ [_1560013, _1560015, _1560017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560013, _1560013)), _1560015), _1560017)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560013, _1560013)), _1560015), c_Transitive__Closure_Otrancl(_1560013, _1560017))))], (39987 ^ _779448) ^ [_1560138] : [-(c_Transitive__Closure_Otrancl(_1560138, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1560138, _1560138), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1560138, _1560138), tc_HOL_Obool)))], (39989 ^ _779448) ^ [_1560180, _1560182] : [-(hAPP(c_Relation_ODomain(_1560180, _1560180), c_Transitive__Closure_Otrancl(_1560180, _1560182)) = hAPP(c_Relation_ODomain(_1560180, _1560180), _1560182))], (39991 ^ _779448) ^ [_1560220, _1560222] : [-(hAPP(c_Relation_ORange(_1560220, _1560220), c_Transitive__Closure_Otrancl(_1560220, _1560222)) = hAPP(c_Relation_ORange(_1560220, _1560220), _1560222))], (39993 ^ _779448) ^ [_1560275, _1560277] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560275, _1560275)), c_Transitive__Closure_Otrancl(_1560275, _1560277))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560275, _1560275)), _1560277)))], (39999 ^ _779448) ^ [_1560382, _1560384] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560382, _1560382)), _1560384)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560382, _1560382)), c_Transitive__Closure_Otrancl(_1560382, _1560384))))], (40005 ^ _779448) ^ [_1560495, _1560497, _1560499, _1560501, _1560503] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560495, _1560495)), hAPP(hAPP(c_Product__Type_OPair(_1560495, _1560495), _1560497), _1560499)), c_Transitive__Closure_Otrancl(_1560495, _1560501))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560495, _1560495)), hAPP(hAPP(c_Product__Type_OPair(_1560495, _1560495), _1560499), _1560503)), c_Transitive__Closure_Otrancl(_1560495, _1560501))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560495, _1560495)), hAPP(hAPP(c_Product__Type_OPair(_1560495, _1560495), _1560497), _1560503)), c_Transitive__Closure_Otrancl(_1560495, _1560501))))], (40015 ^ _779448) ^ [_1560768, _1560770, _1560772, _1560774, _1560776] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1560768, _1560768)), hAPP(hAPP(c_Product__Type_OPair(_1560768, _1560768), _1560770), _1560772)), c_Transitive__Closure_Otrancl(_1560768, _1560774))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560768, _1560768)), hAPP(hAPP(c_Product__Type_OPair(_1560768, _1560768), _1560772), _1560776)), _1560774)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560768, _1560768)), hAPP(hAPP(c_Product__Type_OPair(_1560768, _1560768), _1560770), _1560776)), c_Transitive__Closure_Otrancl(_1560768, _1560774))))], (40025 ^ _779448) ^ [_1561035, _1561037, _1561039, _1561041, _1561043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561035, _1561035)), hAPP(hAPP(c_Product__Type_OPair(_1561035, _1561035), _1561037), _1561039)), _1561041)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1561035, _1561035)), hAPP(hAPP(c_Product__Type_OPair(_1561035, _1561035), _1561039), _1561043)), c_Transitive__Closure_Otrancl(_1561035, _1561041))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561035, _1561035)), hAPP(hAPP(c_Product__Type_OPair(_1561035, _1561035), _1561037), _1561043)), c_Transitive__Closure_Otrancl(_1561035, _1561041))))], (40035 ^ _779448) ^ [_1561302, _1561304, _1561306, _1561308, _1561310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561302, _1561302)), hAPP(hAPP(c_Product__Type_OPair(_1561302, _1561302), _1561304), _1561306)), _1561308)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1561302, _1561302)), hAPP(hAPP(c_Product__Type_OPair(_1561302, _1561302), _1561306), _1561310)), _1561308)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561302, _1561302)), hAPP(hAPP(c_Product__Type_OPair(_1561302, _1561302), _1561304), _1561310)), c_Transitive__Closure_Otrancl(_1561302, _1561308))))], (40045 ^ _779448) ^ [_1561563, _1561565, _1561567, _1561569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561563, _1561563)), _1561565), c_Transitive__Closure_Otrancl(_1561563, _1561567))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561563, _1561563), tc_HOL_Obool)), _1561567), _1561569)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561563, _1561563)), _1561565), c_Transitive__Closure_Otrancl(_1561563, _1561569))))], (40055 ^ _779448) ^ [_1561778, _1561780] : [-(c_Transitive__Closure_Otrancl(_1561778, _1561780) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1561778, _1561778), tc_HOL_Obool)), _1561780), hAPP(hAPP(c_Relation_Orel__comp(_1561778, _1561778, _1561778), c_Transitive__Closure_Otrancl(_1561778, _1561780)), _1561780)))], (40057 ^ _779448) ^ [_1561833, _1561835, _1561837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561833, _1561833), tc_HOL_Obool)), _1561835), hAPP(hAPP(c_Product__Type_OSigma(_1561833, _1561833), _1561837), hAPP(c_COMBK(tc_fun(_1561833, tc_HOL_Obool), _1561833), _1561837)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1561833, _1561833), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1561833, _1561835)), hAPP(hAPP(c_Product__Type_OSigma(_1561833, _1561833), _1561837), hAPP(c_COMBK(tc_fun(_1561833, tc_HOL_Obool), _1561833), _1561837)))))], (40063 ^ _779448) ^ [_1562060, _1562062, _1562064, _1562066, _1562068] : [_1562060 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1562062, _1562064, _1562060, _1562066), _1562068) = hAPP(c_Product__Type_OPair(_1562062, _1562064), _1562068))], (40069 ^ _779448) ^ [_1562165, _1562167, _1562169, _1562171, _1562173] : [-(_1562165 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1562167, _1562169, _1562165, _1562171), _1562173) = hAPP(hAPP(c_Product__Type_Oscomp(_1562169, _1562167, _1562169, tc_prod(_1562167, _1562169)), hAPP(_1562171, _1562173)), c_Random_Oiterate(_1562167, _1562169, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1562165), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1562171)))], (40075 ^ _779448) ^ [_1562245, _1562247, _1562249, _1562251] : [-(c_Transitive__Closure_Otrancl(_1562245, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1562245, _1562245)), hAPP(hAPP(c_Product__Type_OPair(_1562245, _1562245), _1562247), _1562249)), _1562251)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562245, _1562245), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1562245, _1562251)), hAPP(c_Set_OCollect(tc_prod(_1562245, _1562245)), hAPP(c_Product__Type_Oprod_Oprod__case(_1562245, _1562245, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1562245, tc_fun(_1562245, tc_HOL_Obool), tc_fun(_1562245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1562245, tc_HOL_Obool), tc_fun(_1562245, tc_HOL_Obool)), _1562245), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562245)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562245), c_fconj), hAPP(hAPP(c_COMBC(_1562245, tc_fun(tc_prod(_1562245, _1562245), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1562245, _1562245), tc_fun(tc_fun(tc_prod(_1562245, _1562245), tc_HOL_Obool), tc_HOL_Obool), _1562245), c_member(tc_prod(_1562245, _1562245))), hAPP(hAPP(c_COMBC(_1562245, _1562245, tc_prod(_1562245, _1562245)), c_Product__Type_OPair(_1562245, _1562245)), _1562247))), c_Transitive__Closure_Ortrancl(_1562245, _1562251))))), hAPP(hAPP(c_COMBC(_1562245, tc_fun(tc_prod(_1562245, _1562245), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1562245, _1562245), tc_fun(tc_fun(tc_prod(_1562245, _1562245), tc_HOL_Obool), tc_HOL_Obool), _1562245), c_member(tc_prod(_1562245, _1562245))), hAPP(c_Product__Type_OPair(_1562245, _1562245), _1562249))), c_Transitive__Closure_Ortrancl(_1562245, _1562251)))))))], (40077 ^ _779448) ^ [_1562513, _1562515, _1562517, _1562519] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562513, tc_fun(_1562513, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1562513, tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_fun(_1562513, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562513, tc_fun(tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_fun(_1562513, tc_HOL_Obool)), _1562513), c_COMBC(_1562513, tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562513, tc_prod(_1562513, _1562513)), tc_fun(_1562513, tc_fun(tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_HOL_Obool)), _1562513), hAPP(c_COMBB(tc_prod(_1562513, _1562513), tc_fun(tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool), tc_HOL_Obool), _1562513), c_member(tc_prod(_1562513, _1562513)))), c_Product__Type_OPair(_1562513, _1562513)))), _1562515)), c_fequal), _1562517), _1562519)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562513, _1562513)), hAPP(hAPP(c_Product__Type_OPair(_1562513, _1562513), _1562517), _1562519)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562513, _1562513), tc_HOL_Obool)), _1562515), c_Relation_OId(_1562513)))))], (40083 ^ _779448) ^ [_1562934, _1562936, _1562938, _1562940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562934, _1562934)), hAPP(hAPP(c_Product__Type_OPair(_1562934, _1562934), _1562938), _1562940)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool)), _1562936), c_Relation_OId(_1562934)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1562934, tc_fun(_1562934, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1562934, tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_fun(_1562934, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562934, tc_fun(tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_fun(_1562934, tc_HOL_Obool)), _1562934), c_COMBC(_1562934, tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562934, tc_prod(_1562934, _1562934)), tc_fun(_1562934, tc_fun(tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_HOL_Obool)), _1562934), hAPP(c_COMBB(tc_prod(_1562934, _1562934), tc_fun(tc_fun(tc_prod(_1562934, _1562934), tc_HOL_Obool), tc_HOL_Obool), _1562934), c_member(tc_prod(_1562934, _1562934)))), c_Product__Type_OPair(_1562934, _1562934)))), _1562936)), c_fequal), _1562938), _1562940)))], (40089 ^ _779448) ^ [_1563361, _1563363, _1563365] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563361, _1563361)), _1563363), _1563365)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563361, _1563361)), _1563363), c_Transitive__Closure_Ortrancl(_1563361, _1563365))))], (40095 ^ _779448) ^ [_1563486, _1563488, _1563490] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563486, _1563486)), hAPP(hAPP(c_Product__Type_OPair(_1563486, _1563486), _1563488), _1563488)), c_Transitive__Closure_Ortrancl(_1563486, _1563490))))], (40097 ^ _779448) ^ [_1563535, _1563537] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563535, _1563535)), hAPP(hAPP(c_Product__Type_OPair(_1563535, _1563535), _1563537), _1563537)), c_Relation_OId(_1563535))))], (40099 ^ _779448) ^ [_1563581, _1563583, _1563585, _1563587] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563581, _1563581)), hAPP(hAPP(c_Product__Type_OPair(_1563581, _1563581), _1563583), _1563585)), c_Transitive__Closure_Otrancl(_1563581, _1563587))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563581, _1563581)), hAPP(hAPP(c_Product__Type_OPair(_1563581, _1563581), _1563583), _1563585)), c_Transitive__Closure_Ortrancl(_1563581, _1563587))))], (40105 ^ _779448) ^ [_1563750, _1563752] : [-(c_Transitive__Closure_Otrancl(_1563750, c_Transitive__Closure_Ortrancl(_1563750, _1563752)) = c_Transitive__Closure_Ortrancl(_1563750, _1563752))], (40107 ^ _779448) ^ [_1563784, _1563786] : [-(c_Transitive__Closure_Ortrancl(_1563784, c_Transitive__Closure_Otrancl(_1563784, _1563786)) = c_Transitive__Closure_Ortrancl(_1563784, _1563786))], (40109 ^ _779448) ^ [_1563818, _1563820] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563818, _1563818), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1563818, _1563820)), c_Relation_OId(_1563818)) = c_Transitive__Closure_Ortrancl(_1563818, _1563820))], (40111 ^ _779448) ^ [_1563865, _1563867] : [-(c_Transitive__Closure_Otrancl(_1563865, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1563865, _1563865), tc_HOL_Obool)), _1563867), c_Relation_OId(_1563865))) = c_Transitive__Closure_Ortrancl(_1563865, _1563867))], (40113 ^ _779448) ^ [_1563912, _1563914] : [-(c_Transitive__Closure_Otrancl(_1563912, _1563914) = hAPP(hAPP(c_Relation_Orel__comp(_1563912, _1563912, _1563912), _1563914), c_Transitive__Closure_Ortrancl(_1563912, _1563914)))], (40115 ^ _779448) ^ [_1563953, _1563955] : [-(c_Transitive__Closure_Otrancl(_1563953, _1563955) = hAPP(hAPP(c_Relation_Orel__comp(_1563953, _1563953, _1563953), c_Transitive__Closure_Ortrancl(_1563953, _1563955)), _1563955))], (40117 ^ _779448) ^ [_1563994] : [-(c_Transitive__Closure_Ortrancl(_1563994, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1563994, _1563994), tc_HOL_Obool))) = c_Relation_OId(_1563994))], (40119 ^ _779448) ^ [_1564030, _1564032, _1564034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564030, _1564030), tc_HOL_Obool)), c_Relation_OId(_1564030)), _1564032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564030, _1564030), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564030, _1564030, _1564030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1564030, _1564030), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564030, _1564034)), _1564032)), _1564034)), _1564032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564030, _1564030), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564030, _1564034)), _1564032)))], (40129 ^ _779448) ^ [_1564305, _1564307] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1564305, _1564305, _1564305), c_Transitive__Closure_Ortrancl(_1564305, _1564307)), c_Transitive__Closure_Ortrancl(_1564305, _1564307)) = c_Transitive__Closure_Ortrancl(_1564305, _1564307))], (40131 ^ _779448) ^ [_1564349, _1564351] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1564349, _1564349, _1564349), _1564351), c_Transitive__Closure_Ortrancl(_1564349, _1564351)) = hAPP(hAPP(c_Relation_Orel__comp(_1564349, _1564349, _1564349), c_Transitive__Closure_Ortrancl(_1564349, _1564351)), _1564351))], (40133 ^ _779448) ^ [_1564400, _1564402] : [-(c_Transitive__Closure_Ortrancl(_1564400, _1564402) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564400, _1564400), tc_HOL_Obool)), c_Relation_OId(_1564400)), hAPP(hAPP(c_Relation_Orel__comp(_1564400, _1564400, _1564400), c_Transitive__Closure_Ortrancl(_1564400, _1564402)), _1564402)))], (40135 ^ _779448) ^ [_1564457, _1564459] : [-(c_Transitive__Closure_Ortrancl(_1564457, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564457, _1564457), tc_HOL_Obool)), _1564459), c_Relation_OId(_1564457))) = c_Transitive__Closure_Ortrancl(_1564457, _1564459))], (40137 ^ _779448) ^ [_1564504, _1564506, _1564508] : [-(c_Transitive__Closure_Ortrancl(_1564504, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564504, _1564504), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564504, _1564506)), c_Transitive__Closure_Ortrancl(_1564504, _1564508))) = c_Transitive__Closure_Ortrancl(_1564504, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564504, _1564504), tc_HOL_Obool)), _1564506), _1564508)))], (40139 ^ _779448) ^ [_1564571, _1564573] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564571, _1564571), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564571, _1564573)), c_Relation_OId(_1564571)) = c_Transitive__Closure_Ortrancl(_1564571, _1564573))], (40141 ^ _779448) ^ [_1564618, _1564620, _1564622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564618, _1564618), tc_HOL_Obool)), _1564620), c_Transitive__Closure_Ortrancl(_1564618, _1564622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564618, _1564618), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564618, _1564620)), c_Transitive__Closure_Ortrancl(_1564618, _1564622))))], (40147 ^ _779448) ^ [_1564767, _1564769, _1564771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564767, _1564767), tc_HOL_Obool)), _1564769), _1564771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564767, _1564767), tc_HOL_Obool)), _1564771), c_Transitive__Closure_Ortrancl(_1564767, _1564769))), -(c_Transitive__Closure_Ortrancl(_1564767, _1564771) = c_Transitive__Closure_Ortrancl(_1564767, _1564769))], (40157 ^ _779448) ^ [_1564970, _1564972, _1564974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564970, _1564970), tc_HOL_Obool)), _1564972), _1564974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564970, _1564970), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1564970, _1564972)), c_Transitive__Closure_Ortrancl(_1564970, _1564974))))], (40163 ^ _779448) ^ [_1565113, _1565115, _1565117] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565113, _1565113), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565113, _1565113), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565113, _1565115)), c_Transitive__Closure_Ortrancl(_1565113, _1565117))), c_Transitive__Closure_Ortrancl(_1565113, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565113, _1565113), tc_HOL_Obool)), _1565115), _1565117)))))], (40165 ^ _779448) ^ [_1565190, _1565192, _1565194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565190, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1565190, _1565190, _1565192), _1565194)), _1565194)), -(hAPP(c_Relation_OImage(_1565190, _1565190, c_Transitive__Closure_Ortrancl(_1565190, _1565192)), _1565194) = _1565194)], (40171 ^ _779448) ^ [_1565323, _1565325, _1565327, _1565329] : [40172 ^ _779448 : [(40173 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565323, _1565323)), _1565325), c_Transitive__Closure_Ortrancl(_1565323, _1565327)))], (40175 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565323, _1565323)), _1565325), c_Transitive__Closure_Ortrancl(_1565323, _1565329)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565323, _1565323)), _1565325), c_Transitive__Closure_Ortrancl(_1565323, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565323, _1565323), tc_HOL_Obool)), _1565327), _1565329)))))], (40179 ^ _779448) ^ [_1565548, _1565550] : [-(c_Relation_Orefl__on(_1565548, c_Orderings_Otop__class_Otop(tc_fun(_1565548, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1565548, _1565550)))], (40181 ^ _779448) ^ [_1565582, _1565584, _1565586, _1565588, _1565590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565582, _1565582)), hAPP(hAPP(c_Product__Type_OPair(_1565582, _1565582), _1565584), _1565586)), c_Transitive__Closure_Ortrancl(_1565582, _1565588))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565582, _1565582)), hAPP(hAPP(c_Product__Type_OPair(_1565582, _1565582), _1565586), _1565590)), c_Transitive__Closure_Ortrancl(_1565582, _1565588))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565582, _1565582)), hAPP(hAPP(c_Product__Type_OPair(_1565582, _1565582), _1565584), _1565590)), c_Transitive__Closure_Ortrancl(_1565582, _1565588))))], (40191 ^ _779448) ^ [_1565855, _1565857, _1565859, _1565861, _1565863] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565855, _1565855)), hAPP(hAPP(c_Product__Type_OPair(_1565855, _1565855), _1565857), _1565859)), c_Transitive__Closure_Ortrancl(_1565855, _1565861))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565855, _1565855)), hAPP(hAPP(c_Product__Type_OPair(_1565855, _1565855), _1565859), _1565863)), _1565861)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565855, _1565855)), hAPP(hAPP(c_Product__Type_OPair(_1565855, _1565855), _1565857), _1565863)), c_Transitive__Closure_Ortrancl(_1565855, _1565861))))], (40201 ^ _779448) ^ [_1566122, _1566124, _1566126, _1566128, _1566130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566122, _1566122)), hAPP(hAPP(c_Product__Type_OPair(_1566122, _1566122), _1566124), _1566126)), _1566128)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566122, _1566122)), hAPP(hAPP(c_Product__Type_OPair(_1566122, _1566122), _1566126), _1566130)), c_Transitive__Closure_Ortrancl(_1566122, _1566128))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566122, _1566122)), hAPP(hAPP(c_Product__Type_OPair(_1566122, _1566122), _1566124), _1566130)), c_Transitive__Closure_Ortrancl(_1566122, _1566128))))], (40211 ^ _779448) ^ [_1566389, _1566391] : [-(c_Transitive__Closure_Ortrancl(_1566389, c_Transitive__Closure_Ortrancl(_1566389, _1566391)) = c_Transitive__Closure_Ortrancl(_1566389, _1566391))], (40213 ^ _779448) ^ [_1566423, _1566425] : [-(c_Transitive__Closure_Ortrancl(_1566423, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1566423, _1566423), tc_HOL_Obool)), _1566425), c_Relation_OId(_1566423))) = c_Transitive__Closure_Ortrancl(_1566423, _1566425))], (40215 ^ _779448) ^ [_1566470, _1566472] : [-(hAPP(c_Relation_ORange(_1566470, _1566470), c_Transitive__Closure_Ortrancl(_1566470, _1566472)) = c_Orderings_Otop__class_Otop(tc_fun(_1566470, tc_HOL_Obool)))], (40217 ^ _779448) ^ [_1566509, _1566511] : [-(hAPP(c_Relation_ODomain(_1566509, _1566509), c_Transitive__Closure_Ortrancl(_1566509, _1566511)) = c_Orderings_Otop__class_Otop(tc_fun(_1566509, tc_HOL_Obool)))], (40219 ^ _779448) ^ [_1566548, _1566550] : [-(hAPP(c_Relation_OImage(_1566548, _1566548, c_Relation_OId(_1566548)), _1566550) = _1566550)], (40221 ^ _779448) ^ [_1566582, _1566584, _1566586] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1566582, _1566584, _1566584), _1566586), c_Relation_OId(_1566584)) = _1566586)], (40223 ^ _779448) ^ [_1566621, _1566623, _1566625] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1566621, _1566621, _1566623), c_Relation_OId(_1566621)), _1566625) = _1566625)], (40225 ^ _779448) ^ [_1566678, _1566680, _1566682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566678, _1566678)), hAPP(hAPP(c_Product__Type_OPair(_1566678, _1566678), _1566680), _1566682)), c_Relation_OId(_1566678))), -(_1566680 = _1566682)], (40231 ^ _779448) ^ [_1566795, _1566797, _1566799] : [_1566797 = _1566799, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566795, _1566795)), hAPP(hAPP(c_Product__Type_OPair(_1566795, _1566795), _1566797), _1566799)), c_Relation_OId(_1566795))))], (40237 ^ _779448) ^ [_1566918, _1566920, _1566922, _1566924, _1566926] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566918, _1566918)), hAPP(hAPP(c_Product__Type_OPair(_1566918, _1566918), _1566920), _1566922)), c_Transitive__Closure_Ortrancl(_1566918, _1566924))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1566918, _1566918)), hAPP(hAPP(c_Product__Type_OPair(_1566918, _1566918), _1566922), _1566926)), c_Transitive__Closure_Otrancl(_1566918, _1566924))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566918, _1566918)), hAPP(hAPP(c_Product__Type_OPair(_1566918, _1566918), _1566920), _1566926)), c_Transitive__Closure_Otrancl(_1566918, _1566924))))], (40247 ^ _779448) ^ [_1567191, _1567193, _1567195, _1567197, _1567199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567191, _1567191)), hAPP(hAPP(c_Product__Type_OPair(_1567191, _1567191), _1567193), _1567195)), c_Transitive__Closure_Otrancl(_1567191, _1567197))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567191, _1567191)), hAPP(hAPP(c_Product__Type_OPair(_1567191, _1567191), _1567195), _1567199)), c_Transitive__Closure_Ortrancl(_1567191, _1567197))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567191, _1567191)), hAPP(hAPP(c_Product__Type_OPair(_1567191, _1567191), _1567193), _1567199)), c_Transitive__Closure_Otrancl(_1567191, _1567197))))], (40257 ^ _779448) ^ [_1567464, _1567466, _1567468, _1567470, _1567472] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567464, _1567464)), hAPP(hAPP(c_Product__Type_OPair(_1567464, _1567464), _1567466), _1567468)), c_Transitive__Closure_Ortrancl(_1567464, _1567470))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567464, _1567464)), hAPP(hAPP(c_Product__Type_OPair(_1567464, _1567464), _1567468), _1567472)), _1567470)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567464, _1567464)), hAPP(hAPP(c_Product__Type_OPair(_1567464, _1567464), _1567466), _1567472)), c_Transitive__Closure_Otrancl(_1567464, _1567470))))], (40267 ^ _779448) ^ [_1567731, _1567733, _1567735, _1567737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567731, _1567731)), hAPP(hAPP(c_Product__Type_OPair(_1567731, _1567731), _1567733), _1567735)), c_Transitive__Closure_Ortrancl(_1567731, _1567737))), -(_1567733 = _1567735), 40274 ^ _779448 : [(40275 ^ _779448) ^ [] : [_1567733 = _1567735], (40277 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567731, _1567731)), hAPP(hAPP(c_Product__Type_OPair(_1567731, _1567731), _1567733), _1567735)), c_Transitive__Closure_Otrancl(_1567731, _1567737))))]]], (40279 ^ _779448) ^ [_1567993, _1567995, _1567997, _1567999, _1568001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567993, _1567993)), hAPP(hAPP(c_Product__Type_OPair(_1567993, _1567993), _1567995), _1567997)), _1567999)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567993, _1567993)), hAPP(hAPP(c_Product__Type_OPair(_1567993, _1567993), _1567997), _1568001)), c_Transitive__Closure_Ortrancl(_1567993, _1567999))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567993, _1567993)), hAPP(hAPP(c_Product__Type_OPair(_1567993, _1567993), _1567995), _1568001)), c_Transitive__Closure_Otrancl(_1567993, _1567999))))], (40289 ^ _779448) ^ [_1568281, _1568283, _1568285, _1568287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568281, _1568281)), hAPP(hAPP(c_Product__Type_OPair(_1568281, _1568281), _1568283), _1568285)), c_Transitive__Closure_Ortrancl(_1568281, _1568287))), -(_1568283 = _1568285), 40296 ^ _779448 : [(40297 ^ _779448) ^ [] : [_1568283 = _1568285], (40299 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568281, _1568281)), hAPP(hAPP(c_Product__Type_OPair(_1568281, _1568281), _1568283), _1568285)), c_Transitive__Closure_Otrancl(_1568281, _1568287))))]]], (40301 ^ _779448) ^ [_1568539, _1568541, _1568543, _1568545] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568539, _1568539)), hAPP(hAPP(c_Product__Type_OPair(_1568539, _1568539), _1568541), _1568543)), c_Transitive__Closure_Ortrancl(_1568539, _1568545)))), 40302 ^ _779448 : [(40303 ^ _779448) ^ [] : [_1568541 = _1568543], (40305 ^ _779448) ^ [] : [-(_1568541 = _1568543), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568539, _1568539)), hAPP(hAPP(c_Product__Type_OPair(_1568539, _1568539), _1568541), _1568543)), c_Transitive__Closure_Otrancl(_1568539, _1568545)))]]], (40313 ^ _779448) ^ [_1568805] : [-(hAPP(c_Relation_ODomain(_1568805, _1568805), c_Relation_OId(_1568805)) = c_Orderings_Otop__class_Otop(tc_fun(_1568805, tc_HOL_Obool)))], (40315 ^ _779448) ^ [_1568841] : [-(hAPP(c_Relation_ORange(_1568841, _1568841), c_Relation_OId(_1568841)) = c_Orderings_Otop__class_Otop(tc_fun(_1568841, tc_HOL_Obool)))], (40317 ^ _779448) ^ [_1568877] : [-(c_Relation_Orefl__on(_1568877, c_Orderings_Otop__class_Otop(tc_fun(_1568877, tc_HOL_Obool)), c_Relation_OId(_1568877)))], (40319 ^ _779448) ^ [] : [-(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))))], (40321 ^ _779448) ^ [_1568925, _1568927, _1568929, _1568931] : [-(hBOOL(hAPP(hAPP(c_member(_1568925), _1568927), hAPP(c_Relation_ODomain(_1568925, _1568925), _1568929)))), 40324 ^ _779448 : [(40325 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568925, _1568925)), hAPP(hAPP(c_Product__Type_OPair(_1568925, _1568925), _1568927), _1568931)), c_Transitive__Closure_Ortrancl(_1568925, _1568929))), -(_1568927 = _1568931)], (40331 ^ _779448) ^ [] : [_1568927 = _1568931, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568925, _1568925)), hAPP(hAPP(c_Product__Type_OPair(_1568925, _1568925), _1568927), _1568931)), c_Transitive__Closure_Ortrancl(_1568925, _1568929))))]]], (40337 ^ _779448) ^ [_1569221, _1569223, _1569225, _1569227] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569221, _1569221)), hAPP(hAPP(c_Product__Type_OPair(_1569221, _1569221), _1569223), _1569225)), c_Transitive__Closure_Ortrancl(_1569221, _1569227))), hBOOL(hAPP(hAPP(c_member(_1569221), _1569225), c_Wellfounded_Oacc(_1569221, _1569227))), -(hBOOL(hAPP(hAPP(c_member(_1569221), _1569223), c_Wellfounded_Oacc(_1569221, _1569227))))], (40347 ^ _779448) ^ [_1569442, _1569444, _1569446, _1569448] : [hBOOL(hAPP(hAPP(c_member(_1569442), _1569444), c_Wellfounded_Oacc(_1569442, _1569446))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569442, _1569442)), hAPP(hAPP(c_Product__Type_OPair(_1569442, _1569442), _1569448), _1569444)), c_Transitive__Closure_Ortrancl(_1569442, _1569446))), -(hBOOL(hAPP(hAPP(c_member(_1569442), _1569448), c_Wellfounded_Oacc(_1569442, _1569446))))], (40357 ^ _779448) ^ [_1569684, _1569686, _1569688, _1569690] : [c_Wellfounded_Owf(_1569684, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1569684, _1569684)), hAPP(hAPP(c_Product__Type_OPair(_1569684, _1569684), _1569686), _1569688)), _1569690)), 40360 ^ _779448 : [(40361 ^ _779448) ^ [] : [-(c_Wellfounded_Owf(_1569684, _1569690))], (40363 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569684, _1569684)), hAPP(hAPP(c_Product__Type_OPair(_1569684, _1569684), _1569688), _1569686)), c_Transitive__Closure_Ortrancl(_1569684, _1569690)))]]], (40365 ^ _779448) ^ [_1569879, _1569881, _1569883, _1569885] : [-(c_Wellfounded_Owf(_1569879, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1569879, _1569879)), hAPP(hAPP(c_Product__Type_OPair(_1569879, _1569879), _1569881), _1569883)), _1569885))), c_Wellfounded_Owf(_1569879, _1569885), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569879, _1569879)), hAPP(hAPP(c_Product__Type_OPair(_1569879, _1569879), _1569883), _1569881)), c_Transitive__Closure_Ortrancl(_1569879, _1569885))))], (40375 ^ _779448) ^ [_1570126, _1570128, _1570130, _1570132] : [c_Wellfounded_Oacyclic(_1570126, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1570126, _1570126)), hAPP(hAPP(c_Product__Type_OPair(_1570126, _1570126), _1570128), _1570130)), _1570132)), 40378 ^ _779448 : [(40379 ^ _779448) ^ [] : [-(c_Wellfounded_Oacyclic(_1570126, _1570132))], (40381 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570126, _1570126)), hAPP(hAPP(c_Product__Type_OPair(_1570126, _1570126), _1570130), _1570128)), c_Transitive__Closure_Ortrancl(_1570126, _1570132)))]]], (40383 ^ _779448) ^ [_1570321, _1570323, _1570325, _1570327] : [-(c_Wellfounded_Oacyclic(_1570321, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1570321, _1570321)), hAPP(hAPP(c_Product__Type_OPair(_1570321, _1570321), _1570323), _1570325)), _1570327))), c_Wellfounded_Oacyclic(_1570321, _1570327), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570321, _1570321)), hAPP(hAPP(c_Product__Type_OPair(_1570321, _1570321), _1570325), _1570323)), c_Transitive__Closure_Ortrancl(_1570321, _1570327))))], (40393 ^ _779448) ^ [_1570547, _1570549] : [-(c_Relation_Orefl__on(_1570547, c_Orderings_Otop__class_Otop(tc_fun(_1570547, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1570547, _1570547), tc_HOL_Obool)), _1570549), c_Relation_OId(_1570547))))], (40395 ^ _779448) ^ [_1570594] : [-(c_Relation_OId(_1570594) = hAPP(c_Set_OCollect(tc_prod(_1570594, _1570594)), hAPP(hAPP(c_COMBB(tc_fun(_1570594, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1570594, _1570594)), c_HOL_OEx(_1570594)), hAPP(hAPP(c_COMBC(tc_prod(_1570594, _1570594), tc_fun(_1570594, tc_prod(_1570594, _1570594)), tc_fun(_1570594, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1570594, _1570594), tc_HOL_Obool), tc_fun(tc_fun(_1570594, tc_prod(_1570594, _1570594)), tc_fun(_1570594, tc_HOL_Obool)), tc_prod(_1570594, _1570594)), c_COMBB(tc_prod(_1570594, _1570594), tc_HOL_Obool, _1570594)), c_fequal)), hAPP(hAPP(c_COMBS(_1570594, _1570594, tc_prod(_1570594, _1570594)), c_Product__Type_OPair(_1570594, _1570594)), c_COMBI(_1570594))))))], (40397 ^ _779448) ^ [_1570723, _1570725] : [-(c_Relation_Oirrefl(_1570723, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1570723, _1570723), tc_HOL_Obool)), _1570725), c_Relation_OId(_1570723))))], (40399 ^ _779448) ^ [_1570779, _1570781] : [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), _1570779), _1570781)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1570779), _1570781)))], (40405 ^ _779448) ^ [_1570884, _1570886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1570884), _1570886)), -(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), _1570884), _1570886)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40411 ^ _779448) ^ [_1570995, _1570997, _1570999, _1571001, _1571003] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570995, _1570995)), hAPP(hAPP(c_Product__Type_OPair(_1570995, _1570995), _1570997), _1570999)), c_Transitive__Closure_Ortrancl(_1570995, _1571001))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1570995, _1570995), tc_HOL_Obool)), _1571001), hAPP(hAPP(c_Product__Type_OSigma(_1570995, _1570995), _1571003), hAPP(c_COMBK(tc_fun(_1570995, tc_HOL_Obool), _1570995), _1571003)))), -(_1570997 = _1570999), -(hBOOL(hAPP(hAPP(c_member(_1570995), _1570997), _1571003)))], (40425 ^ _779448) ^ [_1571278, _1571280] : [40426 ^ _779448 : [(40427 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1571278), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40429 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571280), _1571278))]], -(c_Random_Olog(_1571278, _1571280) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40433 ^ _779448) ^ [_1571413, _1571415] : [-(c_Random_Olog(_1571413, _1571415) = 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(_1571413, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1571415), _1571413)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1571413), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571415), _1571413)))], (40443 ^ _779448) ^ [_1571495, _1571497, _1571499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571495), _1571497)), -(c_Random_Ominus__shift(_1571499, _1571495, _1571497) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1571499), _1571495)), _1571497))], (40449 ^ _779448) ^ [_1571610, _1571612, _1571614] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1571610), _1571612))), -(c_Random_Ominus__shift(_1571614, _1571610, _1571612) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1571610), _1571612))], (40455 ^ _779448) ^ [_1571674, _1571676] : [_1571674 = _1571676, -(c_Random_Oinc__shift(_1571674, _1571676) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40461 ^ _779448) ^ [_1571751, _1571753] : [-(_1571751 = _1571753), -(c_Random_Oinc__shift(_1571751, _1571753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1571753), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40467 ^ _779448) ^ [_1571798, _1571800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1571798)), -(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(_1571798), _1571800))), _1571798)))], (40473 ^ _779448) ^ [_1571905, _1571907, _1571909] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1571905, _1571905), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1571905, _1571905), _1571907)), c_Transitive__Closure_Ortrancl(_1571905, _1571907)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1571905, _1571905), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571905, _1571905)), hAPP(hAPP(c_Product__Type_OPair(_1571905, _1571905), _1571909), _1571909)), c_Transitive__Closure_Otrancl(_1571905, _1571907)))], (40479 ^ _779448) ^ [_1572091, _1572093] : [-(c_Transitive__Closure_Ortrancl(_1572091, hAPP(c_Relation_Oconverse(_1572091, _1572091), _1572093)) = hAPP(c_Relation_Oconverse(_1572091, _1572091), c_Transitive__Closure_Ortrancl(_1572091, _1572093)))], (40481 ^ _779448) ^ [_1572134] : [-(hAPP(c_Relation_Oconverse(_1572134, _1572134), c_Relation_OId(_1572134)) = c_Relation_OId(_1572134))], (40483 ^ _779448) ^ [_1572167, _1572169, _1572171, _1572173] : [-(hAPP(c_Relation_Oconverse(_1572167, _1572169), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572167, _1572169), tc_HOL_Obool)), _1572171), _1572173)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572169, _1572167), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1572167, _1572169), _1572171)), hAPP(c_Relation_Oconverse(_1572167, _1572169), _1572173)))], (40485 ^ _779448) ^ [_1572242, _1572244] : [-(c_Transitive__Closure_Otrancl(_1572242, hAPP(c_Relation_Oconverse(_1572242, _1572242), _1572244)) = hAPP(c_Relation_Oconverse(_1572242, _1572242), c_Transitive__Closure_Otrancl(_1572242, _1572244)))], (40487 ^ _779448) ^ [_1572300, _1572302] : [c_Wellfounded_Oacyclic(_1572300, hAPP(c_Relation_Oconverse(_1572300, _1572300), _1572302)), -(c_Wellfounded_Oacyclic(_1572300, _1572302))], (40493 ^ _779448) ^ [_1572385, _1572387] : [c_Wellfounded_Oacyclic(_1572385, _1572387), -(c_Wellfounded_Oacyclic(_1572385, hAPP(c_Relation_Oconverse(_1572385, _1572385), _1572387)))], (40499 ^ _779448) ^ [_1572476, _1572478, _1572480, _1572482] : [-(hAPP(c_Relation_Oconverse(_1572476, _1572476), hAPP(hAPP(c_Relation_Oinv__image(_1572478, _1572476), _1572480), _1572482)) = hAPP(hAPP(c_Relation_Oinv__image(_1572478, _1572476), hAPP(c_Relation_Oconverse(_1572478, _1572478), _1572480)), _1572482))], (40501 ^ _779448) ^ [_1572535, _1572537, _1572539] : [-(hAPP(c_Relation_Oconverse(_1572535, _1572537), hAPP(c_Relation_Oconverse(_1572537, _1572535), _1572539)) = _1572539)], (40503 ^ _779448) ^ [_1572574, _1572576] : [-(hAPP(c_Relation_OField(_1572574), hAPP(c_Relation_Oconverse(_1572574, _1572574), _1572576)) = hAPP(c_Relation_OField(_1572574), _1572576))], (40505 ^ _779448) ^ [_1572615, _1572617] : [-(hAPP(c_Relation_Oconverse(_1572615, _1572615), c_Relation_OId__on(_1572615, _1572617)) = c_Relation_OId__on(_1572615, _1572617))], (40507 ^ _779448) ^ [_1572652, _1572654, _1572656, _1572658] : [-(hAPP(c_Relation_Oconverse(_1572652, _1572654), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1572652, _1572654), tc_HOL_Obool)), _1572656), _1572658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1572654, _1572652), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1572652, _1572654), _1572656)), hAPP(c_Relation_Oconverse(_1572652, _1572654), _1572658)))], (40509 ^ _779448) ^ [_1572745, _1572747, _1572749] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572745, _1572747)), hAPP(c_Relation_Oconverse(_1572747, _1572745), _1572749))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572747, _1572745)), _1572749)))], (40515 ^ _779448) ^ [_1572860, _1572862, _1572864] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572862, _1572860)), _1572864)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1572860, _1572862)), hAPP(c_Relation_Oconverse(_1572862, _1572860), _1572864))))], (40521 ^ _779448) ^ [_1572999, _1573001, _1573003] : [c_Relation_Orefl__on(_1572999, _1573001, hAPP(c_Relation_Oconverse(_1572999, _1572999), _1573003)), -(c_Relation_Orefl__on(_1572999, _1573001, _1573003))], (40527 ^ _779448) ^ [_1573090, _1573092, _1573094] : [c_Relation_Orefl__on(_1573090, _1573092, _1573094), -(c_Relation_Orefl__on(_1573090, _1573092, hAPP(c_Relation_Oconverse(_1573090, _1573090), _1573094)))], (40533 ^ _779448) ^ [_1573187, _1573189, _1573191, _1573193, _1573195] : [-(hAPP(c_Relation_Oconverse(_1573187, _1573189), hAPP(hAPP(c_Relation_Orel__comp(_1573187, _1573191, _1573189), _1573193), _1573195)) = hAPP(hAPP(c_Relation_Orel__comp(_1573189, _1573191, _1573187), hAPP(c_Relation_Oconverse(_1573191, _1573189), _1573195)), hAPP(c_Relation_Oconverse(_1573187, _1573191), _1573193)))], (40535 ^ _779448) ^ [_1573280, _1573282, _1573284, _1573286, _1573288] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573280, _1573282)), hAPP(hAPP(c_Product__Type_OPair(_1573280, _1573282), _1573284), _1573286)), hAPP(c_Relation_Oconverse(_1573282, _1573280), _1573288))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573282, _1573280)), hAPP(hAPP(c_Product__Type_OPair(_1573282, _1573280), _1573286), _1573284)), _1573288)))], (40541 ^ _779448) ^ [_1573447, _1573449, _1573451, _1573453, _1573455] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573449, _1573447)), hAPP(hAPP(c_Product__Type_OPair(_1573449, _1573447), _1573453), _1573451)), _1573455)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573447, _1573449)), hAPP(hAPP(c_Product__Type_OPair(_1573447, _1573449), _1573451), _1573453)), hAPP(c_Relation_Oconverse(_1573449, _1573447), _1573455))))], (40547 ^ _779448) ^ [_1573620, _1573622, _1573624, _1573626, _1573628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573620, _1573622)), hAPP(hAPP(c_Product__Type_OPair(_1573620, _1573622), _1573624), _1573626)), _1573628)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573622, _1573620)), hAPP(hAPP(c_Product__Type_OPair(_1573622, _1573620), _1573626), _1573624)), hAPP(c_Relation_Oconverse(_1573620, _1573622), _1573628))))], (40553 ^ _779448) ^ [_1573791, _1573793, _1573795, _1573797, _1573799] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573791, _1573793)), hAPP(hAPP(c_Product__Type_OPair(_1573791, _1573793), _1573795), _1573797)), hAPP(c_Relation_Oconverse(_1573793, _1573791), _1573799))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573793, _1573791)), hAPP(hAPP(c_Product__Type_OPair(_1573793, _1573791), _1573797), _1573795)), _1573799)))], (40559 ^ _779448) ^ [_1573962, _1573964, _1573966, _1573968, _1573970] : [-(hAPP(c_Relation_Oconverse(_1573962, _1573964), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1573966, tc_fun(tc_prod(_1573962, _1573964), tc_HOL_Obool)), _1573968), _1573970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1573966, tc_fun(tc_prod(_1573964, _1573962), tc_HOL_Obool)), _1573968), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1573962, _1573964), tc_HOL_Obool), tc_fun(tc_prod(_1573964, _1573962), tc_HOL_Obool), _1573966), c_Relation_Oconverse(_1573962, _1573964)), _1573970)))], (40561 ^ _779448) ^ [_1574054, _1574056, _1574058, _1574060, _1574062] : [-(hAPP(c_Relation_Oconverse(_1574054, _1574056), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574058, tc_fun(tc_prod(_1574054, _1574056), tc_HOL_Obool)), _1574060), _1574062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574058, tc_fun(tc_prod(_1574056, _1574054), tc_HOL_Obool)), _1574060), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1574054, _1574056), tc_HOL_Obool), tc_fun(tc_prod(_1574056, _1574054), tc_HOL_Obool), _1574058), c_Relation_Oconverse(_1574054, _1574056)), _1574062)))], (40563 ^ _779448) ^ [_1574146, _1574148] : [c_Wellfounded_Owf(_1574146, hAPP(c_Relation_Oconverse(_1574146, _1574146), _1574148)), -(c_Wellfounded_Owf(_1574146, hAPP(c_Relation_Oconverse(_1574146, _1574146), c_Transitive__Closure_Otrancl(_1574146, _1574148))))], (40569 ^ _779448) ^ [_1574253, _1574255, _1574257] : [c_Equiv__Relations_Oequiv(_1574253, _1574255, _1574257), -(hAPP(hAPP(c_Relation_Orel__comp(_1574253, _1574253, _1574253), hAPP(c_Relation_Oconverse(_1574253, _1574253), _1574257)), _1574257) = _1574257)], (40575 ^ _779448) ^ [_1574366, _1574368, _1574370] : [-(hAPP(c_Relation_ORange(_1574366, _1574368), hAPP(c_Relation_Oconverse(_1574368, _1574366), _1574370)) = hAPP(c_Relation_ODomain(_1574368, _1574366), _1574370))], (40577 ^ _779448) ^ [_1574411, _1574413, _1574415] : [-(hAPP(c_Relation_ODomain(_1574411, _1574413), hAPP(c_Relation_Oconverse(_1574413, _1574411), _1574415)) = hAPP(c_Relation_ORange(_1574413, _1574411), _1574415))], (40579 ^ _779448) ^ [_1574456, _1574458, _1574460] : [-(hAPP(c_Relation_ORange(_1574456, _1574458), _1574460) = hAPP(c_Relation_ODomain(_1574458, _1574456), hAPP(c_Relation_Oconverse(_1574456, _1574458), _1574460)))], (40581 ^ _779448) ^ [_1574501, _1574503, _1574505, _1574507] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574501, _1574501)), hAPP(hAPP(c_Product__Type_OPair(_1574501, _1574501), _1574503), _1574505)), c_Transitive__Closure_Ortrancl(_1574501, hAPP(c_Relation_Oconverse(_1574501, _1574501), _1574507)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574501, _1574501)), hAPP(hAPP(c_Product__Type_OPair(_1574501, _1574501), _1574505), _1574503)), c_Transitive__Closure_Ortrancl(_1574501, _1574507))))], (40587 ^ _779448) ^ [_1574682, _1574684, _1574686, _1574688] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574682, _1574682)), hAPP(hAPP(c_Product__Type_OPair(_1574682, _1574682), _1574684), _1574686)), c_Transitive__Closure_Ortrancl(_1574682, _1574688))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574682, _1574682)), hAPP(hAPP(c_Product__Type_OPair(_1574682, _1574682), _1574686), _1574684)), c_Transitive__Closure_Ortrancl(_1574682, hAPP(c_Relation_Oconverse(_1574682, _1574682), _1574688)))))], (40593 ^ _779448) ^ [_1574863, _1574865, _1574867, _1574869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574863, _1574863)), hAPP(hAPP(c_Product__Type_OPair(_1574863, _1574863), _1574865), _1574867)), c_Transitive__Closure_Otrancl(_1574863, hAPP(c_Relation_Oconverse(_1574863, _1574863), _1574869)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574863, _1574863)), hAPP(hAPP(c_Product__Type_OPair(_1574863, _1574863), _1574865), _1574867)), hAPP(c_Relation_Oconverse(_1574863, _1574863), c_Transitive__Closure_Otrancl(_1574863, _1574869)))))], (40599 ^ _779448) ^ [_1575056, _1575058, _1575060, _1575062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575056, _1575056)), hAPP(hAPP(c_Product__Type_OPair(_1575056, _1575056), _1575058), _1575060)), hAPP(c_Relation_Oconverse(_1575056, _1575056), c_Transitive__Closure_Otrancl(_1575056, _1575062)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575056, _1575056)), hAPP(hAPP(c_Product__Type_OPair(_1575056, _1575056), _1575058), _1575060)), c_Transitive__Closure_Otrancl(_1575056, hAPP(c_Relation_Oconverse(_1575056, _1575056), _1575062)))))], (40605 ^ _779448) ^ [_1575273, _1575275, _1575277, _1575279, _1575281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575273, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575275, _1575273, _1575277), _1575279)), _1575281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575275, tc_HOL_Obool)), _1575279), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575275, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575273, _1575275, hAPP(c_Relation_Oconverse(_1575275, _1575273), _1575277)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575273, tc_HOL_Obool)), _1575281))))))], (40611 ^ _779448) ^ [_1575464, _1575466, _1575468, _1575470, _1575472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575466, tc_HOL_Obool)), _1575470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575466, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575464, _1575466, hAPP(c_Relation_Oconverse(_1575466, _1575464), _1575468)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1575464, tc_HOL_Obool)), _1575472))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575464, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1575466, _1575464, _1575468), _1575470)), _1575472)))], (40617 ^ _779448) ^ [_1575661, _1575663, _1575665] : [c_Relation_Orefl__on(_1575661, _1575663, _1575665), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575661, _1575661), tc_HOL_Obool)), _1575665), hAPP(hAPP(c_Relation_Orel__comp(_1575661, _1575661, _1575661), hAPP(c_Relation_Oconverse(_1575661, _1575661), _1575665)), _1575665))))], (40623 ^ _779448) ^ [_1575800, _1575802, _1575804] : [hAPP(hAPP(c_Relation_Orel__comp(_1575800, _1575800, _1575800), hAPP(c_Relation_Oconverse(_1575800, _1575800), _1575802)), _1575802) = _1575802, hAPP(c_Relation_ODomain(_1575800, _1575800), _1575802) = _1575804, -(c_Equiv__Relations_Oequiv(_1575800, _1575804, _1575802))], (40633 ^ _779448) ^ [_1575979, _1575981] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1575979, _1575979)), _1575981)), c_Wellfounded_Oacyclic(_1575979, _1575981), -(c_Wellfounded_Owf(_1575979, hAPP(c_Relation_Oconverse(_1575979, _1575979), _1575981)))], (40643 ^ _779448) ^ [_1576134, _1576136, _1576138] : [-(hAPP(c_Relation_Oconverse(_1576134, _1576136), _1576138) = hAPP(c_Set_OCollect(tc_prod(_1576136, _1576134)), hAPP(c_Product__Type_Oprod_Oprod__case(_1576136, _1576134, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1576136, tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_fun(_1576134, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576134, tc_fun(tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_fun(_1576134, tc_HOL_Obool)), _1576136), c_COMBC(_1576134, tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576134, tc_prod(_1576134, _1576136)), tc_fun(_1576134, tc_fun(tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_HOL_Obool)), _1576136), hAPP(c_COMBB(tc_prod(_1576134, _1576136), tc_fun(tc_fun(tc_prod(_1576134, _1576136), tc_HOL_Obool), tc_HOL_Obool), _1576134), c_member(tc_prod(_1576134, _1576136)))), hAPP(c_COMBC(_1576134, _1576136, tc_prod(_1576134, _1576136)), c_Product__Type_OPair(_1576134, _1576136))))), _1576138))))], (40645 ^ _779448) ^ [_1576310, _1576312, _1576314, _1576316, _1576318, _1576320] : [c_Relation_Osingle__valued(_1576310, _1576312, hAPP(c_Relation_Oconverse(_1576312, _1576310), _1576314)), -(_1576316 = c_Orderings_Obot__class_Obot(tc_fun(_1576318, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1576312, _1576310, _1576314), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576318, tc_fun(_1576312, tc_HOL_Obool)), _1576316), _1576320)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576318, tc_fun(_1576310, tc_HOL_Obool)), _1576316), hAPP(hAPP(c_COMBB(tc_fun(_1576312, tc_HOL_Obool), tc_fun(_1576310, tc_HOL_Obool), _1576318), c_Relation_OImage(_1576312, _1576310, _1576314)), _1576320)))], (40655 ^ _779448) ^ [_1576536, _1576538, _1576540, _1576542, _1576544] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576536, _1576536)), hAPP(hAPP(c_Product__Type_OPair(_1576536, _1576536), hAPP(_1576538, hAPP(c_Nat_OSuc, 40656 ^ [_1576536, _1576538, _1576540, _1576542, _1576544]))), hAPP(_1576538, 40656 ^ [_1576536, _1576538, _1576540, _1576542, _1576544]))), c_Transitive__Closure_Ortrancl(_1576536, _1576540))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576536, _1576536)), hAPP(hAPP(c_Product__Type_OPair(_1576536, _1576536), hAPP(_1576538, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1576542), _1576544))), hAPP(_1576538, _1576542))), c_Transitive__Closure_Ortrancl(_1576536, _1576540))))], (40662 ^ _779448) ^ [_1576829, _1576831, _1576833, _1576835, _1576837] : [c_Relation_Osingle__valued(_1576829, _1576831, _1576833), c_Relation_Osingle__valued(_1576831, _1576835, _1576837), -(c_Relation_Osingle__valued(_1576829, _1576835, hAPP(hAPP(c_Relation_Orel__comp(_1576829, _1576831, _1576835), _1576833), _1576837)))], (40672 ^ _779448) ^ [_1576996] : [-(c_Relation_Osingle__valued(_1576996, _1576996, c_Relation_OId(_1576996)))], (40674 ^ _779448) ^ [_1577022, _1577024, _1577026, _1577028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1577022, _1577024), tc_HOL_Obool)), _1577026), _1577028)), c_Relation_Osingle__valued(_1577022, _1577024, _1577028), -(c_Relation_Osingle__valued(_1577022, _1577024, _1577026))], (40684 ^ _779448) ^ [_1577189, _1577191] : [-(c_Relation_Osingle__valued(_1577189, _1577189, c_Relation_OId__on(_1577189, _1577191)))], (40700 ^ _779448) ^ [_1577610, _1577612, _1577614] : [40703 ^ _779448 : [(40704 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577610, _1577612)), hAPP(hAPP(c_Product__Type_OPair(_1577610, _1577612), 40701 ^ [_1577610, _1577612, _1577614]), 40702 ^ [_1577610, _1577612, _1577614])), _1577614)))], (40707 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577610, _1577612)), hAPP(hAPP(c_Product__Type_OPair(_1577610, _1577612), 40701 ^ [_1577610, _1577612, _1577614]), 40705 ^ [_1577610, _1577612, _1577614])), _1577614)))], (40709 ^ _779448) ^ [] : [40702 ^ [_1577610, _1577612, _1577614] = 40705 ^ [_1577610, _1577612, _1577614]]], -(c_Relation_Osingle__valued(_1577610, _1577612, _1577614))], (40686 ^ _779448) ^ [_1577236, _1577238, _1577240] : [c_Relation_Osingle__valued(_1577236, _1577238, _1577240), 40689 ^ _779448 : [(40690 ^ _779448) ^ [_1577357, _1577359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577236, _1577238)), hAPP(hAPP(c_Product__Type_OPair(_1577236, _1577238), _1577359), _1577357)), _1577240)), 40693 ^ _779448 : [(40694 ^ _779448) ^ [_1577483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577236, _1577238)), hAPP(hAPP(c_Product__Type_OPair(_1577236, _1577238), _1577359), _1577483)), _1577240)), -(_1577357 = _1577483)]]]]], (40713 ^ _779448) ^ [_1577980, _1577982, _1577984, _1577986, _1577988, _1577990] : [c_Relation_Osingle__valued(_1577980, _1577982, _1577984), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577980, _1577982)), hAPP(hAPP(c_Product__Type_OPair(_1577980, _1577982), _1577986), _1577988)), _1577984)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577980, _1577982)), hAPP(hAPP(c_Product__Type_OPair(_1577980, _1577982), _1577986), _1577990)), _1577984)), -(_1577988 = _1577990)], (40727 ^ _779448) ^ [_1578263, _1578265, _1578267, _1578269, _1578271] : [c_Relation_Osingle__valued(_1578263, _1578263, _1578265), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578263, _1578263)), hAPP(hAPP(c_Product__Type_OPair(_1578263, _1578263), _1578267), _1578269)), c_Transitive__Closure_Ortrancl(_1578263, _1578265))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578263, _1578263)), hAPP(hAPP(c_Product__Type_OPair(_1578263, _1578263), _1578267), _1578271)), c_Transitive__Closure_Ortrancl(_1578263, _1578265))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578263, _1578263)), hAPP(hAPP(c_Product__Type_OPair(_1578263, _1578263), _1578269), _1578271)), c_Transitive__Closure_Ortrancl(_1578263, _1578265)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578263, _1578263)), hAPP(hAPP(c_Product__Type_OPair(_1578263, _1578263), _1578271), _1578269)), c_Transitive__Closure_Ortrancl(_1578263, _1578265))))], (40745 ^ _779448) ^ [_1578653, _1578655, _1578657, _1578659, _1578661] : [c_Relation_Osingle__valued(_1578653, _1578655, hAPP(c_Relation_Oconverse(_1578655, _1578653), _1578657)), -(hAPP(c_Relation_OImage(_1578655, _1578653, _1578657), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1578655, tc_HOL_Obool)), _1578659), _1578661)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1578653, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1578655, _1578653, _1578657), _1578659)), hAPP(c_Relation_OImage(_1578655, _1578653, _1578657), _1578661)))], (40751 ^ _779448) ^ [_1578854, _1578856, _1578858] : [c_Relation_Ototal__on(_1578854, _1578856, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1578854, _1578854), tc_HOL_Obool)), _1578858), c_Relation_OId(_1578854))), -(c_Relation_Ototal__on(_1578854, _1578856, _1578858))], (40757 ^ _779448) ^ [_1578965, _1578967, _1578969] : [c_Relation_Ototal__on(_1578965, _1578967, _1578969), -(c_Relation_Ototal__on(_1578965, _1578967, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1578965, _1578965), tc_HOL_Obool)), _1578969), c_Relation_OId(_1578965))))], (40763 ^ _779448) ^ [_1579082, _1579084, _1579086] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579082, _1579082)), _1579084), c_Transitive__Closure_Ortrancl(_1579082, _1579086))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579082, _1579082)), _1579084), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1579082, _1579082), 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(_1579082, _1579082), tc_HOL_Obool), tc_fun(tc_prod(_1579082, _1579082), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1579082, _1579082), tc_HOL_Obool)), _1579086)))))], (40769 ^ _779448) ^ [_1579293, _1579295, _1579297] : [c_Relation_Osingle__valued(_1579293, _1579293, _1579295), -(c_Relation_Osingle__valued(_1579293, _1579293, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579293, _1579293), tc_HOL_Obool), _1579297), _1579295)))], (40775 ^ _779448) ^ [_1579400, _1579402, _1579404] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1579400, _1579400, _1579400), _1579402), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579400, _1579400), tc_HOL_Obool), _1579404), _1579402)) = hAPP(hAPP(c_Relation_Orel__comp(_1579400, _1579400, _1579400), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579400, _1579400), tc_HOL_Obool), _1579404), _1579402)), _1579402))], (40777 ^ _779448) ^ [_1579471, _1579473] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579471, _1579471), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1579473) = _1579473)], (40779 ^ _779448) ^ [_1579508, _1579510, _1579512, _1579514] : [-(hAPP(_1579508, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1579510, _1579510), _1579512), _1579508), _1579514)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1579510, _1579510), _1579512), _1579508), hAPP(_1579508, _1579514)))], (40781 ^ _779448) ^ [_1579567, _1579569, _1579571, _1579573] : [-(hAPP(hAPP(c_Nat_Ocompow(_1579567, _1579567), _1579569), hAPP(hAPP(c_Nat_Ocompow(_1579567, _1579567), _1579571), _1579573)) = hAPP(hAPP(c_Nat_Ocompow(_1579567, _1579567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1579571), _1579569)), _1579573))], (40783 ^ _779448) ^ [_1579629, _1579631, _1579633, _1579635] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1579629, _1579631), tc_fun(_1579629, _1579631)), _1579633), c_Fun_Ocomp(_1579631, _1579631, _1579629, _1579635)) = c_Fun_Ocomp(_1579631, _1579631, _1579629, hAPP(hAPP(c_Nat_Ocompow(_1579631, _1579631), _1579633), _1579635)))], (40785 ^ _779448) ^ [_1579692, _1579694, _1579696] : [c_Wellfounded_Owf(_1579692, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579692, _1579692), tc_HOL_Obool), _1579694), _1579696)), -(c_Wellfounded_Owf(_1579692, _1579696))], (40791 ^ _779448) ^ [_1579795, _1579797, _1579799, _1579801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579795, _1579795)), _1579797), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579795, _1579795), tc_HOL_Obool), _1579799), _1579801))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579795, _1579795)), _1579797), c_Transitive__Closure_Ortrancl(_1579795, _1579801))))], (40797 ^ _779448) ^ [_1579964, _1579966, _1579968] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579964, _1579964)), _1579966), c_Transitive__Closure_Ortrancl(_1579964, _1579968))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579964, _1579964)), _1579966), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1579964, _1579964), tc_HOL_Obool), 40800 ^ [_1579964, _1579966, _1579968]), _1579968))))], (40804 ^ _779448) ^ [_1580123, _1580125, _1580127] : [40805 ^ _779448 : [(40806 ^ _779448) ^ [_1580199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580123, _1580123)), _1580125), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580123, _1580123), tc_HOL_Obool), _1580199), _1580127)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580123, _1580123)), _1580125), c_Transitive__Closure_Ortrancl(_1580123, _1580127))))], (40810 ^ _779448) ^ [_1580287, _1580289, _1580291] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580287, _1580287), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1580289)), _1580291) = hAPP(hAPP(c_Relation_Orel__comp(_1580287, _1580287, _1580287), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580287, _1580287), tc_HOL_Obool), _1580289), _1580291)), _1580291))], (40812 ^ _779448) ^ [_1580351, _1580353, _1580355, _1580357] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580351, _1580351), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1580353), _1580355)), _1580357) = hAPP(hAPP(c_Relation_Orel__comp(_1580351, _1580351, _1580351), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580351, _1580351), tc_HOL_Obool), _1580353), _1580357)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580351, _1580351), tc_HOL_Obool), _1580355), _1580357)))], (40814 ^ _779448) ^ [_1580432, _1580434] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580432, _1580432), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1580434) = c_Relation_OId(_1580432))], (40816 ^ _779448) ^ [_1580471, _1580473] : [-(c_Relation_Ototal__on(_1580471, c_Orderings_Obot__class_Obot(tc_fun(_1580471, tc_HOL_Obool)), _1580473))], (40818 ^ _779448) ^ [_1580520, _1580522, _1580524] : [c_Relation_Ototal__on(_1580520, _1580522, hAPP(c_Relation_Oconverse(_1580520, _1580520), _1580524)), -(c_Relation_Ototal__on(_1580520, _1580522, _1580524))], (40824 ^ _779448) ^ [_1580611, _1580613, _1580615] : [c_Relation_Ototal__on(_1580611, _1580613, _1580615), -(c_Relation_Ototal__on(_1580611, _1580613, hAPP(c_Relation_Oconverse(_1580611, _1580611), _1580615)))], (40830 ^ _779448) ^ [_1580708, _1580710, _1580712, _1580714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580708, _1580708)), hAPP(hAPP(c_Product__Type_OPair(_1580708, _1580708), _1580710), _1580712)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580708, _1580708), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1580714))), -(_1580710 = _1580712)], (40836 ^ _779448) ^ [_1580851, _1580853, _1580855] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580851, _1580851)), hAPP(hAPP(c_Product__Type_OPair(_1580851, _1580851), _1580853), _1580853)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580851, _1580851), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1580855))))], (40838 ^ _779448) ^ [_1580909, _1580911, _1580913, _1580915, _1580917, _1580919] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580909, _1580909)), hAPP(hAPP(c_Product__Type_OPair(_1580909, _1580909), _1580911), _1580913)), _1580915)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1580909, _1580909)), hAPP(hAPP(c_Product__Type_OPair(_1580909, _1580909), _1580913), _1580917)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580909, _1580909), tc_HOL_Obool), _1580919), _1580915))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580909, _1580909)), hAPP(hAPP(c_Product__Type_OPair(_1580909, _1580909), _1580911), _1580917)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1580909, _1580909), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1580919)), _1580915))))], (40848 ^ _779448) ^ [_1581222, _1581224, _1581226, _1581228, _1581230, _1581232] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581222, _1581222)), hAPP(hAPP(c_Product__Type_OPair(_1581222, _1581222), _1581224), _1581226)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581222, _1581222), tc_HOL_Obool), _1581228), _1581230))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1581222, _1581222)), hAPP(hAPP(c_Product__Type_OPair(_1581222, _1581222), _1581226), _1581232)), _1581230)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581222, _1581222)), hAPP(hAPP(c_Product__Type_OPair(_1581222, _1581222), _1581224), _1581232)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581222, _1581222), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1581228)), _1581230))))], (40858 ^ _779448) ^ [_1581535, _1581537, _1581539] : [-(hAPP(hAPP(c_Nat_Ocompow(_1581535, _1581535), hAPP(c_Nat_OSuc, _1581537)), _1581539) = hAPP(c_Fun_Ocomp(_1581535, _1581535, _1581535, _1581539), hAPP(hAPP(c_Nat_Ocompow(_1581535, _1581535), _1581537), _1581539)))], (40860 ^ _779448) ^ [_1581591, _1581593, _1581595, _1581597] : [-(hAPP(hAPP(c_Nat_Ocompow(_1581591, _1581591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1581593), _1581595)), _1581597) = hAPP(c_Fun_Ocomp(_1581591, _1581591, _1581591, hAPP(hAPP(c_Nat_Ocompow(_1581591, _1581591), _1581593), _1581597)), hAPP(hAPP(c_Nat_Ocompow(_1581591, _1581591), _1581595), _1581597)))], (40862 ^ _779448) ^ [_1581661, _1581663] : [-(hAPP(hAPP(c_Nat_Ocompow(_1581661, _1581661), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1581663) = c_Fun_Oid(_1581661))], (40864 ^ _779448) ^ [_1581715, _1581717, _1581719] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581715, _1581715)), _1581717), c_Transitive__Closure_Otrancl(_1581715, _1581719))), 40868 ^ _779448 : [(40869 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40867 ^ [_1581715, _1581717, _1581719])))], (40871 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581715, _1581715)), _1581717), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581715, _1581715), tc_HOL_Obool), 40867 ^ [_1581715, _1581717, _1581719]), _1581719))))]]], (40873 ^ _779448) ^ [_1581913, _1581915, _1581917] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581913, _1581913)), _1581915), c_Transitive__Closure_Otrancl(_1581913, _1581917)))), 40874 ^ _779448 : [(40875 ^ _779448) ^ [_1581992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1581992)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1581913, _1581913)), _1581915), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581913, _1581913), tc_HOL_Obool), _1581992), _1581917)))]]], (40905 ^ _779448) ^ [_1582670, _1582672, _1582674] : [40907 ^ _779448 : [(40908 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582670), 40906 ^ [_1582670, _1582672, _1582674]), _1582672)))], (40911 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582670), 40909 ^ [_1582670, _1582672, _1582674]), _1582672)))], (40913 ^ _779448) ^ [] : [40906 ^ [_1582670, _1582672, _1582674] = 40909 ^ [_1582670, _1582672, _1582674]], (40915 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582670, _1582670)), hAPP(hAPP(c_Product__Type_OPair(_1582670, _1582670), 40906 ^ [_1582670, _1582672, _1582674]), 40909 ^ [_1582670, _1582672, _1582674])), _1582674))], (40917 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582670, _1582670)), hAPP(hAPP(c_Product__Type_OPair(_1582670, _1582670), 40909 ^ [_1582670, _1582672, _1582674]), 40906 ^ [_1582670, _1582672, _1582674])), _1582674))]], -(c_Relation_Ototal__on(_1582670, _1582672, _1582674))], (40883 ^ _779448) ^ [_1582181, _1582183, _1582185] : [c_Relation_Ototal__on(_1582181, _1582183, _1582185), 40886 ^ _779448 : [(40887 ^ _779448) ^ [_1582325] : [hBOOL(hAPP(hAPP(c_member(_1582181), _1582325), _1582183)), 40890 ^ _779448 : [(40891 ^ _779448) ^ [_1582465] : [hBOOL(hAPP(hAPP(c_member(_1582181), _1582465), _1582183)), -(_1582325 = _1582465), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582181, _1582181)), hAPP(hAPP(c_Product__Type_OPair(_1582181, _1582181), _1582325), _1582465)), _1582185))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582181, _1582181)), hAPP(hAPP(c_Product__Type_OPair(_1582181, _1582181), _1582465), _1582325)), _1582185)))]]]]], (40921 ^ _779448) ^ [_1583252, _1583254] : [-(c_Transitive__Closure_Ortrancl(_1583252, _1583254) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1583252, _1583252), 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(_1583252, _1583252), tc_HOL_Obool), tc_fun(tc_prod(_1583252, _1583252), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1583252, _1583252), tc_HOL_Obool)), _1583254)))], (40923 ^ _779448) ^ [_1583323] : [-(c_Nat_Ofunpow(_1583323) = c_Nat_Ocompow(_1583323, _1583323))], (40925 ^ _779448) ^ [_1583351, _1583353, _1583355, _1583357, _1583359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), _1583353), _1583355)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583351, _1583351), tc_HOL_Obool), _1583357), _1583359))), 40930 ^ _779448 : [(40931 ^ _779448) ^ [] : [-(_1583357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40933 ^ _779448) ^ [] : [-(_1583353 = _1583355)]], 40936 ^ _779448 : [(40937 ^ _779448) ^ [] : [-(_1583357 = hAPP(c_Nat_OSuc, 40935 ^ [_1583351, _1583353, _1583355, _1583357, _1583359]))], (40939 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), _1583353), 40934 ^ [_1583351, _1583353, _1583355, _1583357, _1583359])), _1583359)))], (40941 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583351, _1583351)), hAPP(hAPP(c_Product__Type_OPair(_1583351, _1583351), 40934 ^ [_1583351, _1583353, _1583355, _1583357, _1583359]), _1583355)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583351, _1583351), tc_HOL_Obool), 40935 ^ [_1583351, _1583353, _1583355, _1583357, _1583359]), _1583359))))]]], (40943 ^ _779448) ^ [_1583793, _1583795, _1583797, _1583799, _1583801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583793, _1583793)), hAPP(hAPP(c_Product__Type_OPair(_1583793, _1583793), _1583795), _1583797)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583793, _1583793), tc_HOL_Obool), _1583799), _1583801))), 40948 ^ _779448 : [(40949 ^ _779448) ^ [] : [-(_1583799 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40951 ^ _779448) ^ [] : [-(_1583795 = _1583797)]], 40954 ^ _779448 : [(40955 ^ _779448) ^ [] : [-(_1583799 = hAPP(c_Nat_OSuc, 40953 ^ [_1583793, _1583795, _1583797, _1583799, _1583801]))], (40957 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583793, _1583793)), hAPP(hAPP(c_Product__Type_OPair(_1583793, _1583793), _1583795), 40952 ^ [_1583793, _1583795, _1583797, _1583799, _1583801])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583793, _1583793), tc_HOL_Obool), 40953 ^ [_1583793, _1583795, _1583797, _1583799, _1583801]), _1583801))))], (40959 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583793, _1583793)), hAPP(hAPP(c_Product__Type_OPair(_1583793, _1583793), 40952 ^ [_1583793, _1583795, _1583797, _1583799, _1583801]), _1583797)), _1583801)))]]], (40961 ^ _779448) ^ [_1584231, _1584233] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584231, _1584231)), hAPP(hAPP(c_Product__Type_OPair(_1584231, _1584231), 40962 ^ [_1584231, _1584233]), 40962 ^ [_1584231, _1584233])), c_Transitive__Closure_Otrancl(_1584231, _1584233)))), -(c_Wellfounded_Oacyclic(_1584231, _1584233))], (40968 ^ _779448) ^ [_1584303, _1584305, _1584307, _1584309, _1584311] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584303, _1584303)), hAPP(hAPP(c_Product__Type_OPair(_1584303, _1584303), _1584305), _1584307)), c_Transitive__Closure_Ortrancl(_1584303, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584303, _1584303), tc_HOL_Obool)), _1584309), _1584311)))), 40974 ^ _779448 : [(40975 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584303, _1584303)), hAPP(hAPP(c_Product__Type_OPair(_1584303, _1584303), 40973 ^ [_1584303, _1584305, _1584307, _1584309, _1584311]), _1584307)), c_Transitive__Closure_Ortrancl(_1584303, _1584309))))], (40978 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584303, _1584303)), hAPP(hAPP(c_Product__Type_OPair(_1584303, _1584303), 40976 ^ [_1584303, _1584305, _1584307, _1584309, _1584311]), 40973 ^ [_1584303, _1584305, _1584307, _1584309, _1584311])), _1584311)))], (40980 ^ _779448) ^ [] : [40976 ^ [_1584303, _1584305, _1584307, _1584309, _1584311] = 40973 ^ [_1584303, _1584305, _1584307, _1584309, _1584311]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584303, _1584303)), hAPP(hAPP(c_Product__Type_OPair(_1584303, _1584303), _1584305), _1584307)), c_Transitive__Closure_Ortrancl(_1584303, _1584309))))], (40984 ^ _779448) ^ [_1584862, _1584864, _1584866, _1584868, _1584870] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584862, _1584862)), hAPP(hAPP(c_Product__Type_OPair(_1584862, _1584862), _1584864), _1584866)), c_Transitive__Closure_Ortrancl(_1584862, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584862, _1584862), tc_HOL_Obool)), _1584868), _1584870)))), 40990 ^ _779448 : [(40991 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584862, _1584862)), hAPP(hAPP(c_Product__Type_OPair(_1584862, _1584862), _1584864), 40989 ^ [_1584862, _1584864, _1584866, _1584868, _1584870])), c_Transitive__Closure_Ortrancl(_1584862, _1584868))))], (40994 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584862, _1584862)), hAPP(hAPP(c_Product__Type_OPair(_1584862, _1584862), 40989 ^ [_1584862, _1584864, _1584866, _1584868, _1584870]), 40992 ^ [_1584862, _1584864, _1584866, _1584868, _1584870])), _1584870)))], (40996 ^ _779448) ^ [] : [40989 ^ [_1584862, _1584864, _1584866, _1584868, _1584870] = 40992 ^ [_1584862, _1584864, _1584866, _1584868, _1584870]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584862, _1584862)), hAPP(hAPP(c_Product__Type_OPair(_1584862, _1584862), _1584864), _1584866)), c_Transitive__Closure_Ortrancl(_1584862, _1584868))))], (41000 ^ _779448) ^ [_1585421, _1585423, _1585425, _1585427, _1585429] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585421, _1585421)), hAPP(hAPP(c_Product__Type_OPair(_1585421, _1585421), _1585423), _1585425)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585421, _1585421), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585427)), _1585429))), 41004 ^ _779448 : [(41005 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585421, _1585421)), hAPP(hAPP(c_Product__Type_OPair(_1585421, _1585421), _1585423), 41003 ^ [_1585421, _1585423, _1585425, _1585427, _1585429])), _1585429)))], (41007 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585421, _1585421)), hAPP(hAPP(c_Product__Type_OPair(_1585421, _1585421), 41003 ^ [_1585421, _1585423, _1585425, _1585427, _1585429]), _1585425)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585421, _1585421), tc_HOL_Obool), _1585427), _1585429))))]]], (41009 ^ _779448) ^ [_1585729, _1585731, _1585733, _1585735, _1585737] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585729, _1585729)), hAPP(hAPP(c_Product__Type_OPair(_1585729, _1585729), _1585731), _1585733)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585729, _1585729), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1585735)), _1585737))), 41013 ^ _779448 : [(41014 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585729, _1585729)), hAPP(hAPP(c_Product__Type_OPair(_1585729, _1585729), _1585731), 41012 ^ [_1585729, _1585731, _1585733, _1585735, _1585737])), _1585737)))], (41016 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585729, _1585729)), hAPP(hAPP(c_Product__Type_OPair(_1585729, _1585729), 41012 ^ [_1585729, _1585731, _1585733, _1585735, _1585737]), _1585733)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585729, _1585729), tc_HOL_Obool), _1585735), _1585737))))]]], (41018 ^ _779448) ^ [_1586041, _1586043, _1586045, _1586047, _1586049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586041, _1586041)), hAPP(hAPP(c_Product__Type_OPair(_1586041, _1586041), _1586043), _1586045)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586041, _1586041), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1586047)), _1586049))), 41022 ^ _779448 : [(41023 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586041, _1586041)), hAPP(hAPP(c_Product__Type_OPair(_1586041, _1586041), _1586043), 41021 ^ [_1586041, _1586043, _1586045, _1586047, _1586049])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586041, _1586041), tc_HOL_Obool), _1586047), _1586049))))], (41025 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586041, _1586041)), hAPP(hAPP(c_Product__Type_OPair(_1586041, _1586041), 41021 ^ [_1586041, _1586043, _1586045, _1586047, _1586049]), _1586045)), _1586049)))]]], (41027 ^ _779448) ^ [_1586353, _1586355, _1586357, _1586359] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586353, _1586353)), hAPP(hAPP(c_Product__Type_OPair(_1586353, _1586353), _1586355), _1586357)), c_Transitive__Closure_Otrancl(_1586353, _1586359))), 41031 ^ _779448 : [(41032 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586353, _1586353)), hAPP(hAPP(c_Product__Type_OPair(_1586353, _1586353), _1586355), 41030 ^ [_1586353, _1586355, _1586357, _1586359])), _1586359)))], (41034 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586353, _1586353)), hAPP(hAPP(c_Product__Type_OPair(_1586353, _1586353), 41030 ^ [_1586353, _1586355, _1586357, _1586359]), _1586357)), c_Transitive__Closure_Ortrancl(_1586353, _1586359))))]]], (41036 ^ _779448) ^ [_1586613, _1586615, _1586617, _1586619] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586613, _1586613)), hAPP(hAPP(c_Product__Type_OPair(_1586613, _1586613), _1586615), _1586617)), c_Transitive__Closure_Otrancl(_1586613, _1586619))), 41040 ^ _779448 : [(41041 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586613, _1586613)), hAPP(hAPP(c_Product__Type_OPair(_1586613, _1586613), _1586615), 41039 ^ [_1586613, _1586615, _1586617, _1586619])), c_Transitive__Closure_Ortrancl(_1586613, _1586619))))], (41043 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586613, _1586613)), hAPP(hAPP(c_Product__Type_OPair(_1586613, _1586613), 41039 ^ [_1586613, _1586615, _1586617, _1586619]), _1586617)), _1586619)))]]], (41045 ^ _779448) ^ [_1586873, _1586875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586873, _1586873)), _1586875), c_Relation_OId(_1586873))), -(_1586875 = hAPP(hAPP(c_Product__Type_OPair(_1586873, _1586873), 41048 ^ [_1586873, _1586875]), 41048 ^ [_1586873, _1586875]))], (41052 ^ _779448) ^ [_1587015, _1587017, _1587019, _1587021] : [41054 ^ _779448 : [(41055 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1587015), 41053 ^ [_1587015, _1587017, _1587019, _1587021])))], (41057 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41053 ^ [_1587015, _1587017, _1587019, _1587021]), _1587017)))], (41059 ^ _779448) ^ [] : [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(_1587019, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41053 ^ [_1587015, _1587017, _1587019, _1587021]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1587019, 41053 ^ [_1587015, _1587017, _1587019, _1587021])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1587015), _1587017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1587019, _1587015)), _1587021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1587021), hAPP(_1587019, _1587017))), 41073 ^ _779448 : [(41074 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1587015), 41072 ^ [_1587015, _1587017, _1587019, _1587021])))], (41076 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41072 ^ [_1587015, _1587017, _1587019, _1587021]), _1587017)))], (41078 ^ _779448) ^ [] : [-(hAPP(_1587019, 41072 ^ [_1587015, _1587017, _1587019, _1587021]) = _1587021)]]], (41080 ^ _779448) ^ [_1587641, _1587643, _1587645] : [class_Divides_Osemiring__div(_1587641), -(_1587643 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1587641), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1587641), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1587641), _1587643), _1587645)), _1587645)), c_Divides_Odiv__class_Omod(_1587641, _1587643, _1587645)))], (41103 ^ _779448) ^ [_1588308, _1588310] : [-(c_Wellfounded_Owf(_1588308, _1588310)), 41106 ^ _779448 : [(41107 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588308), 41105 ^ [_1588308, _1588310]), 41104 ^ [_1588308, _1588310])))], (41109 ^ _779448) ^ [_1588528] : [hBOOL(hAPP(hAPP(c_member(_1588308), _1588528), 41104 ^ [_1588308, _1588310])), 41113 ^ _779448 : [(41114 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588308, _1588308)), hAPP(hAPP(c_Product__Type_OPair(_1588308, _1588308), 41112 ^ [_1588308, _1588310, _1588528]), _1588528)), _1588310)))], (41116 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588308), 41112 ^ [_1588308, _1588310, _1588528]), 41104 ^ [_1588308, _1588310])))]]]]], (41086 ^ _779448) ^ [_1587789, _1587791] : [c_Wellfounded_Owf(_1587789, _1587791), 41089 ^ _779448 : [(41090 ^ _779448) ^ [_1587921] : [41091 ^ _779448 : [(41092 ^ _779448) ^ [_1588026] : [hBOOL(hAPP(hAPP(c_member(_1587789), _1588026), _1587921))]], 41094 ^ _779448 : [(41095 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587789), 41093 ^ [_1587789, _1587791, _1587921]), _1587921)))], (41097 ^ _779448) ^ [_1588148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587789, _1587789)), hAPP(hAPP(c_Product__Type_OPair(_1587789, _1587789), _1588148), 41093 ^ [_1587789, _1587791, _1587921])), _1587791)), hBOOL(hAPP(hAPP(c_member(_1587789), _1588148), _1587921))]]]]], (41120 ^ _779448) ^ [_1588784, _1588786] : [-(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)))), _1588784)) = 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)))), _1588786))), 41122 ^ _779448 : [(41123 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41121 ^ [_1588784, _1588786])))], (41125 ^ _779448) ^ [] : [41126 ^ _779448 : [(41127 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1588784, 41121 ^ [_1588784, _1588786])))], (41129 ^ _779448) ^ [] : [hBOOL(hAPP(_1588786, 41121 ^ [_1588784, _1588786]))]], 41130 ^ _779448 : [(41131 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1588786, 41121 ^ [_1588784, _1588786])))], (41133 ^ _779448) ^ [] : [hBOOL(hAPP(_1588784, 41121 ^ [_1588784, _1588786]))]]]]], (41137 ^ _779448) ^ [_1589105, _1589107, _1589109, _1589111, _1589113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589105, tc_HOL_Obool)), _1589107), _1589109)), 41143 ^ _779448 : [(41144 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589105), 41142 ^ [_1589105, _1589107, _1589109, _1589111, _1589113]), _1589107)))], (41146 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1589111, 41142 ^ [_1589105, _1589107, _1589109, _1589111, _1589113])))], (41148 ^ _779448) ^ [] : [hBOOL(hAPP(_1589113, 41142 ^ [_1589105, _1589107, _1589109, _1589111, _1589113]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1589105, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589105, tc_HOL_Obool)), _1589107), hAPP(c_Set_OCollect(_1589105), _1589111))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1589105, tc_HOL_Obool)), _1589109), hAPP(c_Set_OCollect(_1589105), _1589113)))))], (41152 ^ _779448) ^ [_1589505, _1589507, _1589509] : [hBOOL(hAPP(hAPP(c_member(_1589505), _1589507), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1589505, tc_HOL_Obool), _1589509))), 41156 ^ _779448 : [(41157 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589505), _1589507), 41155 ^ [_1589505, _1589507, _1589509])))], (41159 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1589505, tc_HOL_Obool)), 41155 ^ [_1589505, _1589507, _1589509]), _1589509)))]]], (41161 ^ _779448) ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589697, _1589699)), _1589701), hAPP(hAPP(c_Relation_Orel__comp(_1589697, _1589703, _1589699), _1589705), _1589707))), 41167 ^ _779448 : [(41168 ^ _779448) ^ [] : [-(_1589701 = hAPP(hAPP(c_Product__Type_OPair(_1589697, _1589699), 41164 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707]), 41166 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707]))], (41170 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589697, _1589703)), hAPP(hAPP(c_Product__Type_OPair(_1589697, _1589703), 41164 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707]), 41165 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707])), _1589705)))], (41172 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589703, _1589699)), hAPP(hAPP(c_Product__Type_OPair(_1589703, _1589699), 41165 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707]), 41166 ^ [_1589697, _1589699, _1589701, _1589703, _1589705, _1589707])), _1589707)))]]], (41174 ^ _779448) ^ [_1590075, _1590077, _1590079, _1590081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590075, _1590077)), _1590079), hAPP(c_Relation_Oconverse(_1590077, _1590075), _1590081))), 41179 ^ _779448 : [(41180 ^ _779448) ^ [] : [-(_1590079 = hAPP(hAPP(c_Product__Type_OPair(_1590075, _1590077), 41178 ^ [_1590075, _1590077, _1590079, _1590081]), 41177 ^ [_1590075, _1590077, _1590079, _1590081]))], (41182 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590077, _1590075)), hAPP(hAPP(c_Product__Type_OPair(_1590077, _1590075), 41177 ^ [_1590075, _1590077, _1590079, _1590081]), 41178 ^ [_1590075, _1590077, _1590079, _1590081])), _1590081)))]]], (41184 ^ _779448) ^ [_1590328, _1590330, _1590332] : [-(c_Nitpick_Oplus__frac(_1590328, _1590330, _1590332) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1590328), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1590328), _1590330), hAPP(c_Nitpick_Odenom(_1590328), _1590332))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1590328), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1590328), tc_Int_Oint), c_Nitpick_Ofrac(_1590328)), 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(_1590328), _1590330))), 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(_1590328), _1590330))))), 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(_1590328), _1590332))), 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(_1590328), _1590332)))))), c_COMBI(tc_Int_Oint))))], (41186 ^ _779448) ^ [_1590459, _1590461, _1590463, _1590465] : [class_Rings_Olinordered__semidom(_1590459), 41192 ^ _779448 : [(41193 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590461), 41191 ^ [_1590459, _1590461, _1590463, _1590465]), _1590463)))], (41195 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590459), c_Groups_Ozero__class_Ozero(_1590459)), hAPP(_1590465, 41191 ^ [_1590459, _1590461, _1590463, _1590465])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590459), c_Groups_Ozero__class_Ozero(_1590459)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1590461, _1590459), _1590465), _1590463))))], (41199 ^ _779448) ^ [_1590755, _1590757, _1590759] : [-(c_Nitpick_Otimes__frac(_1590755, _1590757, _1590759) = hAPP(hAPP(c_Nitpick_Ofrac(_1590755), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590755), _1590757)), hAPP(c_Nitpick_Onum(_1590755), _1590759))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1590755), _1590757)), hAPP(c_Nitpick_Odenom(_1590755), _1590759))))], (41201 ^ _779448) ^ [_1590826, _1590828, _1590830] : [-(c_Nitpick_Oof__frac(_1590828, _1590826, _1590830) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1590826), hAPP(c_Int_Oring__1__class_Oof__int(_1590826), hAPP(c_Nitpick_Onum(_1590828), _1590830))), hAPP(c_Int_Oring__1__class_Oof__int(_1590826), hAPP(c_Nitpick_Odenom(_1590828), _1590830)))), class_Rings_Oinverse(_1590826), class_Rings_Oring__1(_1590826)], (41211 ^ _779448) ^ [_1591019, _1591021] : [-(c_Nitpick_Oinverse__frac(_1591019, _1591021) = hAPP(hAPP(c_Nitpick_Ofrac(_1591019), hAPP(c_Nitpick_Odenom(_1591019), _1591021)), hAPP(c_Nitpick_Onum(_1591019), _1591021)))], (41213 ^ _779448) ^ [_1591065, _1591067] : [-(c_Nitpick_Ouminus__frac(_1591065, _1591067) = c_Nitpick_OAbs__Frac(_1591065, 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(_1591065), _1591067))), hAPP(c_Nitpick_Odenom(_1591065), _1591067))))], (41215 ^ _779448) ^ [_1591133, _1591135, _1591137] : [c_Nitpick_Oless__frac(_1591133, _1591135, _1591137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591133), c_Nitpick_Oplus__frac(_1591133, _1591135, c_Nitpick_Ouminus__frac(_1591133, _1591137)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41221 ^ _779448) ^ [_1591244, _1591246, _1591248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591244), c_Nitpick_Oplus__frac(_1591244, _1591246, c_Nitpick_Ouminus__frac(_1591244, _1591248)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1591244, _1591246, _1591248))], (41227 ^ _779448) ^ [_1591379, _1591381, _1591383] : [c_Nitpick_Oless__eq__frac(_1591379, _1591381, _1591383), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591379), c_Nitpick_Oplus__frac(_1591379, _1591381, c_Nitpick_Ouminus__frac(_1591379, _1591383)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41233 ^ _779448) ^ [_1591490, _1591492, _1591494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591490), c_Nitpick_Oplus__frac(_1591490, _1591492, c_Nitpick_Ouminus__frac(_1591490, _1591494)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1591490, _1591492, _1591494))], (41239 ^ _779448) ^ [_1591607] : [-(c_Nitpick_Odenom(_1591607) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591607, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591607)))], (41241 ^ _779448) ^ [_1591642] : [-(c_Nitpick_Onum(_1591642) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591642, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591642)))], (41243 ^ _779448) ^ [_1591677, _1591679, _1591681] : [-(c_Product__Type_Ointernal__split(_1591677, _1591679, _1591681) = c_Product__Type_Oprod_Oprod__case(_1591677, _1591679, _1591681))], (41245 ^ _779448) ^ [_1591712, _1591714, _1591716, _1591718] : [class_Rings_Olinordered__semidom(_1591712), 41251 ^ _779448 : [(41252 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591714), 41250 ^ [_1591712, _1591714, _1591716, _1591718]), _1591716)))], (41254 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591712), c_Groups_Ozero__class_Ozero(_1591712)), hAPP(_1591718, 41250 ^ [_1591712, _1591714, _1591716, _1591718])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591712), c_Groups_Ozero__class_Ozero(_1591712)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1591714, _1591712), _1591718), _1591716))))], (41258 ^ _779448) ^ [_1592008, _1592010, _1592012, _1592014, _1592016, _1592018] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1592008, _1592010, _1592012), _1592014), hAPP(hAPP(c_Product__Type_OPair(_1592008, _1592010), _1592016), _1592018)) = hAPP(hAPP(_1592014, _1592016), _1592018))], (41260 ^ _779448) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41262 ^ _779448) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41264 ^ _779448) ^ [_1592102, _1592104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41265 ^ [_1592102, _1592104]), hAPP(_1592102, 41265 ^ [_1592102, _1592104]))), -(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)), _1592102)), _1592104)))))], (41271 ^ _779448) ^ [_1592262, _1592264] : [-(c_List_Olenlex(_1592262, _1592264) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1592262)), tc_List_Olist(_1592262)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1592262), c_Wellfounded_Oless__than, c_List_Olex(_1592262, _1592264))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592262), tc_List_Olist(_1592262), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592262))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1592262), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592262))), tc_List_Olist(_1592262)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1592262))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592262)))), c_COMBI(tc_List_Olist(_1592262)))))], (41273 ^ _779448) ^ [_1592370, _1592372, _1592374, _1592376, _1592378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592370), tc_List_Olist(_1592370))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592370), tc_List_Olist(_1592370)), _1592372), _1592374)), hAPP(c_List_Olexn(_1592370, _1592376), _1592378))), 41276 ^ _779448 : [(41277 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592370)), _1592372) = _1592378)], (41279 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592370)), _1592374) = _1592378)]]], (41281 ^ _779448) ^ [_1592572, _1592574, _1592576] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592572)), _1592574) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592572)), _1592576)), _1592574 = _1592576], (41287 ^ _779448) ^ [_1592664, _1592666] : [-(c_List_Olenlex(_1592664, _1592666) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1592664), tc_List_Olist(_1592664), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592664), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), tc_List_Olist(_1592664)), c_COMBS(tc_List_Olist(_1592664), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592664)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592664)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592664), tc_fun(tc_List_Olist(_1592664), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592664), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), tc_List_Olist(_1592664)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592664))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592664)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1592664))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592664)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592664), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), tc_List_Olist(_1592664)), c_COMBS(tc_List_Olist(_1592664), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592664)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592664)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592664), tc_fun(tc_List_Olist(_1592664), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592664), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), tc_List_Olist(_1592664)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592664))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592664)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1592664))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592664)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592664), tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592664), tc_HOL_Obool)), tc_List_Olist(_1592664)), c_COMBC(tc_List_Olist(_1592664), tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592664), tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664))), tc_fun(tc_List_Olist(_1592664), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1592664)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1592664)), c_member(tc_prod(tc_List_Olist(_1592664), tc_List_Olist(_1592664))))), c_Product__Type_OPair(tc_List_Olist(_1592664), tc_List_Olist(_1592664))))), c_List_Olex(_1592664, _1592666)))))))], (41289 ^ _779448) ^ [_1593220, _1593222, _1593224] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593220)), c_List_Osublist(_1593220, _1593222, _1593224)) = 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(_1593220)), _1593222)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1593224)))))], (41291 ^ _779448) ^ [_1593286, _1593288, _1593290] : [-(hAPP(c_List_Olexn(_1593286, _1593288), hAPP(c_Nat_OSuc, _1593290)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1593286), tc_List_Olist(_1593286)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1593286, tc_List_Olist(_1593286)), tc_prod(_1593286, tc_List_Olist(_1593286))), tc_prod(tc_List_Olist(_1593286), tc_List_Olist(_1593286)), c_Product__Type_Omap__pair(tc_prod(_1593286, tc_List_Olist(_1593286)), tc_List_Olist(_1593286), tc_prod(_1593286, tc_List_Olist(_1593286)), tc_List_Olist(_1593286), hAPP(c_Product__Type_Oprod_Oprod__case(_1593286, tc_List_Olist(_1593286), tc_List_Olist(_1593286)), c_List_Olist_OCons(_1593286)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593286, tc_List_Olist(_1593286), tc_List_Olist(_1593286)), c_List_Olist_OCons(_1593286)))), c_Wellfounded_Olex__prod(_1593286, tc_List_Olist(_1593286), _1593288, hAPP(c_List_Olexn(_1593286, _1593288), _1593290)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593286), tc_List_Olist(_1593286))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593286), tc_List_Olist(_1593286), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593286), tc_fun(tc_List_Olist(_1593286), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593286), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593286), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593286), tc_HOL_Obool)), tc_List_Olist(_1593286)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1593286))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593286)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593286), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593286)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593286)))), hAPP(c_Nat_OSuc, _1593290))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593286), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593286)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593286)))), hAPP(c_Nat_OSuc, _1593290)))))))], (41293 ^ _779448) ^ [_1593577, _1593579, _1593581, _1593583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593577)), _1593579)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593577)), _1593581))), _1593579 = hAPP(hAPP(c_List_Olist_OCons(_1593577), _1593583), _1593581)], (41299 ^ _779448) ^ [_1593728, _1593730, _1593732] : [_1593728 = hAPP(hAPP(c_List_Olist_OCons(_1593730), _1593732), _1593728)], (41301 ^ _779448) ^ [_1593778, _1593780, _1593782] : [hAPP(hAPP(c_List_Olist_OCons(_1593778), _1593780), _1593782) = _1593782], (41303 ^ _779448) ^ [_1593837, _1593839, _1593841, _1593843, _1593845] : [hAPP(hAPP(c_List_Olist_OCons(_1593837), _1593839), _1593841) = hAPP(hAPP(c_List_Olist_OCons(_1593837), _1593843), _1593845), 41306 ^ _779448 : [(41307 ^ _779448) ^ [] : [-(_1593839 = _1593843)], (41309 ^ _779448) ^ [] : [-(_1593841 = _1593845)]]], (41311 ^ _779448) ^ [_1593974, _1593976, _1593978, _1593980, _1593982] : [-(hAPP(hAPP(c_List_Olist_OCons(_1593974), _1593976), _1593978) = hAPP(hAPP(c_List_Olist_OCons(_1593974), _1593980), _1593982)), _1593976 = _1593980, _1593978 = _1593982], (41321 ^ _779448) ^ [_1594149, _1594151, _1594153] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594149)), hAPP(hAPP(c_List_Olist_OCons(_1594149), _1594151), _1594153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594149)), _1594153)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41323 ^ _779448) ^ [_1594231, _1594233, _1594235, _1594237, _1594239, _1594241] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594231), tc_List_Olist(_1594231))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594231), tc_List_Olist(_1594231)), hAPP(hAPP(c_List_Olist_OCons(_1594231), _1594233), _1594235)), hAPP(hAPP(c_List_Olist_OCons(_1594231), _1594237), _1594239))), c_List_Olex(_1594231, _1594241))), 41328 ^ _779448 : [(41329 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594231, _1594231)), hAPP(hAPP(c_Product__Type_OPair(_1594231, _1594231), _1594233), _1594237)), _1594241)))], (41331 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594231)), _1594235) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594231)), _1594239))]], 41332 ^ _779448 : [(41333 ^ _779448) ^ [] : [-(_1594233 = _1594237)], (41335 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594231), tc_List_Olist(_1594231))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594231), tc_List_Olist(_1594231)), _1594235), _1594239)), c_List_Olex(_1594231, _1594241))))]]], (41337 ^ _779448) ^ [_1594629, _1594631, _1594633, _1594635, _1594637, _1594639] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594629), tc_List_Olist(_1594629))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594629), tc_List_Olist(_1594629)), hAPP(hAPP(c_List_Olist_OCons(_1594629), _1594631), _1594633)), hAPP(hAPP(c_List_Olist_OCons(_1594629), _1594635), _1594637))), c_List_Olex(_1594629, _1594639)))), 41338 ^ _779448 : [(41339 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594629, _1594629)), hAPP(hAPP(c_Product__Type_OPair(_1594629, _1594629), _1594631), _1594635)), _1594639)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594629)), _1594633) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594629)), _1594637)], (41345 ^ _779448) ^ [] : [_1594631 = _1594635, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594629), tc_List_Olist(_1594629))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594629), tc_List_Olist(_1594629)), _1594633), _1594637)), c_List_Olex(_1594629, _1594639)))]]], (41353 ^ _779448) ^ [_1595085, _1595087, _1595089] : [-(c_List_Oset__Cons(_1595085, _1595087, _1595089) = hAPP(c_Set_OCollect(tc_List_Olist(_1595085)), hAPP(hAPP(c_COMBB(tc_fun(_1595085, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1595085)), c_HOL_OEx(_1595085)), hAPP(hAPP(c_COMBB(tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_fun(_1595085, tc_HOL_Obool), tc_List_Olist(_1595085)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_HOL_Obool, _1595085), c_HOL_OEx(tc_List_Olist(_1595085)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595085), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595085, tc_fun(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), tc_fun(tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), tc_List_Olist(_1595085)), c_COMBS(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1595085, tc_fun(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), tc_List_Olist(_1595085)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595085), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), _1595085), c_COMBS(tc_List_Olist(_1595085), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1595085)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1595085), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1595085)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595085), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_List_Olist(_1595085))), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1595085), tc_List_Olist(_1595085)), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_fun(tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_List_Olist(_1595085))), tc_fun(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool))), tc_List_Olist(_1595085)), c_COMBB(tc_fun(tc_List_Olist(_1595085), tc_List_Olist(_1595085)), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), _1595085)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595085), tc_List_Olist(_1595085)), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), tc_List_Olist(_1595085)), c_COMBB(tc_List_Olist(_1595085), tc_HOL_Obool, tc_List_Olist(_1595085))), c_fequal))), c_List_Olist_OCons(_1595085)))))), hAPP(hAPP(c_COMBC(_1595085, tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool)), _1595085), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1595085))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595085), c_fconj), hAPP(hAPP(c_COMBC(_1595085, tc_fun(_1595085, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595085)), _1595087)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595085), tc_fun(tc_List_Olist(_1595085), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1595085))), _1595089)))))))], (41355 ^ _779448) ^ [_1595635, _1595637, _1595639, _1595641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595635), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595637), _1595639))), -(hAPP(c_Random_Opick(_1595637, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595637)), _1595639), _1595641)), _1595635) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1595637), _1595639))], (41361 ^ _779448) ^ [_1595778, _1595780, _1595782, _1595784] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595778), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595780), _1595782)))), -(hAPP(c_Random_Opick(_1595780, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595780)), _1595782), _1595784)), _1595778) = hAPP(c_Random_Opick(_1595780, _1595784), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1595778), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595780), _1595782))))], (41367 ^ _779448) ^ [_1595866, _1595868, _1595870] : [-(c_Random_Oselect__weight(_1595866, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595866)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1595866), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1595868)), _1595870)) = c_Random_Oselect__weight(_1595866, _1595870))], (41369 ^ _779448) ^ [_1595946, _1595948, _1595950, _1595952, _1595954, _1595956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595946), tc_List_Olist(_1595946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595946), tc_List_Olist(_1595946)), hAPP(hAPP(c_List_Olist_OCons(_1595946), _1595948), _1595950)), hAPP(hAPP(c_List_Olist_OCons(_1595946), _1595952), _1595954))), c_List_Olexord(_1595946, _1595956))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595946, _1595946)), hAPP(hAPP(c_Product__Type_OPair(_1595946, _1595946), _1595948), _1595952)), _1595956))), 41376 ^ _779448 : [(41377 ^ _779448) ^ [] : [-(_1595948 = _1595952)], (41379 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595946), tc_List_Olist(_1595946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595946), tc_List_Olist(_1595946)), _1595950), _1595954)), c_List_Olexord(_1595946, _1595956))))]]], (41381 ^ _779448) ^ [_1596273, _1596275, _1596277, _1596279, _1596281, _1596283] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596273), tc_List_Olist(_1596273))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596273), tc_List_Olist(_1596273)), hAPP(hAPP(c_List_Olist_OCons(_1596273), _1596275), _1596277)), hAPP(hAPP(c_List_Olist_OCons(_1596273), _1596279), _1596281))), c_List_Olexord(_1596273, _1596283)))), 41382 ^ _779448 : [(41383 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596273, _1596273)), hAPP(hAPP(c_Product__Type_OPair(_1596273, _1596273), _1596275), _1596279)), _1596283))], (41385 ^ _779448) ^ [] : [_1596275 = _1596279, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596273), tc_List_Olist(_1596273))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596273), tc_List_Olist(_1596273)), _1596277), _1596281)), c_List_Olexord(_1596273, _1596283)))]]], (41393 ^ _779448) ^ [_1596667, _1596669, _1596671, _1596673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596667), tc_List_Olist(_1596667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596667), tc_List_Olist(_1596667)), _1596669), _1596671)), c_List_Olex(_1596667, _1596673))), 41396 ^ _779448 : [(41397 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596667), tc_List_Olist(_1596667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596667), tc_List_Olist(_1596667)), _1596669), _1596671)), c_List_Olexord(_1596667, _1596673))))], (41399 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596667)), _1596669) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596667)), _1596671))]]], (41401 ^ _779448) ^ [_1596918, _1596920, _1596922, _1596924] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596918), tc_List_Olist(_1596918))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596918), tc_List_Olist(_1596918)), _1596920), _1596922)), c_List_Olex(_1596918, _1596924)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596918), tc_List_Olist(_1596918))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596918), tc_List_Olist(_1596918)), _1596920), _1596922)), c_List_Olexord(_1596918, _1596924))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596918)), _1596920) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596918)), _1596922)], (41411 ^ _779448) ^ [_1597205, _1597207, _1597209, _1597211, _1597213, _1597215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597205, _1597205)), hAPP(hAPP(c_Product__Type_OPair(_1597205, _1597205), _1597207), _1597209)), c_Transitive__Closure_Ortrancl(_1597205, _1597211))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597205), tc_List_Olist(_1597205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597205), tc_List_Olist(_1597205)), _1597213), _1597215)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597205), c_List_Olistrel1(_1597205, _1597211)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597205), tc_List_Olist(_1597205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597205), tc_List_Olist(_1597205)), hAPP(hAPP(c_List_Olist_OCons(_1597205), _1597207), _1597213)), hAPP(hAPP(c_List_Olist_OCons(_1597205), _1597209), _1597215))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597205), c_List_Olistrel1(_1597205, _1597211)))))], (41421 ^ _779448) ^ [_1597566, _1597568, _1597570, _1597572] : [-(c_List_Olist_Olist__size(_1597566, _1597568, hAPP(hAPP(c_List_Olist_OCons(_1597566), _1597570), _1597572)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1597568, _1597570)), c_List_Olist_Olist__size(_1597566, _1597568, _1597572))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41423 ^ _779448) ^ [_1597626, _1597628, _1597630, _1597632] : [hBOOL(hAPP(hAPP(c_member(_1597626), _1597628), c_Wellfounded_Oacc(_1597626, _1597630))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597626)), _1597632), c_Wellfounded_Oacc(tc_List_Olist(_1597626), c_List_Olistrel1(_1597626, _1597630)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597626)), hAPP(hAPP(c_List_Olist_OCons(_1597626), _1597628), _1597632)), c_Wellfounded_Oacc(tc_List_Olist(_1597626), c_List_Olistrel1(_1597626, _1597630)))))], (41433 ^ _779448) ^ [_1597867, _1597869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1597867), tc_List_Olist(_1597867)), tc_HOL_Obool)), c_List_Olistrel1(_1597867, c_Transitive__Closure_Ortrancl(_1597867, _1597869))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597867), c_List_Olistrel1(_1597867, _1597869)))))], (41435 ^ _779448) ^ [_1597923, _1597925, _1597927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597923, _1597923), tc_HOL_Obool)), _1597925), _1597927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1597923), tc_List_Olist(_1597923)), tc_HOL_Obool)), c_List_Olistrel1(_1597923, _1597925)), c_List_Olistrel1(_1597923, _1597927))))], (41441 ^ _779448) ^ [_1598074, _1598076] : [-(c_List_Olistrel1(_1598074, hAPP(c_Relation_Oconverse(_1598074, _1598074), _1598076)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1598074), tc_List_Olist(_1598074)), c_List_Olistrel1(_1598074, _1598076)))], (41443 ^ _779448) ^ [_1598121, _1598123, _1598125, _1598127, _1598129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598121), tc_List_Olist(_1598121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598121), tc_List_Olist(_1598121)), _1598123), _1598125)), c_List_Olistrel1(_1598121, _1598127))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598121), tc_List_Olist(_1598121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598121), tc_List_Olist(_1598121)), hAPP(hAPP(c_List_Olist_OCons(_1598121), _1598129), _1598123)), hAPP(hAPP(c_List_Olist_OCons(_1598121), _1598129), _1598125))), c_List_Olistrel1(_1598121, _1598127))))], (41449 ^ _779448) ^ [_1598356, _1598358, _1598360, _1598362, _1598364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598356), tc_List_Olist(_1598356))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598356), tc_List_Olist(_1598356)), _1598358), _1598360)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598356), c_List_Olistrel1(_1598356, _1598362)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598356), tc_List_Olist(_1598356))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598356), tc_List_Olist(_1598356)), hAPP(hAPP(c_List_Olist_OCons(_1598356), _1598364), _1598358)), hAPP(hAPP(c_List_Olist_OCons(_1598356), _1598364), _1598360))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598356), c_List_Olistrel1(_1598356, _1598362)))))], (41455 ^ _779448) ^ [_1598611, _1598613, _1598615, _1598617] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598611), tc_List_Olist(_1598611))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598611), tc_List_Olist(_1598611)), _1598613), _1598615)), c_List_Olistrel1(_1598611, _1598617))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598611)), _1598613) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598611)), _1598615))], (41461 ^ _779448) ^ [_1598780, _1598782, _1598784, _1598786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598780), tc_List_Olist(_1598780))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598780), tc_List_Olist(_1598780)), _1598782), _1598784)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598780), c_List_Olistrel1(_1598780, _1598786)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598780)), _1598782) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598780)), _1598784))], (41467 ^ _779448) ^ [_1598980, _1598982, _1598984, _1598986] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598980), tc_List_Olist(_1598980))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598980), tc_List_Olist(_1598980)), _1598982), _1598984)), c_List_Olistrel1(_1598980, hAPP(c_Relation_Oconverse(_1598980, _1598980), _1598986)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598980), tc_List_Olist(_1598980))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598980), tc_List_Olist(_1598980)), _1598982), _1598984)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1598980), tc_List_Olist(_1598980)), c_List_Olistrel1(_1598980, _1598986)))))], (41473 ^ _779448) ^ [_1599209, _1599211, _1599213, _1599215] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599209), tc_List_Olist(_1599209))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599209), tc_List_Olist(_1599209)), _1599211), _1599213)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599209), tc_List_Olist(_1599209)), c_List_Olistrel1(_1599209, _1599215)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599209), tc_List_Olist(_1599209))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599209), tc_List_Olist(_1599209)), _1599211), _1599213)), c_List_Olistrel1(_1599209, hAPP(c_Relation_Oconverse(_1599209, _1599209), _1599215)))))], (41479 ^ _779448) ^ [_1599471, _1599473, _1599475, _1599477, _1599479, _1599481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599471), tc_List_Olist(_1599471))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599471), tc_List_Olist(_1599471)), hAPP(hAPP(c_List_Olist_OCons(_1599471), _1599473), _1599475)), hAPP(hAPP(c_List_Olist_OCons(_1599471), _1599477), _1599479))), c_List_Olistrel1(_1599471, _1599481))), 41484 ^ _779448 : [(41485 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599471, _1599471)), hAPP(hAPP(c_Product__Type_OPair(_1599471, _1599471), _1599473), _1599477)), _1599481)))], (41487 ^ _779448) ^ [] : [-(_1599475 = _1599479)]], 41488 ^ _779448 : [(41489 ^ _779448) ^ [] : [-(_1599473 = _1599477)], (41491 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599471), tc_List_Olist(_1599471))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599471), tc_List_Olist(_1599471)), _1599475), _1599479)), c_List_Olistrel1(_1599471, _1599481))))]]], (41493 ^ _779448) ^ [_1599841, _1599843, _1599845, _1599847, _1599849, _1599851] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599841), tc_List_Olist(_1599841))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599841), tc_List_Olist(_1599841)), hAPP(hAPP(c_List_Olist_OCons(_1599841), _1599843), _1599845)), hAPP(hAPP(c_List_Olist_OCons(_1599841), _1599847), _1599849))), c_List_Olistrel1(_1599841, _1599851)))), 41494 ^ _779448 : [(41495 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599841, _1599841)), hAPP(hAPP(c_Product__Type_OPair(_1599841, _1599841), _1599843), _1599847)), _1599851)), _1599845 = _1599849], (41501 ^ _779448) ^ [] : [_1599843 = _1599847, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599841), tc_List_Olist(_1599841))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599841), tc_List_Olist(_1599841)), _1599845), _1599849)), c_List_Olistrel1(_1599841, _1599851)))]]], (41509 ^ _779448) ^ [_1600269, _1600271, _1600273, _1600275, _1600277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600269, _1600269)), hAPP(hAPP(c_Product__Type_OPair(_1600269, _1600269), _1600271), _1600273)), _1600275)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600269), tc_List_Olist(_1600269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600269), tc_List_Olist(_1600269)), hAPP(hAPP(c_List_Olist_OCons(_1600269), _1600271), _1600277)), hAPP(hAPP(c_List_Olist_OCons(_1600269), _1600273), _1600277))), c_List_Olistrel1(_1600269, _1600275))))], (41515 ^ _779448) ^ [_1600482, _1600484, _1600486, _1600488] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1600482), tc_List_Olist(_1600482), c_List_Olistrel(_1600482, _1600484)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600482)), hAPP(hAPP(c_List_Olist_OCons(_1600482), _1600486), _1600488)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600482), tc_HOL_Obool)))) = c_List_Oset__Cons(_1600482, hAPP(c_Relation_OImage(_1600482, _1600482, _1600484), hAPP(hAPP(c_Set_Oinsert(_1600482), _1600486), c_Orderings_Obot__class_Obot(tc_fun(_1600482, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1600482), tc_List_Olist(_1600482), c_List_Olistrel(_1600482, _1600484)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600482)), _1600488), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600482), tc_HOL_Obool))))))], (41517 ^ _779448) ^ [_1600605, _1600607, _1600609, _1600611] : [41520 ^ _779448 : [(41521 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600605, _1600605)), hAPP(hAPP(c_Product__Type_OPair(_1600605, _1600605), 41518 ^ [_1600605, _1600607, _1600609, _1600611]), 41519 ^ [_1600605, _1600607, _1600609, _1600611])), _1600607))], (41523 ^ _779448) ^ [] : [41518 ^ [_1600605, _1600607, _1600609, _1600611] = 41519 ^ [_1600605, _1600607, _1600609, _1600611]], (41525 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600605, _1600605)), hAPP(hAPP(c_Product__Type_OPair(_1600605, _1600605), 41519 ^ [_1600605, _1600607, _1600609, _1600611]), 41518 ^ [_1600605, _1600607, _1600609, _1600611])), _1600607))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600605), tc_List_Olist(_1600605))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600605), tc_List_Olist(_1600605)), _1600609), _1600611)), c_List_Olexord(_1600605, _1600607)))), -(_1600609 = _1600611), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600605), tc_List_Olist(_1600605))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600605), tc_List_Olist(_1600605)), _1600611), _1600609)), c_List_Olexord(_1600605, _1600607))))], (41537 ^ _779448) ^ [_1601152, _1601154, _1601156] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601152), tc_List_Olist(_1601152))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601152), tc_List_Olist(_1601152)), _1601154), _1601154)), c_List_Olistrel(_1601152, c_Transitive__Closure_Ortrancl(_1601152, _1601156)))))], (41539 ^ _779448) ^ [_1601212, _1601214, _1601216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601212, _1601212), tc_HOL_Obool)), _1601214), _1601216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601212), tc_List_Olist(_1601212)), tc_HOL_Obool)), c_List_Olistrel(_1601212, _1601214)), c_List_Olistrel(_1601212, _1601216))))], (41545 ^ _779448) ^ [_1601363, _1601365] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601363), tc_List_Olist(_1601363)), tc_HOL_Obool)), c_List_Olistrel(_1601363, _1601365)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601363), c_List_Olistrel1(_1601363, _1601365)))))], (41547 ^ _779448) ^ [_1601416, _1601418, _1601420, _1601422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601416), tc_List_Olist(_1601416))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601416), tc_List_Olist(_1601416)), _1601418), _1601420)), c_List_Olistrel(_1601416, _1601422))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601416)), _1601418) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601416)), _1601420))], (41553 ^ _779448) ^ [_1601585, _1601587, _1601589, _1601591, _1601593] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601585), tc_List_Olist(_1601585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601585), tc_List_Olist(_1601585)), _1601587), _1601589)), c_List_Olistrel(_1601585, c_Transitive__Closure_Ortrancl(_1601585, _1601591)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601585), tc_List_Olist(_1601585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601585), tc_List_Olist(_1601585)), _1601589), _1601593)), c_List_Olistrel(_1601585, c_Transitive__Closure_Ortrancl(_1601585, _1601591)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601585), tc_List_Olist(_1601585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601585), tc_List_Olist(_1601585)), _1601587), _1601593)), c_List_Olistrel(_1601585, c_Transitive__Closure_Ortrancl(_1601585, _1601591)))))], (41563 ^ _779448) ^ [_1601924, _1601926] : [-(c_List_Olistrel(_1601924, c_Transitive__Closure_Ortrancl(_1601924, _1601926)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601924), c_List_Olistrel1(_1601924, _1601926)))], (41565 ^ _779448) ^ [_1601963, _1601965, _1601967, _1601969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601963), tc_List_Olist(_1601963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601963), tc_List_Olist(_1601963)), _1601965), _1601967)), c_List_Olistrel1(_1601963, _1601969))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601963), tc_List_Olist(_1601963))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601963), tc_List_Olist(_1601963)), _1601965), _1601967)), c_List_Olistrel(_1601963, c_Transitive__Closure_Ortrancl(_1601963, _1601969)))))], (41571 ^ _779448) ^ [_1602170, _1602172, _1602174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602170, _1602170), tc_HOL_Obool)), _1602172), _1602174)), c_Relation_Orefl__on(_1602170, c_Orderings_Otop__class_Otop(tc_fun(_1602170, tc_HOL_Obool)), _1602174), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602170), tc_List_Olist(_1602170)), tc_HOL_Obool)), c_List_Olistrel1(_1602170, _1602172)), c_List_Olistrel(_1602170, _1602174))))], (41581 ^ _779448) ^ [_1602387, _1602389, _1602391, _1602393] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602387), tc_List_Olist(_1602387))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602387), tc_List_Olist(_1602387)), _1602389), _1602391)), c_List_Olistrel(_1602387, _1602393))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602387), tc_List_Olist(_1602387))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602387), tc_List_Olist(_1602387)), _1602389), _1602391)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602387), c_List_Olistrel1(_1602387, _1602393)))))], (41587 ^ _779448) ^ [_1602598, _1602600, _1602602, _1602604, _1602606, _1602608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602598, _1602598)), hAPP(hAPP(c_Product__Type_OPair(_1602598, _1602598), _1602600), _1602602)), _1602604)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602598), tc_List_Olist(_1602598))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602598), tc_List_Olist(_1602598)), _1602606), _1602608)), c_List_Olistrel(_1602598, _1602604))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602598), tc_List_Olist(_1602598))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602598), tc_List_Olist(_1602598)), hAPP(hAPP(c_List_Olist_OCons(_1602598), _1602600), _1602606)), hAPP(hAPP(c_List_Olist_OCons(_1602598), _1602602), _1602608))), c_List_Olistrel(_1602598, _1602604))))], (41597 ^ _779448) ^ [_1602954, _1602956, _1602958, _1602960] : [c_List_Olistrelp(_1602954, hAPP(hAPP(c_COMBC(_1602954, tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_fun(_1602954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602954, tc_fun(tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_fun(_1602954, tc_HOL_Obool)), _1602954), c_COMBC(_1602954, tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602954, tc_prod(_1602954, _1602954)), tc_fun(_1602954, tc_fun(tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_HOL_Obool)), _1602954), hAPP(c_COMBB(tc_prod(_1602954, _1602954), tc_fun(tc_fun(tc_prod(_1602954, _1602954), tc_HOL_Obool), tc_HOL_Obool), _1602954), c_member(tc_prod(_1602954, _1602954)))), c_Product__Type_OPair(_1602954, _1602954)))), _1602956), _1602958, _1602960), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602954), tc_List_Olist(_1602954))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602954), tc_List_Olist(_1602954)), _1602958), _1602960)), c_List_Olistrel(_1602954, _1602956))))], (41603 ^ _779448) ^ [_1603331, _1603333, _1603335, _1603337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603331), tc_List_Olist(_1603331))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603331), tc_List_Olist(_1603331)), _1603335), _1603337)), c_List_Olistrel(_1603331, _1603333))), -(c_List_Olistrelp(_1603331, hAPP(hAPP(c_COMBC(_1603331, tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_fun(_1603331, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603331, tc_fun(tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_fun(_1603331, tc_HOL_Obool)), _1603331), c_COMBC(_1603331, tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603331, tc_prod(_1603331, _1603331)), tc_fun(_1603331, tc_fun(tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_HOL_Obool)), _1603331), hAPP(c_COMBB(tc_prod(_1603331, _1603331), tc_fun(tc_fun(tc_prod(_1603331, _1603331), tc_HOL_Obool), tc_HOL_Obool), _1603331), c_member(tc_prod(_1603331, _1603331)))), c_Product__Type_OPair(_1603331, _1603331)))), _1603333), _1603335, _1603337))], (41609 ^ _779448) ^ [_1603714, _1603716, _1603718, _1603720, _1603722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603714), tc_List_Olist(_1603714))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603714), tc_List_Olist(_1603714)), hAPP(hAPP(c_List_Olist_OCons(_1603714), _1603716), _1603718)), _1603720)), c_List_Olistrel(_1603714, _1603722))), 41614 ^ _779448 : [(41615 ^ _779448) ^ [] : [-(_1603720 = hAPP(hAPP(c_List_Olist_OCons(_1603714), 41612 ^ [_1603714, _1603716, _1603718, _1603720, _1603722]), 41613 ^ [_1603714, _1603716, _1603718, _1603720, _1603722]))], (41617 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603714, _1603714)), hAPP(hAPP(c_Product__Type_OPair(_1603714, _1603714), _1603716), 41612 ^ [_1603714, _1603716, _1603718, _1603720, _1603722])), _1603722)))], (41619 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603714), tc_List_Olist(_1603714))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603714), tc_List_Olist(_1603714)), _1603718), 41613 ^ [_1603714, _1603716, _1603718, _1603720, _1603722])), c_List_Olistrel(_1603714, _1603722))))]]], (41621 ^ _779448) ^ [_1604103, _1604105, _1604107, _1604109, _1604111, _1604113] : [hBOOL(hAPP(hAPP(_1604103, _1604105), _1604107)), c_List_Olistrelp(_1604109, _1604103, _1604111, _1604113), -(c_List_Olistrelp(_1604109, _1604103, hAPP(hAPP(c_List_Olist_OCons(_1604109), _1604105), _1604111), hAPP(hAPP(c_List_Olist_OCons(_1604109), _1604107), _1604113)))], (41631 ^ _779448) ^ [_1604325, _1604327, _1604329, _1604331, _1604333, _1604335] : [c_List_Olistrelp(_1604325, _1604327, hAPP(hAPP(c_List_Olist_OCons(_1604325), _1604329), _1604331), hAPP(hAPP(c_List_Olist_OCons(_1604325), _1604333), _1604335)), 41634 ^ _779448 : [(41635 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1604327, _1604329), _1604333)))], (41637 ^ _779448) ^ [] : [-(c_List_Olistrelp(_1604325, _1604327, _1604331, _1604335))]]], (41639 ^ _779448) ^ [_1604482, _1604484, _1604486, _1604488, _1604490, _1604492] : [-(c_List_Olistrelp(_1604482, _1604484, hAPP(hAPP(c_List_Olist_OCons(_1604482), _1604486), _1604488), hAPP(hAPP(c_List_Olist_OCons(_1604482), _1604490), _1604492))), hBOOL(hAPP(hAPP(_1604484, _1604486), _1604490)), c_List_Olistrelp(_1604482, _1604484, _1604488, _1604492)], (41649 ^ _779448) ^ [_1604679, _1604681, _1604683, _1604685, _1604687] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604679), tc_List_Olist(_1604679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604679), tc_List_Olist(_1604679)), _1604681), hAPP(hAPP(c_List_Olist_OCons(_1604679), _1604683), _1604685))), c_List_Olistrel(_1604679, _1604687))), 41654 ^ _779448 : [(41655 ^ _779448) ^ [] : [-(_1604681 = hAPP(hAPP(c_List_Olist_OCons(_1604679), 41652 ^ [_1604679, _1604681, _1604683, _1604685, _1604687]), 41653 ^ [_1604679, _1604681, _1604683, _1604685, _1604687]))], (41657 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604679, _1604679)), hAPP(hAPP(c_Product__Type_OPair(_1604679, _1604679), 41652 ^ [_1604679, _1604681, _1604683, _1604685, _1604687]), _1604683)), _1604687)))], (41659 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604679), tc_List_Olist(_1604679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604679), tc_List_Olist(_1604679)), 41653 ^ [_1604679, _1604681, _1604683, _1604685, _1604687]), _1604685)), c_List_Olistrel(_1604679, _1604687))))]]], (41661 ^ _779448) ^ [_1605068, _1605070, _1605072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605068, _1605068), tc_HOL_Obool)), _1605070), hAPP(hAPP(c_Product__Type_OSigma(_1605068, _1605068), _1605072), hAPP(c_COMBK(tc_fun(_1605068, tc_HOL_Obool), _1605068), _1605072)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1605068), tc_List_Olist(_1605068)), tc_HOL_Obool)), c_List_Olistrel(_1605068, _1605070)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1605068), tc_List_Olist(_1605068)), c_List_Olists(_1605068, _1605072)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1605068), tc_HOL_Obool), tc_List_Olist(_1605068)), c_List_Olists(_1605068, _1605072))))))], (41667 ^ _779448) ^ [_1605313] : [-(c_List_Olists(_1605313, c_Orderings_Otop__class_Otop(tc_fun(_1605313, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1605313), tc_HOL_Obool)))], (41669 ^ _779448) ^ [_1605351, _1605353, _1605355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605351, tc_HOL_Obool)), _1605353), _1605355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1605351), tc_HOL_Obool)), c_List_Olists(_1605351, _1605353)), c_List_Olists(_1605351, _1605355))))], (41675 ^ _779448) ^ [_1605486, _1605488, _1605490] : [c_Equiv__Relations_Oequiv(_1605486, _1605488, _1605490), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1605486), c_List_Olists(_1605486, _1605488), c_List_Olistrel(_1605486, _1605490)))], (41681 ^ _779448) ^ [_1605585, _1605587, _1605589] : [c_Relation_Orefl__on(_1605585, _1605587, _1605589), -(c_Relation_Orefl__on(tc_List_Olist(_1605585), c_List_Olists(_1605585, _1605587), c_List_Olistrel(_1605585, _1605589)))], (41687 ^ _779448) ^ [_1605705, _1605707, _1605709, _1605711] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605705)), hAPP(hAPP(c_List_Olist_OCons(_1605705), _1605707), _1605709)), c_List_Olists(_1605705, _1605711))), 41690 ^ _779448 : [(41691 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605705), _1605707), _1605711)))], (41693 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605705)), _1605709), c_List_Olists(_1605705, _1605711))))]]], (41695 ^ _779448) ^ [_1605886, _1605888, _1605890, _1605892] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605886)), hAPP(hAPP(c_List_Olist_OCons(_1605886), _1605888), _1605890)), c_List_Olists(_1605886, _1605892)))), hBOOL(hAPP(hAPP(c_member(_1605886), _1605888), _1605892)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605886)), _1605890), c_List_Olists(_1605886, _1605892)))], (41705 ^ _779448) ^ [_1606103, _1606105, _1606107] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606103)), _1606105), c_Wellfounded_Oacc(tc_List_Olist(_1606103), c_List_Olistrel1(_1606103, _1606107)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606103)), _1606105), c_List_Olists(_1606103, c_Wellfounded_Oacc(_1606103, _1606107)))))], (41711 ^ _779448) ^ [_1606246, _1606248, _1606250] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606246)), _1606248), c_List_Olists(_1606246, c_Wellfounded_Oacc(_1606246, _1606250)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606246)), _1606248), c_Wellfounded_Oacc(tc_List_Olist(_1606246), c_List_Olistrel1(_1606246, _1606250)))))], (41717 ^ _779448) ^ [_1606410, _1606412, _1606414, _1606416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606410), tc_List_Olist(_1606410))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606410), tc_List_Olist(_1606410)), _1606412), _1606414)), c_List_Olistrel(_1606410, _1606416))), 41720 ^ _779448 : [(41721 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606410)), _1606412) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606410)), _1606414))], (41723 ^ _779448) ^ [_1606639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606639), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606410)), _1606412))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606410, _1606410)), hAPP(hAPP(c_Product__Type_OPair(_1606410, _1606410), hAPP(hAPP(c_List_Onth(_1606410), _1606412), _1606639)), hAPP(hAPP(c_List_Onth(_1606410), _1606414), _1606639))), _1606416)))]]], (41729 ^ _779448) ^ [_1606818, _1606820, _1606822, _1606824] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606818), tc_List_Olist(_1606818))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606818), tc_List_Olist(_1606818)), _1606820), _1606822)), c_List_Olistrel(_1606818, _1606824)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606818)), _1606820) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606818)), _1606822), 41735 ^ _779448 : [(41736 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41734 ^ [_1606818, _1606820, _1606822, _1606824]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606818)), _1606820))))], (41738 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606818, _1606818)), hAPP(hAPP(c_Product__Type_OPair(_1606818, _1606818), hAPP(hAPP(c_List_Onth(_1606818), _1606820), 41734 ^ [_1606818, _1606820, _1606822, _1606824])), hAPP(hAPP(c_List_Onth(_1606818), _1606822), 41734 ^ [_1606818, _1606820, _1606822, _1606824]))), _1606824))]]], (41742 ^ _779448) ^ [_1607261, _1607263, _1607265] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607261, _1607261)), hAPP(hAPP(c_Product__Type_OPair(_1607261, _1607261), 41743 ^ [_1607261, _1607263, _1607265]), 41743 ^ [_1607261, _1607263, _1607265])), _1607263))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607261), tc_List_Olist(_1607261))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607261), tc_List_Olist(_1607261)), _1607265), _1607265)), c_List_Olexord(_1607261, _1607263)))], (41749 ^ _779448) ^ [_1607445] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1607445)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1607445), tc_HOL_Obool))))], (41751 ^ _779448) ^ [_1607499, _1607501, _1607503] : [_1607499 = _1607501, 41754 ^ _779448 : [(41755 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607503)), _1607499) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607503)), _1607501))], (41757 ^ _779448) ^ [_1607647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607647), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607503)), _1607499))), -(hAPP(hAPP(c_List_Onth(_1607503), _1607499), _1607647) = hAPP(hAPP(c_List_Onth(_1607503), _1607501), _1607647))]]], (41763 ^ _779448) ^ [_1607786, _1607788, _1607790] : [-(_1607786 = _1607788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607790)), _1607786) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607790)), _1607788), 41769 ^ _779448 : [(41770 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41768 ^ [_1607786, _1607788, _1607790]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607790)), _1607786))))], (41772 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Onth(_1607790), _1607786), 41768 ^ [_1607786, _1607788, _1607790]) = hAPP(hAPP(c_List_Onth(_1607790), _1607788), 41768 ^ [_1607786, _1607788, _1607790])]]], (41776 ^ _779448) ^ [_1608101, _1608103, _1608105] : [-(hAPP(hAPP(c_List_Onth(_1608101), hAPP(hAPP(c_List_Olist_OCons(_1608101), _1608103), _1608105)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1608103)], (41778 ^ _779448) ^ [_1608144, _1608146, _1608148, _1608150] : [-(hAPP(hAPP(c_List_Onth(_1608144), hAPP(hAPP(c_List_Olist_OCons(_1608144), _1608146), _1608148)), hAPP(c_Nat_OSuc, _1608150)) = hAPP(hAPP(c_List_Onth(_1608144), _1608148), _1608150))], (41780 ^ _779448) ^ [_1608200, _1608202, _1608204, _1608206] : [-(hAPP(hAPP(c_List_Onth(_1608200), hAPP(hAPP(c_List_Olist_OCons(_1608200), _1608202), _1608204)), _1608206) = c_Nat_Onat_Onat__case(_1608200, _1608202, hAPP(c_List_Onth(_1608200), _1608204), _1608206))], (41782 ^ _779448) ^ [_1608270, _1608272, _1608274, _1608276] : [_1608270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608272), hAPP(hAPP(c_List_Olist_OCons(_1608272), _1608274), _1608276)), _1608270) = _1608274)], (41788 ^ _779448) ^ [_1608377, _1608379, _1608381, _1608383] : [-(_1608377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608379), hAPP(hAPP(c_List_Olist_OCons(_1608379), _1608381), _1608383)), _1608377) = hAPP(hAPP(c_List_Onth(_1608379), _1608383), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1608377), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41794 ^ _779448) ^ [_1608464, _1608466, _1608468, _1608470] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608464) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608466), hAPP(hAPP(c_List_Olist_OCons(_1608466), _1608468), _1608470)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608464)) = _1608468)], (41800 ^ _779448) ^ [_1608583, _1608585, _1608587, _1608589] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608583) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608585), hAPP(hAPP(c_List_Olist_OCons(_1608585), _1608587), _1608589)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608583)) = hAPP(hAPP(c_List_Onth(_1608585), _1608589), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608583)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41806 ^ _779448) ^ [_1608685, _1608687, _1608689, _1608691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608685), tc_List_Olist(_1608685))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608685), tc_List_Olist(_1608685)), _1608687), _1608689)), c_List_Olexord(_1608685, _1608691))), 41811 ^ _779448 : [(41812 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608685)), _1608687)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608685)), _1608689))))], (41814 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608685), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608685)), _1608687)), _1608689) = _1608687)]], 41816 ^ _779448 : [(41817 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41815 ^ [_1608685, _1608687, _1608689, _1608691]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608685)), _1608687)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608685)), _1608689)))))], (41819 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608685), 41815 ^ [_1608685, _1608687, _1608689, _1608691]), _1608687) = hAPP(hAPP(c_List_Otake(_1608685), 41815 ^ [_1608685, _1608687, _1608689, _1608691]), _1608689))], (41821 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608685, _1608685)), hAPP(hAPP(c_Product__Type_OPair(_1608685, _1608685), hAPP(hAPP(c_List_Onth(_1608685), _1608687), 41815 ^ [_1608685, _1608687, _1608689, _1608691])), hAPP(hAPP(c_List_Onth(_1608685), _1608689), 41815 ^ [_1608685, _1608687, _1608689, _1608691]))), _1608691)))]]], (41823 ^ _779448) ^ [_1609225, _1609227, _1609229, _1609231] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609225), tc_List_Olist(_1609225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609225), tc_List_Olist(_1609225)), _1609227), _1609229)), c_List_Olexord(_1609225, _1609231)))), 41824 ^ _779448 : [(41825 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609225)), _1609227)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609225)), _1609229))), hAPP(hAPP(c_List_Otake(_1609225), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609225)), _1609227)), _1609229) = _1609227], (41831 ^ _779448) ^ [_1609532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1609532), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609225)), _1609227)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609225)), _1609229)))), hAPP(hAPP(c_List_Otake(_1609225), _1609532), _1609227) = hAPP(hAPP(c_List_Otake(_1609225), _1609532), _1609229), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609225, _1609225)), hAPP(hAPP(c_Product__Type_OPair(_1609225, _1609225), hAPP(hAPP(c_List_Onth(_1609225), _1609227), _1609532)), hAPP(hAPP(c_List_Onth(_1609225), _1609229), _1609532))), _1609231))]]], (41843 ^ _779448) ^ [_1609886, _1609888, _1609890] : [-(hAPP(c_List_Oset(_1609886), c_List_Osublist(_1609886, _1609888, _1609890)) = hAPP(c_Set_OCollect(_1609886), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1609886), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1609886, 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)), _1609886), 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)), _1609886), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1609886, tc_fun(tc_Nat_Onat, _1609886), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609886, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1609886), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1609886), c_COMBB(_1609886, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1609886), _1609888))))), 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(_1609886)), _1609888)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1609890))))))], (41845 ^ _779448) ^ [_1610030, _1610032] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610030), hAPP(c_List_Oset(_1610030), _1610032))))], (41847 ^ _779448) ^ [_1610064, _1610066, _1610068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610064, tc_HOL_Obool)), hAPP(c_List_Oset(_1610064), _1610066)), hAPP(c_List_Oset(_1610064), hAPP(hAPP(c_List_Olist_OCons(_1610064), _1610068), _1610066)))))], (41849 ^ _779448) ^ [_1610119, _1610121, _1610123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610119)), _1610121)), _1610123)), -(hAPP(hAPP(c_List_Otake(_1610119), _1610123), _1610121) = _1610121)], (41855 ^ _779448) ^ [_1610238, _1610240, _1610242] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610238, tc_HOL_Obool)), hAPP(c_List_Oset(_1610238), hAPP(hAPP(c_List_Otake(_1610238), _1610240), _1610242))), hAPP(c_List_Oset(_1610238), _1610242))))], (41857 ^ _779448) ^ [_1610293, _1610295, _1610297, _1610299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1610293), _1610295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610297, tc_HOL_Obool)), hAPP(c_List_Oset(_1610297), hAPP(hAPP(c_List_Otake(_1610297), _1610293), _1610299))), hAPP(c_List_Oset(_1610297), hAPP(hAPP(c_List_Otake(_1610297), _1610295), _1610299)))))], (41863 ^ _779448) ^ [_1610456, _1610458, _1610460] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610456, tc_HOL_Obool)), hAPP(c_List_Oset(_1610456), c_List_Osublist(_1610456, _1610458, _1610460))), hAPP(c_List_Oset(_1610456), _1610458))))], (41865 ^ _779448) ^ [_1610507, _1610509, _1610511, _1610513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610507), _1610509)), -(hAPP(hAPP(c_List_Onth(_1610511), hAPP(hAPP(c_List_Otake(_1610511), _1610509), _1610513)), _1610507) = hAPP(hAPP(c_List_Onth(_1610511), _1610513), _1610507))], (41871 ^ _779448) ^ [_1610645, _1610647, _1610649, _1610651] : [-(hBOOL(hAPP(hAPP(c_member(_1610645), _1610647), hAPP(c_List_Oset(_1610645), _1610649)))), hBOOL(hAPP(hAPP(c_member(_1610645), _1610647), hAPP(c_List_Oset(_1610645), c_List_Osublist(_1610645, _1610649, _1610651))))], (41877 ^ _779448) ^ [_1610769, _1610771, _1610773, _1610775] : [hBOOL(hAPP(hAPP(c_member(_1610769), _1610771), hAPP(c_List_Oset(_1610769), hAPP(hAPP(c_List_Otake(_1610769), _1610773), _1610775)))), -(hBOOL(hAPP(hAPP(c_member(_1610769), _1610771), hAPP(c_List_Oset(_1610769), _1610775))))], (41883 ^ _779448) ^ [_1610914, _1610916, _1610918, _1610920] : [hBOOL(hAPP(hAPP(c_member(_1610914), _1610916), hAPP(c_List_Oset(_1610914), c_List_Osublist(_1610914, _1610918, _1610920)))), -(hBOOL(hAPP(hAPP(c_member(_1610914), _1610916), hAPP(c_List_Oset(_1610914), _1610918))))], (41889 ^ _779448) ^ [_1611051, _1611053, _1611055, _1611057] : [hBOOL(hAPP(hAPP(c_member(_1611051), _1611053), hAPP(c_List_Oset(_1611051), hAPP(hAPP(c_List_Olist_OCons(_1611051), _1611055), _1611057)))), -(_1611053 = _1611055), -(hBOOL(hAPP(hAPP(c_member(_1611051), _1611053), hAPP(c_List_Oset(_1611051), _1611057))))], (41899 ^ _779448) ^ [_1611209, _1611211, _1611213, _1611215] : [-(hAPP(hAPP(c_List_Otake(_1611209), hAPP(c_Nat_OSuc, _1611211)), hAPP(hAPP(c_List_Olist_OCons(_1611209), _1611213), _1611215)) = hAPP(hAPP(c_List_Olist_OCons(_1611209), _1611213), hAPP(hAPP(c_List_Otake(_1611209), _1611211), _1611215)))], (41901 ^ _779448) ^ [_1611273, _1611275, _1611277] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611273)), hAPP(hAPP(c_List_Otake(_1611273), _1611275), _1611277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611273)), _1611277)), _1611275))], (41903 ^ _779448) ^ [_1611328, _1611330, _1611332, _1611334] : [-(hAPP(hAPP(c_List_Otake(_1611328), _1611330), hAPP(hAPP(c_List_Otake(_1611328), _1611332), _1611334)) = hAPP(hAPP(c_List_Otake(_1611328), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1611330), _1611332)), _1611334))], (41905 ^ _779448) ^ [_1611387, _1611389, _1611391] : [-(hAPP(c_List_Oset(_1611387), hAPP(hAPP(c_List_Olist_OCons(_1611387), _1611389), _1611391)) = hAPP(hAPP(c_Set_Oinsert(_1611387), _1611389), hAPP(c_List_Oset(_1611387), _1611391)))], (41907 ^ _779448) ^ [_1611440, _1611442, _1611444] : [-(c_List_Osublist(_1611440, _1611442, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1611444)) = hAPP(hAPP(c_List_Otake(_1611440), _1611444), _1611442))], (41909 ^ _779448) ^ [_1611482, _1611484] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1611482), hAPP(c_List_Oset(_1611482), _1611484))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611482)), _1611484))))], (41911 ^ _779448) ^ [_1611547, _1611549, _1611551] : [41913 ^ _779448 : [(41914 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611547), 41912 ^ [_1611547, _1611549, _1611551]), hAPP(c_List_Oset(_1611547), _1611549))))], (41916 ^ _779448) ^ [] : [hBOOL(hAPP(_1611551, 41912 ^ [_1611547, _1611549, _1611551]))]], 41917 ^ _779448 : [(41918 ^ _779448) ^ [_1611731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611731), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611547)), _1611549))), -(hBOOL(hAPP(_1611551, hAPP(hAPP(c_List_Onth(_1611547), _1611549), _1611731))))]]], (41924 ^ _779448) ^ [_1611858, _1611860, _1611862] : [41926 ^ _779448 : [(41927 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41925 ^ [_1611858, _1611860, _1611862]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611858)), _1611860))))], (41929 ^ _779448) ^ [] : [hBOOL(hAPP(_1611862, hAPP(hAPP(c_List_Onth(_1611858), _1611860), 41925 ^ [_1611858, _1611860, _1611862])))]], 41930 ^ _779448 : [(41931 ^ _779448) ^ [_1612060] : [hBOOL(hAPP(hAPP(c_member(_1611858), _1612060), hAPP(c_List_Oset(_1611858), _1611860))), -(hBOOL(hAPP(_1611862, _1612060)))]]], (41937 ^ _779448) ^ [_1612177, _1612179, _1612181, _1612183, _1612185] : [hBOOL(hAPP(hAPP(c_member(_1612177), _1612179), hAPP(c_List_Oset(_1612177), _1612181))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612183), hAPP(_1612185, _1612179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612183), c_List_Olist_Olist__size(_1612177, _1612185, _1612181))))], (41947 ^ _779448) ^ [_1612376, _1612378, _1612380, _1612382, _1612384] : [hBOOL(hAPP(hAPP(c_member(_1612376), _1612378), hAPP(c_List_Oset(_1612376), _1612380))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612382), hAPP(_1612384, _1612378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612382), c_List_Olist_Olist__size(_1612376, _1612384, _1612380))))], (41967 ^ _779448) ^ [_1612820, _1612822, _1612824] : [41969 ^ _779448 : [(41970 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612820), 41968 ^ [_1612820, _1612822, _1612824]), hAPP(c_List_Oset(_1612820), _1612822))))], (41972 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1612820), 41968 ^ [_1612820, _1612822, _1612824]), _1612824))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612820)), _1612822), c_List_Olists(_1612820, _1612824))))], (41957 ^ _779448) ^ [_1612593, _1612595, _1612597] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612593)), _1612595), c_List_Olists(_1612593, _1612597))), 41960 ^ _779448 : [(41961 ^ _779448) ^ [_1612701] : [hBOOL(hAPP(hAPP(c_member(_1612593), _1612701), hAPP(c_List_Oset(_1612593), _1612595))), -(hBOOL(hAPP(hAPP(c_member(_1612593), _1612701), _1612597)))]]], (41976 ^ _779448) ^ [_1613040, _1613042, _1613044] : [hBOOL(hAPP(hAPP(c_member(_1613040), _1613042), hAPP(c_List_Oset(_1613040), _1613044))), -(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(_1613040)), _1613044))))], (41982 ^ _779448) ^ [_1613161, _1613163, _1613165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613161), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613163)), _1613165))), -(hBOOL(hAPP(hAPP(c_member(_1613163), hAPP(hAPP(c_List_Onth(_1613163), _1613165), _1613161)), hAPP(c_List_Oset(_1613163), _1613165))))], (41988 ^ _779448) ^ [_1613322, _1613324, _1613326] : [hBOOL(hAPP(hAPP(c_member(_1613322), _1613324), hAPP(c_List_Oset(_1613322), _1613326))), 41992 ^ _779448 : [(41993 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41991 ^ [_1613322, _1613324, _1613326]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613322)), _1613326))))], (41995 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613322), _1613326), 41991 ^ [_1613322, _1613324, _1613326]) = _1613324)]]], (41997 ^ _779448) ^ [_1613510, _1613512, _1613514] : [-(hBOOL(hAPP(hAPP(c_member(_1613510), _1613512), hAPP(c_List_Oset(_1613510), _1613514)))), 41998 ^ _779448 : [(41999 ^ _779448) ^ [_1613584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613584), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613510)), _1613514))), hAPP(hAPP(c_List_Onth(_1613510), _1613514), _1613584) = _1613512]]], (42007 ^ _779448) ^ [_1613746, _1613748] : [-(c_List_Olists(_1613746, _1613748) = hAPP(c_Set_OCollect(tc_List_Olist(_1613746)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613746), tc_fun(_1613746, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613746, tc_HOL_Obool), tc_fun(tc_fun(_1613746, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613746)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613746, tc_HOL_Obool))), c_List_Oset(_1613746))), _1613748)))], (42009 ^ _779448) ^ [_1613824, _1613826] : [-(hAPP(c_List_Oset(_1613824), _1613826) = hAPP(c_Set_OCollect(_1613824), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1613824), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1613824, 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)), _1613824), 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)), _1613824), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1613824, tc_fun(tc_Nat_Onat, _1613824), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613824, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1613824), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1613824), c_COMBB(_1613824, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1613824), _1613826))))), 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(_1613824)), _1613826))))))], (42011 ^ _779448) ^ [_1613950, _1613952, _1613954] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1613950), _1613952)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1613950)), hAPP(c_Set_OCollect(tc_List_Olist(_1613950)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1613950), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1613950)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613950), tc_fun(_1613950, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613950, tc_HOL_Obool), tc_fun(tc_fun(_1613950, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613950)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613950, tc_HOL_Obool))), c_List_Oset(_1613950))), _1613952))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613950), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1613950)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1613950)))), _1613954))))))], (42017 ^ _779448) ^ [_1614253, _1614255, _1614257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614253), _1614255)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614253)), hAPP(c_Set_OCollect(tc_List_Olist(_1614253)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614253), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614253)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614253), tc_fun(_1614253, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614253, tc_HOL_Obool), tc_fun(tc_fun(_1614253, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614253)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614253, tc_HOL_Obool))), c_List_Oset(_1614253))), _1614255))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614253), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614253)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1614253)))), _1614257))))))], (42023 ^ _779448) ^ [_1614577, _1614579, _1614581, _1614583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614577), tc_List_Olist(_1614577))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614577), tc_List_Olist(_1614577)), _1614579), _1614581)), c_List_Olistrel(_1614577, _1614583))), 42026 ^ _779448 : [(42027 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614577)), _1614579) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614577)), _1614581))], (42029 ^ _779448) ^ [_1614913] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614577, _1614577)), _1614913), hAPP(c_List_Oset(tc_prod(_1614577, _1614577)), hAPP(hAPP(c_List_Ozip(_1614577, _1614577), _1614579), _1614581)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1614577, _1614577, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1614577, tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_fun(_1614577, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614577, tc_fun(tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_fun(_1614577, tc_HOL_Obool)), _1614577), c_COMBC(_1614577, tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614577, tc_prod(_1614577, _1614577)), tc_fun(_1614577, tc_fun(tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_HOL_Obool)), _1614577), hAPP(c_COMBB(tc_prod(_1614577, _1614577), tc_fun(tc_fun(tc_prod(_1614577, _1614577), tc_HOL_Obool), tc_HOL_Obool), _1614577), c_member(tc_prod(_1614577, _1614577)))), c_Product__Type_OPair(_1614577, _1614577)))), _1614583)), _1614913)))]]], (42035 ^ _779448) ^ [_1615306, _1615308, _1615310, _1615312] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615306), tc_List_Olist(_1615306))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615306), tc_List_Olist(_1615306)), _1615308), _1615310)), c_List_Olistrel(_1615306, _1615312)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615306)), _1615308) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615306)), _1615310), 42041 ^ _779448 : [(42042 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615306, _1615306)), 42040 ^ [_1615306, _1615308, _1615310, _1615312]), hAPP(c_List_Oset(tc_prod(_1615306, _1615306)), hAPP(hAPP(c_List_Ozip(_1615306, _1615306), _1615308), _1615310)))))], (42044 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615306, _1615306, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615306, tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_fun(_1615306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615306, tc_fun(tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_fun(_1615306, tc_HOL_Obool)), _1615306), c_COMBC(_1615306, tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615306, tc_prod(_1615306, _1615306)), tc_fun(_1615306, tc_fun(tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_HOL_Obool)), _1615306), hAPP(c_COMBB(tc_prod(_1615306, _1615306), tc_fun(tc_fun(tc_prod(_1615306, _1615306), tc_HOL_Obool), tc_HOL_Obool), _1615306), c_member(tc_prod(_1615306, _1615306)))), c_Product__Type_OPair(_1615306, _1615306)))), _1615312)), 42040 ^ [_1615306, _1615308, _1615310, _1615312]))]]], (42048 ^ _779448) ^ [_1616044, _1616046, _1616048, _1616050] : [-(hAPP(c_List_Oset(tc_prod(_1616044, _1616046)), hAPP(hAPP(c_List_Ozip(_1616044, _1616046), _1616048), _1616050)) = hAPP(c_Set_OCollect(tc_prod(_1616044, _1616046)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1616044, _1616046)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1616044, _1616046), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616044, _1616046)), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_prod(_1616044, _1616046)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(tc_prod(_1616044, _1616046), tc_fun(tc_Nat_Onat, tc_prod(_1616044, _1616046)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616044, _1616046), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1616044, _1616046)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616044, _1616046)), c_COMBB(tc_prod(_1616044, _1616046), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1616046, tc_prod(_1616044, _1616046)), hAPP(hAPP(c_COMBB(_1616044, tc_fun(_1616046, tc_prod(_1616044, _1616046)), tc_Nat_Onat), c_Product__Type_OPair(_1616044, _1616046)), hAPP(c_List_Onth(_1616044), _1616048))), hAPP(c_List_Onth(_1616046), _1616050)))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616044)), _1616048)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616046)), _1616050)))))))], (42050 ^ _779448) ^ [_1616269, _1616271, _1616273, _1616275, _1616277] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1616269, _1616271)), _1616273), hAPP(hAPP(c_List_Ozip(_1616269, _1616271), _1616275), _1616277)) = hAPP(hAPP(c_List_Ozip(_1616269, _1616271), hAPP(hAPP(c_List_Otake(_1616269), _1616273), _1616275)), hAPP(hAPP(c_List_Otake(_1616271), _1616273), _1616277)))], (42052 ^ _779448) ^ [_1616345, _1616347, _1616349, _1616351] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1616345, _1616347))), hAPP(hAPP(c_List_Ozip(_1616345, _1616347), _1616349), _1616351)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616345)), _1616349)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616347)), _1616351)))], (42054 ^ _779448) ^ [_1616413, _1616415, _1616417, _1616419, _1616421, _1616423] : [-(hAPP(hAPP(c_List_Ozip(_1616413, _1616415), hAPP(hAPP(c_List_Olist_OCons(_1616413), _1616417), _1616419)), hAPP(hAPP(c_List_Olist_OCons(_1616415), _1616421), _1616423)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1616413, _1616415)), hAPP(hAPP(c_Product__Type_OPair(_1616413, _1616415), _1616417), _1616421)), hAPP(hAPP(c_List_Ozip(_1616413, _1616415), _1616419), _1616423)))], (42056 ^ _779448) ^ [_1616518, _1616520, _1616522] : [_1616518 = _1616520, 42059 ^ _779448 : [(42060 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616522)), _1616518) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616522)), _1616520))], (42062 ^ _779448) ^ [_1616674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616522, _1616522)), _1616674), hAPP(c_List_Oset(tc_prod(_1616522, _1616522)), hAPP(hAPP(c_List_Ozip(_1616522, _1616522), _1616518), _1616520)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616522, _1616522, tc_HOL_Obool), c_fequal), _1616674)))]]], (42068 ^ _779448) ^ [_1616829, _1616831, _1616833] : [-(_1616829 = _1616831), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616833)), _1616829) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616833)), _1616831), 42074 ^ _779448 : [(42075 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616833, _1616833)), 42073 ^ [_1616829, _1616831, _1616833]), hAPP(c_List_Oset(tc_prod(_1616833, _1616833)), hAPP(hAPP(c_List_Ozip(_1616833, _1616833), _1616829), _1616831)))))], (42077 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616833, _1616833, tc_HOL_Obool), c_fequal), 42073 ^ [_1616829, _1616831, _1616833]))]]], (42081 ^ _779448) ^ [_1617143, _1617145, _1617147, _1617149, _1617151, _1617153] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617143, _1617145)), hAPP(hAPP(c_Product__Type_OPair(_1617143, _1617145), _1617147), _1617149)), hAPP(c_List_Oset(tc_prod(_1617143, _1617145)), hAPP(hAPP(c_List_Ozip(_1617143, _1617145), _1617151), _1617153)))), 42084 ^ _779448 : [(42085 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617143), _1617147), hAPP(c_List_Oset(_1617143), _1617151))))], (42087 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617145), _1617149), hAPP(c_List_Oset(_1617145), _1617153))))]]], (42089 ^ _779448) ^ [_1617378, _1617380, _1617382, _1617384, _1617386, _1617388] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617378, _1617380)), hAPP(hAPP(c_Product__Type_OPair(_1617378, _1617380), _1617382), _1617384)), hAPP(c_List_Oset(tc_prod(_1617378, _1617380)), hAPP(hAPP(c_List_Ozip(_1617378, _1617380), _1617386), _1617388)))), -(hBOOL(hAPP(hAPP(c_member(_1617380), _1617384), hAPP(c_List_Oset(_1617380), _1617388))))], (42095 ^ _779448) ^ [_1617559, _1617561, _1617563, _1617565, _1617567, _1617569] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617559, _1617561)), hAPP(hAPP(c_Product__Type_OPair(_1617559, _1617561), _1617563), _1617565)), hAPP(c_List_Oset(tc_prod(_1617559, _1617561)), hAPP(hAPP(c_List_Ozip(_1617559, _1617561), _1617567), _1617569)))), -(hBOOL(hAPP(hAPP(c_member(_1617559), _1617563), hAPP(c_List_Oset(_1617559), _1617567))))], (42101 ^ _779448) ^ [_1617761, _1617763, _1617765, _1617767] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617761, _1617761)), hAPP(hAPP(c_Product__Type_OPair(_1617761, _1617761), _1617763), _1617765)), hAPP(c_List_Oset(tc_prod(_1617761, _1617761)), hAPP(hAPP(c_List_Ozip(_1617761, _1617761), _1617767), _1617767)))), 42104 ^ _779448 : [(42105 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617761), _1617763), hAPP(c_List_Oset(_1617761), _1617767))))], (42107 ^ _779448) ^ [] : [-(_1617763 = _1617765)]]], (42109 ^ _779448) ^ [_1617960, _1617962, _1617964, _1617966] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617960, _1617960)), hAPP(hAPP(c_Product__Type_OPair(_1617960, _1617960), _1617962), _1617964)), hAPP(c_List_Oset(tc_prod(_1617960, _1617960)), hAPP(hAPP(c_List_Ozip(_1617960, _1617960), _1617966), _1617966))))), hBOOL(hAPP(hAPP(c_member(_1617960), _1617962), hAPP(c_List_Oset(_1617960), _1617966))), _1617962 = _1617964], (42119 ^ _779448) ^ [_1618195, _1618197, _1618199, _1618201, _1618203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618197)), _1618199))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618201)), _1618203))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1618197, _1618201)), hAPP(hAPP(c_List_Ozip(_1618197, _1618201), _1618199), _1618203)), _1618195) = hAPP(hAPP(c_Product__Type_OPair(_1618197, _1618201), hAPP(hAPP(c_List_Onth(_1618197), _1618199), _1618195)), hAPP(hAPP(c_List_Onth(_1618201), _1618203), _1618195)))], (42129 ^ _779448) ^ [_1618474, _1618476] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1618474, _1618476) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1618474), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1618476), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42131 ^ _779448) ^ [_1618521, _1618523] : [class_Groups_Ocomm__monoid__add(_1618521), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1618521), _1618523) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1618521), hAPP(c_List_Onth(_1618521), _1618523)), 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(_1618521)), _1618523))))], (42147 ^ _779448) ^ [_1618834] : [42149 ^ _779448 : [(42150 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42148 ^ [_1618834]), hAPP(c_List_Oset(tc_Nat_Onat), _1618834))))], (42152 ^ _779448) ^ [] : [42148 ^ [_1618834] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42137 ^ _779448) ^ [_1618666] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618666) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42140 ^ _779448 : [(42141 ^ _779448) ^ [_1618741] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1618741), hAPP(c_List_Oset(tc_Nat_Onat), _1618666))), -(_1618741 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42156 ^ _779448) ^ [_1618990, _1618992] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1618990, _1618992)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1618990, _1618992))], (42158 ^ _779448) ^ [_1619025, _1619027] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619025, _1619027) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619025, _1619027)))], (42160 ^ _779448) ^ [_1619060, _1619062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619062), _1619060)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619062))))], (42166 ^ _779448) ^ [_1619181, _1619183, _1619185] : [class_Groups_Omonoid__add(_1619181), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619181), hAPP(hAPP(c_List_Olist_OCons(_1619181), _1619183), _1619185)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619181), _1619183), hAPP(c_List_Omonoid__add__class_Olistsum(_1619181), _1619185)))], (42172 ^ _779448) ^ [_1619310, _1619312] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1619310), _1619312) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619312), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42174 ^ _779448) ^ [_1619353, _1619355] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1619353, _1619355) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619353), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1619355)))], (42176 ^ _779448) ^ [_1619406] : [c_List_Onat__list(_1619406), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619406)))], (42182 ^ _779448) ^ [_1619479] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619479)), -(c_List_Onat__list(_1619479))], (42188 ^ _779448) ^ [_1619558, _1619560, _1619562, _1619564] : [42190 ^ _779448 : [(42191 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619558), 42189 ^ [_1619558, _1619560, _1619562, _1619564]), hAPP(c_List_Oset(_1619558), _1619560))))], (42193 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1619562, 42189 ^ [_1619558, _1619560, _1619562, _1619564])), hAPP(_1619564, 42189 ^ [_1619558, _1619560, _1619562, _1619564])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1619558, _1619562, _1619560)), c_List_Olist_Olist__size(_1619558, _1619564, _1619560))))], (42197 ^ _779448) ^ [_1619808, _1619810, _1619812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619808), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619810))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1619810), _1619808), _1619812)) = 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), _1619810)), _1619812)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619810), _1619808)))], (42203 ^ _779448) ^ [_1619969, _1619971, _1619973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1619969), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619971)), _1619973))), -(c_List_Obutlast(_1619971, hAPP(hAPP(c_List_Otake(_1619971), _1619969), _1619973)) = hAPP(hAPP(c_List_Otake(_1619971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1619969), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1619973))], (42209 ^ _779448) ^ [_1620122, _1620124, _1620126, _1620128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620122)), _1620124)), _1620126)), -(hAPP(hAPP(c_List_Olist__update(_1620122, _1620124), _1620126), _1620128) = _1620124)], (42215 ^ _779448) ^ [_1620241, _1620243, _1620245, _1620247, _1620249] : [-(_1620241 = _1620243), -(hAPP(hAPP(c_List_Onth(_1620245), hAPP(hAPP(c_List_Olist__update(_1620245, _1620247), _1620241), _1620249)), _1620243) = hAPP(hAPP(c_List_Onth(_1620245), _1620247), _1620243))], (42221 ^ _779448) ^ [_1620308, _1620310, _1620312] : [-(hAPP(hAPP(c_List_Olist__update(_1620308, _1620310), _1620312), hAPP(hAPP(c_List_Onth(_1620308), _1620310), _1620312)) = _1620310)], (42223 ^ _779448) ^ [_1620367, _1620369, _1620371, _1620373] : [_1620367 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620369)), _1620371)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1620369, hAPP(hAPP(c_List_Olist__update(_1620369, _1620371), _1620367), _1620373)) = c_List_Obutlast(_1620369, _1620371))], (42229 ^ _779448) ^ [_1620498, _1620500, _1620502, _1620504] : [-(_1620498 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620500)), _1620502)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1620500, hAPP(hAPP(c_List_Olist__update(_1620500, _1620502), _1620498), _1620504)) = hAPP(hAPP(c_List_Olist__update(_1620500, c_List_Obutlast(_1620500, _1620502)), _1620498), _1620504))], (42235 ^ _779448) ^ [_1620577, _1620579, _1620581, _1620583] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620577)), hAPP(hAPP(c_List_Olist__update(_1620577, _1620579), _1620581), _1620583)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620577)), _1620579))], (42237 ^ _779448) ^ [_1620629, _1620631, _1620633, _1620635, _1620637, _1620639, _1620641] : [-(hAPP(hAPP(c_List_Ozip(_1620629, _1620631), hAPP(hAPP(c_List_Olist__update(_1620629, _1620633), _1620635), _1620637)), hAPP(hAPP(c_List_Olist__update(_1620631, _1620639), _1620635), _1620641)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1620629, _1620631), hAPP(hAPP(c_List_Ozip(_1620629, _1620631), _1620633), _1620639)), _1620635), hAPP(hAPP(c_Product__Type_OPair(_1620629, _1620631), _1620637), _1620641)))], (42239 ^ _779448) ^ [_1620721, _1620723, _1620725, _1620727, _1620729, _1620731] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1620721, _1620723), hAPP(hAPP(c_List_Ozip(_1620721, _1620723), _1620725), _1620727)), _1620729), _1620731) = hAPP(hAPP(c_List_Ozip(_1620721, _1620723), hAPP(hAPP(c_List_Olist__update(_1620721, _1620725), _1620729), hAPP(c_Product__Type_Ofst(_1620721, _1620723), _1620731))), hAPP(hAPP(c_List_Olist__update(_1620723, _1620727), _1620729), hAPP(c_Product__Type_Osnd(_1620721, _1620723), _1620731))))], (42241 ^ _779448) ^ [_1620814, _1620816, _1620818, _1620820, _1620822] : [-(hAPP(hAPP(c_List_Olist__update(_1620814, hAPP(hAPP(c_List_Olist__update(_1620814, _1620816), _1620818), _1620820)), _1620818), _1620822) = hAPP(hAPP(c_List_Olist__update(_1620814, _1620816), _1620818), _1620822))], (42243 ^ _779448) ^ [_1620868, _1620870, _1620872, _1620874, _1620876, _1620878] : [-(_1620868 = _1620870), -(hAPP(hAPP(c_List_Olist__update(_1620872, hAPP(hAPP(c_List_Olist__update(_1620872, _1620874), _1620868), _1620876)), _1620870), _1620878) = hAPP(hAPP(c_List_Olist__update(_1620872, hAPP(hAPP(c_List_Olist__update(_1620872, _1620874), _1620870), _1620878)), _1620868), _1620876))], (42249 ^ _779448) ^ [_1620948, _1620950, _1620952, _1620954] : [-(hAPP(hAPP(c_List_Olist__update(_1620948, hAPP(hAPP(c_List_Olist_OCons(_1620948), _1620950), _1620952)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1620954) = hAPP(hAPP(c_List_Olist_OCons(_1620948), _1620954), _1620952))], (42251 ^ _779448) ^ [_1621002, _1621004, _1621006, _1621008, _1621010] : [-(hAPP(hAPP(c_List_Olist__update(_1621002, hAPP(hAPP(c_List_Olist_OCons(_1621002), _1621004), _1621006)), hAPP(c_Nat_OSuc, _1621008)), _1621010) = hAPP(hAPP(c_List_Olist_OCons(_1621002), _1621004), hAPP(hAPP(c_List_Olist__update(_1621002, _1621006), _1621008), _1621010)))], (42253 ^ _779448) ^ [_1621070, _1621072, _1621074, _1621076, _1621078] : [-(hAPP(hAPP(c_List_Olist__update(_1621070, hAPP(hAPP(c_List_Olist_OCons(_1621070), _1621072), _1621074)), _1621076), _1621078) = c_Nat_Onat_Onat__case(tc_List_Olist(_1621070), hAPP(hAPP(c_List_Olist_OCons(_1621070), _1621078), _1621074), hAPP(hAPP(c_COMBB(tc_List_Olist(_1621070), tc_List_Olist(_1621070), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1621070), _1621072)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1621070, tc_List_Olist(_1621070)), c_List_Olist__update(_1621070, _1621074)), _1621078)), _1621076))], (42255 ^ _779448) ^ [_1621167, _1621169, _1621171] : [hBOOL(hAPP(hAPP(c_member(_1621167), _1621169), hAPP(c_List_Oset(_1621167), c_List_Obutlast(_1621167, _1621171)))), -(hBOOL(hAPP(hAPP(c_member(_1621167), _1621169), hAPP(c_List_Oset(_1621167), _1621171))))], (42261 ^ _779448) ^ [_1621300, _1621302, _1621304, _1621306, _1621308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621300, tc_HOL_Obool)), hAPP(c_List_Oset(_1621300), _1621302)), _1621304)), hBOOL(hAPP(hAPP(c_member(_1621300), _1621306), _1621304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621300, tc_HOL_Obool)), hAPP(c_List_Oset(_1621300), hAPP(hAPP(c_List_Olist__update(_1621300, _1621302), _1621308), _1621306))), _1621304)))], (42271 ^ _779448) ^ [_1621533, _1621535, _1621537, _1621539] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621533, tc_HOL_Obool)), hAPP(c_List_Oset(_1621533), hAPP(hAPP(c_List_Olist__update(_1621533, _1621535), _1621537), _1621539))), hAPP(hAPP(c_Set_Oinsert(_1621533), _1621539), hAPP(c_List_Oset(_1621533), _1621535)))))], (42273 ^ _779448) ^ [_1621599, _1621601, _1621603, _1621605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621599), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621601)), _1621603))), -(hAPP(hAPP(c_List_Onth(_1621601), hAPP(hAPP(c_List_Olist__update(_1621601, _1621603), _1621599), _1621605)), _1621599) = _1621605)], (42279 ^ _779448) ^ [_1621738, _1621740, _1621742, _1621744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621740)), _1621742))), 42282 ^ _779448 : [(42283 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1621740, _1621742), _1621738), _1621744) = _1621742, -(hAPP(hAPP(c_List_Onth(_1621740), _1621742), _1621738) = _1621744)], (42289 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Onth(_1621740), _1621742), _1621738) = _1621744, -(hAPP(hAPP(c_List_Olist__update(_1621740, _1621742), _1621738), _1621744) = _1621742)]]], (42295 ^ _779448) ^ [_1622032, _1622034, _1622036, _1622038, _1622040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622032), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622034)), _1622036))), 42298 ^ _779448 : [(42299 ^ _779448) ^ [] : [_1622032 = _1622038, -(hAPP(hAPP(c_List_Onth(_1622034), hAPP(hAPP(c_List_Olist__update(_1622034, _1622036), _1622032), _1622040)), _1622038) = _1622040)], (42305 ^ _779448) ^ [] : [-(_1622032 = _1622038), -(hAPP(hAPP(c_List_Onth(_1622034), hAPP(hAPP(c_List_Olist__update(_1622034, _1622036), _1622032), _1622040)), _1622038) = hAPP(hAPP(c_List_Onth(_1622034), _1622036), _1622038))]]], (42311 ^ _779448) ^ [_1622328, _1622330, _1622332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622328), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622330)), _1622332))), -(hAPP(hAPP(c_List_Otake(_1622330), _1622328), c_List_Obutlast(_1622330, _1622332)) = hAPP(hAPP(c_List_Otake(_1622330), _1622328), _1622332))], (42317 ^ _779448) ^ [_1622469, _1622471] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622469)), c_List_Obutlast(_1622469, _1622471)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622469)), _1622471)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42319 ^ _779448) ^ [_1622517, _1622519, _1622521, _1622523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622519)), _1622521))), -(hBOOL(hAPP(hAPP(c_member(_1622519), _1622523), hAPP(c_List_Oset(_1622519), hAPP(hAPP(c_List_Olist__update(_1622519, _1622521), _1622517), _1622523)))))], (42325 ^ _779448) ^ [_1622664, _1622666] : [-(c_List_Obutlast(_1622664, _1622666) = hAPP(hAPP(c_List_Otake(_1622664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622664)), _1622666)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1622666))], (42327 ^ _779448) ^ [_1622734, _1622736, _1622738, _1622740] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622734), tc_List_Olist(_1622734))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622734), tc_List_Olist(_1622734)), _1622736), _1622738)), c_List_Olistrel1(_1622734, _1622740))), 42332 ^ _779448 : [(42333 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622734, _1622734)), hAPP(hAPP(c_Product__Type_OPair(_1622734, _1622734), hAPP(hAPP(c_List_Onth(_1622734), _1622736), 42331 ^ [_1622734, _1622736, _1622738, _1622740])), 42330 ^ [_1622734, _1622736, _1622738, _1622740])), _1622740)))], (42335 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42331 ^ [_1622734, _1622736, _1622738, _1622740]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622734)), _1622736))))], (42337 ^ _779448) ^ [] : [-(_1622738 = hAPP(hAPP(c_List_Olist__update(_1622734, _1622736), 42331 ^ [_1622734, _1622736, _1622738, _1622740]), 42330 ^ [_1622734, _1622736, _1622738, _1622740]))]]], (42339 ^ _779448) ^ [_1623082, _1623084, _1623086, _1623088] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623082), tc_List_Olist(_1623082))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623082), tc_List_Olist(_1623082)), _1623084), _1623086)), c_List_Olistrel1(_1623082, _1623088)))), 42340 ^ _779448 : [(42341 ^ _779448) ^ [_1623215, _1623217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623082, _1623082)), hAPP(hAPP(c_Product__Type_OPair(_1623082, _1623082), hAPP(hAPP(c_List_Onth(_1623082), _1623084), _1623215)), _1623217)), _1623088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623215), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623082)), _1623084))), _1623086 = hAPP(hAPP(c_List_Olist__update(_1623082, _1623084), _1623215), _1623217)]]], (42353 ^ _779448) ^ [_1623515, _1623517, _1623519, _1623521] : [hBOOL(hAPP(c_List_Odistinct(_1623515), _1623517)), -(hBOOL(hAPP(hAPP(c_member(_1623515), _1623519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1623515, tc_HOL_Obool)), hAPP(c_List_Oset(_1623515), _1623517)), hAPP(hAPP(c_Set_Oinsert(_1623515), hAPP(hAPP(c_List_Onth(_1623515), _1623517), _1623521)), c_Orderings_Obot__class_Obot(tc_fun(_1623515, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1623515), hAPP(hAPP(c_List_Olist__update(_1623515, _1623517), _1623521), _1623519))))], (42363 ^ _779448) ^ [_1623733, _1623735] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1623733, _1623735))))], (42365 ^ _779448) ^ [_1623763, _1623765, _1623767] : [hBOOL(hAPP(c_List_Odistinct(_1623763), _1623765)), -(hBOOL(hAPP(c_List_Odistinct(_1623763), hAPP(hAPP(c_List_Otake(_1623763), _1623767), _1623765))))], (42371 ^ _779448) ^ [_1623874, _1623876, _1623878] : [hBOOL(hAPP(c_List_Odistinct(_1623874), _1623876)), -(hBOOL(hAPP(c_List_Odistinct(_1623874), c_List_Osublist(_1623874, _1623876, _1623878))))], (42377 ^ _779448) ^ [_1623977, _1623979, _1623981, _1623983] : [hBOOL(hAPP(c_List_Odistinct(_1623977), _1623979)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1623977, _1623981)), hAPP(hAPP(c_List_Ozip(_1623977, _1623981), _1623979), _1623983))))], (42383 ^ _779448) ^ [_1624098, _1624100, _1624102, _1624104] : [hBOOL(hAPP(c_List_Odistinct(_1624098), _1624100)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624102, _1624098)), hAPP(hAPP(c_List_Ozip(_1624102, _1624098), _1624104), _1624100))))], (42389 ^ _779448) ^ [_1624237, _1624239, _1624241] : [hBOOL(hAPP(c_List_Odistinct(_1624237), hAPP(hAPP(c_List_Olist_OCons(_1624237), _1624239), _1624241))), 42392 ^ _779448 : [(42393 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624237), _1624239), hAPP(c_List_Oset(_1624237), _1624241)))], (42395 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1624237), _1624241)))]]], (42397 ^ _779448) ^ [_1624404, _1624406, _1624408] : [-(hBOOL(hAPP(c_List_Odistinct(_1624404), hAPP(hAPP(c_List_Olist_OCons(_1624404), _1624406), _1624408)))), -(hBOOL(hAPP(hAPP(c_member(_1624404), _1624406), hAPP(c_List_Oset(_1624404), _1624408)))), hBOOL(hAPP(c_List_Odistinct(_1624404), _1624408))], (42407 ^ _779448) ^ [_1624598, _1624600] : [hAPP(c_Finite__Set_Ocard(_1624598), hAPP(c_List_Oset(_1624598), _1624600)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624598)), _1624600), -(hBOOL(hAPP(c_List_Odistinct(_1624598), _1624600)))], (42413 ^ _779448) ^ [_1624717, _1624719] : [hBOOL(hAPP(c_List_Odistinct(_1624717), _1624719)), -(hAPP(c_Finite__Set_Ocard(_1624717), hAPP(c_List_Oset(_1624717), _1624719)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624717)), _1624719))], (42419 ^ _779448) ^ [_1624836, _1624838, _1624840, _1624842] : [hBOOL(hAPP(c_List_Odistinct(_1624836), _1624838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624840), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624836)), _1624838))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624842), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624836)), _1624838))), 42430 ^ _779448 : [(42431 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Onth(_1624836), _1624838), _1624840) = hAPP(hAPP(c_List_Onth(_1624836), _1624838), _1624842), -(_1624840 = _1624842)], (42437 ^ _779448) ^ [] : [_1624840 = _1624842, -(hAPP(hAPP(c_List_Onth(_1624836), _1624838), _1624840) = hAPP(hAPP(c_List_Onth(_1624836), _1624838), _1624842))]]], (42461 ^ _779448) ^ [_1625746, _1625748] : [42463 ^ _779448 : [(42464 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42462 ^ [_1625746, _1625748]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625746)), _1625748))))], (42467 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42465 ^ [_1625746, _1625748]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625746)), _1625748))))], (42469 ^ _779448) ^ [] : [42462 ^ [_1625746, _1625748] = 42465 ^ [_1625746, _1625748]], (42471 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1625746), _1625748), 42462 ^ [_1625746, _1625748]) = hAPP(hAPP(c_List_Onth(_1625746), _1625748), 42465 ^ [_1625746, _1625748]))]], -(hBOOL(hAPP(c_List_Odistinct(_1625746), _1625748)))], (42443 ^ _779448) ^ [_1625286, _1625288] : [hBOOL(hAPP(c_List_Odistinct(_1625286), _1625288)), 42446 ^ _779448 : [(42447 ^ _779448) ^ [_1625418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625418), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625286)), _1625288))), 42450 ^ _779448 : [(42451 ^ _779448) ^ [_1625545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625545), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625286)), _1625288))), -(_1625418 = _1625545), hAPP(hAPP(c_List_Onth(_1625286), _1625288), _1625418) = hAPP(hAPP(c_List_Onth(_1625286), _1625288), _1625545)]]]]], (42475 ^ _779448) ^ [_1626178, _1626180] : [class_Groups_Ocomm__monoid__add(_1626178), hBOOL(hAPP(c_List_Odistinct(_1626178), _1626180)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626178), _1626180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626178, _1626178), c_COMBI(_1626178)), hAPP(c_List_Oset(_1626178), _1626180)))], (42485 ^ _779448) ^ [_1626364, _1626366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626364), _1626366)), -(c_Nitpick_Ocard_H(_1626364, _1626366) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626364)), c_Hilbert__Choice_OEps(tc_List_Olist(_1626364), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626364), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626364)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626364), tc_fun(_1626364, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626364, tc_HOL_Obool), tc_fun(tc_fun(_1626364, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626364)), c_fequal), c_List_Oset(_1626364))), _1626366))), c_List_Odistinct(_1626364)))))], (42491 ^ _779448) ^ [_1626601, _1626603] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1626601), _1626603))), -(c_Nitpick_Ocard_H(_1626601, _1626603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42497 ^ _779448) ^ [_1626646, _1626648, _1626650, _1626652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626646), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626648)), _1626650))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626646), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626648)), _1626652))), 42507 ^ _779448 : [(42508 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42506 ^ [_1626646, _1626648, _1626650, _1626652]), _1626646)))], (42510 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Onth(_1626648), _1626650), 42506 ^ [_1626646, _1626648, _1626650, _1626652]) = hAPP(hAPP(c_List_Onth(_1626648), _1626652), 42506 ^ [_1626646, _1626648, _1626650, _1626652])]], -(hAPP(hAPP(c_List_Otake(_1626648), _1626646), _1626650) = hAPP(hAPP(c_List_Otake(_1626648), _1626646), _1626652))], (42514 ^ _779448) ^ [_1627063, _1627065, _1627067] : [hBOOL(hAPP(c_List_Odistinct(_1627063), _1627065)), -(hAPP(c_List_Oset(_1627063), c_List_Oremove1(_1627063, _1627067, _1627065)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627063, tc_HOL_Obool)), hAPP(c_List_Oset(_1627063), _1627065)), hAPP(hAPP(c_Set_Oinsert(_1627063), _1627067), c_Orderings_Obot__class_Obot(tc_fun(_1627063, tc_HOL_Obool)))))], (42520 ^ _779448) ^ [_1627241, _1627243, _1627245, _1627247] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627243), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627241)), hAPP(hAPP(c_List_Olist_OCons(_1627243), _1627245), _1627247)) = c_List_Olist_ONil(_1627243))], (42526 ^ _779448) ^ [_1627364, _1627366, _1627368, _1627370] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627364) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1627366), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627364)), hAPP(hAPP(c_List_Olist_OCons(_1627366), _1627368), _1627370)) = hAPP(hAPP(c_List_Olist_OCons(_1627366), _1627368), hAPP(hAPP(c_List_Otake(_1627366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627364)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627370)))], (42532 ^ _779448) ^ [_1627453, _1627455] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627453)), c_List_Olist_ONil(_1627453)), c_List_Olists(_1627453, _1627455))))], (42534 ^ _779448) ^ [_1627492, _1627494, _1627496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627492), tc_List_Olist(_1627492))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627492), tc_List_Olist(_1627492)), _1627494), c_List_Olist_ONil(_1627492))), c_List_Olistrel(_1627492, _1627496))), -(_1627494 = c_List_Olist_ONil(_1627492))], (42540 ^ _779448) ^ [_1627639, _1627641, _1627643] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627639), tc_List_Olist(_1627639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627639), tc_List_Olist(_1627639)), c_List_Olist_ONil(_1627639)), _1627641)), c_List_Olistrel(_1627639, _1627643))), -(_1627641 = c_List_Olist_ONil(_1627639))], (42546 ^ _779448) ^ [_1627785, _1627787] : [-(_1627785 = c_List_Olist_ONil(_1627787)), hBOOL(hAPP(c_List_Odistinct(_1627787), _1627785)), -(hBOOL(hAPP(c_List_Odistinct(_1627787), c_List_Obutlast(_1627787, _1627785))))], (42556 ^ _779448) ^ [_1627936, _1627938, _1627940] : [hBOOL(hAPP(c_List_Odistinct(_1627936), _1627938)), -(hBOOL(hAPP(c_List_Odistinct(_1627936), c_List_Oremove1(_1627936, _1627940, _1627938))))], (42562 ^ _779448) ^ [_1628039] : [-(hBOOL(hAPP(c_List_Odistinct(_1628039), c_List_Olist_ONil(_1628039))))], (42564 ^ _779448) ^ [_1628068] : [-(c_List_Obutlast(_1628068, c_List_Olist_ONil(_1628068)) = c_List_Olist_ONil(_1628068))], (42566 ^ _779448) ^ [_1628110, _1628112, _1628114] : [_1628110 = c_List_Olist_ONil(_1628112), -(c_List_Obutlast(_1628112, hAPP(hAPP(c_List_Olist_OCons(_1628112), _1628114), _1628110)) = c_List_Olist_ONil(_1628112))], (42572 ^ _779448) ^ [_1628213, _1628215, _1628217] : [-(_1628213 = c_List_Olist_ONil(_1628215)), -(c_List_Obutlast(_1628215, hAPP(hAPP(c_List_Olist_OCons(_1628215), _1628217), _1628213)) = hAPP(hAPP(c_List_Olist_OCons(_1628215), _1628217), c_List_Obutlast(_1628215, _1628213)))], (42578 ^ _779448) ^ [_1628292, _1628294, _1628296] : [c_List_Olist_ONil(_1628292) = hAPP(hAPP(c_List_Olist_OCons(_1628292), _1628294), _1628296)], (42580 ^ _779448) ^ [_1628344, _1628346, _1628348] : [hAPP(hAPP(c_List_Olist_OCons(_1628344), _1628346), _1628348) = c_List_Olist_ONil(_1628344)], (42582 ^ _779448) ^ [_1628396, _1628398, _1628400, _1628402] : [_1628396 = _1628398, -(c_List_Oremove1(_1628400, _1628396, hAPP(hAPP(c_List_Olist_OCons(_1628400), _1628398), _1628402)) = _1628402)], (42588 ^ _779448) ^ [_1628495, _1628497, _1628499, _1628501] : [-(_1628495 = _1628497), -(c_List_Oremove1(_1628499, _1628495, hAPP(hAPP(c_List_Olist_OCons(_1628499), _1628497), _1628501)) = hAPP(hAPP(c_List_Olist_OCons(_1628499), _1628497), c_List_Oremove1(_1628499, _1628495, _1628501)))], (42594 ^ _779448) ^ [_1628561, _1628563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1628561), _1628563)), -(c_List_Oupto(_1628563, _1628561) = c_List_Olist_ONil(tc_Int_Oint))], (42610 ^ _779448) ^ [_1628784, _1628786, _1628788] : [42611 ^ _779448 : [(42612 ^ _779448) ^ [] : [_1628786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42614 ^ _779448) ^ [] : [_1628788 = c_List_Olist_ONil(_1628784)]], -(hAPP(hAPP(c_List_Otake(_1628784), _1628786), _1628788) = c_List_Olist_ONil(_1628784))], (42600 ^ _779448) ^ [_1628672, _1628674, _1628676] : [hAPP(hAPP(c_List_Otake(_1628672), _1628674), _1628676) = c_List_Olist_ONil(_1628672), -(_1628674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1628676 = c_List_Olist_ONil(_1628672))], (42618 ^ _779448) ^ [_1628927, _1628929] : [-(hAPP(hAPP(c_List_Otake(_1628927), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1628929) = c_List_Olist_ONil(_1628927))], (42620 ^ _779448) ^ [_1628962, _1628964] : [-(hAPP(hAPP(c_List_Otake(_1628962), _1628964), c_List_Olist_ONil(_1628962)) = c_List_Olist_ONil(_1628962))], (42622 ^ _779448) ^ [_1628999, _1629001] : [-(c_List_Osublist(_1628999, c_List_Olist_ONil(_1628999), _1629001) = c_List_Olist_ONil(_1628999))], (42624 ^ _779448) ^ [_1629032, _1629034, _1629036, _1629038] : [-(c_List_Oremove1(_1629032, _1629034, c_List_Oremove1(_1629032, _1629036, _1629038)) = c_List_Oremove1(_1629032, _1629036, c_List_Oremove1(_1629032, _1629034, _1629038)))], (42626 ^ _779448) ^ [_1629077, _1629079] : [-(c_List_Oremove1(_1629077, _1629079, c_List_Olist_ONil(_1629077)) = c_List_Olist_ONil(_1629077))], (42628 ^ _779448) ^ [_1629110, _1629112] : [-(c_List_Olistrelp(_1629110, _1629112, c_List_Olist_ONil(_1629110), c_List_Olist_ONil(_1629110)))], (42630 ^ _779448) ^ [_1629141, _1629143] : [-(c_List_Olistrelp(_1629141, _1629143, c_List_Olist_ONil(_1629141), c_List_Olist_ONil(_1629141)))], (42632 ^ _779448) ^ [_1629172, _1629174, _1629176] : [-(hAPP(hAPP(c_List_Ozip(_1629172, _1629174), c_List_Olist_ONil(_1629172)), _1629176) = c_List_Olist_ONil(tc_prod(_1629172, _1629174)))], (42634 ^ _779448) ^ [_1629215, _1629217, _1629219] : [-(hAPP(hAPP(c_List_Ozip(_1629215, _1629217), _1629219), c_List_Olist_ONil(_1629217)) = c_List_Olist_ONil(tc_prod(_1629215, _1629217)))], (42636 ^ _779448) ^ [_1629258] : [class_Groups_Omonoid__add(_1629258), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629258), c_List_Olist_ONil(_1629258)) = c_Groups_Ozero__class_Ozero(_1629258))], (42642 ^ _779448) ^ [_1629364, _1629366] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629364)), _1629366) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1629366 = c_List_Olist_ONil(_1629364))], (42648 ^ _779448) ^ [_1629455, _1629457] : [_1629457 = c_List_Olist_ONil(_1629455), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629455)), _1629457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42654 ^ _779448) ^ [_1629552] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629552)), c_List_Olist_ONil(_1629552)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42656 ^ _779448) ^ [_1629599, _1629601] : [hAPP(c_List_Oset(_1629599), _1629601) = c_Orderings_Obot__class_Obot(tc_fun(_1629599, tc_HOL_Obool)), -(_1629601 = c_List_Olist_ONil(_1629599))], (42662 ^ _779448) ^ [_1629696, _1629698] : [_1629698 = c_List_Olist_ONil(_1629696), -(hAPP(c_List_Oset(_1629696), _1629698) = c_Orderings_Obot__class_Obot(tc_fun(_1629696, tc_HOL_Obool)))], (42668 ^ _779448) ^ [_1629814, _1629816] : [c_Orderings_Obot__class_Obot(tc_fun(_1629814, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629814), _1629816), -(_1629816 = c_List_Olist_ONil(_1629814))], (42674 ^ _779448) ^ [_1629911, _1629913] : [_1629913 = c_List_Olist_ONil(_1629911), -(c_Orderings_Obot__class_Obot(tc_fun(_1629911, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629911), _1629913))], (42680 ^ _779448) ^ [_1630014] : [-(hAPP(c_List_Oset(_1630014), c_List_Olist_ONil(_1630014)) = c_Orderings_Obot__class_Obot(tc_fun(_1630014, tc_HOL_Obool)))], (42682 ^ _779448) ^ [_1630049, _1630051, _1630053] : [-(hAPP(hAPP(c_List_Olist__update(_1630049, c_List_Olist_ONil(_1630049)), _1630051), _1630053) = c_List_Olist_ONil(_1630049))], (42684 ^ _779448) ^ [_1630089, _1630091, _1630093] : [-(hAPP(hAPP(c_List_Olist__update(_1630089, c_List_Olist_ONil(_1630089)), _1630091), _1630093) = c_List_Olist_ONil(_1630089))], (42686 ^ _779448) ^ [_1630150, _1630152, _1630154, _1630156] : [hAPP(hAPP(c_List_Olist__update(_1630150, _1630152), _1630154), _1630156) = c_List_Olist_ONil(_1630150), -(_1630152 = c_List_Olist_ONil(_1630150))], (42692 ^ _779448) ^ [_1630253, _1630255, _1630257, _1630259] : [_1630255 = c_List_Olist_ONil(_1630253), -(hAPP(hAPP(c_List_Olist__update(_1630253, _1630255), _1630257), _1630259) = c_List_Olist_ONil(_1630253))], (42698 ^ _779448) ^ [_1630362, _1630364] : [-(c_List_Olist_Olist__size(_1630362, _1630364, c_List_Olist_ONil(_1630362)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42700 ^ _779448) ^ [_1630389, _1630391, _1630393] : [-(hBOOL(hAPP(hAPP(c_member(_1630389), _1630391), hAPP(c_List_Oset(_1630389), _1630393)))), -(c_List_Oremove1(_1630389, _1630391, _1630393) = _1630393)], (42706 ^ _779448) ^ [_1630442, _1630444, _1630446, _1630448] : [-(hBOOL(hAPP(hAPP(c_member(_1630442), _1630444), hAPP(c_List_Oset(_1630442), _1630446)))), hBOOL(hAPP(hAPP(c_member(_1630442), _1630444), hAPP(c_List_Oset(_1630442), c_List_Oremove1(_1630442, _1630448, _1630446))))], (42712 ^ _779448) ^ [_1630565, _1630567, _1630569, _1630571] : [-(_1630565 = _1630567), 42715 ^ _779448 : [(42716 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630569), _1630565), hAPP(c_List_Oset(_1630569), c_List_Oremove1(_1630569, _1630567, _1630571)))), -(hBOOL(hAPP(hAPP(c_member(_1630569), _1630565), hAPP(c_List_Oset(_1630569), _1630571))))], (42722 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630569), _1630565), hAPP(c_List_Oset(_1630569), _1630571))), -(hBOOL(hAPP(hAPP(c_member(_1630569), _1630565), hAPP(c_List_Oset(_1630569), c_List_Oremove1(_1630569, _1630567, _1630571)))))]]], (42728 ^ _779448) ^ [_1630866, _1630868] : [-(c_List_Osublist(_1630866, _1630868, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1630866))], (42730 ^ _779448) ^ [_1630897, _1630899, _1630901] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630897, tc_HOL_Obool)), hAPP(c_List_Oset(_1630897), c_List_Oremove1(_1630897, _1630899, _1630901))), hAPP(c_List_Oset(_1630897), _1630901))))], (42732 ^ _779448) ^ [_1630963, _1630965] : [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(_1630963)), _1630965))), _1630965 = c_List_Olist_ONil(_1630963)], (42738 ^ _779448) ^ [_1631057, _1631059] : [-(_1631059 = c_List_Olist_ONil(_1631057)), -(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(_1631057)), _1631059))))], (42744 ^ _779448) ^ [_1631106, _1631108, _1631110] : [-(hAPP(hAPP(c_List_Otake(_1631106), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1631106), _1631108), _1631110)) = hAPP(hAPP(c_List_Olist_OCons(_1631106), _1631108), c_List_Olist_ONil(_1631106)))], (42746 ^ _779448) ^ [_1631174, _1631176, _1631178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631174), tc_List_Olist(_1631174))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631174), tc_List_Olist(_1631174)), _1631176), c_List_Olist_ONil(_1631174))), c_List_Olistrel1(_1631174, _1631178)))], (42748 ^ _779448) ^ [_1631248, _1631250, _1631252] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631248), tc_List_Olist(_1631248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631248), tc_List_Olist(_1631248)), c_List_Olist_ONil(_1631248)), _1631250)), c_List_Olistrel1(_1631248, _1631252)))], (42750 ^ _779448) ^ [_1631307, _1631309] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631307), tc_List_Olist(_1631307))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631307), tc_List_Olist(_1631307)), c_List_Olist_ONil(_1631307)), c_List_Olist_ONil(_1631307))), c_List_Olistrel(_1631307, _1631309))))], (42752 ^ _779448) ^ [_1631381, _1631383, _1631385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631381), tc_List_Olist(_1631381))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631381), tc_List_Olist(_1631381)), _1631383), c_List_Olist_ONil(_1631381))), c_List_Olexord(_1631381, _1631385)))], (42754 ^ _779448) ^ [_1631455, _1631457, _1631459] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631455), tc_List_Olist(_1631455))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631455), tc_List_Olist(_1631455)), _1631457), c_List_Olist_ONil(_1631455))), c_List_Olex(_1631455, _1631459)))], (42756 ^ _779448) ^ [_1631529, _1631531, _1631533] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631529), tc_List_Olist(_1631529))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631529), tc_List_Olist(_1631529)), c_List_Olist_ONil(_1631529)), _1631531)), c_List_Olex(_1631529, _1631533)))], (42758 ^ _779448) ^ [_1631588, _1631590, _1631592, _1631594] : [-(hAPP(hAPP(c_List_Otake(_1631588), _1631590), hAPP(hAPP(c_List_Olist_OCons(_1631588), _1631592), _1631594)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1631588), c_List_Olist_ONil(_1631588), hAPP(hAPP(c_COMBB(tc_List_Olist(_1631588), tc_List_Olist(_1631588), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1631588), _1631592)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1631588), tc_List_Olist(_1631588)), c_List_Otake(_1631588)), _1631594)), _1631590))], (42760 ^ _779448) ^ [_1631686, _1631688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631686), _1631688)), -(c_List_Oupto(_1631686, _1631688) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1631686), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631686), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1631688)))], (42766 ^ _779448) ^ [_1631803, _1631805] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631803), _1631805))), -(c_List_Oupto(_1631803, _1631805) = c_List_Olist_ONil(tc_Int_Oint))], (42772 ^ _779448) ^ [_1631861, _1631863, _1631865] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631861)), -(c_List_Osublist(_1631863, hAPP(hAPP(c_List_Olist_OCons(_1631863), _1631865), c_List_Olist_ONil(_1631863)), _1631861) = hAPP(hAPP(c_List_Olist_OCons(_1631863), _1631865), c_List_Olist_ONil(_1631863)))], (42778 ^ _779448) ^ [_1631986, _1631988, _1631990] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631986))), -(c_List_Osublist(_1631988, hAPP(hAPP(c_List_Olist_OCons(_1631988), _1631990), c_List_Olist_ONil(_1631988)), _1631986) = c_List_Olist_ONil(_1631988))], (42784 ^ _779448) ^ [_1632044] : [-(c_List_Olists(_1632044, c_Orderings_Obot__class_Obot(tc_fun(_1632044, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632044)), c_List_Olist_ONil(_1632044)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632044), tc_HOL_Obool))))], (42786 ^ _779448) ^ [_1632109, _1632111, _1632113, _1632115] : [_1632109 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1632111), _1632109), hAPP(hAPP(c_List_Olist_OCons(_1632111), _1632113), _1632115)) = c_List_Olist_ONil(_1632111))], (42792 ^ _779448) ^ [_1632220, _1632222, _1632224, _1632226] : [-(_1632220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1632222), _1632220), hAPP(hAPP(c_List_Olist_OCons(_1632222), _1632224), _1632226)) = hAPP(hAPP(c_List_Olist_OCons(_1632222), _1632224), hAPP(hAPP(c_List_Otake(_1632222), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632220), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632226)))], (42798 ^ _779448) ^ [_1632309, _1632311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632309)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632311))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632309), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632311)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632309)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632309)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632311))))], (42804 ^ _779448) ^ [_1632468, _1632470] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632470)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632470)) = c_List_Olist_ONil(tc_Int_Oint))], (42810 ^ _779448) ^ [_1632526, _1632528] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1632526), tc_List_Olist(_1632526), c_List_Olistrel(_1632526, _1632528)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632526)), c_List_Olist_ONil(_1632526)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632526), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632526)), c_List_Olist_ONil(_1632526)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632526), tc_HOL_Obool))))], (42812 ^ _779448) ^ [_1632603, _1632605] : [-(c_List_Oset__Cons(_1632603, _1632605, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632603)), c_List_Olist_ONil(_1632603)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632603), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1632603, tc_List_Olist(_1632603), hAPP(hAPP(c_COMBC(_1632603, tc_List_Olist(_1632603), tc_List_Olist(_1632603)), c_List_Olist_OCons(_1632603)), c_List_Olist_ONil(_1632603))), _1632605))], (42814 ^ _779448) ^ [_1632690, _1632692, _1632694] : [hBOOL(hAPP(hAPP(c_member(_1632690), _1632692), hAPP(c_List_Oset(_1632690), _1632694))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632690)), c_List_Oremove1(_1632690, _1632692, _1632694)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632690)), _1632694)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42820 ^ _779448) ^ [_1632835, _1632837, _1632839] : [-(hBOOL(hAPP(hAPP(c_member(_1632835), _1632837), hAPP(c_List_Oset(_1632835), _1632839)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632835)), c_List_Oremove1(_1632835, _1632837, _1632839)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632835)), _1632839))], (42826 ^ _779448) ^ [_1632905, _1632907] : [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), _1632905), _1632907))), 42829 ^ _779448 : [(42830 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632905), _1632907)), -(c_List_Oupto(_1632905, _1632907) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1632905), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1632905), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1632907)))], (42836 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632905), _1632907))), -(c_List_Oupto(_1632905, _1632907) = c_List_Olist_ONil(tc_Int_Oint))]]], (42842 ^ _779448) ^ [_1633155, _1633157, _1633159] : [-(_1633155 = c_List_Olist_ONil(_1633157)), -(hBOOL(hAPP(hAPP(c_member(_1633157), hAPP(c_Product__Type_Ofst(_1633157, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633157, _1633155), _1633159))), hAPP(c_List_Oset(_1633157), _1633155))))], (42848 ^ _779448) ^ [_1633219] : [-(c_List_Olistset(_1633219, c_List_Olist_ONil(tc_fun(_1633219, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633219)), c_List_Olist_ONil(_1633219)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633219), tc_HOL_Obool))))], (42850 ^ _779448) ^ [_1633269, _1633271, _1633273, _1633275, _1633277] : [-(hAPP(hAPP(c_List_Ozip(_1633269, _1633271), hAPP(hAPP(c_List_Olist_OCons(_1633269), _1633273), _1633275)), _1633277) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633269, _1633271)), _1633271, c_List_Olist_ONil(tc_prod(_1633269, _1633271)), hAPP(hAPP(c_COMBC(_1633271, tc_fun(tc_List_Olist(_1633271), tc_List_Olist(tc_prod(_1633269, _1633271))), tc_fun(tc_List_Olist(_1633271), tc_List_Olist(tc_prod(_1633269, _1633271)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633269, _1633271)), tc_List_Olist(tc_prod(_1633269, _1633271))), tc_fun(tc_fun(tc_List_Olist(_1633271), tc_List_Olist(tc_prod(_1633269, _1633271))), tc_fun(tc_List_Olist(_1633271), tc_List_Olist(tc_prod(_1633269, _1633271)))), _1633271), c_COMBB(tc_List_Olist(tc_prod(_1633269, _1633271)), tc_List_Olist(tc_prod(_1633269, _1633271)), tc_List_Olist(_1633271))), hAPP(hAPP(c_COMBB(tc_prod(_1633269, _1633271), tc_fun(tc_List_Olist(tc_prod(_1633269, _1633271)), tc_List_Olist(tc_prod(_1633269, _1633271))), _1633271), c_List_Olist_OCons(tc_prod(_1633269, _1633271))), hAPP(c_Product__Type_OPair(_1633269, _1633271), _1633273)))), hAPP(c_List_Ozip(_1633269, _1633271), _1633275))), _1633277))], (42852 ^ _779448) ^ [_1633470, _1633472, _1633474, _1633476, _1633478, _1633480] : [-(hAPP(c_List_Olist_Olist__case(_1633470, _1633472, _1633474, _1633476), hAPP(hAPP(c_List_Olist_OCons(_1633472), _1633478), _1633480)) = hAPP(hAPP(_1633476, _1633478), _1633480))], (42854 ^ _779448) ^ [_1633525, _1633527, _1633529, _1633531] : [-(hAPP(c_List_Olist_Olist__case(_1633525, _1633527, _1633529, _1633531), c_List_Olist_ONil(_1633527)) = _1633529)], (42856 ^ _779448) ^ [_1633564, _1633566, _1633568] : [-(c_List_Olistset(_1633564, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1633564, tc_HOL_Obool)), _1633566), _1633568)) = c_List_Oset__Cons(_1633564, _1633566, c_List_Olistset(_1633564, _1633568)))], (42858 ^ _779448) ^ [_1633612, _1633614, _1633616, _1633618, _1633620] : [-(hAPP(hAPP(c_List_Ozip(_1633612, _1633614), _1633616), hAPP(hAPP(c_List_Olist_OCons(_1633614), _1633618), _1633620)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633612, _1633614)), _1633612, c_List_Olist_ONil(tc_prod(_1633612, _1633614)), hAPP(hAPP(c_COMBC(_1633612, tc_fun(tc_List_Olist(_1633612), tc_List_Olist(tc_prod(_1633612, _1633614))), tc_fun(tc_List_Olist(_1633612), tc_List_Olist(tc_prod(_1633612, _1633614)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633612, _1633614)), tc_List_Olist(tc_prod(_1633612, _1633614))), tc_fun(tc_fun(tc_List_Olist(_1633612), tc_List_Olist(tc_prod(_1633612, _1633614))), tc_fun(tc_List_Olist(_1633612), tc_List_Olist(tc_prod(_1633612, _1633614)))), _1633612), c_COMBB(tc_List_Olist(tc_prod(_1633612, _1633614)), tc_List_Olist(tc_prod(_1633612, _1633614)), tc_List_Olist(_1633612))), hAPP(hAPP(c_COMBB(tc_prod(_1633612, _1633614), tc_fun(tc_List_Olist(tc_prod(_1633612, _1633614)), tc_List_Olist(tc_prod(_1633612, _1633614))), _1633612), c_List_Olist_OCons(tc_prod(_1633612, _1633614))), hAPP(hAPP(c_COMBC(_1633612, _1633614, tc_prod(_1633612, _1633614)), c_Product__Type_OPair(_1633612, _1633614)), _1633618)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1633612), tc_List_Olist(_1633614), tc_List_Olist(tc_prod(_1633612, _1633614))), c_List_Ozip(_1633612, _1633614)), _1633620))), _1633616))], (42860 ^ _779448) ^ [_1633839, _1633841, _1633843] : [class_Orderings_Olinorder(_1633839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633839), _1633841)), -(c_List_Olinorder__class_Osorted__list__of__set(_1633839, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1633839, tc_HOL_Obool)), _1633841), hAPP(hAPP(c_Set_Oinsert(_1633839), _1633843), c_Orderings_Obot__class_Obot(tc_fun(_1633839, tc_HOL_Obool))))) = c_List_Oremove1(_1633839, _1633843, c_List_Olinorder__class_Osorted__list__of__set(_1633839, _1633841)))], (42870 ^ _779448) ^ [_1634046, _1634048, _1634050] : [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), _1634046), _1634048))), -(hBOOL(hAPP(hAPP(_1634050, _1634046), _1634048))), 42877 ^ _779448 : [(42878 ^ _779448) ^ [] : [-(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), 42875 ^ [_1634046, _1634048, _1634050]), 42876 ^ [_1634046, _1634048, _1634050]))))], (42886 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1634050, 42875 ^ [_1634046, _1634048, _1634050]), 42876 ^ [_1634046, _1634048, _1634050]))], (42880 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42875 ^ [_1634046, _1634048, _1634050]), 42876 ^ [_1634046, _1634048, _1634050])), -(hBOOL(hAPP(hAPP(_1634050, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42875 ^ [_1634046, _1634048, _1634050]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42876 ^ [_1634046, _1634048, _1634050])))]]], (42890 ^ _779448) ^ [_1634537] : [class_Orderings_Olinorder(_1634537), -(c_List_Olinorder__class_Osorted__list__of__set(_1634537, c_Orderings_Obot__class_Obot(tc_fun(_1634537, tc_HOL_Obool))) = c_List_Olist_ONil(_1634537))], (42896 ^ _779448) ^ [_1634648, _1634650, _1634652, _1634654, _1634656] : [_1634648 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634650, _1634652, _1634654), _1634648), _1634656) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634652), _1634650), c_List_Olist_ONil(_1634652)), _1634656))], (42902 ^ _779448) ^ [_1634771, _1634773, _1634775, _1634777, _1634779] : [-(_1634771 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634773, _1634775, _1634777), _1634771), _1634779) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1634775), _1634773), tc_prod(_1634775, _1634773), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634775), _1634773), c_List_Olist_ONil(_1634775)), _1634779), hAPP(c_Product__Type_Oprod_Oprod__case(_1634775, _1634773, tc_prod(tc_List_Olist(_1634775), _1634773)), hAPP(hAPP(c_COMBC(_1634775, tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773)), tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1634775), _1634773), tc_prod(tc_List_Olist(_1634775), _1634773)), tc_fun(tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773)), tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773))), _1634775), c_COMBB(tc_prod(tc_List_Olist(_1634775), _1634773), tc_prod(tc_List_Olist(_1634775), _1634773), _1634773)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634775), tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773))), tc_fun(tc_prod(tc_List_Olist(_1634775), _1634773), tc_prod(tc_List_Olist(_1634775), _1634773)), _1634775), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1634775), _1634773, tc_prod(tc_List_Olist(_1634775), _1634773))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634775), tc_List_Olist(_1634775)), tc_fun(tc_List_Olist(_1634775), tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773))), _1634775), hAPP(c_COMBB(tc_List_Olist(_1634775), tc_fun(_1634773, tc_prod(tc_List_Olist(_1634775), _1634773)), tc_List_Olist(_1634775)), c_Product__Type_OPair(tc_List_Olist(_1634775), _1634773))), c_List_Olist_OCons(_1634775))))), hAPP(c_Lazy__Sequence_Oanamorph(_1634773, _1634775, _1634777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1634771), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1634777, _1634779)))], (42908 ^ _779448) ^ [_1635065, _1635067, _1635069, _1635071] : [-(c_List_Osublist(_1635065, hAPP(hAPP(c_List_Olist_OCons(_1635065), _1635067), _1635069), _1635071) = hAPP(hAPP(c_List_Oappend(_1635065), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1635065)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635071)), hAPP(hAPP(c_List_Olist_OCons(_1635065), _1635067), c_List_Olist_ONil(_1635065))), c_List_Olist_ONil(_1635065))), c_List_Osublist(_1635065, _1635069, 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)), _1635071)))))], (42910 ^ _779448) ^ [_1635176, _1635178, _1635180, _1635182, _1635184] : [hAPP(hAPP(c_List_Oappend(_1635176), _1635178), _1635180) = hAPP(hAPP(c_List_Olist_OCons(_1635176), _1635182), _1635184), 42915 ^ _779448 : [(42916 ^ _779448) ^ [] : [-(_1635178 = c_List_Olist_ONil(_1635176))], (42918 ^ _779448) ^ [] : [-(_1635180 = hAPP(hAPP(c_List_Olist_OCons(_1635176), _1635182), _1635184))]], 42920 ^ _779448 : [(42921 ^ _779448) ^ [] : [-(_1635178 = hAPP(hAPP(c_List_Olist_OCons(_1635176), _1635182), 42919 ^ [_1635176, _1635178, _1635180, _1635182, _1635184]))], (42923 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1635176), 42919 ^ [_1635176, _1635178, _1635180, _1635182, _1635184]), _1635180) = _1635184)]]], (42925 ^ _779448) ^ [_1635469, _1635471, _1635473, _1635475, _1635477] : [-(hAPP(hAPP(c_List_Oappend(_1635469), _1635471), _1635473) = hAPP(hAPP(c_List_Olist_OCons(_1635469), _1635475), _1635477)), 42926 ^ _779448 : [(42927 ^ _779448) ^ [] : [_1635471 = c_List_Olist_ONil(_1635469), _1635473 = hAPP(hAPP(c_List_Olist_OCons(_1635469), _1635475), _1635477)], (42933 ^ _779448) ^ [_1635652] : [_1635471 = hAPP(hAPP(c_List_Olist_OCons(_1635469), _1635475), _1635652), hAPP(hAPP(c_List_Oappend(_1635469), _1635652), _1635473) = _1635477]]], (42941 ^ _779448) ^ [_1635840, _1635842, _1635844, _1635846, _1635848] : [hAPP(hAPP(c_List_Olist_OCons(_1635840), _1635842), _1635844) = hAPP(hAPP(c_List_Oappend(_1635840), _1635846), _1635848), 42946 ^ _779448 : [(42947 ^ _779448) ^ [] : [-(_1635846 = c_List_Olist_ONil(_1635840))], (42949 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635840), _1635842), _1635844) = _1635848)]], 42951 ^ _779448 : [(42952 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635840), _1635842), 42950 ^ [_1635840, _1635842, _1635844, _1635846, _1635848]) = _1635846)], (42954 ^ _779448) ^ [] : [-(_1635844 = hAPP(hAPP(c_List_Oappend(_1635840), 42950 ^ [_1635840, _1635842, _1635844, _1635846, _1635848]), _1635848))]]], (42956 ^ _779448) ^ [_1636133, _1636135, _1636137, _1636139, _1636141] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636133), _1636135), _1636137) = hAPP(hAPP(c_List_Oappend(_1636133), _1636139), _1636141)), 42957 ^ _779448 : [(42958 ^ _779448) ^ [] : [_1636139 = c_List_Olist_ONil(_1636133), hAPP(hAPP(c_List_Olist_OCons(_1636133), _1636135), _1636137) = _1636141], (42964 ^ _779448) ^ [_1636316] : [hAPP(hAPP(c_List_Olist_OCons(_1636133), _1636135), _1636316) = _1636139, _1636137 = hAPP(hAPP(c_List_Oappend(_1636133), _1636316), _1636141)]]], (42972 ^ _779448) ^ [_1636504, _1636506, _1636508, _1636510, _1636512] : [hAPP(hAPP(c_List_Oappend(_1636504), _1636506), hAPP(hAPP(c_List_Olist_OCons(_1636504), _1636508), c_List_Olist_ONil(_1636504))) = hAPP(hAPP(c_List_Oappend(_1636504), _1636510), hAPP(hAPP(c_List_Olist_OCons(_1636504), _1636512), c_List_Olist_ONil(_1636504))), 42975 ^ _779448 : [(42976 ^ _779448) ^ [] : [-(_1636506 = _1636510)], (42978 ^ _779448) ^ [] : [-(_1636508 = _1636512)]]], (42980 ^ _779448) ^ [_1636681, _1636683, _1636685, _1636687, _1636689] : [-(hAPP(hAPP(c_List_Oappend(_1636681), _1636683), hAPP(hAPP(c_List_Olist_OCons(_1636681), _1636685), c_List_Olist_ONil(_1636681))) = hAPP(hAPP(c_List_Oappend(_1636681), _1636687), hAPP(hAPP(c_List_Olist_OCons(_1636681), _1636689), c_List_Olist_ONil(_1636681)))), _1636683 = _1636687, _1636685 = _1636689], (42990 ^ _779448) ^ [_1636896, _1636898, _1636900, _1636902] : [-(hAPP(hAPP(c_List_Oappend(_1636896), hAPP(hAPP(c_List_Olist_OCons(_1636896), _1636898), _1636900)), _1636902) = hAPP(hAPP(c_List_Olist_OCons(_1636896), _1636898), hAPP(hAPP(c_List_Oappend(_1636896), _1636900), _1636902)))], (42992 ^ _779448) ^ [_1636957, _1636959, _1636961, _1636963, _1636965, _1636967] : [hAPP(hAPP(c_List_Olist_OCons(_1636957), _1636959), _1636961) = _1636963, _1636965 = hAPP(hAPP(c_List_Oappend(_1636957), _1636961), _1636967), -(hAPP(hAPP(c_List_Olist_OCons(_1636957), _1636959), _1636965) = hAPP(hAPP(c_List_Oappend(_1636957), _1636963), _1636967))], (43002 ^ _779448) ^ [_1637187, _1637189, _1637191, _1637193] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637187)), hAPP(hAPP(c_List_Oappend(_1637187), _1637189), _1637191)), c_List_Olists(_1637187, _1637193))), 43005 ^ _779448 : [(43006 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637187)), _1637189), c_List_Olists(_1637187, _1637193))))], (43008 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637187)), _1637191), c_List_Olists(_1637187, _1637193))))]]], (43010 ^ _779448) ^ [_1637378, _1637380, _1637382, _1637384] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637378)), hAPP(hAPP(c_List_Oappend(_1637378), _1637380), _1637382)), c_List_Olists(_1637378, _1637384)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637378)), _1637380), c_List_Olists(_1637378, _1637384))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637378)), _1637382), c_List_Olists(_1637378, _1637384)))], (43020 ^ _779448) ^ [_1637605, _1637607, _1637609, _1637611, _1637613, _1637615] : [hAPP(hAPP(c_List_Oappend(_1637605), _1637607), _1637609) = _1637611, _1637613 = hAPP(hAPP(c_List_Oappend(_1637605), _1637609), _1637615), -(hAPP(hAPP(c_List_Oappend(_1637605), _1637607), _1637613) = hAPP(hAPP(c_List_Oappend(_1637605), _1637611), _1637615))], (43030 ^ _779448) ^ [_1637835, _1637837, _1637839, _1637841] : [hAPP(hAPP(c_List_Oappend(_1637835), _1637837), _1637839) = hAPP(hAPP(c_List_Oappend(_1637835), _1637841), _1637839), -(_1637837 = _1637841)], (43036 ^ _779448) ^ [_1637944, _1637946, _1637948, _1637950] : [_1637946 = _1637950, -(hAPP(hAPP(c_List_Oappend(_1637944), _1637946), _1637948) = hAPP(hAPP(c_List_Oappend(_1637944), _1637950), _1637948))], (43042 ^ _779448) ^ [_1638080, _1638082, _1638084, _1638086] : [hAPP(hAPP(c_List_Oappend(_1638080), _1638082), _1638084) = hAPP(hAPP(c_List_Oappend(_1638080), _1638082), _1638086), -(_1638084 = _1638086)], (43048 ^ _779448) ^ [_1638189, _1638191, _1638193, _1638195] : [_1638193 = _1638195, -(hAPP(hAPP(c_List_Oappend(_1638189), _1638191), _1638193) = hAPP(hAPP(c_List_Oappend(_1638189), _1638191), _1638195))], (43054 ^ _779448) ^ [_1638328, _1638330, _1638332, _1638334, _1638336] : [hAPP(hAPP(c_List_Oappend(_1638328), _1638330), _1638332) = hAPP(hAPP(c_List_Oappend(_1638328), _1638334), _1638336), 43060 ^ _779448 : [(43061 ^ _779448) ^ [] : [-(_1638330 = hAPP(hAPP(c_List_Oappend(_1638328), _1638334), 43057 ^ [_1638328, _1638330, _1638332, _1638334, _1638336]))], (43063 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638328), 43057 ^ [_1638328, _1638330, _1638332, _1638334, _1638336]), _1638332) = _1638336)]], 43064 ^ _779448 : [(43065 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638328), _1638330), 43057 ^ [_1638328, _1638330, _1638332, _1638334, _1638336]) = _1638334)], (43067 ^ _779448) ^ [] : [-(_1638332 = hAPP(hAPP(c_List_Oappend(_1638328), 43057 ^ [_1638328, _1638330, _1638332, _1638334, _1638336]), _1638336))]]], (43069 ^ _779448) ^ [_1638659, _1638661, _1638663, _1638665, _1638667] : [-(hAPP(hAPP(c_List_Oappend(_1638659), _1638661), _1638663) = hAPP(hAPP(c_List_Oappend(_1638659), _1638665), _1638667)), 43070 ^ _779448 : [(43071 ^ _779448) ^ [_1638771] : [_1638661 = hAPP(hAPP(c_List_Oappend(_1638659), _1638665), _1638771), hAPP(hAPP(c_List_Oappend(_1638659), _1638771), _1638663) = _1638667], (43077 ^ _779448) ^ [_1638883] : [hAPP(hAPP(c_List_Oappend(_1638659), _1638661), _1638883) = _1638665, _1638663 = hAPP(hAPP(c_List_Oappend(_1638659), _1638883), _1638667)]]], (43085 ^ _779448) ^ [_1639047, _1639049, _1639051, _1639053] : [-(hAPP(hAPP(c_List_Oappend(_1639047), hAPP(hAPP(c_List_Oappend(_1639047), _1639049), _1639051)), _1639053) = hAPP(hAPP(c_List_Oappend(_1639047), _1639049), hAPP(hAPP(c_List_Oappend(_1639047), _1639051), _1639053)))], (43087 ^ _779448) ^ [_1639108, _1639110, _1639112] : [class_Groups_Omonoid__add(_1639108), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639108), hAPP(hAPP(c_List_Oappend(_1639108), _1639110), _1639112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639108), hAPP(c_List_Omonoid__add__class_Olistsum(_1639108), _1639110)), hAPP(c_List_Omonoid__add__class_Olistsum(_1639108), _1639112)))], (43093 ^ _779448) ^ [_1639247, _1639249, _1639251] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639247)), hAPP(hAPP(c_List_Oappend(_1639247), _1639249), _1639251)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639247)), _1639249)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639247)), _1639251)))], (43095 ^ _779448) ^ [_1639309, _1639311, _1639313, _1639315, _1639317, _1639319] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639309)), _1639311) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639313)), _1639315), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639309)), _1639317) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639313)), _1639319), -(hAPP(hAPP(c_List_Ozip(_1639309, _1639313), hAPP(hAPP(c_List_Oappend(_1639309), _1639311), _1639317)), hAPP(hAPP(c_List_Oappend(_1639313), _1639315), _1639319)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1639309, _1639313)), hAPP(hAPP(c_List_Ozip(_1639309, _1639313), _1639311), _1639315)), hAPP(hAPP(c_List_Ozip(_1639309, _1639313), _1639317), _1639319)))], (43105 ^ _779448) ^ [_1639618, _1639620, _1639622] : [-(hAPP(c_List_Oset(_1639618), hAPP(hAPP(c_List_Oappend(_1639618), _1639620), _1639622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1639618, tc_HOL_Obool)), hAPP(c_List_Oset(_1639618), _1639620)), hAPP(c_List_Oset(_1639618), _1639622)))], (43107 ^ _779448) ^ [_1639679, _1639681] : [-(hAPP(hAPP(c_List_Oappend(_1639679), c_List_Olist_ONil(_1639679)), _1639681) = _1639681)], (43109 ^ _779448) ^ [_1639732, _1639734, _1639736] : [c_List_Olist_ONil(_1639732) = hAPP(hAPP(c_List_Oappend(_1639732), _1639734), _1639736), 43112 ^ _779448 : [(43113 ^ _779448) ^ [] : [-(_1639734 = c_List_Olist_ONil(_1639732))], (43115 ^ _779448) ^ [] : [-(_1639736 = c_List_Olist_ONil(_1639732))]]], (43117 ^ _779448) ^ [_1639861, _1639863, _1639865] : [-(c_List_Olist_ONil(_1639861) = hAPP(hAPP(c_List_Oappend(_1639861), _1639863), _1639865)), _1639863 = c_List_Olist_ONil(_1639861), _1639865 = c_List_Olist_ONil(_1639861)], (43127 ^ _779448) ^ [_1640024, _1640026] : [-(hAPP(hAPP(c_List_Oappend(_1640024), _1640026), c_List_Olist_ONil(_1640024)) = _1640026)], (43129 ^ _779448) ^ [_1640077, _1640079, _1640081] : [_1640077 = hAPP(hAPP(c_List_Oappend(_1640079), _1640077), _1640081), -(_1640081 = c_List_Olist_ONil(_1640079))], (43135 ^ _779448) ^ [_1640172, _1640174, _1640176] : [_1640176 = c_List_Olist_ONil(_1640174), -(_1640172 = hAPP(hAPP(c_List_Oappend(_1640174), _1640172), _1640176))], (43141 ^ _779448) ^ [_1640291, _1640293, _1640295] : [_1640291 = hAPP(hAPP(c_List_Oappend(_1640293), _1640295), _1640291), -(_1640295 = c_List_Olist_ONil(_1640293))], (43147 ^ _779448) ^ [_1640386, _1640388, _1640390] : [_1640390 = c_List_Olist_ONil(_1640388), -(_1640386 = hAPP(hAPP(c_List_Oappend(_1640388), _1640390), _1640386))], (43153 ^ _779448) ^ [_1640505, _1640507, _1640509] : [hAPP(hAPP(c_List_Oappend(_1640505), _1640507), _1640509) = c_List_Olist_ONil(_1640505), 43156 ^ _779448 : [(43157 ^ _779448) ^ [] : [-(_1640507 = c_List_Olist_ONil(_1640505))], (43159 ^ _779448) ^ [] : [-(_1640509 = c_List_Olist_ONil(_1640505))]]], (43161 ^ _779448) ^ [_1640634, _1640636, _1640638] : [-(hAPP(hAPP(c_List_Oappend(_1640634), _1640636), _1640638) = c_List_Olist_ONil(_1640634)), _1640636 = c_List_Olist_ONil(_1640634), _1640638 = c_List_Olist_ONil(_1640634)], (43171 ^ _779448) ^ [_1640815, _1640817, _1640819] : [hAPP(hAPP(c_List_Oappend(_1640815), _1640817), _1640819) = _1640817, -(_1640819 = c_List_Olist_ONil(_1640815))], (43177 ^ _779448) ^ [_1640910, _1640912, _1640914] : [_1640914 = c_List_Olist_ONil(_1640910), -(hAPP(hAPP(c_List_Oappend(_1640910), _1640912), _1640914) = _1640912)], (43183 ^ _779448) ^ [_1641029, _1641031, _1641033] : [hAPP(hAPP(c_List_Oappend(_1641029), _1641031), _1641033) = _1641033, -(_1641031 = c_List_Olist_ONil(_1641029))], (43189 ^ _779448) ^ [_1641124, _1641126, _1641128] : [_1641126 = c_List_Olist_ONil(_1641124), -(hAPP(hAPP(c_List_Oappend(_1641124), _1641126), _1641128) = _1641128)], (43195 ^ _779448) ^ [_1641225, _1641227, _1641229] : [_1641225 = _1641227, -(_1641225 = hAPP(hAPP(c_List_Oappend(_1641229), c_List_Olist_ONil(_1641229)), _1641227))], (43201 ^ _779448) ^ [_1641336, _1641338, _1641340] : [_1641336 = c_List_Olist_ONil(_1641338), -(c_List_Obutlast(_1641338, hAPP(hAPP(c_List_Oappend(_1641338), _1641340), _1641336)) = c_List_Obutlast(_1641338, _1641340))], (43207 ^ _779448) ^ [_1641441, _1641443, _1641445] : [-(_1641441 = c_List_Olist_ONil(_1641443)), -(c_List_Obutlast(_1641443, hAPP(hAPP(c_List_Oappend(_1641443), _1641445), _1641441)) = hAPP(hAPP(c_List_Oappend(_1641443), _1641445), c_List_Obutlast(_1641443, _1641441)))], (43213 ^ _779448) ^ [_1641505, _1641507, _1641509, _1641511] : [-(hAPP(hAPP(c_List_Onth(_1641505), hAPP(hAPP(c_List_Oappend(_1641505), _1641507), hAPP(hAPP(c_List_Olist_OCons(_1641505), _1641509), _1641511))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641505)), _1641507)) = _1641509)], (43215 ^ _779448) ^ [_1641565, _1641567, _1641569, _1641571] : [-(hAPP(hAPP(c_List_Onth(_1641565), hAPP(hAPP(c_List_Oappend(_1641565), _1641567), _1641569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641565)), _1641567)), _1641571)) = hAPP(hAPP(c_List_Onth(_1641565), _1641569), _1641571))], (43217 ^ _779448) ^ [_1641631, _1641633, _1641635, _1641637] : [-(hAPP(hAPP(c_List_Otake(_1641631), _1641633), hAPP(hAPP(c_List_Oappend(_1641631), _1641635), _1641637)) = hAPP(hAPP(c_List_Oappend(_1641631), hAPP(hAPP(c_List_Otake(_1641631), _1641633), _1641635)), hAPP(hAPP(c_List_Otake(_1641631), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1641633), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641631)), _1641635))), _1641637)))], (43219 ^ _779448) ^ [_1641713, _1641715, _1641717, _1641719, _1641721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641713), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641715)), _1641717))), -(hAPP(hAPP(c_List_Olist__update(_1641715, hAPP(hAPP(c_List_Oappend(_1641715), _1641717), _1641719)), _1641713), _1641721) = hAPP(hAPP(c_List_Oappend(_1641715), hAPP(hAPP(c_List_Olist__update(_1641715, _1641717), _1641713), _1641721)), _1641719))], (43225 ^ _779448) ^ [_1641888, _1641890, _1641892, _1641894, _1641896] : [-(hAPP(hAPP(c_List_Olist__update(_1641888, hAPP(hAPP(c_List_Oappend(_1641888), _1641890), hAPP(hAPP(c_List_Olist_OCons(_1641888), _1641892), _1641894))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641888)), _1641890)), _1641896) = hAPP(hAPP(c_List_Oappend(_1641888), _1641890), hAPP(hAPP(c_List_Olist_OCons(_1641888), _1641896), _1641894)))], (43227 ^ _779448) ^ [_1641982, _1641984, _1641986, _1641988] : [hBOOL(hAPP(hAPP(c_member(_1641982), _1641984), hAPP(c_List_Oset(_1641982), _1641986))), -(c_List_Oremove1(_1641982, _1641984, hAPP(hAPP(c_List_Oappend(_1641982), _1641986), _1641988)) = hAPP(hAPP(c_List_Oappend(_1641982), c_List_Oremove1(_1641982, _1641984, _1641986)), _1641988))], (43233 ^ _779448) ^ [_1642129, _1642131, _1642133, _1642135] : [-(hBOOL(hAPP(hAPP(c_member(_1642129), _1642131), hAPP(c_List_Oset(_1642129), _1642133)))), -(c_List_Oremove1(_1642129, _1642131, hAPP(hAPP(c_List_Oappend(_1642129), _1642133), _1642135)) = hAPP(hAPP(c_List_Oappend(_1642129), _1642133), c_List_Oremove1(_1642129, _1642131, _1642135)))], (43239 ^ _779448) ^ [_1642207, _1642209, _1642211, _1642213] : [43240 ^ _779448 : [(43241 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642207), _1642209), hAPP(c_List_Oset(_1642207), c_List_Obutlast(_1642207, _1642211))))], (43243 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642207), _1642209), hAPP(c_List_Oset(_1642207), c_List_Obutlast(_1642207, _1642213))))]], -(hBOOL(hAPP(hAPP(c_member(_1642207), _1642209), hAPP(c_List_Oset(_1642207), c_List_Obutlast(_1642207, hAPP(hAPP(c_List_Oappend(_1642207), _1642211), _1642213))))))], (43247 ^ _779448) ^ [_1642432, _1642434, _1642436] : [-(c_List_Obutlast(_1642432, hAPP(hAPP(c_List_Oappend(_1642432), _1642434), hAPP(hAPP(c_List_Olist_OCons(_1642432), _1642436), c_List_Olist_ONil(_1642432)))) = _1642434)], (43249 ^ _779448) ^ [_1642480, _1642482, _1642484, _1642486, _1642488, _1642490] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642480), tc_List_Olist(_1642480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642480), tc_List_Olist(_1642480)), hAPP(hAPP(c_List_Oappend(_1642480), _1642482), _1642488)), hAPP(hAPP(c_List_Oappend(_1642480), _1642484), _1642490))), c_List_Olistrel1(_1642480, _1642486)))), 43250 ^ _779448 : [(43251 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642480), tc_List_Olist(_1642480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642480), tc_List_Olist(_1642480)), _1642482), _1642484)), c_List_Olistrel1(_1642480, _1642486))), _1642488 = _1642490], (43257 ^ _779448) ^ [] : [_1642482 = _1642484, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642480), tc_List_Olist(_1642480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642480), tc_List_Olist(_1642480)), _1642488), _1642490)), c_List_Olistrel1(_1642480, _1642486)))]]], (43265 ^ _779448) ^ [_1642928, _1642930, _1642932, _1642934, _1642936] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642928), tc_List_Olist(_1642928))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642928), tc_List_Olist(_1642928)), _1642930), _1642932)), c_List_Olexord(_1642928, _1642934))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642928), tc_List_Olist(_1642928))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642928), tc_List_Olist(_1642928)), hAPP(hAPP(c_List_Oappend(_1642928), _1642936), _1642930)), hAPP(hAPP(c_List_Oappend(_1642928), _1642936), _1642932))), c_List_Olexord(_1642928, _1642934))))], (43271 ^ _779448) ^ [_1643181, _1643183, _1643185] : [hBOOL(hAPP(c_List_Odistinct(_1643181), hAPP(hAPP(c_List_Oappend(_1643181), _1643183), _1643185))), 43274 ^ _779448 : [(43275 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643181), _1643183)))], (43277 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643181), _1643185)))], (43279 ^ _779448) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643181, tc_HOL_Obool)), hAPP(c_List_Oset(_1643181), _1643183)), hAPP(c_List_Oset(_1643181), _1643185)) = c_Orderings_Obot__class_Obot(tc_fun(_1643181, tc_HOL_Obool)))]]], (43281 ^ _779448) ^ [_1643398, _1643400, _1643402] : [-(hBOOL(hAPP(c_List_Odistinct(_1643398), hAPP(hAPP(c_List_Oappend(_1643398), _1643400), _1643402)))), hBOOL(hAPP(c_List_Odistinct(_1643398), _1643400)), hBOOL(hAPP(c_List_Odistinct(_1643398), _1643402)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643398, tc_HOL_Obool)), hAPP(c_List_Oset(_1643398), _1643400)), hAPP(c_List_Oset(_1643398), _1643402)) = c_Orderings_Obot__class_Obot(tc_fun(_1643398, tc_HOL_Obool))], (43295 ^ _779448) ^ [_1643694, _1643696, _1643698, _1643700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643694), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643696)), _1643698))), -(hAPP(hAPP(c_List_Onth(_1643696), hAPP(hAPP(c_List_Oappend(_1643696), _1643698), _1643700)), _1643694) = hAPP(hAPP(c_List_Onth(_1643696), _1643698), _1643694))], (43301 ^ _779448) ^ [_1643841, _1643843, _1643845, _1643847] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643841), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643843)), _1643845)))), -(hAPP(hAPP(c_List_Onth(_1643843), hAPP(hAPP(c_List_Oappend(_1643843), _1643845), _1643847)), _1643841) = hAPP(hAPP(c_List_Onth(_1643843), _1643847), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643841), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643843)), _1643845))))], (43307 ^ _779448) ^ [_1643950, _1643952, _1643954, _1643956, _1643958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643952)), _1643954))), -(hAPP(hAPP(c_List_Olist__update(_1643952, hAPP(hAPP(c_List_Oappend(_1643952), _1643954), _1643956)), _1643950), _1643958) = hAPP(hAPP(c_List_Oappend(_1643952), hAPP(hAPP(c_List_Olist__update(_1643952, _1643954), _1643950), _1643958)), _1643956))], (43313 ^ _779448) ^ [_1644119, _1644121, _1644123, _1644125, _1644127] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644121)), _1644123)))), -(hAPP(hAPP(c_List_Olist__update(_1644121, hAPP(hAPP(c_List_Oappend(_1644121), _1644123), _1644125)), _1644119), _1644127) = hAPP(hAPP(c_List_Oappend(_1644121), _1644123), hAPP(hAPP(c_List_Olist__update(_1644121, _1644125), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644121)), _1644123))), _1644127)))], (43319 ^ _779448) ^ [_1644222, _1644224, _1644226, _1644228] : [-(c_List_Osublist(_1644222, hAPP(hAPP(c_List_Oappend(_1644222), _1644224), _1644226), _1644228) = hAPP(hAPP(c_List_Oappend(_1644222), c_List_Osublist(_1644222, _1644224, _1644228)), c_List_Osublist(_1644222, _1644226, 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(_1644222)), _1644224)))), _1644228)))))], (43321 ^ _779448) ^ [_1644301, _1644303, _1644305, _1644307, _1644309, _1644311, _1644313, _1644315] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644301, _1644301)), hAPP(hAPP(c_Product__Type_OPair(_1644301, _1644301), _1644303), _1644305)), _1644307)), _1644309 = hAPP(hAPP(c_List_Oappend(_1644301), _1644311), hAPP(hAPP(c_List_Olist_OCons(_1644301), _1644303), _1644313)), _1644315 = hAPP(hAPP(c_List_Oappend(_1644301), _1644311), hAPP(hAPP(c_List_Olist_OCons(_1644301), _1644305), _1644313)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644301), tc_List_Olist(_1644301))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644301), tc_List_Olist(_1644301)), _1644309), _1644315)), c_List_Olistrel1(_1644301, _1644307))))], (43335 ^ _779448) ^ [_1644680, _1644682, _1644684, _1644686, _1644688, _1644690, _1644692] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644680, _1644680)), hAPP(hAPP(c_Product__Type_OPair(_1644680, _1644680), _1644682), _1644684)), _1644686)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644680), tc_List_Olist(_1644680))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644680), tc_List_Olist(_1644680)), hAPP(hAPP(c_List_Oappend(_1644680), _1644688), hAPP(hAPP(c_List_Olist_OCons(_1644680), _1644682), _1644690))), hAPP(hAPP(c_List_Oappend(_1644680), _1644688), hAPP(hAPP(c_List_Olist_OCons(_1644680), _1644684), _1644692)))), c_List_Olexord(_1644680, _1644686))))], (43341 ^ _779448) ^ [_1644929, _1644931, _1644933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644929), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644931)), _1644933))), -(hAPP(hAPP(c_List_Otake(_1644931), hAPP(c_Nat_OSuc, _1644929)), _1644933) = hAPP(hAPP(c_List_Oappend(_1644931), hAPP(hAPP(c_List_Otake(_1644931), _1644929), _1644933)), hAPP(hAPP(c_List_Olist_OCons(_1644931), hAPP(hAPP(c_List_Onth(_1644931), _1644933), _1644929)), c_List_Olist_ONil(_1644931))))], (43347 ^ _779448) ^ [_1645149, _1645151, _1645153, _1645155, _1645157, _1645159] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645149), tc_List_Olist(_1645149))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645149), tc_List_Olist(_1645149)), hAPP(hAPP(c_List_Oappend(_1645149), _1645151), hAPP(hAPP(c_List_Olist_OCons(_1645149), _1645153), c_List_Olist_ONil(_1645149)))), hAPP(hAPP(c_List_Oappend(_1645149), _1645155), hAPP(hAPP(c_List_Olist_OCons(_1645149), _1645157), c_List_Olist_ONil(_1645149))))), c_List_Olistrel1(_1645149, _1645159))), 43352 ^ _779448 : [(43353 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645149), tc_List_Olist(_1645149))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645149), tc_List_Olist(_1645149)), _1645151), _1645155)), c_List_Olistrel1(_1645149, _1645159))))], (43355 ^ _779448) ^ [] : [-(_1645153 = _1645157)]], 43356 ^ _779448 : [(43357 ^ _779448) ^ [] : [-(_1645151 = _1645155)], (43359 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645149, _1645149)), hAPP(hAPP(c_Product__Type_OPair(_1645149, _1645149), _1645153), _1645157)), _1645159)))]]], (43361 ^ _779448) ^ [_1645559, _1645561, _1645563, _1645565, _1645567, _1645569] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645559), tc_List_Olist(_1645559))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645559), tc_List_Olist(_1645559)), hAPP(hAPP(c_List_Oappend(_1645559), _1645561), hAPP(hAPP(c_List_Olist_OCons(_1645559), _1645563), c_List_Olist_ONil(_1645559)))), hAPP(hAPP(c_List_Oappend(_1645559), _1645565), hAPP(hAPP(c_List_Olist_OCons(_1645559), _1645567), c_List_Olist_ONil(_1645559))))), c_List_Olistrel1(_1645559, _1645569)))), 43362 ^ _779448 : [(43363 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645559), tc_List_Olist(_1645559))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645559), tc_List_Olist(_1645559)), _1645561), _1645565)), c_List_Olistrel1(_1645559, _1645569))), _1645563 = _1645567], (43369 ^ _779448) ^ [] : [_1645561 = _1645565, hBOOL(hAPP(hAPP(c_member(tc_prod(_1645559, _1645559)), hAPP(hAPP(c_Product__Type_OPair(_1645559, _1645559), _1645563), _1645567)), _1645569))]]], (43377 ^ _779448) ^ [_1646027, _1646029, _1646031, _1646033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646027), tc_List_Olist(_1646027))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646027), tc_List_Olist(_1646027)), _1646029), _1646031)), c_List_Olistrel1(_1646027, _1646033))), 43382 ^ _779448 : [(43383 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646027, _1646027)), hAPP(hAPP(c_Product__Type_OPair(_1646027, _1646027), 43380 ^ [_1646027, _1646029, _1646031, _1646033]), 43381 ^ [_1646027, _1646029, _1646031, _1646033])), _1646033)))], (43387 ^ _779448) ^ [] : [-(_1646029 = hAPP(hAPP(c_List_Oappend(_1646027), 43384 ^ [_1646027, _1646029, _1646031, _1646033]), hAPP(hAPP(c_List_Olist_OCons(_1646027), 43380 ^ [_1646027, _1646029, _1646031, _1646033]), 43385 ^ [_1646027, _1646029, _1646031, _1646033])))], (43389 ^ _779448) ^ [] : [-(_1646031 = hAPP(hAPP(c_List_Oappend(_1646027), 43384 ^ [_1646027, _1646029, _1646031, _1646033]), hAPP(hAPP(c_List_Olist_OCons(_1646027), 43381 ^ [_1646027, _1646029, _1646031, _1646033]), 43385 ^ [_1646027, _1646029, _1646031, _1646033])))]]], (43391 ^ _779448) ^ [_1646432, _1646434, _1646436, _1646438, _1646440] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646432), tc_List_Olist(_1646432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646432), tc_List_Olist(_1646432)), hAPP(hAPP(c_List_Oappend(_1646432), _1646434), _1646436)), hAPP(hAPP(c_List_Oappend(_1646432), _1646434), _1646438))), c_List_Olexord(_1646432, _1646440))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646432, _1646432)), hAPP(hAPP(c_Product__Type_OPair(_1646432, _1646432), 43396 ^ [_1646432, _1646434, _1646436, _1646438, _1646440]), 43396 ^ [_1646432, _1646434, _1646436, _1646438, _1646440])), _1646440))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646432), tc_List_Olist(_1646432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646432), tc_List_Olist(_1646432)), _1646436), _1646438)), c_List_Olexord(_1646432, _1646440))))], (43402 ^ _779448) ^ [_1646751, _1646753] : [-(hAPP(c_List_Orotate1(_1646751), _1646753) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1646751), _1646751, c_List_Olist_ONil(_1646751), hAPP(hAPP(c_COMBB(tc_List_Olist(_1646751), tc_fun(tc_List_Olist(_1646751), tc_List_Olist(_1646751)), _1646751), hAPP(c_COMBC(tc_List_Olist(_1646751), tc_List_Olist(_1646751), tc_List_Olist(_1646751)), c_List_Oappend(_1646751))), hAPP(hAPP(c_COMBC(_1646751, tc_List_Olist(_1646751), tc_List_Olist(_1646751)), c_List_Olist_OCons(_1646751)), c_List_Olist_ONil(_1646751)))), _1646753))], (43404 ^ _779448) ^ [_1646845, _1646847, _1646849, _1646851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1646845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646847)), _1646849))), -(hAPP(hAPP(c_List_Olist__update(_1646847, _1646849), _1646845), _1646851) = hAPP(hAPP(c_List_Oappend(_1646847), hAPP(hAPP(c_List_Otake(_1646847), _1646845), _1646849)), hAPP(hAPP(c_List_Olist_OCons(_1646847), _1646851), hAPP(hAPP(c_List_Odrop(_1646847), hAPP(c_Nat_OSuc, _1646845)), _1646849))))], (43410 ^ _779448) ^ [_1647038, _1647040, _1647042] : [-(hAPP(hAPP(c_List_Oappend(_1647038), hAPP(hAPP(c_List_Otake(_1647038), _1647040), _1647042)), hAPP(hAPP(c_List_Odrop(_1647038), _1647040), _1647042)) = _1647042)], (43412 ^ _779448) ^ [_1647089, _1647091, _1647093] : [-(hAPP(hAPP(c_List_Odrop(_1647089), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647089), _1647091), _1647093)) = _1647093)], (43414 ^ _779448) ^ [_1647132, _1647134, _1647136, _1647138] : [-(hAPP(hAPP(c_List_Odrop(_1647132), hAPP(c_Nat_OSuc, _1647134)), hAPP(hAPP(c_List_Olist_OCons(_1647132), _1647136), _1647138)) = hAPP(hAPP(c_List_Odrop(_1647132), _1647134), _1647138))], (43416 ^ _779448) ^ [_1647188, _1647190, _1647192, _1647194, _1647196] : [hAPP(hAPP(c_List_Odrop(_1647188), _1647190), _1647192) = hAPP(hAPP(c_List_Olist_OCons(_1647188), _1647194), _1647196), -(hAPP(hAPP(c_List_Onth(_1647188), _1647192), _1647190) = _1647194)], (43422 ^ _779448) ^ [_1647319, _1647321, _1647323] : [hBOOL(hAPP(c_List_Odistinct(_1647319), _1647321)), -(hBOOL(hAPP(c_List_Odistinct(_1647319), hAPP(hAPP(c_List_Odrop(_1647319), _1647323), _1647321))))], (43428 ^ _779448) ^ [_1647445, _1647447] : [hBOOL(hAPP(c_List_Odistinct(_1647445), hAPP(c_List_Orotate1(_1647445), _1647447))), -(hBOOL(hAPP(c_List_Odistinct(_1647445), _1647447)))], (43434 ^ _779448) ^ [_1647544, _1647546] : [hBOOL(hAPP(c_List_Odistinct(_1647544), _1647546)), -(hBOOL(hAPP(c_List_Odistinct(_1647544), hAPP(c_List_Orotate1(_1647544), _1647546))))], (43440 ^ _779448) ^ [_1647649, _1647651, _1647653] : [-(c_List_Obutlast(_1647649, hAPP(hAPP(c_List_Odrop(_1647649), _1647651), _1647653)) = hAPP(hAPP(c_List_Odrop(_1647649), _1647651), c_List_Obutlast(_1647649, _1647653)))], (43442 ^ _779448) ^ [_1647698, _1647700, _1647702] : [-(hAPP(hAPP(c_List_Odrop(_1647698), _1647700), c_List_Obutlast(_1647698, _1647702)) = c_List_Obutlast(_1647698, hAPP(hAPP(c_List_Odrop(_1647698), _1647700), _1647702)))], (43444 ^ _779448) ^ [_1647747, _1647749, _1647751, _1647753] : [-(hAPP(hAPP(c_List_Otake(_1647747), _1647749), hAPP(hAPP(c_List_Odrop(_1647747), _1647751), _1647753)) = hAPP(hAPP(c_List_Odrop(_1647747), _1647751), hAPP(hAPP(c_List_Otake(_1647747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647749), _1647751)), _1647753)))], (43446 ^ _779448) ^ [_1647814, _1647816, _1647818, _1647820] : [-(hAPP(hAPP(c_List_Odrop(_1647814), _1647816), hAPP(hAPP(c_List_Otake(_1647814), _1647818), _1647820)) = hAPP(hAPP(c_List_Otake(_1647814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647818), _1647816)), hAPP(hAPP(c_List_Odrop(_1647814), _1647816), _1647820)))], (43448 ^ _779448) ^ [_1647881, _1647883, _1647885, _1647887] : [-(hAPP(hAPP(c_List_Odrop(_1647881), _1647883), hAPP(hAPP(c_List_Odrop(_1647881), _1647885), _1647887)) = hAPP(hAPP(c_List_Odrop(_1647881), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647883), _1647885)), _1647887))], (43450 ^ _779448) ^ [_1647940, _1647942] : [-(hAPP(hAPP(c_List_Odrop(_1647940), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1647942) = _1647942)], (43452 ^ _779448) ^ [_1647973, _1647975, _1647977, _1647979, _1647981] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1647973, _1647975)), _1647977), hAPP(hAPP(c_List_Ozip(_1647973, _1647975), _1647979), _1647981)) = hAPP(hAPP(c_List_Ozip(_1647973, _1647975), hAPP(hAPP(c_List_Odrop(_1647973), _1647977), _1647979)), hAPP(hAPP(c_List_Odrop(_1647975), _1647977), _1647981)))], (43454 ^ _779448) ^ [_1648049, _1648051] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648049)), hAPP(c_List_Orotate1(_1648049), _1648051)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648049)), _1648051))], (43456 ^ _779448) ^ [_1648093, _1648095, _1648097] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648093)), hAPP(hAPP(c_List_Odrop(_1648093), _1648095), _1648097)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648093)), _1648097)), _1648095))], (43458 ^ _779448) ^ [_1648148, _1648150] : [-(hAPP(c_List_Oset(_1648148), hAPP(c_List_Orotate1(_1648148), _1648150)) = hAPP(c_List_Oset(_1648148), _1648150))], (43460 ^ _779448) ^ [_1648188, _1648190, _1648192, _1648194] : [hBOOL(hAPP(hAPP(c_member(_1648188), _1648190), hAPP(c_List_Oset(_1648188), hAPP(hAPP(c_List_Odrop(_1648188), _1648192), _1648194)))), -(hBOOL(hAPP(hAPP(c_member(_1648188), _1648190), hAPP(c_List_Oset(_1648188), _1648194))))], (43466 ^ _779448) ^ [_1648333, _1648335, _1648337] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648333, tc_HOL_Obool)), hAPP(c_List_Oset(_1648333), hAPP(hAPP(c_List_Odrop(_1648333), _1648335), _1648337))), hAPP(c_List_Oset(_1648333), _1648337))))], (43468 ^ _779448) ^ [_1648388, _1648390] : [-(hAPP(hAPP(c_List_Odrop(_1648388), _1648390), c_List_Olist_ONil(_1648388)) = c_List_Olist_ONil(_1648388))], (43470 ^ _779448) ^ [_1648440, _1648442] : [hAPP(c_List_Orotate1(_1648440), _1648442) = c_List_Olist_ONil(_1648440), -(_1648442 = c_List_Olist_ONil(_1648440))], (43476 ^ _779448) ^ [_1648531, _1648533] : [_1648533 = c_List_Olist_ONil(_1648531), -(hAPP(c_List_Orotate1(_1648531), _1648533) = c_List_Olist_ONil(_1648531))], (43482 ^ _779448) ^ [_1648628, _1648630, _1648632, _1648634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648628), _1648630)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648632, tc_HOL_Obool)), hAPP(c_List_Oset(_1648632), hAPP(hAPP(c_List_Odrop(_1648632), _1648630), _1648634))), hAPP(c_List_Oset(_1648632), hAPP(hAPP(c_List_Odrop(_1648632), _1648628), _1648634)))))], (43488 ^ _779448) ^ [_1648809, _1648811, _1648813] : [hAPP(hAPP(c_List_Odrop(_1648809), _1648811), _1648813) = c_List_Olist_ONil(_1648809), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648809)), _1648813)), _1648811)))], (43494 ^ _779448) ^ [_1648928, _1648930, _1648932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648928)), _1648932)), _1648930)), -(hAPP(hAPP(c_List_Odrop(_1648928), _1648930), _1648932) = c_List_Olist_ONil(_1648928))], (43500 ^ _779448) ^ [_1649053, _1649055, _1649057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649053)), _1649055)), _1649057)), -(hAPP(hAPP(c_List_Odrop(_1649053), _1649057), _1649055) = c_List_Olist_ONil(_1649053))], (43506 ^ _779448) ^ [_1649176, _1649178, _1649180, _1649182] : [-(hAPP(hAPP(c_List_Odrop(_1649176), _1649178), hAPP(hAPP(c_List_Oappend(_1649176), _1649180), _1649182)) = hAPP(hAPP(c_List_Oappend(_1649176), hAPP(hAPP(c_List_Odrop(_1649176), _1649178), _1649180)), hAPP(hAPP(c_List_Odrop(_1649176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649176)), _1649180))), _1649182)))], (43508 ^ _779448) ^ [_1649279, _1649281, _1649283, _1649285] : [hAPP(hAPP(c_List_Oappend(_1649279), _1649281), _1649283) = _1649285, 43511 ^ _779448 : [(43512 ^ _779448) ^ [] : [-(_1649281 = hAPP(hAPP(c_List_Otake(_1649279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649279)), _1649281)), _1649285))], (43514 ^ _779448) ^ [] : [-(_1649283 = hAPP(hAPP(c_List_Odrop(_1649279), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649279)), _1649281)), _1649285))]]], (43516 ^ _779448) ^ [_1649458, _1649460, _1649462, _1649464] : [-(hAPP(hAPP(c_List_Oappend(_1649458), _1649460), _1649462) = _1649464), _1649460 = hAPP(hAPP(c_List_Otake(_1649458), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649458)), _1649460)), _1649464), _1649462 = hAPP(hAPP(c_List_Odrop(_1649458), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649458)), _1649460)), _1649464)], (43526 ^ _779448) ^ [_1649673, _1649675, _1649677, _1649679] : [-(hAPP(hAPP(c_List_Odrop(_1649673), _1649675), hAPP(hAPP(c_List_Olist_OCons(_1649673), _1649677), _1649679)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1649673), hAPP(hAPP(c_List_Olist_OCons(_1649673), _1649677), _1649679), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1649673), tc_List_Olist(_1649673)), c_List_Odrop(_1649673)), _1649679), _1649675))], (43528 ^ _779448) ^ [_1649764, _1649766, _1649768, _1649770] : [_1649764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1649766), _1649764), hAPP(hAPP(c_List_Olist_OCons(_1649766), _1649768), _1649770)) = hAPP(hAPP(c_List_Olist_OCons(_1649766), _1649768), _1649770))], (43534 ^ _779448) ^ [_1649887, _1649889, _1649891, _1649893] : [-(_1649887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1649889), _1649887), hAPP(hAPP(c_List_Olist_OCons(_1649889), _1649891), _1649893)) = hAPP(hAPP(c_List_Odrop(_1649889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649887), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1649893))], (43540 ^ _779448) ^ [_1649959, _1649961, _1649963, _1649965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1649959), _1649961)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649963)), _1649965))), -(hAPP(hAPP(c_List_Onth(_1649963), hAPP(hAPP(c_List_Odrop(_1649963), _1649959), _1649965)), _1649961) = hAPP(hAPP(c_List_Onth(_1649963), _1649965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1649959), _1649961)))], (43546 ^ _779448) ^ [_1650160, _1650162, _1650164, _1650166, _1650168] : [hAPP(hAPP(c_List_Oappend(_1650160), _1650162), _1650164) = hAPP(hAPP(c_List_Oappend(_1650160), _1650166), _1650168), 43549 ^ _779448 : [(43550 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650162)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650166))), 43553 ^ _779448 : [(43554 ^ _779448) ^ [] : [-(_1650162 = hAPP(hAPP(c_List_Otake(_1650160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650162)), _1650166))], (43556 ^ _779448) ^ [] : [-(_1650164 = hAPP(hAPP(c_List_Oappend(_1650160), hAPP(hAPP(c_List_Odrop(_1650160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650162)), _1650166)), _1650168))]]], (43558 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650162)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650166)))), 43561 ^ _779448 : [(43562 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650166)), _1650162) = _1650166)], (43564 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650160), hAPP(hAPP(c_List_Odrop(_1650160), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650160)), _1650166)), _1650162)), _1650164) = _1650168)]]]]], (43566 ^ _779448) ^ [_1650673, _1650675, _1650677, _1650679, _1650681] : [-(hAPP(hAPP(c_List_Oappend(_1650673), _1650675), _1650677) = hAPP(hAPP(c_List_Oappend(_1650673), _1650679), _1650681)), 43569 ^ _779448 : [(43570 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650675)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650679))))], (43572 ^ _779448) ^ [] : [_1650675 = hAPP(hAPP(c_List_Otake(_1650673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650675)), _1650679), _1650677 = hAPP(hAPP(c_List_Oappend(_1650673), hAPP(hAPP(c_List_Odrop(_1650673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650675)), _1650679)), _1650681)]], 43577 ^ _779448 : [(43578 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650675)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650679)))], (43580 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Otake(_1650673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650679)), _1650675) = _1650679, hAPP(hAPP(c_List_Oappend(_1650673), hAPP(hAPP(c_List_Odrop(_1650673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650673)), _1650679)), _1650675)), _1650677) = _1650681]]], (43588 ^ _779448) ^ [_1651261, _1651263, _1651265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651261), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651263)), _1651265))), -(hAPP(hAPP(c_List_Olist_OCons(_1651263), hAPP(hAPP(c_List_Onth(_1651263), _1651265), _1651261)), hAPP(hAPP(c_List_Odrop(_1651263), hAPP(c_Nat_OSuc, _1651261)), _1651265)) = hAPP(hAPP(c_List_Odrop(_1651263), _1651261), _1651265))], (43594 ^ _779448) ^ [_1651432, _1651434, _1651436, _1651438] : [-(hAPP(c_List_Orotate1(_1651432), c_List_Olist_ONil(_1651432)) = c_List_Olist_ONil(_1651432))], (43596 ^ _779448) ^ [_1651467, _1651469, _1651471, _1651473] : [-(hAPP(c_List_Orotate1(_1651469), hAPP(hAPP(c_List_Olist_OCons(_1651469), _1651471), _1651473)) = hAPP(hAPP(c_List_Oappend(_1651469), _1651473), hAPP(hAPP(c_List_Olist_OCons(_1651469), _1651471), c_List_Olist_ONil(_1651469))))], (43598 ^ _779448) ^ [_1651544, _1651546, _1651548, _1651550] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1651546), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651544)), hAPP(hAPP(c_List_Olist_OCons(_1651546), _1651548), _1651550)) = hAPP(hAPP(c_List_Olist_OCons(_1651546), _1651548), _1651550))], (43604 ^ _779448) ^ [_1651679, _1651681, _1651683, _1651685] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651679) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1651681), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651679)), hAPP(hAPP(c_List_Olist_OCons(_1651681), _1651683), _1651685)) = hAPP(hAPP(c_List_Odrop(_1651681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651679)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1651685))], (43610 ^ _779448) ^ [_1651760, _1651762, _1651764, _1651766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651760), _1651762)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651764)), _1651766))), -(hAPP(hAPP(c_List_Otake(_1651764), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651760), _1651762)), _1651766) = hAPP(hAPP(c_List_Oappend(_1651764), hAPP(hAPP(c_List_Otake(_1651764), _1651760), _1651766)), hAPP(hAPP(c_List_Otake(_1651764), _1651762), hAPP(hAPP(c_List_Odrop(_1651764), _1651760), _1651766))))], (43616 ^ _779448) ^ [_1651969, _1651971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651969)), _1651971)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1651969), _1651971) = _1651971)], (43622 ^ _779448) ^ [_1652080, _1652082, _1652084, _1652086, _1652088] : [-(hAPP(hAPP(c_List_Ozip(_1652080, _1652082), hAPP(hAPP(c_List_Oappend(_1652080), _1652084), _1652086)), _1652088) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652080, _1652082)), hAPP(hAPP(c_List_Ozip(_1652080, _1652082), _1652084), hAPP(hAPP(c_List_Otake(_1652082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652080)), _1652084)), _1652088))), hAPP(hAPP(c_List_Ozip(_1652080, _1652082), _1652086), hAPP(hAPP(c_List_Odrop(_1652082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652080)), _1652084)), _1652088))))], (43624 ^ _779448) ^ [_1652187, _1652189, _1652191, _1652193, _1652195] : [-(hAPP(hAPP(c_List_Ozip(_1652187, _1652189), _1652191), hAPP(hAPP(c_List_Oappend(_1652189), _1652193), _1652195)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652187, _1652189)), hAPP(hAPP(c_List_Ozip(_1652187, _1652189), hAPP(hAPP(c_List_Otake(_1652187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652189)), _1652193)), _1652191)), _1652193)), hAPP(hAPP(c_List_Ozip(_1652187, _1652189), hAPP(hAPP(c_List_Odrop(_1652187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652189)), _1652193)), _1652191)), _1652195)))], (43626 ^ _779448) ^ [_1652294, _1652296, _1652298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652294), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652296)), _1652298))), -(_1652298 = hAPP(hAPP(c_List_Oappend(_1652296), hAPP(hAPP(c_List_Otake(_1652296), _1652294), _1652298)), hAPP(hAPP(c_List_Olist_OCons(_1652296), hAPP(hAPP(c_List_Onth(_1652296), _1652298), _1652294)), hAPP(hAPP(c_List_Odrop(_1652296), hAPP(c_Nat_OSuc, _1652294)), _1652298))))], (43632 ^ _779448) ^ [_1652483, _1652485, _1652487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652483), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652485)), _1652487))), -(hAPP(hAPP(c_List_Oappend(_1652485), hAPP(hAPP(c_List_Otake(_1652485), _1652483), _1652487)), hAPP(hAPP(c_List_Olist_OCons(_1652485), hAPP(c_List_Ohd(_1652485), hAPP(hAPP(c_List_Odrop(_1652485), _1652483), _1652487))), c_List_Olist_ONil(_1652485))) = hAPP(hAPP(c_List_Otake(_1652485), hAPP(c_Nat_OSuc, _1652483)), _1652487))], (43638 ^ _779448) ^ [_1652685, _1652687, _1652689] : [-(_1652685 = c_List_Olist_ONil(_1652687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652687)), _1652685))), -(hAPP(c_List_Ohd(_1652687), hAPP(hAPP(c_List_Odrop(_1652687), _1652689), _1652685)) = hAPP(hAPP(c_List_Onth(_1652687), _1652685), _1652689))], (43648 ^ _779448) ^ [_1652884, _1652886, _1652888] : [-(hAPP(c_List_Ohd(_1652884), hAPP(hAPP(c_List_Olist_OCons(_1652884), _1652886), _1652888)) = _1652886)], (43650 ^ _779448) ^ [_1652920, _1652922, _1652924] : [-(_1652920 = c_List_Olist_ONil(_1652922)), -(hAPP(c_List_Ohd(_1652922), hAPP(hAPP(c_List_Oappend(_1652922), _1652920), _1652924)) = hAPP(c_List_Ohd(_1652922), _1652920))], (43656 ^ _779448) ^ [_1652990, _1652992, _1652994] : [_1652990 = c_List_Olist_ONil(_1652992), -(hAPP(c_List_Ohd(_1652992), hAPP(hAPP(c_List_Oappend(_1652992), _1652990), _1652994)) = hAPP(c_List_Ohd(_1652992), _1652994))], (43662 ^ _779448) ^ [_1653103, _1653105, _1653107] : [-(_1653103 = c_List_Olist_ONil(_1653105)), -(hAPP(c_List_Ohd(_1653105), hAPP(hAPP(c_List_Oappend(_1653105), _1653103), _1653107)) = hAPP(c_List_Ohd(_1653105), _1653103))], (43668 ^ _779448) ^ [_1653159, _1653161] : [-(_1653159 = c_List_Olist_ONil(_1653161)), -(hBOOL(hAPP(hAPP(c_member(_1653161), hAPP(c_List_Ohd(_1653161), _1653159)), hAPP(c_List_Oset(_1653161), _1653159))))], (43674 ^ _779448) ^ [_1653210, _1653212] : [-(_1653210 = c_List_Olist_ONil(_1653212)), -(hAPP(c_List_Ohd(_1653212), _1653210) = hAPP(hAPP(c_List_Onth(_1653212), _1653210), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43680 ^ _779448) ^ [_1653257, _1653259] : [-(_1653257 = c_List_Olist_ONil(_1653259)), -(hAPP(c_List_Orotate1(_1653259), _1653257) = hAPP(hAPP(c_List_Oappend(_1653259), hAPP(c_List_Otl(_1653259), _1653257)), hAPP(hAPP(c_List_Olist_OCons(_1653259), hAPP(c_List_Ohd(_1653259), _1653257)), c_List_Olist_ONil(_1653259))))], (43686 ^ _779448) ^ [_1653324, _1653326, _1653328] : [-(_1653324 = c_List_Olist_ONil(_1653326)), -(hAPP(c_List_Ohd(_1653326), hAPP(c_List_Orotate(_1653326, _1653328), _1653324)) = hAPP(hAPP(c_List_Onth(_1653326), _1653324), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1653328, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653326)), _1653324))))], (43692 ^ _779448) ^ [_1653394, _1653396, _1653398] : [-(hAPP(hAPP(c_List_Odrop(_1653394), _1653396), hAPP(c_List_Otl(_1653394), _1653398)) = hAPP(c_List_Otl(_1653394), hAPP(hAPP(c_List_Odrop(_1653394), _1653396), _1653398)))], (43694 ^ _779448) ^ [_1653447, _1653449, _1653451] : [-(hAPP(c_List_Otl(_1653447), hAPP(hAPP(c_List_Odrop(_1653447), _1653449), _1653451)) = hAPP(hAPP(c_List_Odrop(_1653447), _1653449), hAPP(c_List_Otl(_1653447), _1653451)))], (43696 ^ _779448) ^ [_1653500, _1653502, _1653504] : [-(hAPP(c_List_Otl(_1653500), hAPP(hAPP(c_List_Olist_OCons(_1653500), _1653502), _1653504)) = _1653504)], (43698 ^ _779448) ^ [_1653540, _1653542] : [hBOOL(hAPP(c_List_Odistinct(_1653540), _1653542)), -(hBOOL(hAPP(c_List_Odistinct(_1653540), hAPP(c_List_Otl(_1653540), _1653542))))], (43704 ^ _779448) ^ [_1653661, _1653663, _1653665] : [hBOOL(hAPP(c_List_Odistinct(_1653661), hAPP(c_List_Orotate(_1653661, _1653663), _1653665))), -(hBOOL(hAPP(c_List_Odistinct(_1653661), _1653665)))], (43710 ^ _779448) ^ [_1653764, _1653766, _1653768] : [hBOOL(hAPP(c_List_Odistinct(_1653764), _1653768)), -(hBOOL(hAPP(c_List_Odistinct(_1653764), hAPP(c_List_Orotate(_1653764, _1653766), _1653768))))], (43716 ^ _779448) ^ [_1653873, _1653875, _1653877] : [-(c_List_Orotate(_1653873, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653875), _1653877)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1653873), tc_List_Olist(_1653873), tc_List_Olist(_1653873), c_List_Orotate(_1653873, _1653875)), c_List_Orotate(_1653873, _1653877)))], (43718 ^ _779448) ^ [_1653929, _1653931, _1653933, _1653935] : [-(hAPP(c_List_Orotate(_1653929, _1653931), hAPP(c_List_Orotate(_1653929, _1653933), _1653935)) = hAPP(c_List_Orotate(_1653929, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653931), _1653933)), _1653935))], (43720 ^ _779448) ^ [_1653982] : [-(c_List_Orotate(_1653982, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1653982)))], (43722 ^ _779448) ^ [_1654012, _1654014, _1654016] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654012)), hAPP(c_List_Orotate(_1654012, _1654014), _1654016)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654012)), _1654016))], (43724 ^ _779448) ^ [_1654059, _1654061, _1654063] : [-(hAPP(c_List_Oset(_1654059), hAPP(c_List_Orotate(_1654059, _1654061), _1654063)) = hAPP(c_List_Oset(_1654059), _1654063))], (43726 ^ _779448) ^ [_1654102] : [-(hAPP(c_List_Otl(_1654102), c_List_Olist_ONil(_1654102)) = c_List_Olist_ONil(_1654102))], (43728 ^ _779448) ^ [_1654152, _1654154, _1654156] : [hAPP(c_List_Orotate(_1654152, _1654154), _1654156) = c_List_Olist_ONil(_1654152), -(_1654156 = c_List_Olist_ONil(_1654152))], (43734 ^ _779448) ^ [_1654247, _1654249, _1654251] : [_1654251 = c_List_Olist_ONil(_1654247), -(hAPP(c_List_Orotate(_1654247, _1654249), _1654251) = c_List_Olist_ONil(_1654247))], (43740 ^ _779448) ^ [_1654348, _1654350, _1654352] : [-(hAPP(c_List_Orotate1(_1654348), hAPP(c_List_Orotate(_1654348, _1654350), _1654352)) = hAPP(c_List_Orotate(_1654348, _1654350), hAPP(c_List_Orotate1(_1654348), _1654352)))], (43742 ^ _779448) ^ [_1654397, _1654399] : [-(c_List_Orotate(_1654397, _1654399) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1654397), tc_List_Olist(_1654397)), _1654399), c_List_Orotate1(_1654397)))], (43744 ^ _779448) ^ [_1654436, _1654438, _1654440] : [-(_1654436 = c_List_Olist_ONil(_1654438)), -(hAPP(c_List_Otl(_1654438), hAPP(hAPP(c_List_Oappend(_1654438), _1654436), _1654440)) = hAPP(hAPP(c_List_Oappend(_1654438), hAPP(c_List_Otl(_1654438), _1654436)), _1654440))], (43750 ^ _779448) ^ [_1654502, _1654504, _1654506] : [-(hAPP(hAPP(c_List_Otake(_1654502), _1654504), hAPP(c_List_Otl(_1654502), _1654506)) = hAPP(c_List_Otl(_1654502), hAPP(hAPP(c_List_Otake(_1654502), hAPP(c_Nat_OSuc, _1654504)), _1654506)))], (43752 ^ _779448) ^ [_1654558, _1654560, _1654562] : [-(hAPP(c_List_Orotate(_1654558, _1654560), _1654562) = hAPP(c_List_Orotate(_1654558, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654560, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654558)), _1654562))), _1654562))], (43754 ^ _779448) ^ [_1654608, _1654610, _1654612] : [-(hAPP(hAPP(c_List_Odrop(_1654608), hAPP(c_Nat_OSuc, _1654610)), _1654612) = hAPP(hAPP(c_List_Odrop(_1654608), _1654610), hAPP(c_List_Otl(_1654608), _1654612)))], (43756 ^ _779448) ^ [_1654659, _1654661, _1654663] : [-(hAPP(c_List_Orotate(_1654659, hAPP(c_Nat_OSuc, _1654661)), _1654663) = hAPP(c_List_Orotate1(_1654659), hAPP(c_List_Orotate(_1654659, _1654661), _1654663)))], (43758 ^ _779448) ^ [_1654706, _1654708, _1654710] : [-(hAPP(c_List_Otl(_1654706), hAPP(hAPP(c_List_Oappend(_1654706), _1654708), _1654710)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1654706), _1654706, hAPP(c_List_Otl(_1654706), _1654710), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1654706), tc_List_Olist(_1654706)), _1654706), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654706), tc_List_Olist(_1654706), tc_List_Olist(_1654706)), c_List_Oappend(_1654706)), _1654710))), _1654708))], (43760 ^ _779448) ^ [_1654792, _1654794, _1654796] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654792, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654794)), _1654796)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1654794, _1654792), _1654796) = _1654796)], (43766 ^ _779448) ^ [_1654905, _1654907, _1654909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654905)), _1654907)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1654905, _1654909), _1654907) = _1654907)], (43772 ^ _779448) ^ [_1655020, _1655022] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655020)), hAPP(c_List_Otl(_1655020), _1655022)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655020)), _1655022)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43774 ^ _779448) ^ [_1655070, _1655072, _1655074] : [-(hAPP(c_List_Otl(_1655070), hAPP(hAPP(c_List_Otake(_1655070), _1655072), _1655074)) = hAPP(hAPP(c_List_Otake(_1655070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655072), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1655070), _1655074)))], (43776 ^ _779448) ^ [_1655125, _1655127, _1655129] : [-(_1655125 = c_List_Olist_ONil(_1655127)), -(hAPP(hAPP(c_List_Otake(_1655127), hAPP(c_Nat_OSuc, _1655129)), _1655125) = hAPP(hAPP(c_List_Olist_OCons(_1655127), hAPP(c_List_Ohd(_1655127), _1655125)), hAPP(hAPP(c_List_Otake(_1655127), _1655129), hAPP(c_List_Otl(_1655127), _1655125))))], (43782 ^ _779448) ^ [_1655202, _1655204, _1655206] : [-(hAPP(c_List_Orotate(_1655202, _1655204), _1655206) = hAPP(hAPP(c_List_Oappend(_1655202), hAPP(hAPP(c_List_Odrop(_1655202), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655204, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655202)), _1655206))), _1655206)), hAPP(hAPP(c_List_Otake(_1655202), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655204, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655202)), _1655206))), _1655206)))], (43784 ^ _779448) ^ [_1655281, _1655283] : [class_Lattices_Oab__semigroup__idem__mult(_1655281), -(_1655283 = c_List_Olist_ONil(_1655281)), -(hAPP(c_Finite__Set_Ofold1(_1655281, c_Groups_Otimes__class_Otimes(_1655281)), hAPP(c_List_Oset(_1655281), _1655283)) = hAPP(c_List_Ofoldl(_1655281, _1655281, c_Groups_Otimes__class_Otimes(_1655281), hAPP(c_List_Ohd(_1655281), _1655283)), hAPP(c_List_Otl(_1655281), _1655283)))], (43794 ^ _779448) ^ [_1655441, _1655443, _1655445, _1655447] : [43795 ^ _779448 : [(43796 ^ _779448) ^ [_1655538, _1655540] : [_1655441 = hAPP(hAPP(c_List_Olist_OCons(_1655443), _1655540), _1655538)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655443), tc_List_Olist(_1655443))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655443), tc_List_Olist(_1655443)), _1655445), hAPP(hAPP(c_List_Oappend(_1655443), _1655445), _1655441))), c_List_Olexord(_1655443, _1655447))))], (43800 ^ _779448) ^ [_1655637, _1655639, _1655641, _1655643] : [-(hAPP(c_List_Ofoldl(_1655637, _1655639, _1655641, _1655643), c_List_Olist_ONil(_1655639)) = _1655643)], (43802 ^ _779448) ^ [_1655676, _1655678, _1655680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655676), _1655678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655676), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655678), _1655680))))], (43808 ^ _779448) ^ [_1655791, _1655793, _1655795] : [class_Groups_Omonoid__add(_1655791), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655791), _1655793), hAPP(c_List_Ofoldl(_1655791, _1655791, c_Groups_Oplus__class_Oplus(_1655791), c_Groups_Ozero__class_Ozero(_1655791)), _1655795)) = hAPP(c_List_Ofoldl(_1655791, _1655791, c_Groups_Oplus__class_Oplus(_1655791), _1655793), _1655795))], (43814 ^ _779448) ^ [_1655928, _1655930, _1655932, _1655934] : [class_Groups_Osemigroup__add(_1655928), -(hAPP(c_List_Ofoldl(_1655928, _1655928, c_Groups_Oplus__class_Oplus(_1655928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655928), _1655930), _1655932)), _1655934) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655928), _1655930), hAPP(c_List_Ofoldl(_1655928, _1655928, c_Groups_Oplus__class_Oplus(_1655928), _1655932), _1655934)))], (43820 ^ _779448) ^ [_1656079, _1656081, _1656083, _1656085, _1656087, _1656089] : [-(hAPP(c_List_Ofoldl(_1656079, _1656081, _1656083, _1656085), hAPP(hAPP(c_List_Olist_OCons(_1656081), _1656087), _1656089)) = hAPP(c_List_Ofoldl(_1656079, _1656081, _1656083, hAPP(hAPP(_1656083, _1656085), _1656087)), _1656089))], (43822 ^ _779448) ^ [_1656142, _1656144, _1656146, _1656148, _1656150, _1656152] : [-(hAPP(c_List_Ofoldl(_1656142, _1656144, _1656146, _1656148), hAPP(hAPP(c_List_Oappend(_1656144), _1656150), _1656152)) = hAPP(c_List_Ofoldl(_1656142, _1656144, _1656146, hAPP(c_List_Ofoldl(_1656142, _1656144, _1656146, _1656148), _1656150)), _1656152))], (43824 ^ _779448) ^ [_1656207] : [class_Groups_Omonoid__add(_1656207), -(c_List_Omonoid__add__class_Olistsum(_1656207) = c_List_Ofoldl(_1656207, _1656207, c_Groups_Oplus__class_Oplus(_1656207), c_Groups_Ozero__class_Ozero(_1656207)))], (43830 ^ _779448) ^ [_1656317, _1656319] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656317), _1656319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43833 ^ _779448 : [(43834 ^ _779448) ^ [] : [-(_1656317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43836 ^ _779448) ^ [_1656431] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1656431), hAPP(c_List_Oset(tc_Nat_Onat), _1656319))), -(_1656431 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43842 ^ _779448) ^ [_1656528, _1656530] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656528), _1656530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1656528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43848 ^ _779448 : [(43849 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43847 ^ [_1656528, _1656530]), hAPP(c_List_Oset(tc_Nat_Onat), _1656530))))], (43851 ^ _779448) ^ [] : [43847 ^ [_1656528, _1656530] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43855 ^ _779448) ^ [_1656754, _1656756, _1656758, _1656760, _1656762] : [c_Finite__Set_Ofun__left__comm__idem(_1656754, _1656756, _1656758), -(hAPP(hAPP(c_Finite__Set_Ofold(_1656754, _1656756, _1656758), _1656760), hAPP(c_List_Oset(_1656754), _1656762)) = hAPP(c_List_Ofoldl(_1656756, _1656754, hAPP(c_COMBC(_1656754, _1656756, _1656756), _1656758), _1656760), _1656762))], (43861 ^ _779448) ^ [_1656899, _1656901] : [class_Complete__Lattice_Ocomplete__lattice(_1656899), -(c_Complete__Lattice_OSup__class_OSup(_1656899, hAPP(c_List_Oset(_1656899), _1656901)) = hAPP(c_List_Ofoldl(_1656899, _1656899, c_Lattices_Osemilattice__sup__class_Osup(_1656899), c_Orderings_Obot__class_Obot(_1656899)), _1656901))], (43867 ^ _779448) ^ [_1657014, _1657016] : [class_Complete__Lattice_Ocomplete__lattice(_1657014), -(c_Complete__Lattice_OInf__class_OInf(_1657014, hAPP(c_List_Oset(_1657014), _1657016)) = hAPP(c_List_Ofoldl(_1657014, _1657014, c_Lattices_Osemilattice__inf__class_Oinf(_1657014), c_Orderings_Otop__class_Otop(_1657014)), _1657016))], (43873 ^ _779448) ^ [_1657129, _1657131, _1657133] : [class_Lattices_Olattice(_1657129), -(c_Big__Operators_Olattice__class_OSup__fin(_1657129, hAPP(c_List_Oset(_1657129), hAPP(hAPP(c_List_Olist_OCons(_1657129), _1657131), _1657133))) = hAPP(c_List_Ofoldl(_1657129, _1657129, c_Lattices_Osemilattice__sup__class_Osup(_1657129), _1657131), _1657133))], (43879 ^ _779448) ^ [_1657258, _1657260, _1657262] : [class_Lattices_Olattice(_1657258), -(c_Big__Operators_Olattice__class_OInf__fin(_1657258, hAPP(c_List_Oset(_1657258), hAPP(hAPP(c_List_Olist_OCons(_1657258), _1657260), _1657262))) = hAPP(c_List_Ofoldl(_1657258, _1657258, c_Lattices_Osemilattice__inf__class_Oinf(_1657258), _1657260), _1657262))], (43885 ^ _779448) ^ [_1657387, _1657389, _1657391] : [class_Orderings_Olinorder(_1657387), -(c_Big__Operators_Olinorder__class_OMin(_1657387, hAPP(c_List_Oset(_1657387), hAPP(hAPP(c_List_Olist_OCons(_1657387), _1657389), _1657391))) = hAPP(c_List_Ofoldl(_1657387, _1657387, c_Orderings_Oord__class_Omin(_1657387), _1657389), _1657391))], (43891 ^ _779448) ^ [_1657516, _1657518, _1657520] : [class_Orderings_Olinorder(_1657516), -(c_Big__Operators_Olinorder__class_OMax(_1657516, hAPP(c_List_Oset(_1657516), hAPP(hAPP(c_List_Olist_OCons(_1657516), _1657518), _1657520))) = hAPP(c_List_Ofoldl(_1657516, _1657516, c_Orderings_Oord__class_Omax(_1657516), _1657518), _1657520))], (43897 ^ _779448) ^ [_1657645, _1657647, _1657649] : [class_Orderings_Olinorder(_1657645), -(c_Big__Operators_Olattice_OInf__fin(_1657645, c_Orderings_Oord__class_Omin(_1657645), hAPP(c_List_Oset(_1657645), hAPP(hAPP(c_List_Olist_OCons(_1657645), _1657647), _1657649))) = hAPP(c_List_Ofoldl(_1657645, _1657645, c_Orderings_Oord__class_Omin(_1657645), _1657647), _1657649))], (43903 ^ _779448) ^ [_1657780, _1657782, _1657784] : [class_Orderings_Olinorder(_1657780), -(c_Big__Operators_Olattice_OSup__fin(_1657780, c_Orderings_Oord__class_Omax(_1657780), hAPP(c_List_Oset(_1657780), hAPP(hAPP(c_List_Olist_OCons(_1657780), _1657782), _1657784))) = hAPP(c_List_Ofoldl(_1657780, _1657780, c_Orderings_Oord__class_Omax(_1657780), _1657782), _1657784))], (43909 ^ _779448) ^ [_1657915, _1657917, _1657919, _1657921] : [class_Complete__Lattice_Ocomplete__lattice(_1657915), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1657917, _1657915), hAPP(c_List_Oset(_1657917), _1657919)), _1657921) = hAPP(c_List_Ofoldl(_1657915, _1657917, hAPP(c_COMBC(_1657917, _1657915, _1657915), hAPP(hAPP(c_COMBB(_1657915, tc_fun(_1657915, _1657915), _1657917), c_Lattices_Osemilattice__sup__class_Osup(_1657915)), _1657921)), c_Orderings_Obot__class_Obot(_1657915)), _1657919))], (43915 ^ _779448) ^ [_1658086, _1658088, _1658090, _1658092] : [class_Complete__Lattice_Ocomplete__lattice(_1658086), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658088, _1658086), hAPP(c_List_Oset(_1658088), _1658090)), _1658092) = hAPP(c_List_Ofoldl(_1658086, _1658088, hAPP(c_COMBC(_1658088, _1658086, _1658086), hAPP(hAPP(c_COMBB(_1658086, tc_fun(_1658086, _1658086), _1658088), c_Lattices_Osemilattice__inf__class_Oinf(_1658086)), _1658092)), c_Orderings_Otop__class_Otop(_1658086)), _1658090))], (43921 ^ _779448) ^ [_1658257, _1658259] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658257), hAPP(c_List_Oset(tc_Nat_Onat), _1658259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658257), 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)), _1658259))))], (43927 ^ _779448) ^ [_1658366, _1658368, _1658370] : [class_Orderings_Olinorder(_1658366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658366), _1658368)), -(c_List_Olinorder__class_Osorted__list__of__set(_1658366, hAPP(hAPP(c_Set_Oinsert(_1658366), _1658370), _1658368)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658366, _1658366, c_COMBI(_1658366)), _1658370), c_List_Olinorder__class_Osorted__list__of__set(_1658366, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658366, tc_HOL_Obool)), _1658368), hAPP(hAPP(c_Set_Oinsert(_1658366), _1658370), c_Orderings_Obot__class_Obot(tc_fun(_1658366, tc_HOL_Obool)))))))], (43937 ^ _779448) ^ [_1658623, _1658625, _1658627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658623), tc_List_Olist(_1658623))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658623), tc_List_Olist(_1658623)), c_List_Olist_ONil(_1658623)), _1658625)), c_List_Olexord(_1658623, _1658627))), -(_1658625 = hAPP(hAPP(c_List_Olist_OCons(_1658623), 43940 ^ [_1658623, _1658625, _1658627]), 43941 ^ [_1658623, _1658625, _1658627]))], (43945 ^ _779448) ^ [_1658806, _1658808, _1658810] : [43946 ^ _779448 : [(43947 ^ _779448) ^ [_1658895, _1658897] : [_1658808 = hAPP(hAPP(c_List_Olist_OCons(_1658806), _1658897), _1658895)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658806), tc_List_Olist(_1658806))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658806), tc_List_Olist(_1658806)), c_List_Olist_ONil(_1658806)), _1658808)), c_List_Olexord(_1658806, _1658810))))], (43951 ^ _779448) ^ [_1658990, _1658992, _1658994, _1658996, _1658998, _1659000] : [class_Orderings_Olinorder(_1658990), 43954 ^ _779448 : [(43955 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658990), hAPP(_1658992, _1658994)), hAPP(_1658992, _1658996))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658998, _1658990, _1658992), _1658994), hAPP(hAPP(c_List_Olist_OCons(_1658998), _1658996), _1659000)) = hAPP(hAPP(c_List_Olist_OCons(_1658998), _1658994), hAPP(hAPP(c_List_Olist_OCons(_1658998), _1658996), _1659000)))], (43961 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658990), hAPP(_1658992, _1658994)), hAPP(_1658992, _1658996)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658998, _1658990, _1658992), _1658994), hAPP(hAPP(c_List_Olist_OCons(_1658998), _1658996), _1659000)) = hAPP(hAPP(c_List_Olist_OCons(_1658998), _1658996), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658998, _1658990, _1658992), _1658994), _1659000)))]]], (43967 ^ _779448) ^ [_1659372, _1659374, _1659376, _1659378] : [class_Orderings_Olinorder(_1659372), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659374, _1659372, _1659376), _1659378), c_List_Olist_ONil(_1659374)) = hAPP(hAPP(c_List_Olist_OCons(_1659374), _1659378), c_List_Olist_ONil(_1659374)))], (43973 ^ _779448) ^ [_1659495, _1659497, _1659499, _1659501, _1659503] : [class_Orderings_Olinorder(_1659495), -(hAPP(c_List_Oset(_1659497), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659497, _1659495, _1659499), _1659501), _1659503)) = hAPP(hAPP(c_Set_Oinsert(_1659497), _1659501), hAPP(c_List_Oset(_1659497), _1659503)))], (43979 ^ _779448) ^ [_1659632, _1659634, _1659636, _1659638, _1659640] : [class_Orderings_Olinorder(_1659632), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659634)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659634, _1659632, _1659636), _1659638), _1659640)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659634)), _1659640)))], (43985 ^ _779448) ^ [_1659767, _1659769, _1659771, _1659773, _1659775, _1659777] : [class_Orderings_Olinorder(_1659767), -(hAPP(_1659769, _1659771) = hAPP(_1659769, _1659773)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659775, _1659767, _1659769), _1659773), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659775, _1659767, _1659769), _1659771), _1659777)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659775, _1659767, _1659769), _1659771), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659775, _1659767, _1659769), _1659773), _1659777)))], (43995 ^ _779448) ^ [_1659957, _1659959, _1659961, _1659963] : [class_Orderings_Olinorder(_1659957), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659957, _1659957, c_COMBI(_1659957)), _1659959), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659957, _1659957, c_COMBI(_1659957)), _1659961), _1659963)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659957, _1659957, c_COMBI(_1659957)), _1659961), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659957, _1659957, c_COMBI(_1659957)), _1659959), _1659963)))], (44001 ^ _779448) ^ [_1660132] : [class_Orderings_Olinorder(_1660132), -(c_Finite__Set_Ofun__left__comm(_1660132, tc_List_Olist(_1660132), c_List_Olinorder__class_Oinsort__key(_1660132, _1660132, c_COMBI(_1660132))))], (44007 ^ _779448) ^ [_1660223, _1660225, _1660227] : [class_Orderings_Olinorder(_1660223), -(c_List_Oremove1(_1660223, _1660225, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660223, _1660223, c_COMBI(_1660223)), _1660225), _1660227)) = _1660227)], (44013 ^ _779448) ^ [_1660332, _1660334, _1660336, _1660338, _1660340] : [class_Orderings_Olinorder(_1660332), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660334, _1660332, _1660336), _1660338), _1660340) = c_List_Olist_ONil(_1660334)], (44019 ^ _779448) ^ [_1660438, _1660440, _1660442, _1660444, _1660446] : [class_Orderings_Olinorder(_1660438), 44022 ^ _779448 : [(44023 ^ _779448) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1660440), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660440, _1660438, _1660442), _1660444), _1660446))), 44026 ^ _779448 : [(44027 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660440), _1660444), hAPP(c_List_Oset(_1660440), _1660446)))], (44029 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660440), _1660446)))]]], (44031 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660440), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660440, _1660438, _1660442), _1660444), _1660446)))), -(hBOOL(hAPP(hAPP(c_member(_1660440), _1660444), hAPP(c_List_Oset(_1660440), _1660446)))), hBOOL(hAPP(c_List_Odistinct(_1660440), _1660446))]]], (44041 ^ _779448) ^ [_1660840, _1660842, _1660844, _1660846, _1660848] : [class_Orderings_Olinorder(_1660840), -(hBOOL(hAPP(hAPP(c_member(_1660840), hAPP(_1660842, _1660844)), hAPP(c_Set_Oimage(_1660846, _1660840, _1660842), hAPP(c_List_Oset(_1660846), _1660848))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1660846, _1660840, _1660842, _1660844, _1660848) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660846, _1660840, _1660842), _1660844), _1660848))], (44051 ^ _779448) ^ [_1661012, _1661014, _1661016] : [class_Orderings_Olinorder(_1661012), -(hBOOL(hAPP(hAPP(c_member(_1661012), _1661014), hAPP(c_List_Oset(_1661012), _1661016)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661012, _1661012, c_COMBI(_1661012), _1661014, _1661016) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661012, _1661012, c_COMBI(_1661012)), _1661014), _1661016))], (44061 ^ _779448) ^ [_1661168, _1661170, _1661172, _1661174, _1661176] : [class_Orderings_Olinorder(_1661168), hBOOL(hAPP(c_List_Odistinct(_1661170), _1661172)), -(hBOOL(hAPP(c_List_Odistinct(_1661170), c_List_Olinorder__class_Oinsort__insert__key(_1661170, _1661168, _1661174, _1661176, _1661172))))], (44071 ^ _779448) ^ [_1661335, _1661337, _1661339] : [class_Orderings_Olinorder(_1661335), hBOOL(hAPP(hAPP(c_member(_1661335), _1661337), hAPP(c_List_Oset(_1661335), _1661339))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661335, _1661335, c_COMBI(_1661335), _1661337, _1661339) = _1661339)], (44081 ^ _779448) ^ [_1661506, _1661508, _1661510] : [class_Orderings_Olinorder(_1661506), -(hAPP(c_List_Oset(_1661506), c_List_Olinorder__class_Oinsort__insert__key(_1661506, _1661506, c_COMBI(_1661506), _1661508, _1661510)) = hAPP(hAPP(c_Set_Oinsert(_1661506), _1661508), hAPP(c_List_Oset(_1661506), _1661510)))], (44087 ^ _779448) ^ [_1661635, _1661637, _1661639, _1661641, _1661643] : [class_Orderings_Olinorder(_1661635), hBOOL(hAPP(hAPP(c_member(_1661635), hAPP(_1661637, _1661639)), hAPP(c_Set_Oimage(_1661641, _1661635, _1661637), hAPP(c_List_Oset(_1661641), _1661643)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661641, _1661635, _1661637, _1661639, _1661643) = _1661643)], (44097 ^ _779448) ^ [_1661829, _1661831, _1661833, _1661835] : [-(_1661829 = c_List_Olist_ONil(_1661831)), 44100 ^ _779448 : [(44101 ^ _779448) ^ [] : [_1661833 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661831)), _1661829)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1661831, hAPP(hAPP(c_List_Olist__update(_1661831, _1661829), _1661833), _1661835)) = _1661835)], (44107 ^ _779448) ^ [] : [-(_1661833 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661831)), _1661829)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1661831, hAPP(hAPP(c_List_Olist__update(_1661831, _1661829), _1661833), _1661835)) = c_List_Olast(_1661831, _1661829))]]], (44113 ^ _779448) ^ [_1662115, _1662117] : [-(_1662115 = c_List_Olist_ONil(_1662117)), -(c_List_Olast(_1662117, _1662115) = hAPP(hAPP(c_List_Onth(_1662117), _1662115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662117)), _1662115)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44119 ^ _779448) ^ [_1662189, _1662191, _1662193] : [_1662189 = c_List_Olist_ONil(_1662191), -(c_List_Olast(_1662191, hAPP(hAPP(c_List_Olist_OCons(_1662191), _1662193), _1662189)) = _1662193)], (44125 ^ _779448) ^ [_1662288, _1662290, _1662292] : [-(_1662288 = c_List_Olist_ONil(_1662290)), -(c_List_Olast(_1662290, hAPP(hAPP(c_List_Olist_OCons(_1662290), _1662292), _1662288)) = c_List_Olast(_1662290, _1662288))], (44131 ^ _779448) ^ [_1662340, _1662342, _1662344] : [-(_1662340 = c_List_Olist_ONil(_1662342)), -(c_List_Olast(_1662342, hAPP(hAPP(c_List_Olist_OCons(_1662342), _1662344), _1662340)) = c_List_Olast(_1662342, _1662340))], (44137 ^ _779448) ^ [_1662394, _1662396, _1662398] : [_1662394 = c_List_Olist_ONil(_1662396), -(c_List_Olast(_1662396, hAPP(hAPP(c_List_Olist_OCons(_1662396), _1662398), _1662394)) = _1662398)], (44143 ^ _779448) ^ [_1662511, _1662513, _1662515] : [_1662511 = c_List_Olist_ONil(_1662513), -(c_List_Olast(_1662513, hAPP(hAPP(c_List_Oappend(_1662513), _1662515), _1662511)) = c_List_Olast(_1662513, _1662515))], (44149 ^ _779448) ^ [_1662616, _1662618, _1662620] : [-(_1662616 = c_List_Olist_ONil(_1662618)), -(c_List_Olast(_1662618, hAPP(hAPP(c_List_Oappend(_1662618), _1662620), _1662616)) = c_List_Olast(_1662618, _1662616))], (44155 ^ _779448) ^ [_1662668, _1662670, _1662672] : [-(_1662668 = c_List_Olist_ONil(_1662670)), -(c_List_Olast(_1662670, hAPP(hAPP(c_List_Oappend(_1662670), _1662672), _1662668)) = c_List_Olast(_1662670, _1662668))], (44161 ^ _779448) ^ [_1662722, _1662724, _1662726] : [_1662722 = c_List_Olist_ONil(_1662724), -(c_List_Olast(_1662724, hAPP(hAPP(c_List_Oappend(_1662724), _1662726), _1662722)) = c_List_Olast(_1662724, _1662726))], (44167 ^ _779448) ^ [_1662829, _1662831] : [-(_1662829 = c_List_Olist_ONil(_1662831)), -(hBOOL(hAPP(hAPP(c_member(_1662831), c_List_Olast(_1662831, _1662829)), hAPP(c_List_Oset(_1662831), _1662829))))], (44173 ^ _779448) ^ [_1662882, _1662884, _1662886] : [-(c_List_Olast(_1662882, hAPP(hAPP(c_List_Oappend(_1662882), _1662884), hAPP(hAPP(c_List_Olist_OCons(_1662882), _1662886), c_List_Olist_ONil(_1662882)))) = _1662886)], (44175 ^ _779448) ^ [_1662930, _1662932, _1662934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662930), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662932)), _1662934))), -(c_List_Olast(_1662932, hAPP(hAPP(c_List_Odrop(_1662932), _1662930), _1662934)) = c_List_Olast(_1662932, _1662934))], (44181 ^ _779448) ^ [_1663057, _1663059] : [-(_1663057 = c_List_Olist_ONil(_1663059)), -(hAPP(hAPP(c_List_Oappend(_1663059), c_List_Obutlast(_1663059, _1663057)), hAPP(hAPP(c_List_Olist_OCons(_1663059), c_List_Olast(_1663059, _1663057)), c_List_Olist_ONil(_1663059))) = _1663057)], (44187 ^ _779448) ^ [_1663140, _1663142, _1663144, _1663146] : [hAPP(hAPP(c_List_Oappend(_1663140), _1663142), hAPP(hAPP(c_List_Olist_OCons(_1663140), _1663144), c_List_Olist_ONil(_1663140))) = _1663146, 44190 ^ _779448 : [(44191 ^ _779448) ^ [] : [_1663146 = c_List_Olist_ONil(_1663140)], (44193 ^ _779448) ^ [] : [-(c_List_Obutlast(_1663140, _1663146) = _1663142)], (44195 ^ _779448) ^ [] : [-(c_List_Olast(_1663140, _1663146) = _1663144)]]], (44197 ^ _779448) ^ [_1663329, _1663331, _1663333, _1663335] : [-(hAPP(hAPP(c_List_Oappend(_1663329), _1663331), hAPP(hAPP(c_List_Olist_OCons(_1663329), _1663333), c_List_Olist_ONil(_1663329))) = _1663335), -(_1663335 = c_List_Olist_ONil(_1663329)), c_List_Obutlast(_1663329, _1663335) = _1663331, c_List_Olast(_1663329, _1663335) = _1663333], (44211 ^ _779448) ^ [_1663597, _1663599, _1663601] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663597)), _1663599), c_List_Olists(_1663597, _1663601))), -(_1663599 = c_List_Olist_ONil(_1663597)), 44220 ^ _779448 : [(44221 ^ _779448) ^ [] : [-(_1663599 = hAPP(hAPP(c_List_Olist_OCons(_1663597), 44218 ^ [_1663597, _1663599, _1663601]), 44219 ^ [_1663597, _1663599, _1663601]))], (44223 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663597), 44218 ^ [_1663597, _1663599, _1663601]), _1663601)))], (44225 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663597)), 44219 ^ [_1663597, _1663599, _1663601]), c_List_Olists(_1663597, _1663601))))]]], (44227 ^ _779448) ^ [_1663880, _1663882, _1663884] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663880)), _1663882), c_List_Olists(_1663880, _1663884)))), 44228 ^ _779448 : [(44229 ^ _779448) ^ [] : [_1663882 = c_List_Olist_ONil(_1663880)], (44231 ^ _779448) ^ [_1664008, _1664010] : [_1663882 = hAPP(hAPP(c_List_Olist_OCons(_1663880), _1664010), _1664008), hBOOL(hAPP(hAPP(c_member(_1663880), _1664010), _1663884)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663880)), _1664008), c_List_Olists(_1663880, _1663884)))]]], (44243 ^ _779448) ^ [_1664242, _1664244] : [-(_1664242 = c_List_Olist_ONil(_1664244)), -(c_Random_Oselect__weight(_1664244, hAPP(hAPP(c_List_Omap(_1664244, tc_prod(tc_Code__Numeral_Ocode__numeral, _1664244)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1664244), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1664242)) = c_Random_Oselect(_1664244, _1664242))], (44249 ^ _779448) ^ [_1664304, _1664306, _1664308] : [c_Fun_Oinj__on(_1664304, _1664306, _1664308, c_Orderings_Otop__class_Otop(tc_fun(_1664304, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1664304), tc_List_Olist(_1664306), hAPP(c_List_Omap(_1664304, _1664306), _1664308), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664304), tc_HOL_Obool))))], (44255 ^ _779448) ^ [_1664431, _1664433, _1664435, _1664437] : [-(_1664431 = c_List_Olist_ONil(_1664433)), -(c_List_Olast(_1664435, hAPP(hAPP(c_List_Omap(_1664433, _1664435), _1664437), _1664431)) = hAPP(_1664437, c_List_Olast(_1664433, _1664431)))], (44261 ^ _779448) ^ [_1664491, _1664493, _1664495, _1664497, _1664499, _1664501, _1664503] : [-(hAPP(c_List_Ofoldl(_1664491, _1664493, _1664495, _1664497), hAPP(hAPP(c_List_Omap(_1664499, _1664493), _1664501), _1664503)) = hAPP(c_List_Ofoldl(_1664491, _1664499, hAPP(hAPP(c_COMBC(_1664491, tc_fun(_1664499, _1664493), tc_fun(_1664499, _1664491)), hAPP(hAPP(c_COMBB(tc_fun(_1664493, _1664491), tc_fun(tc_fun(_1664499, _1664493), tc_fun(_1664499, _1664491)), _1664491), c_COMBB(_1664493, _1664491, _1664499)), _1664495)), _1664501), _1664497), _1664503))], (44263 ^ _779448) ^ [_1664593, _1664595, _1664597, _1664599, _1664601] : [-(hAPP(c_List_Orotate(_1664593, _1664595), hAPP(hAPP(c_List_Omap(_1664597, _1664593), _1664599), _1664601)) = hAPP(hAPP(c_List_Omap(_1664597, _1664593), _1664599), hAPP(c_List_Orotate(_1664597, _1664595), _1664601)))], (44265 ^ _779448) ^ [_1664654, _1664656, _1664658, _1664660] : [-(hAPP(hAPP(c_List_Omap(_1664654, _1664656), _1664658), hAPP(c_List_Otl(_1664654), _1664660)) = hAPP(c_List_Otl(_1664656), hAPP(hAPP(c_List_Omap(_1664654, _1664656), _1664658), _1664660)))], (44267 ^ _779448) ^ [_1664711, _1664713] : [-(hAPP(hAPP(c_List_Ozip(_1664711, _1664711), _1664713), _1664713) = hAPP(hAPP(c_List_Omap(_1664711, tc_prod(_1664711, _1664711)), hAPP(hAPP(c_COMBS(_1664711, _1664711, tc_prod(_1664711, _1664711)), c_Product__Type_OPair(_1664711, _1664711)), c_COMBI(_1664711))), _1664713))], (44269 ^ _779448) ^ [_1664775, _1664777, _1664779, _1664781, _1664783, _1664785, _1664787, _1664789] : [-(hAPP(hAPP(c_List_Ozip(_1664775, _1664777), hAPP(hAPP(c_List_Omap(_1664779, _1664775), _1664781), _1664783)), hAPP(hAPP(c_List_Omap(_1664785, _1664777), _1664787), _1664789)) = hAPP(hAPP(c_List_Omap(tc_prod(_1664779, _1664785), tc_prod(_1664775, _1664777)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664779, _1664785, tc_prod(_1664775, _1664777)), hAPP(hAPP(c_COMBC(_1664779, tc_fun(_1664785, _1664777), tc_fun(_1664785, tc_prod(_1664775, _1664777))), hAPP(hAPP(c_COMBB(tc_fun(_1664777, tc_prod(_1664775, _1664777)), tc_fun(tc_fun(_1664785, _1664777), tc_fun(_1664785, tc_prod(_1664775, _1664777))), _1664779), c_COMBB(_1664777, tc_prod(_1664775, _1664777), _1664785)), hAPP(hAPP(c_COMBB(_1664775, tc_fun(_1664777, tc_prod(_1664775, _1664777)), _1664779), c_Product__Type_OPair(_1664775, _1664777)), _1664781))), _1664787))), hAPP(hAPP(c_List_Ozip(_1664779, _1664785), _1664783), _1664789)))], (44271 ^ _779448) ^ [_1664946, _1664948, _1664950, _1664952, _1664954, _1664956] : [-(hAPP(hAPP(c_List_Ozip(_1664946, _1664948), hAPP(hAPP(c_List_Omap(_1664950, _1664946), _1664952), _1664954)), _1664956) = hAPP(hAPP(c_List_Omap(tc_prod(_1664950, _1664948), tc_prod(_1664946, _1664948)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664950, _1664948, tc_prod(_1664946, _1664948)), hAPP(hAPP(c_COMBB(_1664946, tc_fun(_1664948, tc_prod(_1664946, _1664948)), _1664950), c_Product__Type_OPair(_1664946, _1664948)), _1664952))), hAPP(hAPP(c_List_Ozip(_1664950, _1664948), _1664954), _1664956)))], (44273 ^ _779448) ^ [_1665050, _1665052, _1665054, _1665056, _1665058, _1665060, _1665062, _1665064] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665050, _1665052), _1665054), _1665056), hAPP(hAPP(c_List_Ozip(_1665050, _1665052), hAPP(hAPP(c_List_Omap(_1665058, _1665050), _1665060), _1665062)), _1665064)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665058, _1665052), _1665054), hAPP(c_Product__Type_Oprod_Oprod__case(_1665058, _1665052, _1665054), hAPP(hAPP(c_COMBB(tc_fun(_1665052, tc_prod(_1665050, _1665052)), tc_fun(_1665052, _1665054), _1665058), hAPP(c_COMBB(tc_prod(_1665050, _1665052), _1665054, _1665052), _1665056)), hAPP(hAPP(c_COMBB(_1665050, tc_fun(_1665052, tc_prod(_1665050, _1665052)), _1665058), c_Product__Type_OPair(_1665050, _1665052)), _1665060)))), hAPP(hAPP(c_List_Ozip(_1665058, _1665052), _1665062), _1665064)))], (44275 ^ _779448) ^ [_1665193, _1665195, _1665197, _1665199, _1665201, _1665203, _1665205, _1665207] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665193, _1665195), _1665197), _1665199), hAPP(hAPP(c_List_Ozip(_1665193, _1665195), _1665201), hAPP(hAPP(c_List_Omap(_1665203, _1665195), _1665205), _1665207))) = hAPP(hAPP(c_List_Omap(tc_prod(_1665193, _1665203), _1665197), hAPP(c_Product__Type_Oprod_Oprod__case(_1665193, _1665203, _1665197), hAPP(hAPP(c_COMBB(tc_fun(_1665203, tc_prod(_1665193, _1665195)), tc_fun(_1665203, _1665197), _1665193), hAPP(c_COMBB(tc_prod(_1665193, _1665195), _1665197, _1665203), _1665199)), hAPP(hAPP(c_COMBC(_1665193, tc_fun(_1665203, _1665195), tc_fun(_1665203, tc_prod(_1665193, _1665195))), hAPP(hAPP(c_COMBB(tc_fun(_1665195, tc_prod(_1665193, _1665195)), tc_fun(tc_fun(_1665203, _1665195), tc_fun(_1665203, tc_prod(_1665193, _1665195))), _1665193), c_COMBB(_1665195, tc_prod(_1665193, _1665195), _1665203)), c_Product__Type_OPair(_1665193, _1665195))), _1665205)))), hAPP(hAPP(c_List_Ozip(_1665193, _1665203), _1665201), _1665207)))], (44277 ^ _779448) ^ [_1665374, _1665376, _1665378, _1665380, _1665382, _1665384] : [-(hAPP(hAPP(c_List_Ozip(_1665374, _1665376), _1665378), hAPP(hAPP(c_List_Omap(_1665380, _1665376), _1665382), _1665384)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665374, _1665380), tc_prod(_1665374, _1665376)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665374, _1665380, tc_prod(_1665374, _1665376)), hAPP(hAPP(c_COMBC(_1665374, tc_fun(_1665380, _1665376), tc_fun(_1665380, tc_prod(_1665374, _1665376))), hAPP(hAPP(c_COMBB(tc_fun(_1665376, tc_prod(_1665374, _1665376)), tc_fun(tc_fun(_1665380, _1665376), tc_fun(_1665380, tc_prod(_1665374, _1665376))), _1665374), c_COMBB(_1665376, tc_prod(_1665374, _1665376), _1665380)), c_Product__Type_OPair(_1665374, _1665376))), _1665382))), hAPP(hAPP(c_List_Ozip(_1665374, _1665380), _1665378), _1665384)))], (44279 ^ _779448) ^ [_1665537, _1665539, _1665541, _1665543] : [hAPP(hAPP(c_List_Omap(_1665537, _1665539), _1665541), _1665543) = c_List_Olist_ONil(_1665539), -(_1665543 = c_List_Olist_ONil(_1665537))], (44285 ^ _779448) ^ [_1665640, _1665642, _1665644, _1665646] : [_1665646 = c_List_Olist_ONil(_1665640), -(hAPP(hAPP(c_List_Omap(_1665640, _1665642), _1665644), _1665646) = c_List_Olist_ONil(_1665642))], (44291 ^ _779448) ^ [_1665749, _1665751, _1665753] : [-(hAPP(hAPP(c_List_Omap(_1665749, _1665751), _1665753), c_List_Olist_ONil(_1665749)) = c_List_Olist_ONil(_1665751))], (44293 ^ _779448) ^ [_1665810, _1665812, _1665814, _1665816] : [c_List_Olist_ONil(_1665810) = hAPP(hAPP(c_List_Omap(_1665812, _1665810), _1665814), _1665816), -(_1665816 = c_List_Olist_ONil(_1665812))], (44299 ^ _779448) ^ [_1665913, _1665915, _1665917, _1665919] : [_1665919 = c_List_Olist_ONil(_1665915), -(c_List_Olist_ONil(_1665913) = hAPP(hAPP(c_List_Omap(_1665915, _1665913), _1665917), _1665919))], (44305 ^ _779448) ^ [_1666022, _1666024, _1666026, _1666028, _1666030, _1666032] : [-(hAPP(hAPP(c_List_Omap(_1666022, _1666024), _1666026), hAPP(hAPP(c_List_Olist__update(_1666022, _1666028), _1666030), _1666032)) = hAPP(hAPP(c_List_Olist__update(_1666024, hAPP(hAPP(c_List_Omap(_1666022, _1666024), _1666026), _1666028)), _1666030), hAPP(_1666026, _1666032)))], (44317 ^ _779448) ^ [_1666362, _1666364, _1666366, _1666368, _1666370] : [44319 ^ _779448 : [(44320 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666362), 44318 ^ [_1666362, _1666364, _1666366, _1666368, _1666370]), hAPP(c_List_Oset(_1666362), _1666368))))], (44322 ^ _779448) ^ [] : [hAPP(_1666366, 44318 ^ [_1666362, _1666364, _1666366, _1666368, _1666370]) = hAPP(_1666370, 44318 ^ [_1666362, _1666364, _1666366, _1666368, _1666370])]], -(hAPP(hAPP(c_List_Omap(_1666362, _1666364), _1666366), _1666368) = hAPP(hAPP(c_List_Omap(_1666362, _1666364), _1666370), _1666368))], (44307 ^ _779448) ^ [_1666118, _1666120, _1666122, _1666124, _1666126] : [hAPP(hAPP(c_List_Omap(_1666118, _1666120), _1666122), _1666124) = hAPP(hAPP(c_List_Omap(_1666118, _1666120), _1666126), _1666124), 44310 ^ _779448 : [(44311 ^ _779448) ^ [_1666241] : [hBOOL(hAPP(hAPP(c_member(_1666118), _1666241), hAPP(c_List_Oset(_1666118), _1666124))), -(hAPP(_1666122, _1666241) = hAPP(_1666126, _1666241))]]], (44326 ^ _779448) ^ [_1666619, _1666621, _1666623, _1666625] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666619)), hAPP(hAPP(c_List_Omap(_1666621, _1666619), _1666623), _1666625)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666621)), _1666625))], (44328 ^ _779448) ^ [_1666671, _1666673, _1666675, _1666677, _1666679, _1666681, _1666683] : [hAPP(hAPP(c_List_Omap(_1666671, _1666673), _1666675), _1666677) = hAPP(hAPP(c_List_Omap(_1666679, _1666673), _1666681), _1666683), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666671)), _1666677) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666679)), _1666683))], (44334 ^ _779448) ^ [_1666822, _1666824, _1666826] : [class_Groups_Omonoid__add(_1666822), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666822), hAPP(hAPP(c_List_Omap(_1666824, _1666822), hAPP(c_COMBK(_1666822, _1666824), c_Groups_Ozero__class_Ozero(_1666822))), _1666826)) = c_Groups_Ozero__class_Ozero(_1666822))], (44340 ^ _779448) ^ [_1666947, _1666949, _1666951, _1666953, _1666955] : [class_Rings_Osemiring__0(_1666947), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666947), hAPP(hAPP(c_List_Omap(_1666949, _1666947), hAPP(hAPP(c_COMBB(_1666947, _1666947, _1666949), hAPP(c_Groups_Otimes__class_Otimes(_1666947), _1666951)), _1666953)), _1666955)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1666947), _1666951), hAPP(c_List_Omonoid__add__class_Olistsum(_1666947), hAPP(hAPP(c_List_Omap(_1666949, _1666947), _1666953), _1666955))))], (44346 ^ _779448) ^ [_1667130, _1667132, _1667134, _1667136, _1667138] : [class_Rings_Osemiring__0(_1667130), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667130), hAPP(hAPP(c_List_Omap(_1667132, _1667130), hAPP(hAPP(c_COMBC(_1667132, _1667130, _1667130), hAPP(hAPP(c_COMBB(_1667130, tc_fun(_1667130, _1667130), _1667132), c_Groups_Otimes__class_Otimes(_1667130)), _1667134)), _1667136)), _1667138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667130), hAPP(c_List_Omonoid__add__class_Olistsum(_1667130), hAPP(hAPP(c_List_Omap(_1667132, _1667130), _1667134), _1667138))), _1667136))], (44352 ^ _779448) ^ [_1667333, _1667335, _1667337, _1667339, _1667341] : [class_Groups_Oab__group__add(_1667333), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667333), hAPP(hAPP(c_List_Omap(_1667335, _1667333), hAPP(hAPP(c_COMBS(_1667335, _1667333, _1667333), hAPP(hAPP(c_COMBB(_1667333, tc_fun(_1667333, _1667333), _1667335), c_Groups_Ominus__class_Ominus(_1667333)), _1667337)), _1667339)), _1667341)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1667333), hAPP(c_List_Omonoid__add__class_Olistsum(_1667333), hAPP(hAPP(c_List_Omap(_1667335, _1667333), _1667337), _1667341))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667333), hAPP(hAPP(c_List_Omap(_1667335, _1667333), _1667339), _1667341))))], (44358 ^ _779448) ^ [_1667564, _1667566, _1667568, _1667570, _1667572] : [class_Groups_Ocomm__monoid__add(_1667564), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667564), hAPP(hAPP(c_List_Omap(_1667566, _1667564), hAPP(hAPP(c_COMBS(_1667566, _1667564, _1667564), hAPP(hAPP(c_COMBB(_1667564, tc_fun(_1667564, _1667564), _1667566), c_Groups_Oplus__class_Oplus(_1667564)), _1667568)), _1667570)), _1667572)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667564), hAPP(c_List_Omonoid__add__class_Olistsum(_1667564), hAPP(hAPP(c_List_Omap(_1667566, _1667564), _1667568), _1667572))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667564), hAPP(hAPP(c_List_Omap(_1667566, _1667564), _1667570), _1667572))))], (44364 ^ _779448) ^ [_1667795, _1667797, _1667799, _1667801, _1667803] : [c_Fun_Oinj__on(_1667795, _1667797, _1667799, c_Orderings_Otop__class_Otop(tc_fun(_1667795, tc_HOL_Obool))), 44367 ^ _779448 : [(44368 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Omap(_1667795, _1667797), _1667799), _1667801) = hAPP(hAPP(c_List_Omap(_1667795, _1667797), _1667799), _1667803), -(_1667801 = _1667803)], (44374 ^ _779448) ^ [] : [_1667801 = _1667803, -(hAPP(hAPP(c_List_Omap(_1667795, _1667797), _1667799), _1667801) = hAPP(hAPP(c_List_Omap(_1667795, _1667797), _1667799), _1667803))]]], (44380 ^ _779448) ^ [_1668088, _1668090, _1668092, _1668094, _1668096] : [hAPP(hAPP(c_List_Omap(_1668088, _1668090), _1668092), _1668094) = hAPP(hAPP(c_List_Omap(_1668088, _1668090), _1668092), _1668096), c_Fun_Oinj__on(_1668088, _1668090, _1668092, c_Orderings_Otop__class_Otop(tc_fun(_1668088, tc_HOL_Obool))), -(_1668094 = _1668096)], (44390 ^ _779448) ^ [_1668279, _1668281] : [-(hAPP(hAPP(c_List_Omap(_1668279, _1668279), c_COMBI(_1668279)), _1668281) = _1668281)], (44392 ^ _779448) ^ [_1668315, _1668317, _1668319, _1668321, _1668323] : [-(hAPP(hAPP(c_List_Otake(_1668315), _1668317), hAPP(hAPP(c_List_Omap(_1668319, _1668315), _1668321), _1668323)) = hAPP(hAPP(c_List_Omap(_1668319, _1668315), _1668321), hAPP(hAPP(c_List_Otake(_1668319), _1668317), _1668323)))], (44394 ^ _779448) ^ [_1668380, _1668382, _1668384, _1668386] : [-(hAPP(hAPP(c_List_Omap(_1668380, _1668382), _1668384), c_List_Obutlast(_1668380, _1668386)) = c_List_Obutlast(_1668382, hAPP(hAPP(c_List_Omap(_1668380, _1668382), _1668384), _1668386)))], (44396 ^ _779448) ^ [_1668433, _1668435, _1668437, _1668439] : [-(hAPP(c_List_Oset(_1668433), hAPP(hAPP(c_List_Omap(_1668435, _1668433), _1668437), _1668439)) = hAPP(c_Set_Oimage(_1668435, _1668433, _1668437), hAPP(c_List_Oset(_1668435), _1668439)))], (44398 ^ _779448) ^ [_1668488, _1668490, _1668492, _1668494, _1668496] : [-(hAPP(hAPP(c_List_Omap(_1668488, _1668490), _1668492), hAPP(hAPP(c_List_Olist_OCons(_1668488), _1668494), _1668496)) = hAPP(hAPP(c_List_Olist_OCons(_1668490), hAPP(_1668492, _1668494)), hAPP(hAPP(c_List_Omap(_1668488, _1668490), _1668492), _1668496)))], (44400 ^ _779448) ^ [_1668556, _1668558, _1668560, _1668562, _1668564] : [-(hAPP(hAPP(c_List_Omap(_1668556, _1668558), _1668560), hAPP(hAPP(c_List_Oappend(_1668556), _1668562), _1668564)) = hAPP(hAPP(c_List_Oappend(_1668558), hAPP(hAPP(c_List_Omap(_1668556, _1668558), _1668560), _1668562)), hAPP(hAPP(c_List_Omap(_1668556, _1668558), _1668560), _1668564)))], (44402 ^ _779448) ^ [_1668626, _1668628, _1668630, _1668632] : [-(_1668626 = c_List_Olist_ONil(_1668628)), -(hAPP(c_List_Ohd(_1668630), hAPP(hAPP(c_List_Omap(_1668628, _1668630), _1668632), _1668626)) = hAPP(_1668632, hAPP(c_List_Ohd(_1668628), _1668626)))], (44408 ^ _779448) ^ [_1668690, _1668692, _1668694, _1668696, _1668698] : [-(hAPP(hAPP(c_List_Odrop(_1668690), _1668692), hAPP(hAPP(c_List_Omap(_1668694, _1668690), _1668696), _1668698)) = hAPP(hAPP(c_List_Omap(_1668694, _1668690), _1668696), hAPP(hAPP(c_List_Odrop(_1668694), _1668692), _1668698)))], (44410 ^ _779448) ^ [_1668755, _1668757, _1668759, _1668761, _1668763] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668755), tc_List_Olist(_1668757), tc_List_Olist(_1668759), hAPP(c_List_Omap(_1668755, _1668757), _1668761)), hAPP(c_List_Omap(_1668759, _1668755), _1668763)) = hAPP(c_List_Omap(_1668759, _1668757), hAPP(c_Fun_Ocomp(_1668755, _1668757, _1668759, _1668761), _1668763)))], (44412 ^ _779448) ^ [_1668826, _1668828, _1668830, _1668832, _1668834] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668826), tc_List_Olist(_1668828), tc_List_Olist(_1668830), hAPP(c_List_Omap(_1668826, _1668828), _1668832)), hAPP(c_List_Omap(_1668830, _1668826), _1668834)) = hAPP(c_List_Omap(_1668830, _1668828), hAPP(c_Fun_Ocomp(_1668826, _1668828, _1668830, _1668832), _1668834)))], (44414 ^ _779448) ^ [_1668897, _1668899, _1668901, _1668903, _1668905, _1668907] : [-(hAPP(hAPP(c_List_Omap(_1668897, _1668899), _1668901), hAPP(hAPP(c_List_Omap(_1668903, _1668897), _1668905), _1668907)) = hAPP(hAPP(c_List_Omap(_1668903, _1668899), hAPP(c_Fun_Ocomp(_1668897, _1668899, _1668903, _1668901), _1668905)), _1668907))], (44416 ^ _779448) ^ [_1668965, _1668967, _1668969, _1668971, _1668973, _1668975] : [-(hAPP(hAPP(c_List_Omap(_1668965, _1668967), _1668969), hAPP(hAPP(c_List_Omap(_1668971, _1668965), _1668973), _1668975)) = hAPP(hAPP(c_List_Omap(_1668971, _1668967), hAPP(c_Fun_Ocomp(_1668965, _1668967, _1668971, _1668969), _1668973)), _1668975))], (44418 ^ _779448) ^ [_1669033] : [-(hAPP(c_List_Omap(_1669033, _1669033), c_COMBI(_1669033)) = c_Fun_Oid(tc_List_Olist(_1669033)))], (44420 ^ _779448) ^ [_1669068, _1669070, _1669072, _1669074, _1669076] : [-(c_List_Olist_Olist__size(_1669068, _1669070, hAPP(hAPP(c_List_Omap(_1669072, _1669068), _1669074), _1669076)) = c_List_Olist_Olist__size(_1669072, hAPP(c_Fun_Ocomp(_1669068, tc_Nat_Onat, _1669072, _1669070), _1669074), _1669076))], (44422 ^ _779448) ^ [_1669124] : [-(hAPP(c_List_Omap(_1669124, _1669124), c_Fun_Oid(_1669124)) = c_Fun_Oid(tc_List_Olist(_1669124)))], (44424 ^ _779448) ^ [_1669159, _1669161, _1669163, _1669165, _1669167] : [c_Fun_Oinj__on(_1669159, _1669161, _1669163, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669159, tc_HOL_Obool)), hAPP(c_List_Oset(_1669159), _1669165)), hAPP(c_List_Oset(_1669159), _1669167))), 44427 ^ _779448 : [(44428 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Omap(_1669159, _1669161), _1669163), _1669165) = hAPP(hAPP(c_List_Omap(_1669159, _1669161), _1669163), _1669167), -(_1669165 = _1669167)], (44434 ^ _779448) ^ [] : [_1669165 = _1669167, -(hAPP(hAPP(c_List_Omap(_1669159, _1669161), _1669163), _1669165) = hAPP(hAPP(c_List_Omap(_1669159, _1669161), _1669163), _1669167))]]], (44440 ^ _779448) ^ [_1669484, _1669486, _1669488, _1669490, _1669492] : [hAPP(hAPP(c_List_Omap(_1669484, _1669486), _1669488), _1669490) = hAPP(hAPP(c_List_Omap(_1669484, _1669486), _1669488), _1669492), c_Fun_Oinj__on(_1669484, _1669486, _1669488, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669484, tc_HOL_Obool)), hAPP(c_List_Oset(_1669484), _1669490)), hAPP(c_List_Oset(_1669484), _1669492))), -(_1669490 = _1669492)], (44450 ^ _779448) ^ [_1669707, _1669709, _1669711, _1669713, _1669715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669707), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669709)), _1669711))), -(hAPP(hAPP(c_List_Onth(_1669713), hAPP(hAPP(c_List_Omap(_1669709, _1669713), _1669715), _1669711)), _1669707) = hAPP(_1669715, hAPP(hAPP(c_List_Onth(_1669709), _1669711), _1669707)))], (44456 ^ _779448) ^ [_1669866, _1669868, _1669870, _1669872, _1669874, _1669876] : [-(hBOOL(hAPP(hAPP(c_member(_1669866), _1669868), hAPP(c_List_Oset(_1669866), _1669870)))), -(hAPP(hAPP(c_List_Omap(_1669866, _1669872), c_Fun_Ofun__upd(_1669866, _1669872, _1669874, _1669868, _1669876)), _1669870) = hAPP(hAPP(c_List_Omap(_1669866, _1669872), _1669874), _1669870))], (44462 ^ _779448) ^ [_1669967, _1669969, _1669971, _1669973] : [hBOOL(hAPP(c_List_Odistinct(_1669967), hAPP(hAPP(c_List_Omap(_1669969, _1669967), _1669971), _1669973))), 44465 ^ _779448 : [(44466 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669969), _1669973)))], (44468 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_1669969, _1669967, _1669971, hAPP(c_List_Oset(_1669969), _1669973)))]]], (44470 ^ _779448) ^ [_1670118, _1670120, _1670122, _1670124] : [-(hBOOL(hAPP(c_List_Odistinct(_1670118), hAPP(hAPP(c_List_Omap(_1670120, _1670118), _1670122), _1670124)))), hBOOL(hAPP(c_List_Odistinct(_1670120), _1670124)), c_Fun_Oinj__on(_1670120, _1670118, _1670122, hAPP(c_List_Oset(_1670120), _1670124))], (44480 ^ _779448) ^ [_1670305, _1670307] : [class_Groups_Oordered__ab__group__add__abs(_1670305), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670305), hAPP(c_Groups_Oabs__class_Oabs(_1670305), hAPP(c_List_Omonoid__add__class_Olistsum(_1670305), _1670307))), hAPP(c_List_Omonoid__add__class_Olistsum(_1670305), hAPP(hAPP(c_List_Omap(_1670305, _1670305), c_Groups_Oabs__class_Oabs(_1670305)), _1670307)))))], (44486 ^ _779448) ^ [_1670446, _1670448, _1670450, _1670452] : [class_Groups_Oab__group__add(_1670446), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1670446), hAPP(c_List_Omonoid__add__class_Olistsum(_1670446), hAPP(hAPP(c_List_Omap(_1670448, _1670446), _1670450), _1670452))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1670446), hAPP(hAPP(c_List_Omap(_1670448, _1670446), hAPP(c_Fun_Ocomp(_1670446, _1670446, _1670448, c_Groups_Ouminus__class_Ouminus(_1670446)), _1670450)), _1670452)))], (44492 ^ _779448) ^ [_1670611, _1670613, _1670615, _1670617] : [c_Fun_Oinj__on(_1670611, _1670613, _1670615, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670611, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1670611), tc_fun(_1670611, tc_HOL_Obool), c_List_Oset(_1670611)), _1670617))), -(c_Fun_Oinj__on(tc_List_Olist(_1670611), tc_List_Olist(_1670613), hAPP(c_List_Omap(_1670611, _1670613), _1670615), _1670617))], (44498 ^ _779448) ^ [_1670760, _1670762, _1670764] : [c_Fun_Oinj__on(tc_List_Olist(_1670760), tc_List_Olist(_1670762), hAPP(c_List_Omap(_1670760, _1670762), _1670764), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670760), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1670760, _1670762, _1670764, c_Orderings_Otop__class_Otop(tc_fun(_1670760, tc_HOL_Obool))))], (44504 ^ _779448) ^ [_1670909, _1670911, _1670913] : [c_Fun_Oinj__on(tc_List_Olist(_1670909), tc_List_Olist(_1670911), hAPP(c_List_Omap(_1670909, _1670911), _1670913), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670909), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1670909, _1670911, _1670913, c_Orderings_Otop__class_Otop(tc_fun(_1670909, tc_HOL_Obool))))], (44510 ^ _779448) ^ [_1671036, _1671038, _1671040] : [c_Fun_Oinj__on(_1671036, _1671038, _1671040, c_Orderings_Otop__class_Otop(tc_fun(_1671036, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1671036), tc_List_Olist(_1671038), hAPP(c_List_Omap(_1671036, _1671038), _1671040), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671036), tc_HOL_Obool))))], (44516 ^ _779448) ^ [_1671169, _1671171, _1671173, _1671175] : [class_Groups_Ocomm__monoid__add(_1671169), hBOOL(hAPP(c_List_Odistinct(_1671171), _1671173)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671169), hAPP(hAPP(c_List_Omap(_1671171, _1671169), _1671175), _1671173)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671171, _1671169), _1671175), hAPP(c_List_Oset(_1671171), _1671173)))], (44526 ^ _779448) ^ [_1671368, _1671370, _1671372, _1671374] : [class_Rings_Osemiring__1(_1671368), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671368), hAPP(hAPP(c_List_Omap(_1671370, _1671368), hAPP(c_COMBK(_1671368, _1671370), _1671372)), _1671374)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671368), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1671368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671370)), _1671374))), _1671372))], (44532 ^ _779448) ^ [_1671527, _1671529, _1671531, _1671533, _1671535] : [class_Groups_Ocomm__monoid__add(_1671527), hBOOL(hAPP(hAPP(c_member(_1671529), _1671531), hAPP(c_List_Oset(_1671529), _1671533))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671527), hAPP(hAPP(c_List_Omap(_1671529, _1671527), _1671535), _1671533)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1671527), hAPP(_1671535, _1671531)), hAPP(c_List_Omonoid__add__class_Olistsum(_1671527), hAPP(hAPP(c_List_Omap(_1671529, _1671527), _1671535), c_List_Oremove1(_1671529, _1671531, _1671533)))))], (44542 ^ _779448) ^ [_1671776, _1671778, _1671780, _1671782] : [class_Groups_Ocomm__monoid__add(_1671776), 44545 ^ _779448 : [(44546 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1671778), _1671780)), -(c_Nitpick_Osetsum_H(_1671778, _1671776, _1671782, _1671780) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671776), hAPP(hAPP(c_List_Omap(_1671778, _1671776), _1671782), c_Hilbert__Choice_OEps(tc_List_Olist(_1671778), hAPP(hAPP(c_COMBS(tc_List_Olist(_1671778), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1671778)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671778), tc_fun(_1671778, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1671778, tc_HOL_Obool), tc_fun(tc_fun(_1671778, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1671778)), c_fequal), c_List_Oset(_1671778))), _1671780))), c_List_Odistinct(_1671778))))))], (44552 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1671778), _1671780))), -(c_Nitpick_Osetsum_H(_1671778, _1671776, _1671782, _1671780) = c_Groups_Ozero__class_Ozero(_1671776))]]], (44558 ^ _779448) ^ [_1672164, _1672166, _1672168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672164), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672166)), _1672168))), -(hAPP(c_Random_Opick(_1672166, hAPP(hAPP(c_List_Omap(_1672166, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672166)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672166), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672168)), hAPP(c_Code__Numeral_Oof__nat, _1672164)) = hAPP(hAPP(c_List_Onth(_1672166), _1672168), _1672164))], (44564 ^ _779448) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44566 ^ _779448) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (44568 ^ _779448) ^ [_1672388, _1672390] : [hAPP(c_Code__Numeral_Oof__nat, _1672388) = hAPP(c_Code__Numeral_Oof__nat, _1672390), -(_1672388 = _1672390)], (44574 ^ _779448) ^ [_1672473, _1672475] : [_1672473 = _1672475, -(hAPP(c_Code__Numeral_Oof__nat, _1672473) = hAPP(c_Code__Numeral_Oof__nat, _1672475))], (44580 ^ _779448) ^ [_1672564, _1672566] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672564)), hAPP(c_Code__Numeral_Oof__nat, _1672566)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1672564), _1672566)))], (44582 ^ _779448) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44584 ^ _779448) ^ [_1672643, _1672645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672643)), hAPP(c_Code__Numeral_Oof__nat, _1672645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672643), _1672645)))], (44590 ^ _779448) ^ [_1672748, _1672750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672748), _1672750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672748)), hAPP(c_Code__Numeral_Oof__nat, _1672750))))], (44596 ^ _779448) ^ [_1672859, _1672861] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1672859), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1672861), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44603 ^ _779448 : [(44604 ^ _779448) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1672859) = hAPP(c_Code__Numeral_Oof__nat, _1672861), -(_1672859 = _1672861)], (44610 ^ _779448) ^ [] : [_1672859 = _1672861, -(hAPP(c_Code__Numeral_Oof__nat, _1672859) = hAPP(c_Code__Numeral_Oof__nat, _1672861))]]], (44616 ^ _779448) ^ [_1673156, _1673158, _1673160, _1673162] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673156)), _1673158) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673160)), _1673162), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673156, _1673160), _1673156), c_Product__Type_Ofst(_1673156, _1673160)), hAPP(hAPP(c_List_Ozip(_1673156, _1673160), _1673158), _1673162)) = _1673158)], (44622 ^ _779448) ^ [_1673313, _1673315, _1673317, _1673319] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673313)), _1673315) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673317)), _1673319), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673313, _1673317), _1673317), c_Product__Type_Osnd(_1673313, _1673317)), hAPP(hAPP(c_List_Ozip(_1673313, _1673317), _1673315), _1673319)) = _1673319)], (44628 ^ _779448) ^ [] : [-(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))], (44630 ^ _779448) ^ [_1673488, _1673490, _1673492] : [-(hAPP(hAPP(c_List_Ozip(_1673488, _1673490), hAPP(hAPP(c_List_Omap(tc_prod(_1673488, _1673490), _1673488), c_Product__Type_Ofst(_1673488, _1673490)), _1673492)), hAPP(hAPP(c_List_Omap(tc_prod(_1673488, _1673490), _1673490), c_Product__Type_Osnd(_1673488, _1673490)), _1673492)) = _1673492)], (44632 ^ _779448) ^ [_1673554, _1673556] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673554)), hAPP(c_Code__Numeral_Oof__nat, _1673556)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1673554), _1673556)))], (44634 ^ _779448) ^ [_1673615, _1673617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673615)), hAPP(c_Code__Numeral_Oof__nat, _1673617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673615), _1673617)))], (44640 ^ _779448) ^ [_1673720, _1673722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673720), _1673722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673720)), hAPP(c_Code__Numeral_Oof__nat, _1673722))))], (44646 ^ _779448) ^ [_1673831, _1673833, _1673835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1673831), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1673833), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1673833)), _1673835)))), -(hBOOL(hAPP(hAPP(c_member(_1673833), hAPP(c_Random_Opick(_1673833, _1673835), _1673831)), hAPP(c_List_Oset(_1673833), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1673833), _1673833), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1673833)), _1673835)))))], (44652 ^ _779448) ^ [_1674022, _1674024, _1674026, _1674028, _1674030] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674022)), _1674024) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674026)), _1674028), 44655 ^ _779448 : [(44656 ^ _779448) ^ [] : [hAPP(hAPP(c_List_Ozip(_1674022, _1674026), _1674024), _1674028) = _1674030, 44659 ^ _779448 : [(44660 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674022, _1674026), _1674022), c_Product__Type_Ofst(_1674022, _1674026)), _1674030) = _1674024)], (44662 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674022, _1674026), _1674026), c_Product__Type_Osnd(_1674022, _1674026)), _1674030) = _1674028)]]], (44664 ^ _779448) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1674022, _1674026), _1674024), _1674028) = _1674030), hAPP(hAPP(c_List_Omap(tc_prod(_1674022, _1674026), _1674022), c_Product__Type_Ofst(_1674022, _1674026)), _1674030) = _1674024, hAPP(hAPP(c_List_Omap(tc_prod(_1674022, _1674026), _1674026), c_Product__Type_Osnd(_1674022, _1674026)), _1674030) = _1674028]]], (44674 ^ _779448) ^ [_1674470, _1674472, _1674474] : [-(c_List_Olist_Olist__size(_1674470, _1674472, _1674474) = 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(_1674470, tc_Nat_Onat), _1674472), _1674474))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674470)), _1674474)))], (44676 ^ _779448) ^ [_1674532] : [-(_1674532 = 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)), _1674532)))], (44682 ^ _779448) ^ [_1674564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1674564)), _1674564 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44688 ^ _779448) ^ [_1674646, _1674648, _1674650, _1674652] : [class_Groups_Ocomm__monoid__add(_1674646), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674646), _1674648), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674650, _1674652))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1674646), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674646), _1674648), c_List_Oupto(_1674650, _1674652))))], (44694 ^ _779448) ^ [_1674789, _1674791, _1674793, _1674795] : [class_Groups_Ocomm__monoid__add(_1674789), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1674789), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674789), _1674791), c_List_Oupto(_1674793, _1674795))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674789), _1674791), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674793, _1674795))))], (44700 ^ _779448) ^ [_1674932, _1674934, _1674936] : [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, _1674932), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674932)), _1674934)))), -(hBOOL(hAPP(hAPP(c_member(_1674932), hAPP(c_Product__Type_Ofst(_1674932, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1674932, _1674934), _1674936))), hAPP(c_List_Oset(_1674932), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674932), _1674932), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674932)), _1674934)))))], (44706 ^ _779448) ^ [_1675129, _1675131] : [-(c_Random_Oselect__weight(_1675129, _1675131) = 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(_1675129, 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, _1675129), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675129)), _1675131)))), hAPP(hAPP(c_COMBB(_1675129, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675129, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675129, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1675129, _1675131))))], (44708 ^ _779448) ^ [_1675213, _1675215] : [-(c_Random_Oselect(_1675213, _1675215) = 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(_1675213, 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(_1675213)), _1675215)))), hAPP(hAPP(c_COMBB(_1675213, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675213, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675213, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1675213, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1675213), _1675215)), c_Code__Numeral_Onat__of))))], (44710 ^ _779448) ^ [_1675301, _1675303] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1675301)), hAPP(c_Code__Numeral_Oof__nat, _1675303)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1675301), _1675303)))], (44712 ^ _779448) ^ [_1675347] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675347)) = _1675347)], (44714 ^ _779448) ^ [_1675376] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675376)) = _1675376)], (44716 ^ _779448) ^ [_1675405] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1675405)) = _1675405)], (44718 ^ _779448) ^ [_1675449, _1675451] : [hAPP(c_Code__Numeral_Onat__of, _1675449) = hAPP(c_Code__Numeral_Onat__of, _1675451), -(_1675449 = _1675451)], (44724 ^ _779448) ^ [_1675534, _1675536] : [_1675534 = _1675536, -(hAPP(c_Code__Numeral_Onat__of, _1675534) = hAPP(c_Code__Numeral_Onat__of, _1675536))], (44730 ^ _779448) ^ [_1675640, _1675642] : [hAPP(c_Code__Numeral_Onat__of, _1675640) = hAPP(c_Code__Numeral_Onat__of, _1675642), -(_1675640 = _1675642)], (44736 ^ _779448) ^ [_1675725, _1675727] : [_1675725 = _1675727, -(hAPP(c_Code__Numeral_Onat__of, _1675725) = hAPP(c_Code__Numeral_Onat__of, _1675727))], (44742 ^ _779448) ^ [_1675816, _1675818] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1675816), _1675818) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675816)), hAPP(c_Code__Numeral_Onat__of, _1675818))))], (44744 ^ _779448) ^ [] : [-(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))))], (44746 ^ _779448) ^ [_1675895, _1675897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1675895), _1675897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675895)), hAPP(c_Code__Numeral_Onat__of, _1675897))))], (44752 ^ _779448) ^ [_1676000, _1676002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676000)), hAPP(c_Code__Numeral_Onat__of, _1676002))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1676000), _1676002)))], (44758 ^ _779448) ^ [_1676111] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676111)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (44760 ^ _779448) ^ [_1676142] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1676142)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1676142))], (44762 ^ _779448) ^ [] : [-(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))], (44764 ^ _779448) ^ [_1676207, _1676209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676207), _1676209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676207)), hAPP(c_Code__Numeral_Onat__of, _1676209))))], (44770 ^ _779448) ^ [_1676312, _1676314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676312)), hAPP(c_Code__Numeral_Onat__of, _1676314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676312), _1676314)))], (44776 ^ _779448) ^ [_1676423] : [-(hAPP(c_Code__Numeral_Onat__of, _1676423) = c_Code__Numeral_Onat__of__aux(_1676423, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44778 ^ _779448) ^ [_1676452, _1676454] : [-(c_Code__Numeral_Onat__of__aux(_1676452, _1676454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676452)), _1676454))], (44780 ^ _779448) ^ [_1676489] : [-(c_Code__Numeral_OSuc__code__numeral(_1676489) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1676489))))], (44782 ^ _779448) ^ [_1676523, _1676525] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676523), _1676525) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676523)), hAPP(c_Code__Numeral_Onat__of, _1676525))))], (44784 ^ _779448) ^ [_1676569] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1676569), 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, _1676569)) = _1676569)], (44790 ^ _779448) ^ [_1676666, _1676668] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1676666), _1676668) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676666)), hAPP(c_Code__Numeral_Onat__of, _1676668))))], (44792 ^ _779448) ^ [_1676712, _1676714] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1676712), _1676714) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676712)), hAPP(c_Code__Numeral_Onat__of, _1676714))))], (44794 ^ _779448) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (44796 ^ _779448) ^ [_1676776, _1676778] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676776), _1676778) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1676776), _1676778))], (44798 ^ _779448) ^ [_1676813, _1676815] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1676813, _1676815) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1676813), hAPP(c_Code__Numeral_Onat__of, _1676815))))], (44800 ^ _779448) ^ [_1676851] : [-(_1676851 = 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, _1676851)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1676851))))], (44806 ^ _779448) ^ [_1676902, _1676904, _1676906, _1676908, _1676910] : [class_Groups_Omonoid__add(_1676902), class_Groups_Oordered__ab__semigroup__add(_1676902), 44816 ^ _779448 : [(44817 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676904), 44815 ^ [_1676902, _1676904, _1676906, _1676908, _1676910]), hAPP(c_List_Oset(_1676904), _1676906))))], (44819 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676902), hAPP(_1676908, 44815 ^ [_1676902, _1676904, _1676906, _1676908, _1676910])), hAPP(_1676910, 44815 ^ [_1676902, _1676904, _1676906, _1676908, _1676910])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676902), hAPP(c_List_Omonoid__add__class_Olistsum(_1676902), hAPP(hAPP(c_List_Omap(_1676904, _1676902), _1676908), _1676906))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676902), hAPP(hAPP(c_List_Omap(_1676904, _1676902), _1676910), _1676906)))))], (44823 ^ _779448) ^ [_1677326, _1677328] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1677326), _1677328) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1677326, 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)))), _1677328))))], (44825 ^ _779448) ^ [_1677364, _1677366, _1677368, _1677370, _1677372] : [c_List_Opartition(_1677364, _1677366, _1677368) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677364), tc_List_Olist(_1677364)), _1677370), _1677372), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1677364, tc_HOL_Obool)), hAPP(c_List_Oset(_1677364), _1677370)), hAPP(c_List_Oset(_1677364), _1677372)) = hAPP(c_List_Oset(_1677364), _1677368))], (44831 ^ _779448) ^ [_1677533, _1677535, _1677537] : [-(c_List_Olistsp(_1677533, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1677533, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1677533, tc_fun(_1677533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677533)), _1677535)), hAPP(hAPP(c_COMBC(_1677533, tc_fun(_1677533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677533)), _1677537))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1677533), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677533), tc_fun(tc_List_Olist(_1677533), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677533))), c_List_Olists(_1677533, _1677535))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677533), tc_fun(tc_List_Olist(_1677533), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677533))), c_List_Olists(_1677533, _1677537))))], (44833 ^ _779448) ^ [_1677665, _1677667] : [-(hBOOL(hAPP(c_List_Olistsp(_1677665, _1677667), c_List_Olist_ONil(_1677665))))], (44835 ^ _779448) ^ [_1677697, _1677699] : [-(hBOOL(hAPP(c_List_Olistsp(_1677697, _1677699), c_List_Olist_ONil(_1677697))))], (44847 ^ _779448) ^ [_1677945, _1677947, _1677949] : [44849 ^ _779448 : [(44850 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677945), 44848 ^ [_1677945, _1677947, _1677949]), hAPP(c_List_Oset(_1677945), _1677949))))], (44852 ^ _779448) ^ [] : [hBOOL(hAPP(_1677947, 44848 ^ [_1677945, _1677947, _1677949]))]], -(hBOOL(hAPP(c_List_Olistsp(_1677945, _1677947), _1677949)))], (44837 ^ _779448) ^ [_1677747, _1677749, _1677751] : [hBOOL(hAPP(c_List_Olistsp(_1677747, _1677749), _1677751)), 44840 ^ _779448 : [(44841 ^ _779448) ^ [_1677836] : [hBOOL(hAPP(hAPP(c_member(_1677747), _1677836), hAPP(c_List_Oset(_1677747), _1677751))), -(hBOOL(hAPP(_1677749, _1677836)))]]], (44856 ^ _779448) ^ [_1678156, _1678158, _1678160, _1678162] : [hBOOL(hAPP(c_List_Olistsp(_1678156, hAPP(hAPP(c_COMBS(_1678156, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678156), c_fconj), _1678158)), _1678160)), _1678162)), 44859 ^ _779448 : [(44860 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678156, _1678158), _1678162)))], (44862 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678156, _1678160), _1678162)))]]], (44864 ^ _779448) ^ [_1678329, _1678331, _1678333, _1678335] : [-(hBOOL(hAPP(c_List_Olistsp(_1678329, hAPP(hAPP(c_COMBS(_1678329, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678329), c_fconj), _1678331)), _1678333)), _1678335))), hBOOL(hAPP(c_List_Olistsp(_1678329, _1678331), _1678335)), hBOOL(hAPP(c_List_Olistsp(_1678329, _1678333), _1678335))], (44874 ^ _779448) ^ [_1678538, _1678540, _1678542, _1678544] : [hBOOL(hAPP(c_List_Olistsp(_1678538, _1678540), _1678542)), hBOOL(hAPP(c_List_Olistsp(_1678538, _1678544), _1678542)), -(hBOOL(hAPP(c_List_Olistsp(_1678538, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678538, tc_HOL_Obool)), _1678540), _1678544)), _1678542)))], (44884 ^ _779448) ^ [_1678727, _1678729, _1678731] : [-(c_List_Olistsp(_1678727, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678727, tc_HOL_Obool)), _1678729), _1678731)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1678727), tc_HOL_Obool)), c_List_Olistsp(_1678727, _1678729)), c_List_Olistsp(_1678727, _1678731)))], (44886 ^ _779448) ^ [_1678808, _1678810, _1678812, _1678814] : [hBOOL(hAPP(c_List_Olistsp(_1678808, _1678810), hAPP(hAPP(c_List_Olist_OCons(_1678808), _1678812), _1678814))), 44889 ^ _779448 : [(44890 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1678810, _1678812)))], (44892 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678808, _1678810), _1678814)))]]], (44894 ^ _779448) ^ [_1678951, _1678953, _1678955, _1678957] : [-(hBOOL(hAPP(c_List_Olistsp(_1678951, _1678953), hAPP(hAPP(c_List_Olist_OCons(_1678951), _1678955), _1678957)))), hBOOL(hAPP(_1678953, _1678955)), hBOOL(hAPP(c_List_Olistsp(_1678951, _1678953), _1678957))], (44904 ^ _779448) ^ [_1679151, _1679153, _1679155, _1679157] : [hBOOL(hAPP(c_List_Olistsp(_1679151, _1679153), hAPP(hAPP(c_List_Oappend(_1679151), _1679155), _1679157))), 44907 ^ _779448 : [(44908 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679151, _1679153), _1679155)))], (44910 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679151, _1679153), _1679157)))]]], (44912 ^ _779448) ^ [_1679300, _1679302, _1679304, _1679306] : [-(hBOOL(hAPP(c_List_Olistsp(_1679300, _1679302), hAPP(hAPP(c_List_Oappend(_1679300), _1679304), _1679306)))), hBOOL(hAPP(c_List_Olistsp(_1679300, _1679302), _1679304)), hBOOL(hAPP(c_List_Olistsp(_1679300, _1679302), _1679306))], (44922 ^ _779448) ^ [_1679485, _1679487, _1679489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1679485, tc_HOL_Obool)), _1679487), _1679489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1679485), tc_HOL_Obool)), c_List_Olistsp(_1679485, _1679487)), c_List_Olistsp(_1679485, _1679489))))], (44928 ^ _779448) ^ [_1679620, _1679622, _1679624, _1679626, _1679628] : [c_List_Opartition(_1679620, _1679622, _1679624) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679620), tc_List_Olist(_1679620)), _1679626), _1679628), 44931 ^ _779448 : [(44932 ^ _779448) ^ [_1679773] : [hBOOL(hAPP(hAPP(c_member(_1679620), _1679773), hAPP(c_List_Oset(_1679620), _1679626))), -(hBOOL(hAPP(_1679622, _1679773)))], (44938 ^ _779448) ^ [_1679882] : [hBOOL(hAPP(hAPP(c_member(_1679620), _1679882), hAPP(c_List_Oset(_1679620), _1679628))), hBOOL(hAPP(_1679622, _1679882))]]], (44944 ^ _779448) ^ [_1680002, _1680004] : [-(c_List_Opartition(_1680002, _1680004, c_List_Olist_ONil(_1680002)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680002), tc_List_Olist(_1680002)), c_List_Olist_ONil(_1680002)), c_List_Olist_ONil(_1680002)))], (44946 ^ _779448) ^ [_1680068, _1680070, _1680072] : [hBOOL(hAPP(c_List_Olistsp(_1680068, hAPP(hAPP(c_COMBC(_1680068, tc_fun(_1680068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680068)), _1680070)), _1680072)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680068)), _1680072), c_List_Olists(_1680068, _1680070))))], (44952 ^ _779448) ^ [_1680207, _1680209, _1680211] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680207)), _1680211), c_List_Olists(_1680207, _1680209))), -(hBOOL(hAPP(c_List_Olistsp(_1680207, hAPP(hAPP(c_COMBC(_1680207, tc_fun(_1680207, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680207)), _1680209)), _1680211)))], (44958 ^ _779448) ^ [_1680352, _1680354, _1680356, _1680358] : [-(c_List_Opartition(_1680352, _1680354, hAPP(hAPP(c_List_Olist_OCons(_1680352), _1680356), _1680358)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1680352), tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1680352), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680352), tc_fun(tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), tc_fun(tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), tc_List_Olist(_1680352)), c_COMBS(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_fun(tc_List_Olist(_1680352), tc_fun(tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), tc_List_Olist(_1680352)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_fun(tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_List_Olist(_1680352)), hAPP(c_If(tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), hAPP(_1680354, _1680356)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1680352), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_List_Olist(_1680352)), c_Product__Type_OPair(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), hAPP(c_List_Olist_OCons(_1680352), _1680356))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680352), tc_fun(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352))), tc_fun(tc_fun(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_fun(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), tc_List_Olist(_1680352)), c_COMBB(tc_List_Olist(_1680352), tc_prod(tc_List_Olist(_1680352), tc_List_Olist(_1680352)), tc_List_Olist(_1680352))), c_Product__Type_OPair(tc_List_Olist(_1680352), tc_List_Olist(_1680352)))), hAPP(c_List_Olist_OCons(_1680352), _1680356)))), c_List_Opartition(_1680352, _1680354, _1680358)))], (44960 ^ _779448) ^ [_1680771, _1680773, _1680775, _1680777] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680771)), _1680773), c_List_Olists(_1680771, _1680775))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680771)), _1680773), c_List_Olists(_1680771, _1680777))), -(hBOOL(hAPP(c_List_Olistsp(_1680771, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680771, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1680771, tc_fun(_1680771, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680771)), _1680775)), hAPP(hAPP(c_COMBC(_1680771, tc_fun(_1680771, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680771)), _1680777))), _1680773)))], (44970 ^ _779448) ^ [_1681048, _1681050, _1681052, _1681054, _1681056] : [-(c_Enum_Oproduct(_1681048, _1681050, hAPP(hAPP(c_List_Olist_OCons(_1681048), _1681052), _1681054), _1681056) = hAPP(hAPP(c_List_Oappend(tc_prod(_1681048, _1681050)), hAPP(hAPP(c_List_Omap(_1681050, tc_prod(_1681048, _1681050)), hAPP(c_Product__Type_OPair(_1681048, _1681050), _1681052)), _1681056)), c_Enum_Oproduct(_1681048, _1681050, _1681054, _1681056)))], (44972 ^ _779448) ^ [_1681150, _1681152, _1681154, _1681156, _1681158] : [c_List_Olist__all2(_1681150, _1681152, _1681154, _1681156, _1681158), 44975 ^ _779448 : [(44976 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681150)), _1681156) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681152)), _1681158))], (44978 ^ _779448) ^ [_1681316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681150, _1681152)), _1681316), hAPP(c_List_Oset(tc_prod(_1681150, _1681152)), hAPP(hAPP(c_List_Ozip(_1681150, _1681152), _1681156), _1681158)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681150, _1681152, tc_HOL_Obool), _1681154), _1681316)))]]], (44984 ^ _779448) ^ [_1681475, _1681477, _1681479, _1681481, _1681483] : [-(c_List_Olist__all2(_1681475, _1681477, _1681479, _1681481, _1681483)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681475)), _1681481) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681477)), _1681483), 44990 ^ _779448 : [(44991 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681475, _1681477)), 44989 ^ [_1681475, _1681477, _1681479, _1681481, _1681483]), hAPP(c_List_Oset(tc_prod(_1681475, _1681477)), hAPP(hAPP(c_List_Ozip(_1681475, _1681477), _1681481), _1681483)))))], (44993 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681475, _1681477, tc_HOL_Obool), _1681479), 44989 ^ [_1681475, _1681477, _1681479, _1681481, _1681483]))]]], (44997 ^ _779448) ^ [_1681846, _1681848, _1681850, _1681852, _1681854, _1681856, _1681858] : [c_List_Olist__all2(_1681846, _1681848, _1681850, hAPP(hAPP(c_List_Omap(_1681852, _1681846), _1681854), _1681856), _1681858), -(c_List_Olist__all2(_1681852, _1681848, hAPP(hAPP(c_COMBB(_1681846, tc_fun(_1681848, tc_HOL_Obool), _1681852), _1681850), _1681854), _1681856, _1681858))], (45003 ^ _779448) ^ [_1681985, _1681987, _1681989, _1681991, _1681993, _1681995, _1681997] : [c_List_Olist__all2(_1681991, _1681987, hAPP(hAPP(c_COMBB(_1681985, tc_fun(_1681987, tc_HOL_Obool), _1681991), _1681989), _1681993), _1681995, _1681997), -(c_List_Olist__all2(_1681985, _1681987, _1681989, hAPP(hAPP(c_List_Omap(_1681991, _1681985), _1681993), _1681995), _1681997))], (45009 ^ _779448) ^ [_1682160, _1682162, _1682164, _1682166, _1682168, _1682170, _1682172] : [c_List_Olist__all2(_1682160, _1682162, _1682164, _1682166, hAPP(hAPP(c_List_Omap(_1682168, _1682162), _1682170), _1682172)), -(c_List_Olist__all2(_1682160, _1682168, hAPP(hAPP(c_COMBC(_1682160, tc_fun(_1682168, _1682162), tc_fun(_1682168, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682162, tc_HOL_Obool), tc_fun(tc_fun(_1682168, _1682162), tc_fun(_1682168, tc_HOL_Obool)), _1682160), c_COMBB(_1682162, tc_HOL_Obool, _1682168)), _1682164)), _1682170), _1682166, _1682172))], (45015 ^ _779448) ^ [_1682357, _1682359, _1682361, _1682363, _1682365, _1682367, _1682369] : [c_List_Olist__all2(_1682357, _1682365, hAPP(hAPP(c_COMBC(_1682357, tc_fun(_1682365, _1682359), tc_fun(_1682365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682359, tc_HOL_Obool), tc_fun(tc_fun(_1682365, _1682359), tc_fun(_1682365, tc_HOL_Obool)), _1682357), c_COMBB(_1682359, tc_HOL_Obool, _1682365)), _1682361)), _1682367), _1682363, _1682369), -(c_List_Olist__all2(_1682357, _1682359, _1682361, _1682363, hAPP(hAPP(c_List_Omap(_1682365, _1682359), _1682367), _1682369)))], (45021 ^ _779448) ^ [_1682560, _1682562, _1682564, _1682566, _1682568, _1682570] : [c_List_Olist__all2(_1682560, _1682562, _1682564, _1682566, _1682568), -(c_List_Olist__all2(_1682560, _1682562, _1682564, hAPP(hAPP(c_List_Odrop(_1682560), _1682570), _1682566), hAPP(hAPP(c_List_Odrop(_1682562), _1682570), _1682568)))], (45027 ^ _779448) ^ [_1682689, _1682691, _1682693, _1682695, _1682697, _1682699, _1682701] : [c_List_Olist__all2(_1682689, _1682691, _1682693, _1682695, _1682697), c_List_Olist__all2(_1682689, _1682691, _1682693, _1682699, _1682701), -(c_List_Olist__all2(_1682689, _1682691, _1682693, hAPP(hAPP(c_List_Oappend(_1682689), _1682695), _1682699), hAPP(hAPP(c_List_Oappend(_1682691), _1682697), _1682701)))], (45037 ^ _779448) ^ [_1682888, _1682890, _1682892, _1682894, _1682896, _1682898, _1682900] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682888)), _1682890) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682892)), _1682894), 45040 ^ _779448 : [(45041 ^ _779448) ^ [] : [c_List_Olist__all2(_1682888, _1682892, _1682896, hAPP(hAPP(c_List_Oappend(_1682888), _1682890), _1682898), hAPP(hAPP(c_List_Oappend(_1682892), _1682894), _1682900)), 45044 ^ _779448 : [(45045 ^ _779448) ^ [] : [-(c_List_Olist__all2(_1682888, _1682892, _1682896, _1682890, _1682894))], (45047 ^ _779448) ^ [] : [-(c_List_Olist__all2(_1682888, _1682892, _1682896, _1682898, _1682900))]]], (45049 ^ _779448) ^ [] : [-(c_List_Olist__all2(_1682888, _1682892, _1682896, hAPP(hAPP(c_List_Oappend(_1682888), _1682890), _1682898), hAPP(hAPP(c_List_Oappend(_1682892), _1682894), _1682900))), c_List_Olist__all2(_1682888, _1682892, _1682896, _1682890, _1682894), c_List_Olist__all2(_1682888, _1682892, _1682896, _1682898, _1682900)]]], (45059 ^ _779448) ^ [_1683340, _1683342, _1683344, _1683346, _1683348, _1683350, _1683352] : [c_List_Olist__all2(_1683340, _1683342, _1683344, hAPP(hAPP(c_List_Olist_OCons(_1683340), _1683346), _1683348), hAPP(hAPP(c_List_Olist_OCons(_1683342), _1683350), _1683352)), 45062 ^ _779448 : [(45063 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1683344, _1683346), _1683350)))], (45065 ^ _779448) ^ [] : [-(c_List_Olist__all2(_1683340, _1683342, _1683344, _1683348, _1683352))]]], (45067 ^ _779448) ^ [_1683503, _1683505, _1683507, _1683509, _1683511, _1683513, _1683515] : [-(c_List_Olist__all2(_1683503, _1683505, _1683507, hAPP(hAPP(c_List_Olist_OCons(_1683503), _1683509), _1683511), hAPP(hAPP(c_List_Olist_OCons(_1683505), _1683513), _1683515))), hBOOL(hAPP(hAPP(_1683507, _1683509), _1683513)), c_List_Olist__all2(_1683503, _1683505, _1683507, _1683511, _1683515)], (45077 ^ _779448) ^ [_1683708, _1683710, _1683712, _1683714, _1683716, _1683718] : [c_List_Olist__all2(_1683708, _1683710, _1683712, _1683714, _1683716), -(c_List_Olist__all2(_1683708, _1683710, _1683712, hAPP(hAPP(c_List_Otake(_1683708), _1683718), _1683714), hAPP(hAPP(c_List_Otake(_1683710), _1683718), _1683716)))], (45083 ^ _779448) ^ [_1683855, _1683857, _1683859] : [_1683855 = _1683857, -(c_List_Olist__all2(_1683859, _1683859, c_fequal, _1683855, _1683857))], (45089 ^ _779448) ^ [_1683936, _1683938, _1683940] : [c_List_Olist__all2(_1683940, _1683940, c_fequal, _1683936, _1683938), -(_1683936 = _1683938)], (45095 ^ _779448) ^ [_1684023, _1684025, _1684027, _1684029, _1684031] : [c_List_Olist__all2(_1684023, _1684025, _1684027, _1684029, _1684031), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684023)), _1684029) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684025)), _1684031))], (45101 ^ _779448) ^ [_1684161, _1684163, _1684165, _1684167] : [c_List_Olist__all2(_1684161, _1684163, _1684165, c_List_Olist_ONil(_1684161), _1684167), -(_1684167 = c_List_Olist_ONil(_1684163))], (45107 ^ _779448) ^ [_1684252, _1684254, _1684256, _1684258] : [_1684258 = c_List_Olist_ONil(_1684254), -(c_List_Olist__all2(_1684252, _1684254, _1684256, c_List_Olist_ONil(_1684252), _1684258))], (45113 ^ _779448) ^ [_1684370, _1684372, _1684374, _1684376] : [c_List_Olist__all2(_1684370, _1684372, _1684374, _1684376, c_List_Olist_ONil(_1684372)), -(_1684376 = c_List_Olist_ONil(_1684370))], (45119 ^ _779448) ^ [_1684461, _1684463, _1684465, _1684467] : [_1684467 = c_List_Olist_ONil(_1684461), -(c_List_Olist__all2(_1684461, _1684463, _1684465, _1684467, c_List_Olist_ONil(_1684463)))], (45125 ^ _779448) ^ [_1684558, _1684560, _1684562] : [-(c_Enum_Oproduct(_1684558, _1684560, c_List_Olist_ONil(_1684558), _1684562) = c_List_Olist_ONil(tc_prod(_1684558, _1684560)))], (45127 ^ _779448) ^ [_1684597, _1684599, _1684601, _1684603, _1684605, _1684607] : [c_List_Olist__all2(_1684597, _1684599, _1684601, _1684603, _1684605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684607), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684599)), _1684605))), -(hBOOL(hAPP(hAPP(_1684601, hAPP(hAPP(c_List_Onth(_1684597), _1684603), _1684607)), hAPP(hAPP(c_List_Onth(_1684599), _1684605), _1684607))))], (45137 ^ _779448) ^ [_1684814, _1684816, _1684818, _1684820, _1684822, _1684824] : [c_List_Olist__all2(_1684814, _1684816, _1684818, _1684820, _1684822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684824), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684814)), _1684820))), -(hBOOL(hAPP(hAPP(_1684818, hAPP(hAPP(c_List_Onth(_1684814), _1684820), _1684824)), hAPP(hAPP(c_List_Onth(_1684816), _1684822), _1684824))))], (45147 ^ _779448) ^ [_1685055, _1685057, _1685059, _1685061, _1685063] : [c_List_Olist__all2(_1685055, _1685057, _1685059, _1685061, _1685063), 45150 ^ _779448 : [(45151 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685055)), _1685061) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685057)), _1685063))], (45153 ^ _779448) ^ [_1685218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685218), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685055)), _1685061))), -(hBOOL(hAPP(hAPP(_1685059, hAPP(hAPP(c_List_Onth(_1685055), _1685061), _1685218)), hAPP(hAPP(c_List_Onth(_1685057), _1685063), _1685218))))]]], (45159 ^ _779448) ^ [_1685371, _1685373, _1685375, _1685377, _1685379] : [-(c_List_Olist__all2(_1685371, _1685373, _1685375, _1685377, _1685379)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685371)), _1685377) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685373)), _1685379), 45165 ^ _779448 : [(45166 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45164 ^ [_1685371, _1685373, _1685375, _1685377, _1685379]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685371)), _1685377))))], (45168 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1685375, hAPP(hAPP(c_List_Onth(_1685371), _1685377), 45164 ^ [_1685371, _1685373, _1685375, _1685377, _1685379])), hAPP(hAPP(c_List_Onth(_1685373), _1685379), 45164 ^ [_1685371, _1685373, _1685375, _1685377, _1685379])))]]], (45172 ^ _779448) ^ [_1685731, _1685733, _1685735, _1685737, _1685739, _1685741, _1685743, _1685745] : [c_List_Olist__all2(_1685731, _1685733, _1685735, _1685737, _1685739), hBOOL(hAPP(hAPP(_1685735, _1685741), _1685743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685745), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685733)), _1685739))), -(c_List_Olist__all2(_1685731, _1685733, _1685735, hAPP(hAPP(c_List_Olist__update(_1685731, _1685737), _1685745), _1685741), hAPP(hAPP(c_List_Olist__update(_1685733, _1685739), _1685745), _1685743)))], (45186 ^ _779448) ^ [_1686030, _1686032, _1686034, _1686036, _1686038, _1686040, _1686042, _1686044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686030), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686032)), _1686034))), c_List_Olist__all2(_1686032, _1686036, _1686038, _1686034, _1686040), hBOOL(hAPP(hAPP(_1686038, _1686042), _1686044)), -(c_List_Olist__all2(_1686032, _1686036, _1686038, hAPP(hAPP(c_List_Olist__update(_1686032, _1686034), _1686030), _1686042), hAPP(hAPP(c_List_Olist__update(_1686036, _1686040), _1686030), _1686044)))], (45200 ^ _779448) ^ [_1686329, _1686331, _1686333, _1686335] : [hBOOL(hAPP(c_List_Odistinct(_1686329), _1686331)), hBOOL(hAPP(c_List_Odistinct(_1686333), _1686335)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1686329, _1686333)), c_Enum_Oproduct(_1686329, _1686333, _1686331, _1686335))))], (45210 ^ _779448) ^ [_1686506, _1686508, _1686510, _1686512] : [-(hAPP(c_List_Oset(tc_prod(_1686506, _1686508)), c_Enum_Oproduct(_1686506, _1686508, _1686510, _1686512)) = hAPP(hAPP(c_Product__Type_OSigma(_1686506, _1686508), hAPP(c_List_Oset(_1686506), _1686510)), hAPP(c_COMBK(tc_fun(_1686508, tc_HOL_Obool), _1686506), hAPP(c_List_Oset(_1686508), _1686512))))], (45212 ^ _779448) ^ [_1686576, _1686578] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1686576), tc_fun(_1686576, tc_HOL_Obool), c_List_Oset(_1686576)), hAPP(c_List_Oset(tc_List_Olist(_1686576)), c_Enum_Osublists(_1686576, _1686578))) = hAPP(c_Set_OPow(_1686576), hAPP(c_List_Oset(_1686576), _1686578)))], (45214 ^ _779448) ^ [_1686635, _1686637] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686635))), c_Enum_Osublists(_1686635, _1686637)) = 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(_1686635)), _1686637)))], (45216 ^ _779448) ^ [_1686682] : [-(c_Enum_Osublists(_1686682, c_List_Olist_ONil(_1686682)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1686682)), c_List_Olist_ONil(_1686682)), c_List_Olist_ONil(tc_List_Olist(_1686682))))], (45218 ^ _779448) ^ [_1686726, _1686728, _1686730] : [-(c_Enum_Osublists(_1686726, hAPP(hAPP(c_List_Olist_OCons(_1686726), _1686728), _1686730)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1686726)), tc_List_Olist(tc_List_Olist(_1686726))), c_Enum_Osublists(_1686726, _1686730)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1686726)), tc_List_Olist(tc_List_Olist(_1686726)), tc_List_Olist(tc_List_Olist(_1686726))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1686726)), tc_fun(tc_List_Olist(tc_List_Olist(_1686726)), tc_List_Olist(tc_List_Olist(_1686726))), tc_List_Olist(tc_List_Olist(_1686726))), c_List_Oappend(tc_List_Olist(_1686726))), hAPP(c_List_Omap(tc_List_Olist(_1686726), tc_List_Olist(_1686726)), hAPP(c_List_Olist_OCons(_1686726), _1686728)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1686726))))))], (45220 ^ _779448) ^ [_1686860, _1686862] : [hBOOL(hAPP(c_List_Odistinct(_1686860), _1686862)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1686860, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1686860), tc_fun(_1686860, tc_HOL_Obool)), c_List_Oset(_1686860)), c_Enum_Osublists(_1686860, _1686862)))))], (45226 ^ _779448) ^ [_1686997, _1686999, _1687001] : [-(hAPP(c_List_Oset(tc_List_Olist(_1686997)), c_Enum_On__lists(_1686997, _1686999, _1687001)) = hAPP(c_Set_OCollect(tc_List_Olist(_1686997)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1686997), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1686997)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1686997), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1686997)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1686997)))), _1686999))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1686997), tc_fun(_1686997, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1686997, tc_HOL_Obool), tc_fun(tc_fun(_1686997, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1686997)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1686997, tc_HOL_Obool))), c_List_Oset(_1686997))), hAPP(c_List_Oset(_1686997), _1687001)))))], (45228 ^ _779448) ^ [_1687142, _1687144] : [-(c_Enum_Oenum__the(_1687142, _1687144) = c_HOL_OThe(_1687142, _1687144))], (45230 ^ _779448) ^ [_1687173, _1687175, _1687177] : [hBOOL(hAPP(c_List_Odistinct(_1687173), _1687175)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687173)), c_Enum_On__lists(_1687173, _1687177, _1687175))))], (45236 ^ _779448) ^ [_1687289, _1687291] : [_1687289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1687291, _1687289, c_List_Olist_ONil(_1687291)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687291)), c_List_Olist_ONil(_1687291)), c_List_Olist_ONil(tc_List_Olist(_1687291))))], (45242 ^ _779448) ^ [_1687404, _1687406] : [-(_1687404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1687406, _1687404, c_List_Olist_ONil(_1687406)) = c_List_Olist_ONil(tc_List_Olist(_1687406)))], (45248 ^ _779448) ^ [_1687452, _1687454] : [-(c_Enum_On__lists(_1687452, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1687454) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687452)), c_List_Olist_ONil(_1687452)), c_List_Olist_ONil(tc_List_Olist(_1687452))))], (45250 ^ _779448) ^ [_1687497, _1687499, _1687501] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687497))), c_Enum_On__lists(_1687497, _1687499, _1687501)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687497)), _1687501)), _1687499))], (45252 ^ _779448) ^ [_1687550, _1687552, _1687554, _1687556] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687550)), _1687552), hAPP(c_List_Oset(tc_List_Olist(_1687550)), c_Enum_On__lists(_1687550, _1687554, _1687556)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687550)), _1687552) = _1687554)], (45258 ^ _779448) ^ [_1687685, _1687687, _1687689, _1687691, _1687693] : [45260 ^ _779448 : [(45261 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687685, _1687687)), 45259 ^ [_1687685, _1687687, _1687689, _1687691, _1687693]), hAPP(c_List_Oset(tc_prod(_1687685, _1687687)), hAPP(hAPP(c_List_Ozip(_1687685, _1687687), _1687689), _1687691)))))], (45263 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687685, _1687687, tc_HOL_Obool), _1687693), 45259 ^ [_1687685, _1687687, _1687689, _1687691, _1687693]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687685)), _1687689) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687687)), _1687691), -(c_List_Olist__all2(_1687685, _1687687, _1687693, _1687689, _1687691))], (45271 ^ _779448) ^ [_1688024, _1688026, _1688028, _1688030] : [45273 ^ _779448 : [(45274 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45272 ^ [_1688024, _1688026, _1688028, _1688030]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688024)), _1688026))))], (45276 ^ _779448) ^ [] : [hBOOL(hAPP(_1688028, hAPP(hAPP(c_List_Onth(_1688024), _1688026), 45272 ^ [_1688024, _1688026, _1688028, _1688030])))]], hBOOL(hAPP(hAPP(c_member(_1688024), _1688030), hAPP(c_List_Oset(_1688024), _1688026))), -(hBOOL(hAPP(_1688028, _1688030)))], (45284 ^ _779448) ^ [_1688320, _1688322, _1688324, _1688326, _1688328] : [c_Finite__Set_Ofun__left__comm(_1688320, _1688322, _1688324), -(hAPP(hAPP(c_Finite__Set_Ofold(_1688320, _1688322, _1688324), _1688326), hAPP(c_List_Oset(_1688320), _1688328)) = hAPP(c_List_Ofoldl(_1688322, _1688320, hAPP(c_COMBC(_1688320, _1688322, _1688322), _1688324), _1688326), c_List_Oremdups(_1688320, _1688328)))], (45290 ^ _779448) ^ [_1688471, _1688473, _1688475, _1688477, _1688479] : [c_Fun_Oinj__on(_1688471, _1688473, _1688475, hAPP(hAPP(c_Set_Oinsert(_1688471), _1688477), hAPP(c_List_Oset(_1688471), _1688479))), -(hAPP(hAPP(c_List_Omap(_1688471, _1688473), _1688475), hAPP(c_List_OremoveAll(_1688471, _1688477), _1688479)) = hAPP(c_List_OremoveAll(_1688473, hAPP(_1688475, _1688477)), hAPP(hAPP(c_List_Omap(_1688471, _1688473), _1688475), _1688479)))], (45296 ^ _779448) ^ [_1688650, _1688652] : [-(hBOOL(hAPP(c_List_Odistinct(_1688650), c_List_Oremdups(_1688650, _1688652))))], (45298 ^ _779448) ^ [_1688682, _1688684] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688682)), c_List_Oremdups(_1688682, _1688684))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688682)), _1688684))))], (45300 ^ _779448) ^ [_1688729, _1688731] : [hBOOL(hAPP(c_List_Odistinct(_1688729), _1688731)), -(c_List_Oremdups(_1688729, _1688731) = _1688731)], (45306 ^ _779448) ^ [_1688820, _1688822, _1688824] : [hBOOL(hAPP(c_List_Odistinct(_1688820), _1688822)), -(hBOOL(hAPP(c_List_Odistinct(_1688820), hAPP(c_List_OremoveAll(_1688820, _1688824), _1688822))))], (45312 ^ _779448) ^ [_1688942, _1688944] : [c_List_Oremdups(_1688942, _1688944) = _1688944, -(hBOOL(hAPP(c_List_Odistinct(_1688942), _1688944)))], (45318 ^ _779448) ^ [_1689029, _1689031] : [hBOOL(hAPP(c_List_Odistinct(_1689029), _1689031)), -(c_List_Oremdups(_1689029, _1689031) = _1689031)], (45324 ^ _779448) ^ [_1689122, _1689124] : [-(hAPP(c_List_Oset(_1689122), c_List_Oremdups(_1689122, _1689124)) = hAPP(c_List_Oset(_1689122), _1689124))], (45326 ^ _779448) ^ [_1689175, _1689177] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689175)), c_List_Oremdups(_1689175, _1689177)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689175)), _1689177), -(c_List_Oremdups(_1689175, _1689177) = _1689177)], (45332 ^ _779448) ^ [_1689288, _1689290] : [c_List_Oremdups(_1689288, _1689290) = _1689290, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689288)), c_List_Oremdups(_1689288, _1689290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689288)), _1689290))], (45338 ^ _779448) ^ [_1689407, _1689409] : [-(c_List_Oremdups(_1689407, c_List_Oremdups(_1689407, _1689409)) = c_List_Oremdups(_1689407, _1689409))], (45340 ^ _779448) ^ [_1689456, _1689458] : [c_List_Oremdups(_1689456, _1689458) = c_List_Olist_ONil(_1689456), -(_1689458 = c_List_Olist_ONil(_1689456))], (45346 ^ _779448) ^ [_1689543, _1689545] : [_1689545 = c_List_Olist_ONil(_1689543), -(c_List_Oremdups(_1689543, _1689545) = c_List_Olist_ONil(_1689543))], (45352 ^ _779448) ^ [_1689636, _1689638] : [-(hAPP(c_List_OremoveAll(_1689636, _1689638), c_List_Olist_ONil(_1689636)) = c_List_Olist_ONil(_1689636))], (45354 ^ _779448) ^ [_1689686, _1689688] : [c_List_Olist_ONil(_1689686) = c_List_Oremdups(_1689686, _1689688), -(_1689688 = c_List_Olist_ONil(_1689686))], (45360 ^ _779448) ^ [_1689773, _1689775] : [_1689775 = c_List_Olist_ONil(_1689773), -(c_List_Olist_ONil(_1689773) = c_List_Oremdups(_1689773, _1689775))], (45366 ^ _779448) ^ [_1689866] : [-(c_List_Oremdups(_1689866, c_List_Olist_ONil(_1689866)) = c_List_Olist_ONil(_1689866))], (45368 ^ _779448) ^ [_1689911, _1689913, _1689915, _1689917] : [_1689911 = _1689913, -(hAPP(c_List_OremoveAll(_1689915, _1689911), hAPP(hAPP(c_List_Olist_OCons(_1689915), _1689913), _1689917)) = hAPP(c_List_OremoveAll(_1689915, _1689911), _1689917))], (45374 ^ _779448) ^ [_1690026, _1690028, _1690030, _1690032] : [-(_1690026 = _1690028), -(hAPP(c_List_OremoveAll(_1690030, _1690026), hAPP(hAPP(c_List_Olist_OCons(_1690030), _1690028), _1690032)) = hAPP(hAPP(c_List_Olist_OCons(_1690030), _1690028), hAPP(c_List_OremoveAll(_1690030, _1690026), _1690032)))], (45380 ^ _779448) ^ [_1690096, _1690098, _1690100, _1690102] : [-(hAPP(c_List_OremoveAll(_1690096, _1690098), hAPP(hAPP(c_List_Oappend(_1690096), _1690100), _1690102)) = hAPP(hAPP(c_List_Oappend(_1690096), hAPP(c_List_OremoveAll(_1690096, _1690098), _1690100)), hAPP(c_List_OremoveAll(_1690096, _1690098), _1690102)))], (45382 ^ _779448) ^ [_1690159, _1690161, _1690163, _1690165] : [-(c_List_Oremdups(_1690159, hAPP(hAPP(c_List_Omap(_1690161, _1690159), _1690163), c_List_Oremdups(_1690161, _1690165))) = c_List_Oremdups(_1690159, hAPP(hAPP(c_List_Omap(_1690161, _1690159), _1690163), _1690165)))], (45384 ^ _779448) ^ [_1690215, _1690217, _1690219] : [hBOOL(hAPP(c_List_Odistinct(_1690215), _1690217)), -(c_List_Oremove1(_1690215, _1690219, c_List_Oremdups(_1690215, _1690217)) = c_List_Oremdups(_1690215, c_List_Oremove1(_1690215, _1690219, _1690217)))], (45390 ^ _779448) ^ [_1690326, _1690328, _1690330] : [-(hBOOL(hAPP(hAPP(c_member(_1690326), _1690328), hAPP(c_List_Oset(_1690326), _1690330)))), -(hAPP(c_List_OremoveAll(_1690326, _1690328), _1690330) = _1690330)], (45396 ^ _779448) ^ [_1690382, _1690384, _1690386] : [hBOOL(hAPP(c_List_Odistinct(_1690382), _1690384)), -(c_List_Oremove1(_1690382, _1690386, _1690384) = hAPP(c_List_OremoveAll(_1690382, _1690386), _1690384))], (45402 ^ _779448) ^ [_1690501, _1690503, _1690505] : [hBOOL(hAPP(hAPP(c_member(_1690501), _1690503), hAPP(c_List_Oset(_1690501), _1690505))), -(c_List_Oremdups(_1690501, hAPP(hAPP(c_List_Olist_OCons(_1690501), _1690503), _1690505)) = c_List_Oremdups(_1690501, _1690505))], (45408 ^ _779448) ^ [_1690626, _1690628, _1690630] : [-(hBOOL(hAPP(hAPP(c_member(_1690626), _1690628), hAPP(c_List_Oset(_1690626), _1690630)))), -(c_List_Oremdups(_1690626, hAPP(hAPP(c_List_Olist_OCons(_1690626), _1690628), _1690630)) = hAPP(hAPP(c_List_Olist_OCons(_1690626), _1690628), c_List_Oremdups(_1690626, _1690630)))], (45414 ^ _779448) ^ [_1690700, _1690702] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690700)), c_List_Oremdups(_1690700, _1690702)) = hAPP(c_Finite__Set_Ocard(_1690700), hAPP(c_List_Oset(_1690700), _1690702)))], (45416 ^ _779448) ^ [_1690745, _1690747, _1690749, _1690751, _1690753] : [c_Fun_Oinj__on(_1690745, _1690747, _1690749, c_Orderings_Otop__class_Otop(tc_fun(_1690745, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1690745, _1690747), _1690749), hAPP(c_List_OremoveAll(_1690745, _1690751), _1690753)) = hAPP(c_List_OremoveAll(_1690747, hAPP(_1690749, _1690751)), hAPP(hAPP(c_List_Omap(_1690745, _1690747), _1690749), _1690753)))], (45422 ^ _779448) ^ [_1690908, _1690910, _1690912] : [-(hAPP(c_List_Oset(_1690908), hAPP(c_List_OremoveAll(_1690908, _1690910), _1690912)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1690908, tc_HOL_Obool)), hAPP(c_List_Oset(_1690908), _1690912)), hAPP(hAPP(c_Set_Oinsert(_1690908), _1690910), c_Orderings_Obot__class_Obot(tc_fun(_1690908, tc_HOL_Obool)))))], (45424 ^ _779448) ^ [_1690975, _1690977] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690975)), c_List_Oremdups(_1690975, c_List_Oconcat(_1690975, _1690977))) = hAPP(c_Finite__Set_Ocard(_1690975), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1690975), tc_fun(_1690975, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1690975)), _1690977)), c_List_Oset(_1690975))))], (45426 ^ _779448) ^ [_1691041, _1691043] : [class_Orderings_Olinorder(_1691041), -(c_List_Olinorder__class_Osorted__list__of__set(_1691041, hAPP(c_List_Oset(_1691041), _1691043)) = c_List_Olinorder__class_Osort__key(_1691041, _1691041, c_COMBI(_1691041), c_List_Oremdups(_1691041, _1691043)))], (45432 ^ _779448) ^ [_1691152, _1691154] : [-(c_List_Oconcat(_1691152, _1691154) = hAPP(c_List_Ofoldl(tc_List_Olist(_1691152), tc_List_Olist(_1691152), c_List_Oappend(_1691152), c_List_Olist_ONil(_1691152)), _1691154))], (45434 ^ _779448) ^ [_1691196, _1691198, _1691200] : [class_Orderings_Olinorder(_1691196), -(c_List_Olinorder__class_Osort__key(_1691198, _1691196, _1691200, c_List_Olist_ONil(_1691198)) = c_List_Olist_ONil(_1691198))], (45440 ^ _779448) ^ [_1691291, _1691293, _1691295] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1691291), tc_List_Olist(_1691291), c_List_Oappend(_1691291), _1691293), _1691295) = hAPP(hAPP(c_List_Oappend(_1691291), _1691293), c_List_Oconcat(_1691291, _1691295)))], (45442 ^ _779448) ^ [_1691343, _1691345, _1691347, _1691349] : [class_Orderings_Olinorder(_1691343), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691345)), c_List_Olinorder__class_Osort__key(_1691345, _1691343, _1691347, _1691349)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691345)), _1691349))], (45448 ^ _779448) ^ [_1691460, _1691462, _1691464, _1691466] : [class_Orderings_Olinorder(_1691460), -(hAPP(c_List_Oset(_1691462), c_List_Olinorder__class_Osort__key(_1691462, _1691460, _1691464, _1691466)) = hAPP(c_List_Oset(_1691462), _1691466))], (45454 ^ _779448) ^ [_1691569, _1691571, _1691573, _1691575] : [class_Orderings_Olinorder(_1691569), 45457 ^ _779448 : [(45458 ^ _779448) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691571), c_List_Olinorder__class_Osort__key(_1691571, _1691569, _1691573, _1691575))), -(hBOOL(hAPP(c_List_Odistinct(_1691571), _1691575)))], (45464 ^ _779448) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691571), _1691575)), -(hBOOL(hAPP(c_List_Odistinct(_1691571), c_List_Olinorder__class_Osort__key(_1691571, _1691569, _1691573, _1691575))))]]], (45470 ^ _779448) ^ [_1691825] : [-(c_List_Oconcat(_1691825, c_List_Olist_ONil(tc_List_Olist(_1691825))) = c_List_Olist_ONil(_1691825))], (45472 ^ _779448) ^ [_1691857, _1691859, _1691861] : [-(c_List_Oconcat(_1691857, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1691857)), _1691859), _1691861)) = hAPP(hAPP(c_List_Oappend(_1691857), _1691859), c_List_Oconcat(_1691857, _1691861)))], (45484 ^ _779448) ^ [_1692129, _1692131] : [45486 ^ _779448 : [(45487 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692129)), 45485 ^ [_1692129, _1692131]), hAPP(c_List_Oset(tc_List_Olist(_1692129)), _1692131))))], (45489 ^ _779448) ^ [] : [45485 ^ [_1692129, _1692131] = c_List_Olist_ONil(_1692129)]], -(c_List_Oconcat(_1692129, _1692131) = c_List_Olist_ONil(_1692129))], (45474 ^ _779448) ^ [_1691923, _1691925] : [c_List_Oconcat(_1691923, _1691925) = c_List_Olist_ONil(_1691923), 45477 ^ _779448 : [(45478 ^ _779448) ^ [_1692014] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691923)), _1692014), hAPP(c_List_Oset(tc_List_Olist(_1691923)), _1691925))), -(_1692014 = c_List_Olist_ONil(_1691923))]]], (45503 ^ _779448) ^ [_1692541, _1692543] : [45505 ^ _779448 : [(45506 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692541)), 45504 ^ [_1692541, _1692543]), hAPP(c_List_Oset(tc_List_Olist(_1692541)), _1692543))))], (45508 ^ _779448) ^ [] : [45504 ^ [_1692541, _1692543] = c_List_Olist_ONil(_1692541)]], -(c_List_Olist_ONil(_1692541) = c_List_Oconcat(_1692541, _1692543))], (45493 ^ _779448) ^ [_1692335, _1692337] : [c_List_Olist_ONil(_1692335) = c_List_Oconcat(_1692335, _1692337), 45496 ^ _779448 : [(45497 ^ _779448) ^ [_1692426] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692335)), _1692426), hAPP(c_List_Oset(tc_List_Olist(_1692335)), _1692337))), -(_1692426 = c_List_Olist_ONil(_1692335))]]], (45512 ^ _779448) ^ [_1692732, _1692734, _1692736, _1692738] : [-(hAPP(hAPP(c_List_Omap(_1692732, _1692734), _1692736), c_List_Oconcat(_1692732, _1692738)) = c_List_Oconcat(_1692734, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692732), tc_List_Olist(_1692734)), hAPP(c_List_Omap(_1692732, _1692734), _1692736)), _1692738)))], (45514 ^ _779448) ^ [_1692795, _1692797] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692795)), c_List_Oconcat(_1692795, _1692797)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692795), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1692795))), _1692797)))], (45516 ^ _779448) ^ [_1692848, _1692850] : [-(hAPP(c_List_Oset(_1692848), c_List_Oconcat(_1692848, _1692850)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1692848), tc_fun(_1692848, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1692848)), _1692850)), c_List_Oset(_1692848)))], (45518 ^ _779448) ^ [_1692904, _1692906, _1692908, _1692910, _1692912] : [class_Orderings_Olinorder(_1692904), -(c_List_Olinorder__class_Osort__key(_1692906, _1692904, _1692908, hAPP(hAPP(c_List_Olist_OCons(_1692906), _1692910), _1692912)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1692906, _1692904, _1692908), _1692910), c_List_Olinorder__class_Osort__key(_1692906, _1692904, _1692908, _1692912)))], (45524 ^ _779448) ^ [_1693041, _1693043, _1693045] : [-(c_List_Oconcat(_1693041, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1693041)), _1693043), _1693045)) = hAPP(hAPP(c_List_Oappend(_1693041), c_List_Oconcat(_1693041, _1693043)), c_List_Oconcat(_1693041, _1693045)))], (45526 ^ _779448) ^ [_1693095, _1693097] : [class_Orderings_Olinorder(_1693095), -(c_List_Olinorder__class_Osort__key(_1693095, _1693095, c_COMBI(_1693095), _1693097) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693095), _1693095, hAPP(c_COMBC(_1693095, tc_List_Olist(_1693095), tc_List_Olist(_1693095)), c_List_Olinorder__class_Oinsort__key(_1693095, _1693095, c_COMBI(_1693095))), c_List_Olist_ONil(_1693095)), _1693097))], (45532 ^ _779448) ^ [_1693242, _1693244, _1693246] : [c_List_Oconcat(_1693242, _1693244) = c_List_Oconcat(_1693242, _1693246), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693242))), _1693244) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693242))), _1693246), 45542 ^ _779448 : [(45543 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693242), tc_List_Olist(_1693242))), 45541 ^ [_1693242, _1693244, _1693246]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693242), tc_List_Olist(_1693242))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693242), tc_List_Olist(_1693242)), _1693244), _1693246)))))], (45545 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693242), tc_List_Olist(_1693242), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693242), tc_fun(tc_List_Olist(_1693242), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693242), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693242), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693242), tc_HOL_Obool)), tc_List_Olist(_1693242)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693242))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693242)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693242))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693242)))), 45541 ^ [_1693242, _1693244, _1693246]))]], -(_1693244 = _1693246)], (45549 ^ _779448) ^ [_1693883, _1693885, _1693887] : [45551 ^ _779448 : [(45552 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693883), tc_List_Olist(_1693883))), 45550 ^ [_1693883, _1693885, _1693887]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693883), tc_List_Olist(_1693883))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693883), tc_List_Olist(_1693883)), _1693885), _1693887)))))], (45554 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693883), tc_List_Olist(_1693883), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693883), tc_fun(tc_List_Olist(_1693883), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693883), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693883), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693883), tc_HOL_Obool)), tc_List_Olist(_1693883)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693883))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693883)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693883))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693883)))), 45550 ^ [_1693883, _1693885, _1693887]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693883))), _1693885) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693883))), _1693887), 45559 ^ _779448 : [(45560 ^ _779448) ^ [] : [c_List_Oconcat(_1693883, _1693885) = c_List_Oconcat(_1693883, _1693887), -(_1693885 = _1693887)], (45566 ^ _779448) ^ [] : [_1693885 = _1693887, -(c_List_Oconcat(_1693883, _1693885) = c_List_Oconcat(_1693883, _1693887))]]], (45572 ^ _779448) ^ [_1694610, _1694612, _1694614, _1694616] : [-(c_List_Oconcat(_1694610, hAPP(hAPP(c_List_Omap(_1694612, tc_List_Olist(_1694610)), hAPP(hAPP(c_COMBC(_1694612, tc_List_Olist(_1694610), tc_List_Olist(_1694610)), hAPP(hAPP(c_COMBB(_1694610, tc_fun(tc_List_Olist(_1694610), tc_List_Olist(_1694610)), _1694612), c_List_Olist_OCons(_1694610)), _1694614)), c_List_Olist_ONil(_1694610))), _1694616)) = hAPP(hAPP(c_List_Omap(_1694612, _1694610), _1694614), _1694616))], (45574 ^ _779448) ^ [_1694697, _1694699, _1694701] : [-(c_Enum_On__lists(_1694697, hAPP(c_Nat_OSuc, _1694699), _1694701) = c_List_Oconcat(tc_List_Olist(_1694697), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694697), tc_List_Olist(tc_List_Olist(_1694697))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694697), tc_List_Olist(_1694697), tc_List_Olist(tc_List_Olist(_1694697))), hAPP(hAPP(c_COMBB(tc_fun(_1694697, tc_List_Olist(_1694697)), tc_fun(tc_List_Olist(_1694697), tc_List_Olist(tc_List_Olist(_1694697))), tc_List_Olist(_1694697)), c_List_Omap(_1694697, tc_List_Olist(_1694697))), hAPP(c_COMBC(_1694697, tc_List_Olist(_1694697), tc_List_Olist(_1694697)), c_List_Olist_OCons(_1694697)))), _1694701)), c_Enum_On__lists(_1694697, _1694699, _1694701))))], (45576 ^ _779448) ^ [_1694817, _1694819, _1694821, _1694823] : [-(c_List_Otranspose(_1694817, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694817)), hAPP(hAPP(c_List_Olist_OCons(_1694817), _1694819), _1694821)), _1694823)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694817)), hAPP(hAPP(c_List_Olist_OCons(_1694817), _1694819), c_List_Oconcat(_1694817, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694817), tc_List_Olist(_1694817)), c_List_Olist_Olist__case(tc_List_Olist(_1694817), _1694817, c_List_Olist_ONil(_1694817), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694817), tc_fun(tc_List_Olist(_1694817), tc_List_Olist(_1694817)), _1694817), c_COMBK(tc_List_Olist(_1694817), tc_List_Olist(_1694817))), hAPP(hAPP(c_COMBC(_1694817, tc_List_Olist(_1694817), tc_List_Olist(_1694817)), c_List_Olist_OCons(_1694817)), c_List_Olist_ONil(_1694817))))), _1694823)))), c_List_Otranspose(_1694817, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694817)), _1694821), c_List_Oconcat(tc_List_Olist(_1694817), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694817), tc_List_Olist(tc_List_Olist(_1694817))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1694817)), _1694817, c_List_Olist_ONil(tc_List_Olist(_1694817)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1694817), tc_List_Olist(tc_List_Olist(_1694817))), _1694817), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694817), tc_List_Olist(tc_List_Olist(_1694817)), tc_List_Olist(tc_List_Olist(_1694817))), c_List_Olist_OCons(tc_List_Olist(_1694817))), c_List_Olist_ONil(tc_List_Olist(_1694817)))))), _1694823))))))], (45578 ^ _779448) ^ [_1695043, _1695045] : [-(c_List_Oconcat(_1695043, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695043), tc_List_Olist(_1695043)), c_List_Olist_Olist__case(tc_List_Olist(_1695043), _1695043, c_List_Olist_ONil(_1695043), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695043), tc_fun(tc_List_Olist(_1695043), tc_List_Olist(_1695043)), _1695043), c_COMBK(tc_List_Olist(_1695043), tc_List_Olist(_1695043))), hAPP(hAPP(c_COMBC(_1695043, tc_List_Olist(_1695043), tc_List_Olist(_1695043)), c_List_Olist_OCons(_1695043)), c_List_Olist_ONil(_1695043))))), _1695045)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695043), _1695043), c_List_Ohd(_1695043)), hAPP(c_List_Ofilter(tc_List_Olist(_1695043), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695043)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695043), tc_List_Olist(_1695043), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695043)))), _1695045)))], (45580 ^ _779448) ^ [_1695186, _1695188, _1695190] : [-(hAPP(c_List_Ofilter(_1695186, _1695188), c_List_Oconcat(_1695186, _1695190)) = c_List_Oconcat(_1695186, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695186), tc_List_Olist(_1695186)), c_List_Ofilter(_1695186, _1695188)), _1695190)))], (45582 ^ _779448) ^ [_1695241, _1695243, _1695245, _1695247, _1695249] : [class_Orderings_Olinorder(_1695241), -(hAPP(c_List_Ofilter(_1695243, _1695245), c_List_Olinorder__class_Osort__key(_1695243, _1695241, _1695247, _1695249)) = c_List_Olinorder__class_Osort__key(_1695243, _1695241, _1695247, hAPP(c_List_Ofilter(_1695243, _1695245), _1695249)))], (45588 ^ _779448) ^ [_1695366, _1695368, _1695370] : [hBOOL(hAPP(c_List_Odistinct(_1695366), _1695368)), -(hBOOL(hAPP(c_List_Odistinct(_1695366), hAPP(c_List_Ofilter(_1695366, _1695370), _1695368))))], (45594 ^ _779448) ^ [_1695473, _1695475, _1695477] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695473)), hAPP(c_List_Ofilter(_1695473, _1695475), _1695477))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695473)), hAPP(c_List_Ofilter(_1695473, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1695473), c_fNot), _1695475)), _1695477))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695473)), _1695477))], (45596 ^ _779448) ^ [_1695549, _1695551, _1695553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695549, tc_HOL_Obool)), hAPP(c_List_Oset(_1695549), hAPP(c_List_Ofilter(_1695549, _1695551), _1695553))), hAPP(c_List_Oset(_1695549), _1695553))))], (45608 ^ _779448) ^ [_1695820, _1695822, _1695824] : [45610 ^ _779448 : [(45611 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695820), 45609 ^ [_1695820, _1695822, _1695824]), hAPP(c_List_Oset(_1695820), _1695824))))], (45613 ^ _779448) ^ [] : [hBOOL(hAPP(_1695822, 45609 ^ [_1695820, _1695822, _1695824]))]], -(hAPP(c_List_Ofilter(_1695820, _1695822), _1695824) = _1695824)], (45598 ^ _779448) ^ [_1695620, _1695622, _1695624] : [hAPP(c_List_Ofilter(_1695620, _1695622), _1695624) = _1695624, 45601 ^ _779448 : [(45602 ^ _779448) ^ [_1695711] : [hBOOL(hAPP(hAPP(c_member(_1695620), _1695711), hAPP(c_List_Oset(_1695620), _1695624))), -(hBOOL(hAPP(_1695622, _1695711)))]]], (45617 ^ _779448) ^ [_1696012, _1696014, _1696016] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696012)), hAPP(c_List_Ofilter(_1696012, _1696014), _1696016))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696012)), _1696016))))], (45619 ^ _779448) ^ [_1696064, _1696066, _1696068] : [-(c_List_Opartition(_1696064, _1696066, _1696068) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696064), tc_List_Olist(_1696064)), hAPP(c_List_Ofilter(_1696064, _1696066), _1696068)), hAPP(c_List_Ofilter(_1696064, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1696064, c_fNot), _1696066)), _1696068)))], (45621 ^ _779448) ^ [_1696128, _1696130, _1696132] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1696128), tc_List_Olist(_1696128)), c_List_Opartition(_1696128, _1696130, _1696132)) = hAPP(c_List_Ofilter(_1696128, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1696128, c_fNot), _1696130)), _1696132))], (45623 ^ _779448) ^ [_1696183, _1696185, _1696187] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1696183), tc_List_Olist(_1696183)), c_List_Opartition(_1696183, _1696185, _1696187)) = hAPP(c_List_Ofilter(_1696183, _1696185), _1696187))], (45625 ^ _779448) ^ [_1696230, _1696232, _1696234, _1696236] : [-(hAPP(c_List_Ofilter(_1696230, _1696232), hAPP(c_List_Ofilter(_1696230, _1696234), _1696236)) = hAPP(c_List_Ofilter(_1696230, hAPP(hAPP(c_COMBS(_1696230, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696230), c_fconj), _1696234)), _1696232)), _1696236))], (45627 ^ _779448) ^ [_1696297, _1696299, _1696301, _1696303] : [-(hAPP(c_List_Ofilter(_1696297, _1696299), c_List_Oremove1(_1696297, _1696301, _1696303)) = c_List_Oremove1(_1696297, _1696301, hAPP(c_List_Ofilter(_1696297, _1696299), _1696303)))], (45629 ^ _779448) ^ [_1696342, _1696344, _1696346, _1696348] : [-(hBOOL(hAPP(_1696342, _1696344))), -(c_List_Oremove1(_1696346, _1696344, hAPP(c_List_Ofilter(_1696346, _1696342), _1696348)) = hAPP(c_List_Ofilter(_1696346, _1696342), _1696348))], (45635 ^ _779448) ^ [_1696400, _1696402, _1696404, _1696406, _1696408, _1696410] : [class_Orderings_Olinorder(_1696400), -(hBOOL(hAPP(_1696402, _1696404))), -(hAPP(c_List_Ofilter(_1696406, _1696402), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696406, _1696400, _1696408), _1696404), _1696410)) = hAPP(c_List_Ofilter(_1696406, _1696402), _1696410))], (45645 ^ _779448) ^ [_1696546, _1696548, _1696550, _1696552, _1696554] : [-(hAPP(c_List_Ofilter(_1696546, _1696548), hAPP(hAPP(c_List_Omap(_1696550, _1696546), _1696552), _1696554)) = hAPP(hAPP(c_List_Omap(_1696550, _1696546), _1696552), hAPP(c_List_Ofilter(_1696550, hAPP(c_Fun_Ocomp(_1696546, tc_HOL_Obool, _1696550, _1696548), _1696552)), _1696554)))], (45647 ^ _779448) ^ [_1696615, _1696617] : [-(hAPP(c_List_Ofilter(_1696615, _1696617), c_List_Olist_ONil(_1696615)) = c_List_Olist_ONil(_1696615))], (45649 ^ _779448) ^ [_1696650] : [-(c_List_Otranspose(_1696650, c_List_Olist_ONil(tc_List_Olist(_1696650))) = c_List_Olist_ONil(tc_List_Olist(_1696650)))], (45651 ^ _779448) ^ [_1696699, _1696701, _1696703, _1696705] : [hBOOL(hAPP(_1696699, _1696701)), -(hAPP(c_List_Ofilter(_1696703, _1696699), hAPP(hAPP(c_List_Olist_OCons(_1696703), _1696701), _1696705)) = hAPP(hAPP(c_List_Olist_OCons(_1696703), _1696701), hAPP(c_List_Ofilter(_1696703, _1696699), _1696705)))], (45657 ^ _779448) ^ [_1696834, _1696836, _1696838, _1696840] : [-(hBOOL(hAPP(_1696834, _1696836))), -(hAPP(c_List_Ofilter(_1696838, _1696834), hAPP(hAPP(c_List_Olist_OCons(_1696838), _1696836), _1696840)) = hAPP(c_List_Ofilter(_1696838, _1696834), _1696840))], (45663 ^ _779448) ^ [_1696898, _1696900, _1696902, _1696904] : [-(hAPP(c_List_Ofilter(_1696898, _1696900), hAPP(hAPP(c_List_Oappend(_1696898), _1696902), _1696904)) = hAPP(hAPP(c_List_Oappend(_1696898), hAPP(c_List_Ofilter(_1696898, _1696900), _1696902)), hAPP(c_List_Ofilter(_1696898, _1696900), _1696904)))], (45675 ^ _779448) ^ [_1697184, _1697186, _1697188] : [45677 ^ _779448 : [(45678 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697184), 45676 ^ [_1697184, _1697186, _1697188]), hAPP(c_List_Oset(_1697184), _1697188))))], (45680 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1697186, 45676 ^ [_1697184, _1697186, _1697188])))]], -(hAPP(c_List_Ofilter(_1697184, _1697186), _1697188) = c_List_Olist_ONil(_1697184))], (45665 ^ _779448) ^ [_1696979, _1696981, _1696983] : [hAPP(c_List_Ofilter(_1696979, _1696981), _1696983) = c_List_Olist_ONil(_1696979), 45668 ^ _779448 : [(45669 ^ _779448) ^ [_1697076] : [hBOOL(hAPP(hAPP(c_member(_1696979), _1697076), hAPP(c_List_Oset(_1696979), _1696983))), hBOOL(hAPP(_1696981, _1697076))]]], (45684 ^ _779448) ^ [_1697301, _1697303, _1697305, _1697307, _1697309] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697301)), hAPP(c_List_Ofilter(_1697301, _1697303), hAPP(hAPP(c_List_Omap(_1697305, _1697301), _1697307), _1697309))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697305)), hAPP(c_List_Ofilter(_1697305, hAPP(c_Fun_Ocomp(_1697301, tc_HOL_Obool, _1697305, _1697303), _1697307)), _1697309)))], (45686 ^ _779448) ^ [_1697375, _1697377] : [-(c_List_OremoveAll(_1697375, _1697377) = c_List_Ofilter(_1697375, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1697375), c_fNot), hAPP(c_fequal, _1697377))))], (45688 ^ _779448) ^ [_1697419, _1697421, _1697423] : [-(c_List_Oremdups(_1697419, hAPP(c_List_Ofilter(_1697419, _1697421), _1697423)) = hAPP(c_List_Ofilter(_1697419, _1697421), c_List_Oremdups(_1697419, _1697423)))], (45690 ^ _779448) ^ [_1697460, _1697462, _1697464, _1697466] : [-(hBOOL(hAPP(_1697460, _1697462))), -(hAPP(c_List_OremoveAll(_1697464, _1697462), hAPP(c_List_Ofilter(_1697464, _1697460), _1697466)) = hAPP(c_List_Ofilter(_1697464, _1697460), _1697466))], (45696 ^ _779448) ^ [_1697520, _1697522] : [-(c_List_Otranspose(_1697520, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697520)), c_List_Olist_ONil(_1697520)), _1697522)) = c_List_Otranspose(_1697520, _1697522))], (45698 ^ _779448) ^ [_1697563, _1697565, _1697567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697563), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1697565))), c_List_Otranspose(_1697565, _1697567)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1697565)), c_List_Otranspose(_1697565, _1697567)), _1697563) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697565), _1697565), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697565), tc_Nat_Onat, _1697565), c_List_Onth(_1697565)), _1697563)), hAPP(c_List_Ofilter(tc_List_Olist(_1697565), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1697565)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697563)), c_Nat_Osize__class_Osize(tc_List_Olist(_1697565)))), _1697567)))], (45704 ^ _779448) ^ [_1697806, _1697808, _1697810, _1697812] : [-(c_List_Otranspose(_1697806, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697808), tc_List_Olist(_1697806)), hAPP(c_List_Omap(_1697808, _1697806), _1697810)), _1697812)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697808), tc_List_Olist(_1697806)), hAPP(c_List_Omap(_1697808, _1697806), _1697810)), c_List_Otranspose(_1697808, _1697812)))], (45706 ^ _779448) ^ [_1697879, _1697881, _1697883] : [-(hAPP(c_List_Oset(_1697879), hAPP(c_List_Ofilter(_1697879, _1697881), _1697883)) = hAPP(c_Set_OCollect(_1697879), hAPP(hAPP(c_COMBS(_1697879, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1697879), c_fconj), hAPP(hAPP(c_COMBC(_1697879, tc_fun(_1697879, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697879)), hAPP(c_List_Oset(_1697879), _1697883)))), _1697881)))], (45708 ^ _779448) ^ [_1697962, _1697964, _1697966, _1697968] : [hBOOL(hAPP(hAPP(c_member(_1697962), _1697964), hAPP(c_List_Oset(_1697962), _1697966))), -(hBOOL(hAPP(_1697968, _1697964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697962)), hAPP(c_List_Ofilter(_1697962, _1697968), _1697966))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697962)), _1697966))))], (45718 ^ _779448) ^ [_1698136, _1698138, _1698140] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698136, tc_HOL_Obool)), hAPP(c_List_Oset(_1698136), _1698138)), hAPP(hAPP(c_Set_Oinsert(_1698136), _1698140), c_Orderings_Obot__class_Obot(tc_fun(_1698136, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698136), hAPP(c_List_Ofilter(_1698136, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698136), c_fNot), hAPP(hAPP(c_COMBC(_1698136, _1698136, tc_HOL_Obool), c_fequal), _1698140))), _1698138)))], (45720 ^ _779448) ^ [_1698223, _1698225, _1698227] : [hBOOL(hAPP(c_List_Odistinct(_1698223), _1698225)), -(hAPP(c_List_Ofilter(_1698223, hAPP(hAPP(c_COMBC(_1698223, tc_fun(_1698223, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698223)), hAPP(c_List_Oset(_1698223), c_List_Osublist(_1698223, _1698225, _1698227)))), _1698225) = c_List_Osublist(_1698223, _1698225, _1698227))], (45736 ^ _779448) ^ [_1698603, _1698605] : [45738 ^ _779448 : [(45739 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698603)), 45737 ^ [_1698603, _1698605]), hAPP(c_List_Oset(tc_List_Olist(_1698603)), _1698605))))], (45741 ^ _779448) ^ [] : [45737 ^ [_1698603, _1698605] = c_List_Olist_ONil(_1698603)]], -(c_List_Otranspose(_1698603, _1698605) = c_List_Olist_ONil(tc_List_Olist(_1698603)))], (45726 ^ _779448) ^ [_1698393, _1698395] : [c_List_Otranspose(_1698393, _1698395) = c_List_Olist_ONil(tc_List_Olist(_1698393)), 45729 ^ _779448 : [(45730 ^ _779448) ^ [_1698488] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698393)), _1698488), hAPP(c_List_Oset(tc_List_Olist(_1698393)), _1698395))), -(_1698488 = c_List_Olist_ONil(_1698393))]]], (45745 ^ _779448) ^ [_1698798, _1698800, _1698802] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698798)), hAPP(c_List_Ofilter(_1698798, _1698800), _1698802)) = 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(_1698798)), _1698802)))), hAPP(hAPP(c_COMBB(_1698798, tc_HOL_Obool, tc_Nat_Onat), _1698800), hAPP(c_List_Onth(_1698798), _1698802))))))], (45747 ^ _779448) ^ [_1698878, _1698880] : [-(c_List_Oconcat(tc_List_Olist(_1698878), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698878), tc_List_Olist(tc_List_Olist(_1698878))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1698878)), _1698878, c_List_Olist_ONil(tc_List_Olist(_1698878)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1698878), tc_List_Olist(tc_List_Olist(_1698878))), _1698878), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698878), tc_List_Olist(tc_List_Olist(_1698878)), tc_List_Olist(tc_List_Olist(_1698878))), c_List_Olist_OCons(tc_List_Olist(_1698878))), c_List_Olist_ONil(tc_List_Olist(_1698878)))))), _1698880)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698878), tc_List_Olist(_1698878)), c_List_Otl(_1698878)), hAPP(c_List_Ofilter(tc_List_Olist(_1698878), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1698878)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698878), tc_List_Olist(_1698878), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1698878)))), _1698880)))], (45749 ^ _779448) ^ [_1699030, _1699032, _1699034, _1699036] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699030)), c_List_Otranspose__rel(_1699030)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699030)), hAPP(hAPP(c_List_Olist_OCons(_1699030), _1699032), _1699034)), _1699036))), -(c_List_Otranspose(_1699030, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699030)), hAPP(hAPP(c_List_Olist_OCons(_1699030), _1699032), _1699034)), _1699036)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699030)), hAPP(hAPP(c_List_Olist_OCons(_1699030), _1699032), c_List_Oconcat(_1699030, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699030), tc_List_Olist(_1699030)), c_List_Olist_Olist__case(tc_List_Olist(_1699030), _1699030, c_List_Olist_ONil(_1699030), hAPP(hAPP(c_COMBB(tc_List_Olist(_1699030), tc_fun(tc_List_Olist(_1699030), tc_List_Olist(_1699030)), _1699030), c_COMBK(tc_List_Olist(_1699030), tc_List_Olist(_1699030))), hAPP(hAPP(c_COMBC(_1699030, tc_List_Olist(_1699030), tc_List_Olist(_1699030)), c_List_Olist_OCons(_1699030)), c_List_Olist_ONil(_1699030))))), _1699036)))), c_List_Otranspose(_1699030, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699030)), _1699034), c_List_Oconcat(tc_List_Olist(_1699030), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699030), tc_List_Olist(tc_List_Olist(_1699030))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699030)), _1699030, c_List_Olist_ONil(tc_List_Olist(_1699030)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699030), tc_List_Olist(tc_List_Olist(_1699030))), _1699030), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699030), tc_List_Olist(tc_List_Olist(_1699030)), tc_List_Olist(tc_List_Olist(_1699030))), c_List_Olist_OCons(tc_List_Olist(_1699030))), c_List_Olist_ONil(tc_List_Olist(_1699030)))))), _1699036))))))], (45755 ^ _779448) ^ [_1699563, _1699565] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699563)), c_List_Otranspose__rel(_1699563)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699563)), c_List_Olist_ONil(_1699563)), _1699565))), -(c_List_Otranspose(_1699563, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699563)), c_List_Olist_ONil(_1699563)), _1699565)) = c_List_Otranspose(_1699563, _1699565))], (45761 ^ _779448) ^ [_1699722, _1699724, _1699726, _1699728] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1699722, tc_Nat_Onat), _1699722), c_Product__Type_Ofst(_1699722, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699722, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699722, tc_Nat_Onat)), _1699724), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1699722, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1699722, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1699722, tc_Nat_Onat), _1699726), _1699728))) = hAPP(hAPP(c_List_Omap(tc_prod(_1699722, tc_Nat_Onat), _1699722), c_Product__Type_Ofst(_1699722, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699722, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699722, tc_Nat_Onat)), _1699724), c_Product__Type_Osnd(_1699722, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1699722, tc_Nat_Onat), _1699726), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1699728)))))], (45763 ^ _779448) ^ [_1699865, _1699867] : [-(c_Random_Oselect__weight(_1699865, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1699865), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1699865, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1699865, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1699865)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1699867)) = c_Random_Oselect__weight(_1699865, _1699867))], (45765 ^ _779448) ^ [_1699928, _1699930] : [-(c_Random_Opick(_1699928, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1699928), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1699928, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1699928, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1699928)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1699930)) = c_Random_Opick(_1699928, _1699930))], (45767 ^ _779448) ^ [_1699991] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699991)), c_List_Otranspose__rel(_1699991)), c_List_Olist_ONil(tc_List_Olist(_1699991)))), -(c_List_Otranspose(_1699991, c_List_Olist_ONil(tc_List_Olist(_1699991))) = c_List_Olist_ONil(tc_List_Olist(_1699991)))], (45773 ^ _779448) ^ [_1700118, _1700120] : [-(c_List_Ofoldr(tc_List_Olist(_1700118), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700118)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700118))), c_List_Otranspose(_1700118, _1700120), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700118))), hAPP(c_List_Ofilter(tc_List_Olist(_1700118), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700118)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700118), tc_List_Olist(_1700118), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700118)))), _1700120)))], (45775 ^ _779448) ^ [_1700215, _1700217, _1700219, _1700221] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700215)), _1700217))), c_List_Ofoldr(tc_List_Olist(_1700219), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700219)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700219))), _1700221, 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(_1700215)), _1700217)), c_List_Ofoldr(tc_List_Olist(_1700219), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700219)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700219), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700219)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700219)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700219), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700219)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700219), tc_List_Olist(_1700219), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700219)))), _1700221), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (45777 ^ _779448) ^ [_1700384, _1700386, _1700388, _1700390] : [-(c_List_Ofoldr(_1700384, _1700386, _1700388, c_List_Olist_ONil(_1700384), _1700390) = _1700390)], (45779 ^ _779448) ^ [_1700421, _1700423, _1700425, _1700427, _1700429, _1700431] : [-(c_List_Ofoldr(_1700421, _1700423, _1700425, hAPP(hAPP(c_List_Olist_OCons(_1700421), _1700427), _1700429), _1700431) = hAPP(hAPP(_1700425, _1700427), c_List_Ofoldr(_1700421, _1700423, _1700425, _1700429, _1700431)))], (45781 ^ _779448) ^ [_1700480, _1700482, _1700484, _1700486, _1700488, _1700490] : [-(c_List_Ofoldr(_1700480, _1700482, _1700484, hAPP(hAPP(c_List_Oappend(_1700480), _1700486), _1700488), _1700490) = c_List_Ofoldr(_1700480, _1700482, _1700484, _1700486, c_List_Ofoldr(_1700480, _1700482, _1700484, _1700488, _1700490)))], (45783 ^ _779448) ^ [_1700539, _1700541, _1700543] : [class_Groups_Oab__semigroup__add(_1700539), -(c_List_Ofoldr(_1700539, _1700539, c_Groups_Oplus__class_Oplus(_1700539), _1700541, _1700543) = hAPP(c_List_Ofoldl(_1700539, _1700539, c_Groups_Oplus__class_Oplus(_1700539), _1700543), _1700541))], (45789 ^ _779448) ^ [_1700652, _1700654, _1700656, _1700658, _1700660, _1700662, _1700664] : [-(c_List_Ofoldr(_1700652, _1700654, _1700656, hAPP(hAPP(c_List_Omap(_1700658, _1700652), _1700660), _1700662), _1700664) = c_List_Ofoldr(_1700658, _1700654, hAPP(c_Fun_Ocomp(_1700652, tc_fun(_1700654, _1700654), _1700658, _1700656), _1700660), _1700662, _1700664))], (45791 ^ _779448) ^ [_1700719, _1700721] : [class_Groups_Omonoid__add(_1700719), -(hAPP(c_List_Ofoldl(_1700719, _1700719, c_Groups_Oplus__class_Oplus(_1700719), c_Groups_Ozero__class_Ozero(_1700719)), _1700721) = c_List_Ofoldr(_1700719, _1700719, c_Groups_Oplus__class_Oplus(_1700719), _1700721, c_Groups_Ozero__class_Ozero(_1700719)))], (45797 ^ _779448) ^ [_1700838, _1700840, _1700842] : [class_Groups_Omonoid__add(_1700838), -(hAPP(c_List_Ofoldl(_1700838, _1700838, c_Groups_Oplus__class_Oplus(_1700838), _1700840), _1700842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1700838), _1700840), c_List_Ofoldr(_1700838, _1700838, c_Groups_Oplus__class_Oplus(_1700838), _1700842, c_Groups_Ozero__class_Ozero(_1700838))))], (45803 ^ _779448) ^ [_1700971, _1700973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700971))), c_List_Otranspose(_1700971, _1700973)) = c_List_Ofoldr(tc_List_Olist(_1700971), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700971)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700971))), _1700973, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45805 ^ _779448) ^ [_1701032, _1701034, _1701036] : [-(c_List_Osublist(_1701032, _1701034, _1701036) = hAPP(hAPP(c_List_Omap(tc_prod(_1701032, tc_Nat_Onat), _1701032), c_Product__Type_Ofst(_1701032, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701032, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701032, 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(_1701032, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701032, tc_Nat_Onat))), _1701036)), hAPP(hAPP(c_List_Ozip(_1701032, tc_Nat_Onat), _1701034), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701032)), _1701034))))))], (45807 ^ _779448) ^ [_1701135, _1701137, _1701139, _1701141] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701135, tc_Nat_Onat), _1701135), c_Product__Type_Ofst(_1701135, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701135, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701135, 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(_1701135, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701135, tc_Nat_Onat))), _1701137)), hAPP(hAPP(c_List_Ozip(_1701135, tc_Nat_Onat), _1701139), c_List_Oupt(_1701141, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701141), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701135)), _1701139)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701135, tc_Nat_Onat), _1701135), c_Product__Type_Ofst(_1701135, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701135, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701135, 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(_1701135, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701135, 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(_1701135, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701135, tc_Nat_Onat))), _1701141))), _1701137)), hAPP(hAPP(c_List_Ozip(_1701135, tc_Nat_Onat), _1701139), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701135)), _1701139))))))], (45809 ^ _779448) ^ [_1701340, _1701342] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701340, _1701342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701340), _1701342))], (45811 ^ _779448) ^ [_1701377, _1701379] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701377), _1701379) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701377, _1701379)))], (45813 ^ _779448) ^ [_1701414, _1701416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701414), _1701416)), -(c_List_Oupt(_1701414, hAPP(c_Nat_OSuc, _1701416)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701414, _1701416)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701416), c_List_Olist_ONil(tc_Nat_Onat))))], (45819 ^ _779448) ^ [_1701552, _1701554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701552), _1701554)), -(c_List_Oupt(_1701552, hAPP(c_Nat_OSuc, _1701554)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701552, _1701554)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701554), c_List_Olist_ONil(tc_Nat_Onat))))], (45825 ^ _779448) ^ [_1701675, _1701677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701675), _1701677))), -(c_List_Oupt(_1701675, hAPP(c_Nat_OSuc, _1701677)) = c_List_Olist_ONil(tc_Nat_Onat))], (45831 ^ _779448) ^ [_1701724, _1701726, _1701728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701724), _1701726)), -(c_List_Oupt(_1701724, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701726), _1701728)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701724, _1701726)), c_List_Oupt(_1701726, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701726), _1701728))))], (45837 ^ _779448) ^ [_1701876, _1701878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701876), _1701878)), -(c_List_Oupt(_1701876, _1701878) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701876), c_List_Oupt(hAPP(c_Nat_OSuc, _1701876), _1701878)))], (45843 ^ _779448) ^ [_1701987, _1701989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701987), _1701989))), -(c_List_Oupt(_1701987, _1701989) = c_List_Olist_ONil(tc_Nat_Onat))], (45849 ^ _779448) ^ [_1702033, _1702035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702033), _1702035)), -(c_List_Oupt(_1702033, _1702035) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702033), c_List_Oupt(hAPP(c_Nat_OSuc, _1702033), _1702035)))], (45855 ^ _779448) ^ [_1702150, _1702152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702150), _1702152)), -(c_List_Oupt(_1702152, _1702150) = c_List_Olist_ONil(tc_Nat_Onat))], (45871 ^ _779448) ^ [_1702360, _1702362] : [45872 ^ _779448 : [(45873 ^ _779448) ^ [] : [_1702362 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45875 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702362), _1702360))]], -(c_List_Oupt(_1702360, _1702362) = c_List_Olist_ONil(tc_Nat_Onat))], (45861 ^ _779448) ^ [_1702258, _1702260] : [c_List_Oupt(_1702258, _1702260) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702260), _1702258)))], (45879 ^ _779448) ^ [_1702493] : [-(c_List_Oupt(_1702493, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (45881 ^ _779448) ^ [_1702519, _1702521, _1702523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702519), _1702521)), _1702523)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1702521), c_List_Oupt(_1702519, _1702523)) = c_List_Oupt(_1702519, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702519), _1702521)))], (45887 ^ _779448) ^ [_1702656, _1702658] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1702656), _1702658)) = c_List_Oupt(_1702656, _1702658))], (45889 ^ _779448) ^ [_1702693, _1702695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702693), _1702695)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1702693, _1702695)) = _1702693)], (45895 ^ _779448) ^ [_1702792, _1702794, _1702796] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1702792), c_List_Oupt(_1702794, _1702796)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702794), _1702792), _1702796))], (45897 ^ _779448) ^ [_1702837, _1702839] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1702837, _1702839))))], (45899 ^ _779448) ^ [_1702867, _1702869] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1702867, _1702869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1702869), _1702867))], (45901 ^ _779448) ^ [_1702913, _1702915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702913)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702915))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702913), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702915)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702913)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702913)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702915))))], (45907 ^ _779448) ^ [_1703066, _1703068] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703066)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703068)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703066), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703068)) = c_List_Olist_ONil(tc_Nat_Onat))], (45913 ^ _779448) ^ [_1703145, _1703147, _1703149, _1703151] : [c_List_Oupt(_1703145, _1703147) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703149), _1703151), 45916 ^ _779448 : [(45917 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703145), _1703147)))], (45919 ^ _779448) ^ [] : [-(_1703145 = _1703149)], (45921 ^ _779448) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703145), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703147) = _1703151)]]], (45923 ^ _779448) ^ [_1703318, _1703320, _1703322, _1703324] : [-(c_List_Oupt(_1703318, _1703320) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703322), _1703324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703318), _1703320)), _1703318 = _1703322, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703318), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703320) = _1703324], (45937 ^ _779448) ^ [_1703559, _1703561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703559), _1703561)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1703559, _1703561)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703561), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45943 ^ _779448) ^ [_1703670, _1703672] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1703670, _1703672)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1703670), hAPP(c_Nat_OSuc, _1703672)))], (45945 ^ _779448) ^ [_1703710, _1703712] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1703710, _1703712) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1703710, hAPP(c_Nat_OSuc, _1703712))))], (45947 ^ _779448) ^ [_1703748] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1703748) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1703748)))], (45949 ^ _779448) ^ [_1703780, _1703782, _1703784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703780), _1703782)), _1703784)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1703780, _1703784)), _1703782) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703780), _1703782))], (45955 ^ _779448) ^ [_1703911, _1703913] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1703911, _1703913) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1703911), hAPP(c_Nat_OSuc, _1703913))))], (45957 ^ _779448) ^ [_1703952, _1703954] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1703952, _1703954) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1703952), _1703954)))], (45959 ^ _779448) ^ [_1703990] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1703990) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1703990))))], (45961 ^ _779448) ^ [_1704025, _1704027] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704025), hAPP(c_List_Onth(_1704025), _1704027)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704025)), _1704027))) = _1704027)], (45963 ^ _779448) ^ [_1704074, _1704076, _1704078, _1704080] : [class_Groups_Ocomm__monoid__add(_1704074), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704074), _1704076), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704078, _1704080))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1704074), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704074), _1704076), c_List_Oupt(_1704078, _1704080))))], (45969 ^ _779448) ^ [_1704217, _1704219, _1704221, _1704223] : [class_Groups_Ocomm__monoid__add(_1704217), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704217), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704217), _1704219), c_List_Oupt(_1704221, _1704223))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704217), _1704219), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704221, _1704223))))], (45975 ^ _779448) ^ [_1704360, _1704362, _1704364, _1704366, _1704368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704362), _1704364))), -(hAPP(hAPP(c_List_Onth(_1704366), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704366), _1704368), c_List_Oupt(_1704364, _1704362))), _1704360) = hAPP(_1704368, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704364), _1704360)))], (45981 ^ _779448) ^ [_1704523, _1704525, _1704527] : [45982 ^ _779448 : [(45983 ^ _779448) ^ [] : [-(_1704523 = c_List_Olist_ONil(tc_List_Olist(_1704525)))], (45985 ^ _779448) ^ [] : [_1704527 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 45989 ^ _779448 : [(45990 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45988 ^ [_1704523, _1704525, _1704527]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704525))), _1704523))))], (45992 ^ _779448) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704525)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1704525)), _1704523), 45988 ^ [_1704523, _1704525, _1704527])) = _1704527]], -(c_List_Otranspose(_1704525, _1704523) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1704525)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704525)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1704525), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704525)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1704525)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1704525), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704525), tc_fun(tc_Nat_Onat, _1704525), tc_Nat_Onat), c_List_Onth(_1704525)), hAPP(c_List_Onth(tc_List_Olist(_1704525)), _1704523))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704525))), _1704523)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704527)))], (45996 ^ _779448) ^ [_1705033, _1705035, _1705037, _1705039, _1705041] : [class_Orderings_Olinorder(_1705033), hBOOL(hAPP(hAPP(c_member(_1705035), _1705037), hAPP(c_List_Oset(_1705035), _1705039))), c_List_Olinorder__class_Osorted(_1705033, hAPP(hAPP(c_List_Omap(_1705035, _1705033), _1705041), _1705039)), hAPP(c_List_Ohd(_1705035), hAPP(c_List_Ofilter(_1705035, hAPP(hAPP(c_COMBB(_1705033, tc_HOL_Obool, _1705035), hAPP(c_fequal, hAPP(_1705041, _1705037))), _1705041)), _1705039)) = _1705037, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705035, _1705033, _1705041), _1705037), c_List_Oremove1(_1705035, _1705037, _1705039)) = _1705039)], (46014 ^ _779448) ^ [_1705412] : [class_Orderings_Olinorder(_1705412), -(c_List_Olinorder__class_Osorted(_1705412, c_List_Olist_ONil(_1705412)))], (46020 ^ _779448) ^ [_1705489, _1705491] : [class_Orderings_Olinorder(_1705489), -(c_List_Olinorder__class_Osorted(_1705489, hAPP(hAPP(c_List_Olist_OCons(_1705489), _1705491), c_List_Olist_ONil(_1705489))))], (46026 ^ _779448) ^ [_1705584, _1705586] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1705584, _1705586)))], (46028 ^ _779448) ^ [_1705612, _1705614] : [class_Orderings_Olinorder(_1705612), -(c_List_Olinorder__class_Osorted(_1705612, c_List_Olinorder__class_Osort__key(_1705612, _1705612, c_COMBI(_1705612), _1705614)))], (46034 ^ _779448) ^ [_1705701, _1705703, _1705705] : [class_Orderings_Olinorder(_1705701), c_List_Olinorder__class_Osorted(_1705701, _1705703), -(c_List_Olinorder__class_Osorted(_1705701, c_List_Olinorder__class_Oinsort__insert__key(_1705701, _1705701, c_COMBI(_1705701), _1705705, _1705703)))], (46044 ^ _779448) ^ [_1705848, _1705850, _1705852] : [class_Orderings_Olinorder(_1705848), c_List_Olinorder__class_Osorted(_1705848, _1705850), -(c_List_Olinorder__class_Osorted(_1705848, hAPP(hAPP(c_List_Odrop(_1705848), _1705852), _1705850)))], (46054 ^ _779448) ^ [_1705995, _1705997] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1705995, _1705997)))], (46056 ^ _779448) ^ [_1706023, _1706025, _1706027] : [class_Orderings_Olinorder(_1706023), c_List_Olinorder__class_Osorted(_1706023, _1706025), -(c_List_Olinorder__class_Osorted(_1706023, hAPP(hAPP(c_List_Otake(_1706023), _1706027), _1706025)))], (46066 ^ _779448) ^ [_1706170, _1706172, _1706174] : [class_Orderings_Olinorder(_1706170), c_List_Olinorder__class_Osorted(_1706170, _1706172), -(c_List_Olinorder__class_Osorted(_1706170, c_List_Oremove1(_1706170, _1706174, _1706172)))], (46076 ^ _779448) ^ [_1706309, _1706311] : [class_Orderings_Olinorder(_1706309), c_List_Olinorder__class_Osorted(_1706309, _1706311), -(c_List_Olinorder__class_Osorted(_1706309, hAPP(c_List_Otl(_1706309), _1706311)))], (46086 ^ _779448) ^ [_1706446, _1706448, _1706450] : [class_Orderings_Olinorder(_1706446), 46089 ^ _779448 : [(46090 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1706446, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706446, _1706446, c_COMBI(_1706446)), _1706448), _1706450)), -(c_List_Olinorder__class_Osorted(_1706446, _1706450))], (46096 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1706446, _1706450), -(c_List_Olinorder__class_Osorted(_1706446, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706446, _1706446, c_COMBI(_1706446)), _1706448), _1706450)))]]], (46102 ^ _779448) ^ [_1706693, _1706695] : [class_Orderings_Olinorder(_1706693), -(_1706695 = c_List_Olist_ONil(_1706693)), c_List_Olinorder__class_Osorted(_1706693, _1706695), -(c_List_Olinorder__class_Osorted(_1706693, c_List_Obutlast(_1706693, _1706695)))], (46116 ^ _779448) ^ [_1706885] : [class_Orderings_Olinorder(_1706885), -(c_List_Olinorder__class_Osorted(_1706885, c_List_Olist_ONil(_1706885)))], (46122 ^ _779448) ^ [_1706962, _1706964, _1706966, _1706968] : [class_Orderings_Olinorder(_1706962), 46125 ^ _779448 : [(46126 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1706962, hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706964), hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706966), _1706968))), 46129 ^ _779448 : [(46130 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706962), _1706964), _1706966)))], (46132 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1706962, hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706966), _1706968)))]]], (46134 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1706962, hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706964), hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706966), _1706968)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706962), _1706964), _1706966)), c_List_Olinorder__class_Osorted(_1706962, hAPP(hAPP(c_List_Olist_OCons(_1706962), _1706966), _1706968))]]], (46144 ^ _779448) ^ [_1707348, _1707350, _1707352, _1707354] : [class_Orderings_Olinorder(_1707348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707348), _1707350), _1707352)), c_List_Olinorder__class_Osorted(_1707348, hAPP(hAPP(c_List_Olist_OCons(_1707348), _1707352), _1707354)), -(c_List_Olinorder__class_Osorted(_1707348, hAPP(hAPP(c_List_Olist_OCons(_1707348), _1707350), hAPP(hAPP(c_List_Olist_OCons(_1707348), _1707352), _1707354))))], (46158 ^ _779448) ^ [_1707601, _1707603] : [class_Orderings_Olinorder(_1707601), c_List_Olinorder__class_Osorted(_1707601, _1707603), -(c_List_Olinorder__class_Osorted(_1707601, c_List_Oremdups(_1707601, _1707603)))], (46168 ^ _779448) ^ [_1707734, _1707736, _1707738] : [class_Orderings_Olinorder(_1707734), c_List_Olinorder__class_Osorted(_1707734, _1707736), hBOOL(hAPP(c_List_Odistinct(_1707734), _1707736)), c_List_Olinorder__class_Osorted(_1707734, _1707738), hBOOL(hAPP(c_List_Odistinct(_1707734), _1707738)), hAPP(c_List_Oset(_1707734), _1707736) = hAPP(c_List_Oset(_1707734), _1707738), -(_1707736 = _1707738)], (46194 ^ _779448) ^ [_1708117, _1708119, _1708121, _1708123] : [class_Orderings_Olinorder(_1708117), -(c_List_Olinorder__class_Osorted(_1708117, hAPP(hAPP(c_List_Omap(_1708119, _1708117), _1708121), c_List_Olinorder__class_Osort__key(_1708119, _1708117, _1708121, _1708123))))], (46200 ^ _779448) ^ [_1708224, _1708226, _1708228, _1708230, _1708232] : [class_Orderings_Olinorder(_1708224), c_List_Olinorder__class_Osorted(_1708224, hAPP(hAPP(c_List_Omap(_1708226, _1708224), _1708228), _1708230)), -(c_List_Olinorder__class_Osorted(_1708224, hAPP(hAPP(c_List_Omap(_1708226, _1708224), _1708228), c_List_Olinorder__class_Oinsort__insert__key(_1708226, _1708224, _1708228, _1708232, _1708230))))], (46210 ^ _779448) ^ [_1708411, _1708413, _1708415, _1708417, _1708419] : [class_Orderings_Olinorder(_1708411), c_List_Olinorder__class_Osorted(_1708411, hAPP(hAPP(c_List_Omap(_1708413, _1708411), _1708415), _1708417)), -(c_List_Olinorder__class_Osorted(_1708411, hAPP(hAPP(c_List_Omap(_1708413, _1708411), _1708415), c_List_Oremove1(_1708413, _1708419, _1708417))))], (46220 ^ _779448) ^ [_1708594, _1708596, _1708598, _1708600, _1708602] : [class_Orderings_Olinorder(_1708594), 46223 ^ _779448 : [(46224 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1708594, hAPP(hAPP(c_List_Omap(_1708596, _1708594), _1708598), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708596, _1708594, _1708598), _1708600), _1708602))), -(c_List_Olinorder__class_Osorted(_1708594, hAPP(hAPP(c_List_Omap(_1708596, _1708594), _1708598), _1708602)))], (46230 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1708594, hAPP(hAPP(c_List_Omap(_1708596, _1708594), _1708598), _1708602)), -(c_List_Olinorder__class_Osorted(_1708594, hAPP(hAPP(c_List_Omap(_1708596, _1708594), _1708598), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708596, _1708594, _1708598), _1708600), _1708602))))]]], (46236 ^ _779448) ^ [_1708901, _1708903, _1708905, _1708907, _1708909] : [class_Orderings_Olinorder(_1708901), -(c_List_Olinorder__class_Osorted(_1708901, hAPP(hAPP(c_List_Omap(_1708903, _1708901), _1708905), hAPP(c_List_Ofilter(_1708903, hAPP(hAPP(c_COMBC(_1708903, _1708901, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1708901, tc_fun(_1708901, tc_HOL_Obool), _1708903), c_fequal), _1708905)), hAPP(_1708907, _1708909))), _1708909))))], (46242 ^ _779448) ^ [_1709064, _1709066, _1709068, _1709070, _1709072] : [class_Orderings_Olinorder(_1709064), c_List_Olinorder__class_Osorted(_1709064, hAPP(hAPP(c_List_Omap(_1709066, _1709064), _1709068), _1709070)), -(c_List_Olinorder__class_Osorted(_1709064, hAPP(hAPP(c_List_Omap(_1709066, _1709064), _1709068), hAPP(c_List_Ofilter(_1709066, _1709072), _1709070))))], (46252 ^ _779448) ^ [_1709251, _1709253, _1709255] : [class_Orderings_Olinorder(_1709251), -(c_List_Olinorder__class_Osorted(_1709251, hAPP(c_List_Ofilter(_1709251, hAPP(hAPP(c_COMBC(_1709251, _1709251, tc_HOL_Obool), c_fequal), hAPP(_1709253, _1709255))), _1709255)))], (46258 ^ _779448) ^ [_1709366, _1709368, _1709370] : [class_Orderings_Olinorder(_1709366), 46261 ^ _779448 : [(46262 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1709366, hAPP(hAPP(c_List_Olist_OCons(_1709366), _1709368), _1709370)), 46265 ^ _779448 : [(46266 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709366, _1709370))], (46268 ^ _779448) ^ [_1709552] : [hBOOL(hAPP(hAPP(c_member(_1709366), _1709552), hAPP(c_List_Oset(_1709366), _1709370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709366), _1709368), _1709552)))]]], (46274 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709366, hAPP(hAPP(c_List_Olist_OCons(_1709366), _1709368), _1709370))), c_List_Olinorder__class_Osorted(_1709366, _1709370), 46280 ^ _779448 : [(46281 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709366), 46279 ^ [_1709366, _1709368, _1709370]), hAPP(c_List_Oset(_1709366), _1709370))))], (46283 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709366), _1709368), 46279 ^ [_1709366, _1709368, _1709370]))]]]]], (46287 ^ _779448) ^ [_1709891, _1709893, _1709895] : [class_Orderings_Olinorder(_1709891), 46290 ^ _779448 : [(46291 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1709891, hAPP(hAPP(c_List_Oappend(_1709891), _1709893), _1709895)), 46294 ^ _779448 : [(46295 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709891, _1709893))], (46297 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709891, _1709895))], (46299 ^ _779448) ^ [_1710127] : [hBOOL(hAPP(hAPP(c_member(_1709891), _1710127), hAPP(c_List_Oset(_1709891), _1709893))), 46302 ^ _779448 : [(46303 ^ _779448) ^ [_1710237] : [hBOOL(hAPP(hAPP(c_member(_1709891), _1710237), hAPP(c_List_Oset(_1709891), _1709895))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709891), _1710127), _1710237)))]]]]], (46309 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709891, hAPP(hAPP(c_List_Oappend(_1709891), _1709893), _1709895))), c_List_Olinorder__class_Osorted(_1709891, _1709893), c_List_Olinorder__class_Osorted(_1709891, _1709895), 46319 ^ _779448 : [(46320 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709891), 46318 ^ [_1709891, _1709893, _1709895]), hAPP(c_List_Oset(_1709891), _1709893))))], (46323 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709891), 46321 ^ [_1709891, _1709893, _1709895]), hAPP(c_List_Oset(_1709891), _1709895))))], (46325 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709891), 46318 ^ [_1709891, _1709893, _1709895]), 46321 ^ [_1709891, _1709893, _1709895]))]]]]], (46329 ^ _779448) ^ [_1710739, _1710741, _1710743, _1710745, _1710747, _1710749] : [class_Orderings_Olinorder(_1710739), c_List_Olinorder__class_Osorted(_1710739, hAPP(hAPP(c_List_Omap(_1710741, _1710739), _1710743), _1710745)), hBOOL(hAPP(_1710747, _1710749)), -(hAPP(c_List_Ofilter(_1710741, _1710747), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710741, _1710739, _1710743), _1710749), _1710745)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710741, _1710739, _1710743), _1710749), hAPP(c_List_Ofilter(_1710741, _1710747), _1710745)))], (46343 ^ _779448) ^ [_1711028, _1711030, _1711032] : [class_Orderings_Olinorder(_1711028), 46346 ^ _779448 : [(46347 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1711028, hAPP(hAPP(c_List_Olist_OCons(_1711028), _1711030), _1711032)), 46350 ^ _779448 : [(46357 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711028, _1711032))], (46351 ^ _779448) ^ [_1711196] : [hBOOL(hAPP(hAPP(c_member(_1711028), _1711196), hAPP(c_List_Oset(_1711028), _1711032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711028), _1711030), _1711196)))]]], (46359 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711028, hAPP(hAPP(c_List_Olist_OCons(_1711028), _1711030), _1711032))), 46363 ^ _779448 : [(46364 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711028), 46362 ^ [_1711028, _1711030, _1711032]), hAPP(c_List_Oset(_1711028), _1711032))))], (46366 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711028), _1711030), 46362 ^ [_1711028, _1711030, _1711032]))]], c_List_Olinorder__class_Osorted(_1711028, _1711032)]]], (46372 ^ _779448) ^ [_1711554, _1711556] : [class_Orderings_Olinorder(_1711554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1711554), _1711556)), 46379 ^ _779448 : [(46380 ^ _779448) ^ [] : [-(hAPP(c_List_Oset(_1711554), c_List_Olinorder__class_Osorted__list__of__set(_1711554, _1711556)) = _1711556)], (46382 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711554, c_List_Olinorder__class_Osorted__list__of__set(_1711554, _1711556)))], (46384 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1711554), c_List_Olinorder__class_Osorted__list__of__set(_1711554, _1711556))))]]], (46386 ^ _779448) ^ [_1711775, _1711777, _1711779] : [class_Orderings_Olinorder(_1711775), hBOOL(hAPP(hAPP(c_member(_1711775), _1711777), hAPP(c_List_Oset(_1711775), _1711779))), c_List_Olinorder__class_Osorted(_1711775, _1711779), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711775, _1711775, c_COMBI(_1711775)), _1711777), c_List_Oremove1(_1711775, _1711777, _1711779)) = _1711779)], (46400 ^ _779448) ^ [_1712016, _1712018, _1712020, _1712022] : [class_Orderings_Olinorder(_1712016), c_List_Olinorder__class_Osorted(_1712016, _1712018), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712020), _1712022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712022), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712016)), _1712018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712016), hAPP(hAPP(c_List_Onth(_1712016), _1712018), _1712020)), hAPP(hAPP(c_List_Onth(_1712016), _1712018), _1712022))))], (46418 ^ _779448) ^ [_1712343, _1712345] : [class_Orderings_Olinorder(_1712343), 46421 ^ _779448 : [(46436 ^ _779448) ^ [] : [46438 ^ _779448 : [(46439 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46437 ^ [_1712343, _1712345]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712343)), _1712345))))], (46442 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46440 ^ [_1712343, _1712345]), 46437 ^ [_1712343, _1712345])))], (46444 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712343), hAPP(hAPP(c_List_Onth(_1712343), _1712345), 46440 ^ [_1712343, _1712345])), hAPP(hAPP(c_List_Onth(_1712343), _1712345), 46437 ^ [_1712343, _1712345])))]], -(c_List_Olinorder__class_Osorted(_1712343, _1712345))], (46422 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1712343, _1712345), 46425 ^ _779448 : [(46426 ^ _779448) ^ [_1712514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712343)), _1712345))), 46429 ^ _779448 : [(46430 ^ _779448) ^ [_1712631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712631), _1712514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712343), hAPP(hAPP(c_List_Onth(_1712343), _1712345), _1712631)), hAPP(hAPP(c_List_Onth(_1712343), _1712345), _1712514))))]]]]]]], (46448 ^ _779448) ^ [_1713067, _1713069, _1713071, _1713073, _1713075] : [class_Orderings_Olinorder(_1713067), c_Fun_Oinj__on(_1713069, _1713067, _1713071, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713069, tc_HOL_Obool)), hAPP(c_List_Oset(_1713069), _1713073)), hAPP(c_List_Oset(_1713069), _1713075))), c_List_Olinorder__class_Osorted(_1713067, hAPP(hAPP(c_List_Omap(_1713069, _1713067), _1713071), _1713073)), hBOOL(hAPP(c_List_Odistinct(_1713067), hAPP(hAPP(c_List_Omap(_1713069, _1713067), _1713071), _1713073))), c_List_Olinorder__class_Osorted(_1713067, hAPP(hAPP(c_List_Omap(_1713069, _1713067), _1713071), _1713075)), hBOOL(hAPP(c_List_Odistinct(_1713067), hAPP(hAPP(c_List_Omap(_1713069, _1713067), _1713071), _1713075))), hAPP(c_List_Oset(_1713069), _1713073) = hAPP(c_List_Oset(_1713069), _1713075), -(_1713073 = _1713075)], (46478 ^ _779448) ^ [_1713650, _1713652, _1713654] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713650), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1713650))), _1713652))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713654), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713650))), _1713652))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713650), _1713650), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713650), tc_Nat_Onat, _1713650), c_List_Onth(_1713650)), _1713654)), hAPP(c_List_Ofilter(tc_List_Olist(_1713650), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713650)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713654)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713650)))), c_List_Otranspose(_1713650, _1713652))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713650)), _1713652), _1713654))], (46488 ^ _779448) ^ [_1713977, _1713979, _1713981, _1713983] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713977), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1713977))), _1713979))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713981), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713977))), c_List_Otranspose(_1713977, _1713979)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713983), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713977))), hAPP(c_List_Ofilter(tc_List_Olist(_1713977), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713977)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713981)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713977)))), _1713979)))), -(hAPP(hAPP(c_List_Onth(_1713977), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713977)), c_List_Otranspose(_1713977, _1713979)), _1713981)), _1713983) = hAPP(hAPP(c_List_Onth(_1713977), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713977)), _1713979), _1713983)), _1713981))], (46502 ^ _779448) ^ [_1714400, _1714402] : [-(c_Fun_Oinj__on(tc_List_Olist(_1714400), tc_List_Olist(_1714400), c_List_Orev(_1714400), _1714402))], (46504 ^ _779448) ^ [_1714448, _1714450] : [hBOOL(hAPP(c_List_Odistinct(_1714448), hAPP(c_List_Orev(_1714448), _1714450))), -(hBOOL(hAPP(c_List_Odistinct(_1714448), _1714450)))], (46510 ^ _779448) ^ [_1714547, _1714549] : [hBOOL(hAPP(c_List_Odistinct(_1714547), _1714549)), -(hBOOL(hAPP(c_List_Odistinct(_1714547), hAPP(c_List_Orev(_1714547), _1714549))))], (46516 ^ _779448) ^ [_1714667, _1714669] : [hAPP(c_List_Orev(_1714667), _1714669) = c_List_Olist_ONil(_1714667), -(_1714669 = c_List_Olist_ONil(_1714667))], (46522 ^ _779448) ^ [_1714758, _1714760] : [_1714760 = c_List_Olist_ONil(_1714758), -(hAPP(c_List_Orev(_1714758), _1714760) = c_List_Olist_ONil(_1714758))], (46528 ^ _779448) ^ [_1714870, _1714872] : [c_List_Olist_ONil(_1714870) = hAPP(c_List_Orev(_1714870), _1714872), -(_1714872 = c_List_Olist_ONil(_1714870))], (46534 ^ _779448) ^ [_1714961, _1714963] : [_1714963 = c_List_Olist_ONil(_1714961), -(c_List_Olist_ONil(_1714961) = hAPP(c_List_Orev(_1714961), _1714963))], (46540 ^ _779448) ^ [_1715058] : [-(hAPP(c_List_Orev(_1715058), c_List_Olist_ONil(_1715058)) = c_List_Olist_ONil(_1715058))], (46542 ^ _779448) ^ [_1715108, _1715110, _1715112] : [hAPP(hAPP(c_List_Olist_OCons(_1715108), _1715110), c_List_Olist_ONil(_1715108)) = hAPP(c_List_Orev(_1715108), _1715112), -(_1715112 = hAPP(hAPP(c_List_Olist_OCons(_1715108), _1715110), c_List_Olist_ONil(_1715108)))], (46548 ^ _779448) ^ [_1715233, _1715235, _1715237] : [_1715237 = hAPP(hAPP(c_List_Olist_OCons(_1715233), _1715235), c_List_Olist_ONil(_1715233)), -(hAPP(hAPP(c_List_Olist_OCons(_1715233), _1715235), c_List_Olist_ONil(_1715233)) = hAPP(c_List_Orev(_1715233), _1715237))], (46554 ^ _779448) ^ [_1715382, _1715384, _1715386] : [hAPP(c_List_Orev(_1715382), _1715384) = hAPP(hAPP(c_List_Olist_OCons(_1715382), _1715386), c_List_Olist_ONil(_1715382)), -(_1715384 = hAPP(hAPP(c_List_Olist_OCons(_1715382), _1715386), c_List_Olist_ONil(_1715382)))], (46560 ^ _779448) ^ [_1715507, _1715509, _1715511] : [_1715509 = hAPP(hAPP(c_List_Olist_OCons(_1715507), _1715511), c_List_Olist_ONil(_1715507)), -(hAPP(c_List_Orev(_1715507), _1715509) = hAPP(hAPP(c_List_Olist_OCons(_1715507), _1715511), c_List_Olist_ONil(_1715507)))], (46566 ^ _779448) ^ [_1715638, _1715640, _1715642] : [-(hAPP(c_List_Orev(_1715638), hAPP(hAPP(c_List_Oappend(_1715638), _1715640), _1715642)) = hAPP(hAPP(c_List_Oappend(_1715638), hAPP(c_List_Orev(_1715638), _1715642)), hAPP(c_List_Orev(_1715638), _1715640)))], (46568 ^ _779448) ^ [_1715696, _1715698] : [-(hAPP(c_List_Orev(_1715696), c_List_Oconcat(_1715696, _1715698)) = c_List_Oconcat(_1715696, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715696), tc_List_Olist(_1715696)), c_List_Orev(_1715696)), hAPP(c_List_Orev(tc_List_Olist(_1715696)), _1715698))))], (46570 ^ _779448) ^ [_1715754, _1715756, _1715758, _1715760] : [-(hAPP(c_List_Orev(_1715754), hAPP(hAPP(c_List_Omap(_1715756, _1715754), _1715758), _1715760)) = hAPP(hAPP(c_List_Omap(_1715756, _1715754), _1715758), hAPP(c_List_Orev(_1715756), _1715760)))], (46572 ^ _779448) ^ [_1715811, _1715813, _1715815] : [-(hAPP(c_List_Orev(_1715811), hAPP(c_List_Ofilter(_1715811, _1715813), _1715815)) = hAPP(c_List_Ofilter(_1715811, _1715813), hAPP(c_List_Orev(_1715811), _1715815)))], (46574 ^ _779448) ^ [_1715860, _1715862, _1715864, _1715866] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715860)), _1715862) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715864)), _1715866), -(hAPP(hAPP(c_List_Ozip(_1715860, _1715864), hAPP(c_List_Orev(_1715860), _1715862)), hAPP(c_List_Orev(_1715864), _1715866)) = hAPP(c_List_Orev(tc_prod(_1715860, _1715864)), hAPP(hAPP(c_List_Ozip(_1715860, _1715864), _1715862), _1715866)))], (46580 ^ _779448) ^ [_1716041, _1716043] : [-(hAPP(c_List_Oset(_1716041), hAPP(c_List_Orev(_1716041), _1716043)) = hAPP(c_List_Oset(_1716041), _1716043))], (46582 ^ _779448) ^ [_1716105, _1716107, _1716109, _1716111, _1716113] : [c_List_Olist__all2(_1716105, _1716107, _1716109, hAPP(c_List_Orev(_1716105), _1716111), hAPP(c_List_Orev(_1716107), _1716113)), -(c_List_Olist__all2(_1716105, _1716107, _1716109, _1716111, _1716113))], (46588 ^ _779448) ^ [_1716216, _1716218, _1716220, _1716222, _1716224] : [c_List_Olist__all2(_1716216, _1716218, _1716220, _1716222, _1716224), -(c_List_Olist__all2(_1716216, _1716218, _1716220, hAPP(c_List_Orev(_1716216), _1716222), hAPP(c_List_Orev(_1716218), _1716224)))], (46594 ^ _779448) ^ [_1716357, _1716359, _1716361, _1716363, _1716365] : [c_List_Olist__all2(_1716357, _1716359, _1716361, hAPP(c_List_Orev(_1716357), _1716363), _1716365), -(c_List_Olist__all2(_1716357, _1716359, _1716361, _1716363, hAPP(c_List_Orev(_1716359), _1716365)))], (46600 ^ _779448) ^ [_1716468, _1716470, _1716472, _1716474, _1716476] : [c_List_Olist__all2(_1716468, _1716470, _1716472, _1716474, hAPP(c_List_Orev(_1716470), _1716476)), -(c_List_Olist__all2(_1716468, _1716470, _1716472, hAPP(c_List_Orev(_1716468), _1716474), _1716476))], (46606 ^ _779448) ^ [_1716585, _1716587] : [-(hAPP(c_List_Orev(_1716585), hAPP(c_List_Orev(_1716585), _1716587)) = _1716587)], (46608 ^ _779448) ^ [_1716638, _1716640, _1716642] : [hAPP(c_List_Orev(_1716638), _1716640) = _1716642, -(_1716640 = hAPP(c_List_Orev(_1716638), _1716642))], (46614 ^ _779448) ^ [_1716733, _1716735, _1716737] : [_1716735 = hAPP(c_List_Orev(_1716733), _1716737), -(hAPP(c_List_Orev(_1716733), _1716735) = _1716737)], (46620 ^ _779448) ^ [_1716852, _1716854, _1716856] : [hAPP(c_List_Orev(_1716852), _1716854) = hAPP(c_List_Orev(_1716852), _1716856), -(_1716854 = _1716856)], (46626 ^ _779448) ^ [_1716947, _1716949, _1716951] : [_1716949 = _1716951, -(hAPP(c_List_Orev(_1716947), _1716949) = hAPP(c_List_Orev(_1716947), _1716951))], (46632 ^ _779448) ^ [_1717048, _1717050] : [class_Groups_Ocomm__monoid__add(_1717048), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717048), hAPP(c_List_Orev(_1717048), _1717050)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717048), _1717050))], (46638 ^ _779448) ^ [_1717153, _1717155] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717153)), hAPP(c_List_Orev(_1717153), _1717155)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717153)), _1717155))], (46640 ^ _779448) ^ [_1717197, _1717199, _1717201, _1717203, _1717205] : [-(hAPP(c_List_Ofoldl(_1717197, _1717199, _1717201, _1717203), _1717205) = c_List_Ofoldr(_1717199, _1717197, hAPP(c_COMBC(_1717197, _1717199, _1717197), _1717201), hAPP(c_List_Orev(_1717199), _1717205), _1717203))], (46642 ^ _779448) ^ [_1717254, _1717256, _1717258, _1717260, _1717262] : [-(c_List_Ofoldr(_1717254, _1717256, _1717258, _1717260, _1717262) = hAPP(c_List_Ofoldl(_1717256, _1717254, hAPP(c_COMBC(_1717254, _1717256, _1717256), _1717258), _1717262), hAPP(c_List_Orev(_1717254), _1717260)))], (46644 ^ _779448) ^ [_1717332, _1717334, _1717336, _1717338] : [hAPP(c_List_Orev(_1717332), _1717334) = hAPP(hAPP(c_List_Olist_OCons(_1717332), _1717336), _1717338), -(_1717334 = hAPP(hAPP(c_List_Oappend(_1717332), hAPP(c_List_Orev(_1717332), _1717338)), hAPP(hAPP(c_List_Olist_OCons(_1717332), _1717336), c_List_Olist_ONil(_1717332))))], (46650 ^ _779448) ^ [_1717481, _1717483, _1717485, _1717487] : [_1717483 = hAPP(hAPP(c_List_Oappend(_1717481), hAPP(c_List_Orev(_1717481), _1717487)), hAPP(hAPP(c_List_Olist_OCons(_1717481), _1717485), c_List_Olist_ONil(_1717481))), -(hAPP(c_List_Orev(_1717481), _1717483) = hAPP(hAPP(c_List_Olist_OCons(_1717481), _1717485), _1717487))], (46656 ^ _779448) ^ [_1717636, _1717638, _1717640] : [-(hAPP(c_List_Orev(_1717636), hAPP(hAPP(c_List_Olist_OCons(_1717636), _1717638), _1717640)) = hAPP(hAPP(c_List_Oappend(_1717636), hAPP(c_List_Orev(_1717636), _1717640)), hAPP(hAPP(c_List_Olist_OCons(_1717636), _1717638), c_List_Olist_ONil(_1717636))))], (46658 ^ _779448) ^ [_1717695, _1717697] : [-(_1717695 = c_List_Olist_ONil(_1717697)), -(hAPP(c_List_Ohd(_1717697), hAPP(c_List_Orev(_1717697), _1717695)) = c_List_Olast(_1717697, _1717695))], (46664 ^ _779448) ^ [_1717742, _1717744] : [-(_1717742 = c_List_Olist_ONil(_1717744)), -(c_List_Olast(_1717744, hAPP(c_List_Orev(_1717744), _1717742)) = hAPP(c_List_Ohd(_1717744), _1717742))], (46670 ^ _779448) ^ [_1717793, _1717795] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1717793), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1717793))), c_List_Otranspose(_1717793, _1717795)))))], (46672 ^ _779448) ^ [_1717839, _1717841] : [-(hAPP(c_List_Orev(_1717839), _1717841) = hAPP(c_List_Ofoldl(tc_List_Olist(_1717839), _1717839, hAPP(c_COMBC(_1717839, tc_List_Olist(_1717839), tc_List_Olist(_1717839)), c_List_Olist_OCons(_1717839)), c_List_Olist_ONil(_1717839)), _1717841))], (46674 ^ _779448) ^ [_1717894, _1717896, _1717898] : [-(hAPP(c_List_Orev(_1717894), hAPP(hAPP(c_List_Odrop(_1717894), _1717896), _1717898)) = hAPP(hAPP(c_List_Otake(_1717894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717894)), _1717898)), _1717896)), hAPP(c_List_Orev(_1717894), _1717898)))], (46676 ^ _779448) ^ [_1717960, _1717962, _1717964] : [-(hAPP(c_List_Orev(_1717960), hAPP(hAPP(c_List_Otake(_1717960), _1717962), _1717964)) = hAPP(hAPP(c_List_Odrop(_1717960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717960)), _1717964)), _1717962)), hAPP(c_List_Orev(_1717960), _1717964)))], (46678 ^ _779448) ^ [_1718026, _1718028, _1718030] : [-(hAPP(c_List_Orotate(_1718026, _1718028), hAPP(c_List_Orev(_1718026), _1718030)) = hAPP(c_List_Orev(_1718026), hAPP(c_List_Orotate(_1718026, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718026)), _1718030)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718028, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718026)), _1718030)))), _1718030)))], (46680 ^ _779448) ^ [_1718099, _1718101, _1718103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718099), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718101)), _1718103))), -(hAPP(hAPP(c_List_Onth(_1718101), hAPP(c_List_Orev(_1718101), _1718103)), _1718099) = hAPP(hAPP(c_List_Onth(_1718101), _1718103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718101)), _1718103)), hAPP(c_Nat_OSuc, _1718099))))], (46686 ^ _779448) ^ [_1718276, _1718278, _1718280, _1718282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718276), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718278)), _1718280))), -(hAPP(c_List_Orev(_1718278), hAPP(hAPP(c_List_Olist__update(_1718278, _1718280), _1718276), _1718282)) = hAPP(hAPP(c_List_Olist__update(_1718278, hAPP(c_List_Orev(_1718278), _1718280)), 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(_1718278)), _1718280)), _1718276)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718282))], (46692 ^ _779448) ^ [_1718475, _1718477, _1718479, _1718481] : [class_Orderings_Olinorder(_1718475), c_List_Olinorder__class_Osorted(_1718475, hAPP(c_List_Orev(_1718475), _1718477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718479), _1718481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718475)), _1718477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718475), hAPP(hAPP(c_List_Onth(_1718475), _1718477), _1718481)), hAPP(hAPP(c_List_Onth(_1718475), _1718477), _1718479))))], (46710 ^ _779448) ^ [_1718812, _1718814, _1718816] : [class_Orderings_Olinorder(_1718812), c_List_Olinorder__class_Osorted(_1718812, hAPP(c_List_Orev(_1718812), _1718814)), 46717 ^ _779448 : [(46718 ^ _779448) ^ [] : [_1718814 = c_List_Olist_ONil(_1718812), -(c_List_Ofoldr(_1718812, _1718812, c_Orderings_Oord__class_Omax(_1718812), _1718814, _1718816) = _1718816)], (46724 ^ _779448) ^ [] : [-(_1718814 = c_List_Olist_ONil(_1718812)), -(c_List_Ofoldr(_1718812, _1718812, c_Orderings_Oord__class_Omax(_1718812), _1718814, _1718816) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1718812), hAPP(hAPP(c_List_Onth(_1718812), _1718814), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1718816))]]], (46730 ^ _779448) ^ [_1719126, _1719128] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719126), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719126))), _1719128))), 46733 ^ _779448 : [(46734 ^ _779448) ^ [] : [_1719128 = c_List_Olist_ONil(tc_List_Olist(_1719126)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719126))), c_List_Otranspose(_1719126, _1719128)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46740 ^ _779448) ^ [] : [-(_1719128 = c_List_Olist_ONil(tc_List_Olist(_1719126))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719126))), c_List_Otranspose(_1719126, _1719128)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719126)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719126)), _1719128), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (46746 ^ _779448) ^ [_1719436, _1719438, _1719440] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719436), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719436))), _1719438))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719440), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719436))), _1719438))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719436))), hAPP(c_List_Ofilter(tc_List_Olist(_1719436), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719436)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719440)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719436)))), c_List_Otranspose(_1719436, _1719438))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719436)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719436)), _1719438), _1719440)))], (46756 ^ _779448) ^ [_1719745, _1719747] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719745), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719745))), _1719747))), -(c_List_Otranspose(_1719745, c_List_Otranspose(_1719745, _1719747)) = c_List_OtakeWhile(tc_List_Olist(_1719745), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719745)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719745), tc_List_Olist(_1719745), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1719745))), _1719747))], (46762 ^ _779448) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (46764 ^ _779448) ^ [_1719956, _1719958, _1719960] : [class_Orderings_Olinorder(_1719956), c_List_Olinorder__class_Osorted(_1719956, _1719958), -(c_List_Olinorder__class_Osorted(_1719956, c_List_OtakeWhile(_1719956, _1719960, _1719958)))], (46774 ^ _779448) ^ [_1720095, _1720097, _1720099] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720095)), c_List_OtakeWhile(_1720095, _1720097, _1720099))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720095)), _1720099))))], (46786 ^ _779448) ^ [_1720359, _1720361, _1720363] : [46788 ^ _779448 : [(46789 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720359), 46787 ^ [_1720359, _1720361, _1720363]), hAPP(c_List_Oset(_1720359), _1720363))))], (46791 ^ _779448) ^ [] : [hBOOL(hAPP(_1720361, 46787 ^ [_1720359, _1720361, _1720363]))]], -(c_List_OtakeWhile(_1720359, _1720361, _1720363) = _1720363)], (46776 ^ _779448) ^ [_1720163, _1720165, _1720167] : [c_List_OtakeWhile(_1720163, _1720165, _1720167) = _1720167, 46779 ^ _779448 : [(46780 ^ _779448) ^ [_1720250] : [hBOOL(hAPP(hAPP(c_member(_1720163), _1720250), hAPP(c_List_Oset(_1720163), _1720167))), -(hBOOL(hAPP(_1720165, _1720250)))]]], (46795 ^ _779448) ^ [_1720547, _1720549, _1720551, _1720553] : [hBOOL(hAPP(hAPP(c_member(_1720547), _1720549), hAPP(c_List_Oset(_1720547), c_List_OtakeWhile(_1720547, _1720551, _1720553)))), 46798 ^ _779448 : [(46799 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720547), _1720549), hAPP(c_List_Oset(_1720547), _1720553))))], (46801 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1720551, _1720549)))]]], (46803 ^ _779448) ^ [_1720714, _1720716, _1720718, _1720720, _1720722] : [-(hAPP(hAPP(c_List_Ozip(_1720714, _1720716), _1720718), c_List_OtakeWhile(_1720716, _1720720, _1720722)) = c_List_OtakeWhile(tc_prod(_1720714, _1720716), hAPP(c_Fun_Ocomp(_1720716, tc_HOL_Obool, tc_prod(_1720714, _1720716), _1720720), c_Product__Type_Osnd(_1720714, _1720716)), hAPP(hAPP(c_List_Ozip(_1720714, _1720716), _1720718), _1720722)))], (46805 ^ _779448) ^ [_1720788, _1720790, _1720792, _1720794, _1720796] : [-(hAPP(hAPP(c_List_Ozip(_1720788, _1720790), c_List_OtakeWhile(_1720788, _1720792, _1720794)), _1720796) = c_List_OtakeWhile(tc_prod(_1720788, _1720790), hAPP(c_Fun_Ocomp(_1720788, tc_HOL_Obool, tc_prod(_1720788, _1720790), _1720792), c_Product__Type_Ofst(_1720788, _1720790)), hAPP(hAPP(c_List_Ozip(_1720788, _1720790), _1720794), _1720796)))], (46807 ^ _779448) ^ [_1720862, _1720864, _1720866, _1720868, _1720870] : [-(c_List_OtakeWhile(_1720862, _1720864, hAPP(hAPP(c_List_Omap(_1720866, _1720862), _1720868), _1720870)) = hAPP(hAPP(c_List_Omap(_1720866, _1720862), _1720868), c_List_OtakeWhile(_1720866, hAPP(c_Fun_Ocomp(_1720862, tc_HOL_Obool, _1720866, _1720864), _1720868), _1720870)))], (46809 ^ _779448) ^ [_1720923, _1720925, _1720927, _1720929, _1720931] : [-(hBOOL(hAPP(_1720923, _1720925))), -(c_List_OtakeWhile(_1720927, _1720923, hAPP(hAPP(c_List_Oappend(_1720927), _1720929), hAPP(hAPP(c_List_Olist_OCons(_1720927), _1720925), _1720931))) = c_List_OtakeWhile(_1720927, _1720923, _1720929))], (46815 ^ _779448) ^ [_1721006, _1721008, _1721010, _1721012] : [hBOOL(hAPP(_1721006, _1721008)), -(c_List_OtakeWhile(_1721010, _1721006, hAPP(hAPP(c_List_Olist_OCons(_1721010), _1721008), _1721012)) = hAPP(hAPP(c_List_Olist_OCons(_1721010), _1721008), c_List_OtakeWhile(_1721010, _1721006, _1721012)))], (46821 ^ _779448) ^ [_1721133, _1721135, _1721137, _1721139] : [-(hBOOL(hAPP(_1721133, _1721135))), -(c_List_OtakeWhile(_1721137, _1721133, hAPP(hAPP(c_List_Olist_OCons(_1721137), _1721135), _1721139)) = c_List_Olist_ONil(_1721137))], (46827 ^ _779448) ^ [_1721191, _1721193] : [-(c_List_OtakeWhile(_1721191, _1721193, c_List_Olist_ONil(_1721191)) = c_List_Olist_ONil(_1721191))], (46829 ^ _779448) ^ [_1721224, _1721226, _1721228] : [-(c_List_OtakeWhile(_1721224, _1721226, _1721228) = hAPP(hAPP(c_List_Otake(_1721224), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721224)), c_List_OtakeWhile(_1721224, _1721226, _1721228))), _1721228))], (46831 ^ _779448) ^ [_1721274, _1721276, _1721278] : [hBOOL(hAPP(c_List_Odistinct(_1721274), _1721276)), -(hBOOL(hAPP(c_List_Odistinct(_1721274), c_List_OtakeWhile(_1721274, _1721278, _1721276))))], (46837 ^ _779448) ^ [_1721377] : [-(c_List_Oreturn__list(_1721377) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1721377))], (46839 ^ _779448) ^ [_1721405, _1721407, _1721409, _1721411, _1721413] : [hBOOL(hAPP(hAPP(c_member(_1721405), _1721407), hAPP(c_List_Oset(_1721405), _1721409))), -(hBOOL(hAPP(_1721411, _1721407))), -(c_List_OtakeWhile(_1721405, _1721411, hAPP(hAPP(c_List_Oappend(_1721405), _1721409), _1721413)) = c_List_OtakeWhile(_1721405, _1721411, _1721409))], (46849 ^ _779448) ^ [_1721563, _1721565, _1721567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721563)), c_List_OtakeWhile(_1721563, _1721565, _1721567))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721563)), _1721567))), hBOOL(hAPP(_1721565, hAPP(hAPP(c_List_Onth(_1721563), _1721567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721563)), c_List_OtakeWhile(_1721563, _1721565, _1721567)))))], (46855 ^ _779448) ^ [_1721731, _1721733, _1721735, _1721737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721731), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721733)), c_List_OtakeWhile(_1721733, _1721735, _1721737)))), -(hAPP(hAPP(c_List_Onth(_1721733), c_List_OtakeWhile(_1721733, _1721735, _1721737)), _1721731) = hAPP(hAPP(c_List_Onth(_1721733), _1721737), _1721731))], (46861 ^ _779448) ^ [_1721883, _1721885] : [-(_1721883 = c_List_Olist_ONil(_1721885)), hBOOL(hAPP(c_List_Odistinct(_1721885), _1721883)), -(c_List_OtakeWhile(_1721885, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1721885), c_fNot), hAPP(hAPP(c_COMBC(_1721885, _1721885, tc_HOL_Obool), c_fequal), c_List_Olast(_1721885, _1721883))), _1721883) = c_List_Obutlast(_1721885, _1721883))], (46871 ^ _779448) ^ [_1722080, _1722082, _1722084, _1722086, _1722088] : [class_Orderings_Olinorder(_1722080), c_List_Olinorder__class_Osorted(_1722080, hAPP(c_List_Orev(_1722080), hAPP(hAPP(c_List_Omap(_1722082, _1722080), _1722084), _1722086))), -(hAPP(c_List_Ofilter(_1722082, hAPP(hAPP(c_COMBB(_1722080, tc_HOL_Obool, _1722082), hAPP(c_Orderings_Oord__class_Oless(_1722080), _1722088)), _1722084)), _1722086) = c_List_OtakeWhile(_1722082, hAPP(hAPP(c_COMBB(_1722080, tc_HOL_Obool, _1722082), hAPP(c_Orderings_Oord__class_Oless(_1722080), _1722088)), _1722084), _1722086))], (46881 ^ _779448) ^ [_1722327] : [c_List_Onat__list(_1722327), -(c_List_Oembed__list(c_List_Oreturn__list(_1722327)) = _1722327)], (46887 ^ _779448) ^ [_1722408, _1722410] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1722408), _1722410) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1722408)), c_List_Oembed__list(_1722410))))], (46889 ^ _779448) ^ [_1722451] : [-(c_List_Oembed__list(_1722451) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1722451))], (46891 ^ _779448) ^ [_1722479, _1722481, _1722483] : [hBOOL(hAPP(c_List_Odistinct(_1722479), _1722481)), hBOOL(hAPP(hAPP(c_member(_1722479), _1722483), hAPP(c_List_Oset(_1722479), _1722481))), -(c_List_OtakeWhile(_1722479, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722479), c_fNot), hAPP(hAPP(c_COMBC(_1722479, _1722479, tc_HOL_Obool), c_fequal), _1722483)), hAPP(c_List_Orev(_1722479), _1722481)) = hAPP(c_List_Orev(_1722479), hAPP(c_List_Otl(_1722479), c_List_OdropWhile(_1722479, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722479), c_fNot), hAPP(hAPP(c_COMBC(_1722479, _1722479, tc_HOL_Obool), c_fequal), _1722483)), _1722481))))], (46901 ^ _779448) ^ [_1722770, _1722772, _1722774] : [hBOOL(hAPP(c_List_Odistinct(_1722770), _1722772)), hBOOL(hAPP(hAPP(c_member(_1722770), _1722774), hAPP(c_List_Oset(_1722770), _1722772))), -(c_List_OdropWhile(_1722770, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722770), c_fNot), hAPP(hAPP(c_COMBC(_1722770, _1722770, tc_HOL_Obool), c_fequal), _1722774)), hAPP(c_List_Orev(_1722770), _1722772)) = hAPP(hAPP(c_List_Olist_OCons(_1722770), _1722774), hAPP(c_List_Orev(_1722770), c_List_OtakeWhile(_1722770, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722770), c_fNot), hAPP(hAPP(c_COMBC(_1722770, _1722770, tc_HOL_Obool), c_fequal), _1722774)), _1722772))))], (46911 ^ _779448) ^ [_1723067, _1723069, _1723071] : [-(hAPP(hAPP(c_List_Oappend(_1723067), c_List_OtakeWhile(_1723067, _1723069, _1723071)), c_List_OdropWhile(_1723067, _1723069, _1723071)) = _1723071)], (46913 ^ _779448) ^ [_1723110, _1723112, _1723114] : [class_Orderings_Olinorder(_1723110), c_List_Olinorder__class_Osorted(_1723110, _1723112), -(c_List_Olinorder__class_Osorted(_1723110, c_List_OdropWhile(_1723110, _1723114, _1723112)))], (46923 ^ _779448) ^ [_1723249, _1723251, _1723253] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723249)), c_List_OdropWhile(_1723249, _1723251, _1723253))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723249)), _1723253))))], (46935 ^ _779448) ^ [_1723517, _1723519, _1723521] : [46937 ^ _779448 : [(46938 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723517), 46936 ^ [_1723517, _1723519, _1723521]), hAPP(c_List_Oset(_1723517), _1723521))))], (46940 ^ _779448) ^ [] : [hBOOL(hAPP(_1723519, 46936 ^ [_1723517, _1723519, _1723521]))]], -(c_List_OdropWhile(_1723517, _1723519, _1723521) = c_List_Olist_ONil(_1723517))], (46925 ^ _779448) ^ [_1723317, _1723319, _1723321] : [c_List_OdropWhile(_1723317, _1723319, _1723321) = c_List_Olist_ONil(_1723317), 46928 ^ _779448 : [(46929 ^ _779448) ^ [_1723408] : [hBOOL(hAPP(hAPP(c_member(_1723317), _1723408), hAPP(c_List_Oset(_1723317), _1723321))), -(hBOOL(hAPP(_1723319, _1723408)))]]], (46944 ^ _779448) ^ [_1723724, _1723726, _1723728, _1723730] : [hBOOL(hAPP(_1723724, _1723726)), -(c_List_OdropWhile(_1723728, _1723724, hAPP(hAPP(c_List_Olist_OCons(_1723728), _1723726), _1723730)) = c_List_OdropWhile(_1723728, _1723724, _1723730))], (46950 ^ _779448) ^ [_1723835, _1723837, _1723839, _1723841] : [-(hBOOL(hAPP(_1723835, _1723837))), -(c_List_OdropWhile(_1723839, _1723835, hAPP(hAPP(c_List_Olist_OCons(_1723839), _1723837), _1723841)) = hAPP(hAPP(c_List_Olist_OCons(_1723839), _1723837), _1723841))], (46956 ^ _779448) ^ [_1723899, _1723901] : [-(c_List_OdropWhile(_1723899, _1723901, c_List_Olist_ONil(_1723899)) = c_List_Olist_ONil(_1723899))], (46958 ^ _779448) ^ [_1723932, _1723934, _1723936] : [hBOOL(hAPP(c_List_Odistinct(_1723932), _1723934)), -(hBOOL(hAPP(c_List_Odistinct(_1723932), c_List_OdropWhile(_1723932, _1723936, _1723934))))], (46964 ^ _779448) ^ [_1724034, _1724036, _1724038] : [-(c_List_OdropWhile(_1724034, _1724036, _1724038) = c_List_Olist_ONil(_1724034)), hBOOL(hAPP(_1724036, hAPP(c_List_Ohd(_1724034), c_List_OdropWhile(_1724034, _1724036, _1724038))))], (46970 ^ _779448) ^ [_1724140, _1724142, _1724144, _1724146, _1724148] : [-(c_List_OdropWhile(_1724140, _1724142, hAPP(hAPP(c_List_Omap(_1724144, _1724140), _1724146), _1724148)) = hAPP(hAPP(c_List_Omap(_1724144, _1724140), _1724146), c_List_OdropWhile(_1724144, hAPP(c_Fun_Ocomp(_1724140, tc_HOL_Obool, _1724144, _1724142), _1724146), _1724148)))], (46972 ^ _779448) ^ [_1724205, _1724207, _1724209, _1724211, _1724213] : [hBOOL(hAPP(hAPP(c_member(_1724205), _1724207), hAPP(c_List_Oset(_1724205), _1724209))), -(hBOOL(hAPP(_1724211, _1724207))), -(c_List_OdropWhile(_1724205, _1724211, hAPP(hAPP(c_List_Oappend(_1724205), _1724209), _1724213)) = hAPP(hAPP(c_List_Oappend(_1724205), c_List_OdropWhile(_1724205, _1724211, _1724209)), _1724213))], (46982 ^ _779448) ^ [_1724403, _1724405, _1724407, _1724409, _1724411] : [c_List_OdropWhile(_1724403, _1724405, _1724407) = hAPP(hAPP(c_List_Olist_OCons(_1724403), _1724409), _1724411), 46985 ^ _779448 : [(46986 ^ _779448) ^ [] : [-(_1724407 = hAPP(hAPP(c_List_Oappend(_1724403), c_List_OtakeWhile(_1724403, _1724405, _1724407)), hAPP(hAPP(c_List_Olist_OCons(_1724403), _1724409), _1724411)))], (46988 ^ _779448) ^ [] : [hBOOL(hAPP(_1724405, _1724409))]]], (46990 ^ _779448) ^ [_1724584, _1724586, _1724588, _1724590, _1724592] : [-(c_List_OdropWhile(_1724584, _1724586, _1724588) = hAPP(hAPP(c_List_Olist_OCons(_1724584), _1724590), _1724592)), _1724588 = hAPP(hAPP(c_List_Oappend(_1724584), c_List_OtakeWhile(_1724584, _1724586, _1724588)), hAPP(hAPP(c_List_Olist_OCons(_1724584), _1724590), _1724592)), -(hBOOL(hAPP(_1724586, _1724590)))], (47000 ^ _779448) ^ [_1724798, _1724800, _1724802] : [-(c_List_OdropWhile(_1724798, _1724800, _1724802) = hAPP(hAPP(c_List_Odrop(_1724798), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724798)), c_List_OtakeWhile(_1724798, _1724800, _1724802))), _1724802))], (47002 ^ _779448) ^ [_1724848, _1724850, _1724852, _1724854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724850)), c_List_OdropWhile(_1724850, _1724852, _1724854)))), -(hAPP(hAPP(c_List_Onth(_1724850), c_List_OdropWhile(_1724850, _1724852, _1724854)), _1724848) = hAPP(hAPP(c_List_Onth(_1724850), _1724854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1724848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724850)), c_List_OtakeWhile(_1724850, _1724852, _1724854)))))], (47008 ^ _779448) ^ [_1725035, _1725037, _1725039, _1725041, _1725043] : [class_Groups_Omonoid__add(_1725035), 47014 ^ _779448 : [(47015 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725037), 47013 ^ [_1725035, _1725037, _1725039, _1725041, _1725043]), hAPP(c_List_Oset(_1725037), _1725039))))], (47017 ^ _779448) ^ [] : [hBOOL(hAPP(_1725041, 47013 ^ [_1725035, _1725037, _1725039, _1725041, _1725043]))], (47019 ^ _779448) ^ [] : [hAPP(_1725043, 47013 ^ [_1725035, _1725037, _1725039, _1725041, _1725043]) = c_Groups_Ozero__class_Ozero(_1725035)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1725035), hAPP(hAPP(c_List_Omap(_1725037, _1725035), _1725043), hAPP(c_List_Ofilter(_1725037, _1725041), _1725039))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1725035), hAPP(hAPP(c_List_Omap(_1725037, _1725035), _1725043), _1725039)))], (47023 ^ _779448) ^ [_1725426, _1725428] : [class_Orderings_Olinorder(_1725426), 47030 ^ _779448 : [(47031 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47028 ^ [_1725426, _1725428]), 47029 ^ [_1725426, _1725428])))], (47033 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47029 ^ [_1725426, _1725428]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725426)), _1725428))))], (47035 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725426), hAPP(hAPP(c_List_Onth(_1725426), _1725428), 47028 ^ [_1725426, _1725428])), hAPP(hAPP(c_List_Onth(_1725426), _1725428), 47029 ^ [_1725426, _1725428])))]], -(c_List_Olinorder__class_Osorted(_1725426, _1725428))], (47039 ^ _779448) ^ [_1725797, _1725799, _1725801] : [47041 ^ _779448 : [(47042 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725797), 47040 ^ [_1725797, _1725799, _1725801]), hAPP(c_List_Oset(_1725797), c_List_OdropWhile(_1725797, _1725799, _1725801)))))], (47044 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1725799, 47040 ^ [_1725797, _1725799, _1725801])))]], -(c_List_OtakeWhile(_1725797, _1725799, _1725801) = hAPP(c_List_Ofilter(_1725797, _1725799), _1725801))], (47048 ^ _779448) ^ [_1725918, _1725920, _1725922, _1725924] : [47050 ^ _779448 : [(47051 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47049 ^ [_1725918, _1725920, _1725922, _1725924]), _1725918)))], (47053 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47049 ^ [_1725918, _1725920, _1725922, _1725924]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725920)), _1725922))))], (47055 ^ _779448) ^ [] : [hBOOL(hAPP(_1725924, hAPP(hAPP(c_List_Onth(_1725920), _1725922), 47049 ^ [_1725918, _1725920, _1725922, _1725924])))]], 47058 ^ _779448 : [(47059 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725918), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725920)), _1725922))))], (47061 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1725924, hAPP(hAPP(c_List_Onth(_1725920), _1725922), _1725918))))]], -(c_List_OtakeWhile(_1725920, _1725924, _1725922) = hAPP(hAPP(c_List_Otake(_1725920), _1725918), _1725922))], (47065 ^ _779448) ^ [_1726322, _1726324, _1726326, _1726328] : [47067 ^ _779448 : [(47068 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47066 ^ [_1726322, _1726324, _1726326, _1726328]), _1726322)))], (47070 ^ _779448) ^ [] : [hBOOL(hAPP(_1726324, hAPP(hAPP(c_List_Onth(_1726326), _1726328), 47066 ^ [_1726322, _1726324, _1726326, _1726328])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726322), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726326)), _1726328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726322), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726326)), c_List_OtakeWhile(_1726326, _1726324, _1726328)))))], (47078 ^ _779448) ^ [_1726630, _1726632] : [class_Orderings_Olinorder(_1726630), 47081 ^ _779448 : [(47082 ^ _779448) ^ [] : [c_List_Olinorder__class_Osorted(_1726630, _1726632), -(_1726632 = c_List_Olist_ONil(_1726630)), 47091 ^ _779448 : [(47092 ^ _779448) ^ [] : [-(_1726632 = hAPP(hAPP(c_List_Olist_OCons(_1726630), 47090 ^ [_1726630, _1726632]), 47089 ^ [_1726630, _1726632]))], (47100 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726630, 47089 ^ [_1726630, _1726632]))], (47094 ^ _779448) ^ [_1726964] : [hBOOL(hAPP(hAPP(c_member(_1726630), _1726964), hAPP(c_List_Oset(_1726630), 47089 ^ [_1726630, _1726632]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726630), 47090 ^ [_1726630, _1726632]), _1726964)))]]], (47102 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726630, _1726632)), 47103 ^ _779448 : [(47104 ^ _779448) ^ [] : [_1726632 = c_List_Olist_ONil(_1726630)], (47106 ^ _779448) ^ [_1727190, _1727192] : [_1726632 = hAPP(hAPP(c_List_Olist_OCons(_1726630), _1727190), _1727192), 47112 ^ _779448 : [(47113 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726630), 47111 ^ [_1726630, _1726632, _1727190, _1727192]), hAPP(c_List_Oset(_1726630), _1727192))))], (47115 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726630), _1727190), 47111 ^ [_1726630, _1726632, _1727190, _1727192]))]], c_List_Olinorder__class_Osorted(_1726630, _1727192)]]]]], (47121 ^ _779448) ^ [_1727511, _1727513, _1727515] : [hBOOL(hAPP(hAPP(c_member(_1727511), _1727513), hAPP(c_List_Oset(_1727511), _1727515))), -(c_List_Oinsert(_1727511, _1727513, _1727515) = _1727515)], (47127 ^ _779448) ^ [_1727616, _1727618, _1727620] : [-(hBOOL(hAPP(hAPP(c_member(_1727616), _1727618), hAPP(c_List_Oset(_1727616), _1727620)))), -(c_List_Oinsert(_1727616, _1727618, _1727620) = hAPP(hAPP(c_List_Olist_OCons(_1727616), _1727618), _1727620))], (47133 ^ _779448) ^ [_1727676, _1727678, _1727680] : [-(hBOOL(hAPP(hAPP(c_member(_1727676), _1727678), hAPP(c_List_Oset(_1727676), _1727680)))), -(c_List_Oinsert(_1727676, _1727678, _1727680) = hAPP(hAPP(c_List_Olist_OCons(_1727676), _1727678), _1727680))], (47139 ^ _779448) ^ [_1727738, _1727740, _1727742] : [-(c_List_Oinsert(_1727738, _1727740, c_List_Oremdups(_1727738, _1727742)) = c_List_Oremdups(_1727738, c_List_Oinsert(_1727738, _1727740, _1727742)))], (47141 ^ _779448) ^ [_1727779, _1727781, _1727783] : [hBOOL(hAPP(c_List_Odistinct(_1727779), _1727781)), -(hBOOL(hAPP(c_List_Odistinct(_1727779), c_List_Oinsert(_1727779, _1727783, _1727781))))], (47147 ^ _779448) ^ [_1727882, _1727884, _1727886] : [hBOOL(hAPP(hAPP(c_member(_1727882), _1727884), hAPP(c_List_Oset(_1727882), _1727886))), -(c_List_Oinsert(_1727882, _1727884, _1727886) = _1727886)], (47153 ^ _779448) ^ [_1727993, _1727995, _1727997] : [-(hAPP(c_List_Oset(_1727993), c_List_Oinsert(_1727993, _1727995, _1727997)) = hAPP(hAPP(c_Set_Oinsert(_1727993), _1727995), hAPP(c_List_Oset(_1727993), _1727997)))], (47155 ^ _779448) ^ [_1728042, _1728044] : [-(c_List_Oinsert(_1728042, _1728044, c_List_Olist_ONil(_1728042)) = hAPP(hAPP(c_List_Olist_OCons(_1728042), _1728044), c_List_Olist_ONil(_1728042)))], (47157 ^ _779448) ^ [_1728083, _1728085, _1728087, _1728089] : [-(c_List_Omaps(_1728083, _1728085, _1728087, _1728089) = c_List_Oconcat(_1728085, hAPP(hAPP(c_List_Omap(_1728083, tc_List_Olist(_1728085)), _1728087), _1728089)))], (47159 ^ _779448) ^ [_1728131, _1728133, _1728135, _1728137] : [-(c_List_Oconcat(_1728131, hAPP(hAPP(c_List_Omap(_1728133, tc_List_Olist(_1728131)), _1728135), _1728137)) = c_List_Omaps(_1728133, _1728131, _1728135, _1728137))], (47161 ^ _779448) ^ [_1728179, _1728181, _1728183] : [-(c_List_Omaps(_1728179, _1728181, _1728183, c_List_Olist_ONil(_1728179)) = c_List_Olist_ONil(_1728181))], (47163 ^ _779448) ^ [_1728215, _1728217, _1728219, _1728221, _1728223] : [-(c_List_Omaps(_1728215, _1728217, _1728219, hAPP(hAPP(c_List_Olist_OCons(_1728215), _1728221), _1728223)) = hAPP(hAPP(c_List_Oappend(_1728217), hAPP(_1728219, _1728221)), c_List_Omaps(_1728215, _1728217, _1728219, _1728223)))], (47165 ^ _779448) ^ [_1728275, _1728277] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1728275)), _1728277)), 47171 ^ _779448 : [(47172 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728275)), 47170 ^ [_1728275, _1728277]), hAPP(c_List_Oset(tc_List_Olist(_1728275)), _1728277))))], (47174 ^ _779448) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1728275), 47170 ^ [_1728275, _1728277]))]], 47178 ^ _779448 : [(47179 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728275)), 47177 ^ [_1728275, _1728277]), hAPP(c_List_Oset(tc_List_Olist(_1728275)), _1728277))))], (47182 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728275)), 47180 ^ [_1728275, _1728277]), hAPP(c_List_Oset(tc_List_Olist(_1728275)), _1728277))))], (47184 ^ _779448) ^ [] : [47177 ^ [_1728275, _1728277] = 47180 ^ [_1728275, _1728277]], (47186 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728275, tc_HOL_Obool)), hAPP(c_List_Oset(_1728275), 47177 ^ [_1728275, _1728277])), hAPP(c_List_Oset(_1728275), 47180 ^ [_1728275, _1728277])) = c_Orderings_Obot__class_Obot(tc_fun(_1728275, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1728275), c_List_Oconcat(_1728275, _1728277))))], (47190 ^ _779448) ^ [_1728992, _1728994, _1728996, _1728998, _1729000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1728992, _1728994)), hAPP(_1728992, _1728996))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1728998, _1728998)), hAPP(hAPP(c_Product__Type_OPair(_1728998, _1728998), _1728994), _1728996)), c_List_Omeasures(_1728998, _1729000))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1728998, _1728998)), hAPP(hAPP(c_Product__Type_OPair(_1728998, _1728998), _1728994), _1728996)), c_List_Omeasures(_1728998, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1728998, tc_Nat_Onat)), _1728992), _1729000)))))], (47200 ^ _779448) ^ [_1729265, _1729267] : [-(c_Wellfounded_Owf(_1729265, c_List_Omeasures(_1729265, _1729267)))], (47202 ^ _779448) ^ [_1729308, _1729310, _1729312] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729308, _1729308)), hAPP(hAPP(c_Product__Type_OPair(_1729308, _1729308), _1729310), _1729312)), c_List_Omeasures(_1729308, c_List_Olist_ONil(tc_fun(_1729308, tc_Nat_Onat)))))], (47204 ^ _779448) ^ [_1729362, _1729364] : [-(c_List_Omeasures(_1729362, _1729364) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1729362), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1729362, tc_List_Olist(tc_fun(_1729362, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729362, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1729362, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1729362), c_List_Omap(tc_fun(_1729362, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1729362, tc_Nat_Onat), _1729362, tc_Nat_Onat), c_COMBI(tc_fun(_1729362, tc_Nat_Onat))))), _1729364)))], (47206 ^ _779448) ^ [_1729459, _1729461, _1729463, _1729465, _1729467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729459, _1729461)), hAPP(_1729459, _1729463))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729465, _1729465)), hAPP(hAPP(c_Product__Type_OPair(_1729465, _1729465), _1729461), _1729463)), c_List_Omeasures(_1729465, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729465, tc_Nat_Onat)), _1729459), _1729467)))))], (47212 ^ _779448) ^ [_1729654, _1729656, _1729658, _1729660, _1729662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729654, _1729654)), hAPP(hAPP(c_Product__Type_OPair(_1729654, _1729654), _1729656), _1729658)), c_List_Omeasures(_1729654, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729654, tc_Nat_Onat)), _1729660), _1729662)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729660, _1729656)), hAPP(_1729660, _1729658)))), 47219 ^ _779448 : [(47220 ^ _779448) ^ [] : [-(hAPP(_1729660, _1729656) = hAPP(_1729660, _1729658))], (47222 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729654, _1729654)), hAPP(hAPP(c_Product__Type_OPair(_1729654, _1729654), _1729656), _1729658)), c_List_Omeasures(_1729654, _1729662))))]]], (47224 ^ _779448) ^ [_1729933, _1729935, _1729937, _1729939, _1729941] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729933, _1729933)), hAPP(hAPP(c_Product__Type_OPair(_1729933, _1729933), _1729935), _1729937)), c_List_Omeasures(_1729933, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729933, tc_Nat_Onat)), _1729939), _1729941))))), 47225 ^ _779448 : [(47226 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729939, _1729935)), hAPP(_1729939, _1729937)))], (47228 ^ _779448) ^ [] : [hAPP(_1729939, _1729935) = hAPP(_1729939, _1729937), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729933, _1729933)), hAPP(hAPP(c_Product__Type_OPair(_1729933, _1729933), _1729935), _1729937)), c_List_Omeasures(_1729933, _1729941)))]]], (47236 ^ _779448) ^ [_1730256, _1730258, _1730260, _1730262, _1730264, _1730266, _1730268, _1730270] : [47238 ^ _779448 : [(47239 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730256), 47237 ^ [_1730256, _1730258, _1730260, _1730262, _1730264, _1730266, _1730268, _1730270]), hAPP(c_List_Oset(_1730256), _1730258))))], (47241 ^ _779448) ^ [] : [hAPP(c_Fun_Ocomp(_1730260, _1730260, _1730262, hAPP(_1730264, 47237 ^ [_1730256, _1730258, _1730260, _1730262, _1730264, _1730266, _1730268, _1730270])), _1730266) = hAPP(c_Fun_Ocomp(_1730262, _1730260, _1730262, _1730266), hAPP(_1730268, 47237 ^ [_1730256, _1730258, _1730260, _1730262, _1730264, _1730266, _1730268, _1730270]))]], -(hAPP(c_List_Ofoldl(_1730260, _1730256, hAPP(c_COMBC(_1730256, _1730260, _1730260), _1730264), hAPP(_1730266, _1730270)), _1730258) = hAPP(_1730266, hAPP(c_List_Ofoldl(_1730262, _1730256, hAPP(c_COMBC(_1730256, _1730262, _1730262), _1730268), _1730270), _1730258)))], (47245 ^ _779448) ^ [_1730625, _1730627, _1730629, _1730631] : [class_Orderings_Oorder(_1730625), class_Enum_Oenum(_1730627), 47252 ^ _779448 : [(47253 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730627, _1730625)), _1730629), _1730631)), 47256 ^ _779448 : [(47257 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730627, _1730625)), _1730629), _1730631)))], (47259 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730627), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730627), c_fNot), hAPP(hAPP(c_COMBS(_1730627, _1730625, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730625, tc_fun(_1730625, tc_HOL_Obool), _1730627), c_fequal), _1730629)), _1730631)))))]]], (47261 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730627, _1730625)), _1730629), _1730631))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730627, _1730625)), _1730629), _1730631)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730627), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730627), c_fNot), hAPP(hAPP(c_COMBS(_1730627, _1730625, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730625, tc_fun(_1730625, tc_HOL_Obool), _1730627), c_fequal), _1730629)), _1730631))))]]], (47271 ^ _779448) ^ [_1731145, _1731147, _1731149] : [class_Enum_Oenum(_1731145), class_Enum_Oenum(_1731147), 47278 ^ _779448 : [(47279 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731147, _1731145)), _1731149)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731147), hAPP(hAPP(c_COMBB(tc_fun(_1731145, tc_HOL_Obool), tc_HOL_Obool, _1731147), c_Enum_Oenum__class_Oenum__ex(_1731145)), hAPP(hAPP(c_COMBB(tc_fun(_1731145, tc_prod(_1731147, _1731145)), tc_fun(_1731145, tc_HOL_Obool), _1731147), hAPP(c_COMBB(tc_prod(_1731147, _1731145), tc_HOL_Obool, _1731145), _1731149)), c_Product__Type_OPair(_1731147, _1731145))))))], (47285 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731147), hAPP(hAPP(c_COMBB(tc_fun(_1731145, tc_HOL_Obool), tc_HOL_Obool, _1731147), c_Enum_Oenum__class_Oenum__ex(_1731145)), hAPP(hAPP(c_COMBB(tc_fun(_1731145, tc_prod(_1731147, _1731145)), tc_fun(_1731145, tc_HOL_Obool), _1731147), hAPP(c_COMBB(tc_prod(_1731147, _1731145), tc_HOL_Obool, _1731145), _1731149)), c_Product__Type_OPair(_1731147, _1731145))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731147, _1731145)), _1731149)))]]], (47291 ^ _779448) ^ [_1731584, _1731586] : [class_Enum_Oenum(_1731584), 47294 ^ _779448 : [(47295 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731584), _1731586)), -(hBOOL(hAPP(_1731586, 47298 ^ [_1731584, _1731586])))], (47302 ^ _779448) ^ [] : [47303 ^ _779448 : [(47304 ^ _779448) ^ [_1731764] : [hBOOL(hAPP(_1731586, _1731764))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731584), _1731586)))]]], (47308 ^ _779448) ^ [_1731827, _1731829] : [class_Enum_Oenum(_1731827), 47311 ^ _779448 : [(47312 ^ _779448) ^ [] : [47313 ^ _779448 : [(47314 ^ _779448) ^ [_1731929] : [hBOOL(hAPP(_1731829, _1731929))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731827), _1731829)))], (47318 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731827), _1731829)), -(hBOOL(hAPP(_1731829, 47321 ^ [_1731827, _1731829])))]]], (47325 ^ _779448) ^ [_1732070, _1732072, _1732074, _1732076, _1732078] : [47326 ^ _779448 : [(47327 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732070)), hAPP(hAPP(c_List_Otake(_1732070), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732070)), _1732072)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732074)), _1732076))), _1732072)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732074)), hAPP(hAPP(c_List_Otake(_1732074), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732070)), _1732072)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732074)), _1732076))), _1732076)))], (47329 ^ _779448) ^ [] : [hBOOL(hAPP(_1732078, hAPP(hAPP(c_List_Ozip(_1732070, _1732074), hAPP(hAPP(c_List_Otake(_1732070), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732070)), _1732072)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732074)), _1732076))), _1732072)), hAPP(hAPP(c_List_Otake(_1732074), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732070)), _1732072)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732074)), _1732076))), _1732076))))]], -(hBOOL(hAPP(_1732078, hAPP(hAPP(c_List_Ozip(_1732070, _1732074), _1732072), _1732076))))], (47333 ^ _779448) ^ [_1732482, _1732484, _1732486, _1732488] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1732482, _1732484, _1732486, _1732488) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1732482, _1732484), _1732486), _1732488)))], (47335 ^ _779448) ^ [_1732527, _1732529, _1732531, _1732533] : [47337 ^ _779448 : [(47338 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732527), 47336 ^ [_1732527, _1732529, _1732531, _1732533]), hAPP(c_List_Oset(_1732527), _1732529))))], (47340 ^ _779448) ^ [] : [hBOOL(hAPP(_1732531, 47336 ^ [_1732527, _1732529, _1732531, _1732533]))]], -(c_List_OdropWhile(_1732527, _1732531, hAPP(hAPP(c_List_Oappend(_1732527), _1732529), _1732533)) = c_List_OdropWhile(_1732527, _1732531, _1732533))], (47344 ^ _779448) ^ [_1732745, _1732747, _1732749, _1732751, _1732753] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732745)), _1732747) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732749)), _1732751), 47350 ^ _779448 : [(47351 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47349 ^ [_1732745, _1732747, _1732749, _1732751, _1732753]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732745)), _1732747))))], (47353 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1732753, hAPP(hAPP(c_List_Onth(_1732745), _1732747), 47349 ^ [_1732745, _1732747, _1732749, _1732751, _1732753])), hAPP(hAPP(c_List_Onth(_1732749), _1732751), 47349 ^ [_1732745, _1732747, _1732749, _1732751, _1732753])))]], -(c_List_Olist__all2(_1732745, _1732749, _1732753, _1732747, _1732751))], (47357 ^ _779448) ^ [_1733103, _1733105] : [class_Orderings_Olinorder(_1733103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1733103), _1733105)), 47365 ^ _779448 : [(47366 ^ _779448) ^ [] : [-(hAPP(c_List_Oset(_1733103), 47364 ^ [_1733103, _1733105]) = _1733105)], (47368 ^ _779448) ^ [] : [-(c_List_Olinorder__class_Osorted(_1733103, 47364 ^ [_1733103, _1733105]))], (47370 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1733103), 47364 ^ [_1733103, _1733105])))], (47372 ^ _779448) ^ [_1733429] : [-(_1733429 = 47364 ^ [_1733103, _1733105]), hAPP(c_List_Oset(_1733103), _1733429) = _1733105, c_List_Olinorder__class_Osorted(_1733103, _1733429), hBOOL(hAPP(c_List_Odistinct(_1733103), _1733429))]]], (47386 ^ _779448) ^ [_1733660, _1733662, _1733664, _1733666] : [47388 ^ _779448 : [(47389 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733660), 47387 ^ [_1733660, _1733662, _1733664, _1733666]), hAPP(c_List_Oset(_1733660), _1733662))))], (47391 ^ _779448) ^ [] : [hBOOL(hAPP(_1733664, 47387 ^ [_1733660, _1733662, _1733664, _1733666]))]], -(c_List_OtakeWhile(_1733660, _1733664, hAPP(hAPP(c_List_Oappend(_1733660), _1733662), _1733666)) = hAPP(hAPP(c_List_Oappend(_1733660), _1733662), c_List_OtakeWhile(_1733660, _1733664, _1733666)))], (47395 ^ _779448) ^ [_1733894, _1733896, _1733898, _1733900, _1733902] : [class_Orderings_Olinorder(_1733894), 47401 ^ _779448 : [(47402 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733896), 47400 ^ [_1733894, _1733896, _1733898, _1733900, _1733902]), hAPP(c_List_Oset(_1733896), _1733898))))], (47404 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1733894), hAPP(_1733900, _1733902)), hAPP(_1733900, 47400 ^ [_1733894, _1733896, _1733898, _1733900, _1733902])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733896, _1733894, _1733900), _1733902), _1733898) = hAPP(hAPP(c_List_Olist_OCons(_1733896), _1733902), _1733898))], (47408 ^ _779448) ^ [_1734237, _1734239, _1734241, _1734243, _1734245] : [hAPP(hAPP(c_List_Olist_OCons(_1734237), _1734239), _1734241) = hAPP(c_List_Ofilter(_1734237, _1734243), _1734245), 47413 ^ _779448 : [(47414 ^ _779448) ^ [] : [-(_1734245 = hAPP(hAPP(c_List_Oappend(_1734237), 47411 ^ [_1734237, _1734239, _1734241, _1734243, _1734245]), hAPP(hAPP(c_List_Olist_OCons(_1734237), _1734239), 47412 ^ [_1734237, _1734239, _1734241, _1734243, _1734245])))], (47422 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1734243, _1734239)))], (47424 ^ _779448) ^ [] : [-(_1734241 = hAPP(c_List_Ofilter(_1734237, _1734243), 47412 ^ [_1734237, _1734239, _1734241, _1734243, _1734245]))], (47416 ^ _779448) ^ [_1734551] : [hBOOL(hAPP(hAPP(c_member(_1734237), _1734551), hAPP(c_List_Oset(_1734237), 47411 ^ [_1734237, _1734239, _1734241, _1734243, _1734245]))), hBOOL(hAPP(_1734243, _1734551))]]], (47426 ^ _779448) ^ [_1734755, _1734757, _1734759, _1734761, _1734763] : [-(hAPP(hAPP(c_List_Olist_OCons(_1734755), _1734757), _1734759) = hAPP(c_List_Ofilter(_1734755, _1734761), _1734763)), 47427 ^ _779448 : [(47428 ^ _779448) ^ [_1734883, _1734885] : [_1734763 = hAPP(hAPP(c_List_Oappend(_1734755), _1734885), hAPP(hAPP(c_List_Olist_OCons(_1734755), _1734757), _1734883)), 47434 ^ _779448 : [(47435 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734755), 47433 ^ [_1734755, _1734757, _1734759, _1734761, _1734763, _1734883, _1734885]), hAPP(c_List_Oset(_1734755), _1734885))))], (47437 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1734761, 47433 ^ [_1734755, _1734757, _1734759, _1734761, _1734763, _1734883, _1734885])))]], hBOOL(hAPP(_1734761, _1734757)), _1734759 = hAPP(c_List_Ofilter(_1734755, _1734761), _1734883)]]], (47447 ^ _779448) ^ [_1735305, _1735307, _1735309, _1735311, _1735313] : [hAPP(c_List_Ofilter(_1735305, _1735307), _1735309) = hAPP(hAPP(c_List_Olist_OCons(_1735305), _1735311), _1735313), 47452 ^ _779448 : [(47453 ^ _779448) ^ [] : [-(_1735309 = hAPP(hAPP(c_List_Oappend(_1735305), 47450 ^ [_1735305, _1735307, _1735309, _1735311, _1735313]), hAPP(hAPP(c_List_Olist_OCons(_1735305), _1735311), 47451 ^ [_1735305, _1735307, _1735309, _1735311, _1735313])))], (47461 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1735307, _1735311)))], (47463 ^ _779448) ^ [] : [-(_1735313 = hAPP(c_List_Ofilter(_1735305, _1735307), 47451 ^ [_1735305, _1735307, _1735309, _1735311, _1735313]))], (47455 ^ _779448) ^ [_1735619] : [hBOOL(hAPP(hAPP(c_member(_1735305), _1735619), hAPP(c_List_Oset(_1735305), 47450 ^ [_1735305, _1735307, _1735309, _1735311, _1735313]))), hBOOL(hAPP(_1735307, _1735619))]]], (47465 ^ _779448) ^ [_1735823, _1735825, _1735827, _1735829, _1735831] : [-(hAPP(c_List_Ofilter(_1735823, _1735825), _1735827) = hAPP(hAPP(c_List_Olist_OCons(_1735823), _1735829), _1735831)), 47466 ^ _779448 : [(47467 ^ _779448) ^ [_1735951, _1735953] : [_1735827 = hAPP(hAPP(c_List_Oappend(_1735823), _1735953), hAPP(hAPP(c_List_Olist_OCons(_1735823), _1735829), _1735951)), 47473 ^ _779448 : [(47474 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735823), 47472 ^ [_1735823, _1735825, _1735827, _1735829, _1735831, _1735951, _1735953]), hAPP(c_List_Oset(_1735823), _1735953))))], (47476 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1735825, 47472 ^ [_1735823, _1735825, _1735827, _1735829, _1735831, _1735951, _1735953])))]], hBOOL(hAPP(_1735825, _1735829)), _1735831 = hAPP(c_List_Ofilter(_1735823, _1735825), _1735951)]]], (47486 ^ _779448) ^ [_1736349, _1736351, _1736353, _1736355] : [class_Orderings_Oorder(_1736349), class_Enum_Oenum(_1736351), 47493 ^ _779448 : [(47494 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736351, _1736349)), _1736353), _1736355)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736351), hAPP(hAPP(c_COMBS(_1736351, _1736349, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736349, tc_fun(_1736349, tc_HOL_Obool), _1736351), c_Orderings_Oord__class_Oless__eq(_1736349)), _1736353)), _1736355))))], (47500 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736351), hAPP(hAPP(c_COMBS(_1736351, _1736349, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736349, tc_fun(_1736349, tc_HOL_Obool), _1736351), c_Orderings_Oord__class_Oless__eq(_1736349)), _1736353)), _1736355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736351, _1736349)), _1736353), _1736355)))]]], (47506 ^ _779448) ^ [_1736739, _1736741] : [class_Enum_Oenum(_1736739), 47509 ^ _779448 : [(47510 ^ _779448) ^ [] : [hBOOL(hAPP(_1736741, 47511 ^ [_1736739, _1736741])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736739), _1736741)))], (47517 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736739), _1736741)), 47520 ^ _779448 : [(47521 ^ _779448) ^ [_1736957] : [-(hBOOL(hAPP(_1736741, _1736957)))]]]]], (47523 ^ _779448) ^ [_1736992, _1736994] : [class_Enum_Oenum(_1736992), 47526 ^ _779448 : [(47527 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736992), _1736994)), 47530 ^ _779448 : [(47531 ^ _779448) ^ [_1737118] : [-(hBOOL(hAPP(_1736994, _1737118)))]]], (47533 ^ _779448) ^ [] : [hBOOL(hAPP(_1736994, 47534 ^ [_1736992, _1736994])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736992), _1736994)))]]], (47540 ^ _779448) ^ [_1737245, _1737247, _1737249] : [class_Enum_Oenum(_1737245), class_Enum_Oenum(_1737247), 47547 ^ _779448 : [(47548 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737247, _1737245)), _1737249)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737247), hAPP(hAPP(c_COMBB(tc_fun(_1737245, tc_HOL_Obool), tc_HOL_Obool, _1737247), c_Enum_Oenum__class_Oenum__all(_1737245)), hAPP(hAPP(c_COMBB(tc_fun(_1737245, tc_prod(_1737247, _1737245)), tc_fun(_1737245, tc_HOL_Obool), _1737247), hAPP(c_COMBB(tc_prod(_1737247, _1737245), tc_HOL_Obool, _1737245), _1737249)), c_Product__Type_OPair(_1737247, _1737245))))))], (47554 ^ _779448) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737247), hAPP(hAPP(c_COMBB(tc_fun(_1737245, tc_HOL_Obool), tc_HOL_Obool, _1737247), c_Enum_Oenum__class_Oenum__all(_1737245)), hAPP(hAPP(c_COMBB(tc_fun(_1737245, tc_prod(_1737247, _1737245)), tc_fun(_1737245, tc_HOL_Obool), _1737247), hAPP(c_COMBB(tc_prod(_1737247, _1737245), tc_HOL_Obool, _1737245), _1737249)), c_Product__Type_OPair(_1737247, _1737245))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737247, _1737245)), _1737249)))]]], (47560 ^ _779448) ^ [_1737684, _1737686, _1737688, _1737690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737686)), _1737688))), 47566 ^ _779448 : [(47567 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737686), 47565 ^ [_1737684, _1737686, _1737688, _1737690]), hAPP(c_List_Oset(_1737686), _1737688))))], (47569 ^ _779448) ^ [] : [hBOOL(hAPP(_1737690, 47565 ^ [_1737684, _1737686, _1737688, _1737690]))]], -(hBOOL(hAPP(_1737690, hAPP(hAPP(c_List_Onth(_1737686), _1737688), _1737684))))], (47573 ^ _779448) ^ [_1737970, _1737972, _1737974] : [class_Orderings_Olinorder(_1737970), 47579 ^ _779448 : [(47580 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737970), 47578 ^ [_1737970, _1737972, _1737974]), hAPP(c_List_Oset(_1737970), _1737972))))], (47582 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1737970), _1737974), 47578 ^ [_1737970, _1737972, _1737974]))]], c_List_Olinorder__class_Osorted(_1737970, _1737972), -(c_List_Olinorder__class_Osorted(_1737970, hAPP(hAPP(c_List_Olist_OCons(_1737970), _1737974), _1737972)))], (47590 ^ _779448) ^ [_1738304, _1738306, _1738308] : [c_List_Olist__ex(_1738304, _1738306, _1738308), 47594 ^ _779448 : [(47595 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47593 ^ [_1738304, _1738306, _1738308]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738304)), _1738308))))], (47597 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1738306, hAPP(hAPP(c_List_Onth(_1738304), _1738308), 47593 ^ [_1738304, _1738306, _1738308]))))]]], (47599 ^ _779448) ^ [_1738474, _1738476, _1738478] : [-(c_List_Olist__ex(_1738474, _1738476, _1738478)), 47600 ^ _779448 : [(47601 ^ _779448) ^ [_1738539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738539), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738474)), _1738478))), hBOOL(hAPP(_1738476, hAPP(hAPP(c_List_Onth(_1738474), _1738478), _1738539)))]]], (47609 ^ _779448) ^ [_1738712, _1738714, _1738716] : [hBOOL(hAPP(hAPP(c_member(_1738712), _1738714), hAPP(c_List_Oset(_1738712), _1738716))), -(_1738716 = hAPP(hAPP(c_List_Oappend(_1738712), 47612 ^ [_1738712, _1738714, _1738716]), hAPP(hAPP(c_List_Olist_OCons(_1738712), _1738714), 47613 ^ [_1738712, _1738714, _1738716])))], (47617 ^ _779448) ^ [_1738871, _1738873, _1738875] : [47618 ^ _779448 : [(47619 ^ _779448) ^ [_1738948, _1738950] : [_1738875 = hAPP(hAPP(c_List_Oappend(_1738871), _1738950), hAPP(hAPP(c_List_Olist_OCons(_1738871), _1738873), _1738948))]], -(hBOOL(hAPP(hAPP(c_member(_1738871), _1738873), hAPP(c_List_Oset(_1738871), _1738875))))], (47623 ^ _779448) ^ [_1739043, _1739045] : [c_List_Olist__ex(_1739043, _1739045, c_List_Olist_ONil(_1739043))], (47635 ^ _779448) ^ [_1739204, _1739206, _1739208, _1739210] : [47636 ^ _779448 : [(47637 ^ _779448) ^ [] : [c_List_Olist__ex(_1739204, _1739206, _1739208)], (47639 ^ _779448) ^ [] : [c_List_Olist__ex(_1739204, _1739206, _1739210)]], -(c_List_Olist__ex(_1739204, _1739206, hAPP(hAPP(c_List_Oappend(_1739204), _1739208), _1739210)))], (47625 ^ _779448) ^ [_1739092, _1739094, _1739096, _1739098] : [c_List_Olist__ex(_1739092, _1739094, hAPP(hAPP(c_List_Oappend(_1739092), _1739096), _1739098)), -(c_List_Olist__ex(_1739092, _1739094, _1739096)), -(c_List_Olist__ex(_1739092, _1739094, _1739098))], (47643 ^ _779448) ^ [_1739365, _1739367, _1739369] : [c_List_Olist__ex(_1739365, _1739367, _1739369), 47647 ^ _779448 : [(47648 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739365), 47646 ^ [_1739365, _1739367, _1739369]), hAPP(c_List_Oset(_1739365), _1739369))))], (47650 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1739367, 47646 ^ [_1739365, _1739367, _1739369])))]]], (47652 ^ _779448) ^ [_1739519, _1739521, _1739523] : [-(c_List_Olist__ex(_1739519, _1739521, _1739523)), 47653 ^ _779448 : [(47654 ^ _779448) ^ [_1739576] : [hBOOL(hAPP(hAPP(c_member(_1739519), _1739576), hAPP(c_List_Oset(_1739519), _1739523))), hBOOL(hAPP(_1739521, _1739576))]]], (47662 ^ _779448) ^ [_1739733, _1739735, _1739737] : [c_List_Olist__ex(_1739733, _1739735, hAPP(c_List_Orev(_1739733), _1739737)), -(c_List_Olist__ex(_1739733, _1739735, _1739737))], (47668 ^ _779448) ^ [_1739822, _1739824, _1739826] : [c_List_Olist__ex(_1739822, _1739824, _1739826), -(c_List_Olist__ex(_1739822, _1739824, hAPP(c_List_Orev(_1739822), _1739826)))], (47684 ^ _779448) ^ [_1740052, _1740054, _1740056, _1740058] : [47685 ^ _779448 : [(47686 ^ _779448) ^ [] : [hBOOL(hAPP(_1740054, _1740056))], (47688 ^ _779448) ^ [] : [c_List_Olist__ex(_1740052, _1740054, _1740058)]], -(c_List_Olist__ex(_1740052, _1740054, hAPP(hAPP(c_List_Olist_OCons(_1740052), _1740056), _1740058)))], (47674 ^ _779448) ^ [_1739938, _1739940, _1739942, _1739944] : [c_List_Olist__ex(_1739938, _1739940, hAPP(hAPP(c_List_Olist_OCons(_1739938), _1739942), _1739944)), -(hBOOL(hAPP(_1739940, _1739942))), -(c_List_Olist__ex(_1739938, _1739940, _1739944))], (47692 ^ _779448) ^ [_1740215, _1740217, _1740219] : [hBOOL(hAPP(hAPP(c_member(_1740215), _1740217), hAPP(c_List_Oset(_1740215), _1740219))), 47697 ^ _779448 : [(47698 ^ _779448) ^ [] : [-(_1740219 = hAPP(hAPP(c_List_Oappend(_1740215), 47695 ^ [_1740215, _1740217, _1740219]), hAPP(hAPP(c_List_Olist_OCons(_1740215), _1740217), 47696 ^ [_1740215, _1740217, _1740219])))], (47700 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740215), _1740217), hAPP(c_List_Oset(_1740215), 47695 ^ [_1740215, _1740217, _1740219])))]]], (47702 ^ _779448) ^ [_1740470, _1740472, _1740474] : [-(hBOOL(hAPP(hAPP(c_member(_1740470), _1740472), hAPP(c_List_Oset(_1740470), _1740474)))), 47703 ^ _779448 : [(47704 ^ _779448) ^ [_1740559] : [47705 ^ _779448 : [(47706 ^ _779448) ^ [_1740632] : [_1740474 = hAPP(hAPP(c_List_Oappend(_1740470), _1740559), hAPP(hAPP(c_List_Olist_OCons(_1740470), _1740472), _1740632))]], -(hBOOL(hAPP(hAPP(c_member(_1740470), _1740472), hAPP(c_List_Oset(_1740470), _1740559))))]]], (47712 ^ _779448) ^ [_1740771, _1740773, _1740775] : [hBOOL(hAPP(hAPP(c_member(_1740771), _1740773), hAPP(c_List_Oset(_1740771), _1740775))), 47717 ^ _779448 : [(47718 ^ _779448) ^ [] : [-(_1740775 = hAPP(hAPP(c_List_Oappend(_1740771), 47715 ^ [_1740771, _1740773, _1740775]), hAPP(hAPP(c_List_Olist_OCons(_1740771), _1740773), 47716 ^ [_1740771, _1740773, _1740775])))], (47720 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740771), _1740773), hAPP(c_List_Oset(_1740771), 47716 ^ [_1740771, _1740773, _1740775])))]]], (47722 ^ _779448) ^ [_1741026, _1741028, _1741030] : [-(hBOOL(hAPP(hAPP(c_member(_1741026), _1741028), hAPP(c_List_Oset(_1741026), _1741030)))), 47723 ^ _779448 : [(47724 ^ _779448) ^ [_1741115, _1741117] : [_1741030 = hAPP(hAPP(c_List_Oappend(_1741026), _1741117), hAPP(hAPP(c_List_Olist_OCons(_1741026), _1741028), _1741115)), -(hBOOL(hAPP(hAPP(c_member(_1741026), _1741028), hAPP(c_List_Oset(_1741026), _1741115))))]]], (47742 ^ _779448) ^ [_1741530, _1741532, _1741534] : [47744 ^ _779448 : [(47745 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47743 ^ [_1741530, _1741532, _1741534]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741530)), _1741534))))], (47747 ^ _779448) ^ [] : [hBOOL(hAPP(_1741532, hAPP(hAPP(c_List_Onth(_1741530), _1741534), 47743 ^ [_1741530, _1741532, _1741534])))]], -(c_List_Olist__all(_1741530, _1741532, _1741534))], (47732 ^ _779448) ^ [_1741316, _1741318, _1741320] : [c_List_Olist__all(_1741316, _1741318, _1741320), 47735 ^ _779448 : [(47736 ^ _779448) ^ [_1741405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741405), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741316)), _1741320))), -(hBOOL(hAPP(_1741318, hAPP(hAPP(c_List_Onth(_1741316), _1741320), _1741405))))]]], (47751 ^ _779448) ^ [] : [-(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))))], (47753 ^ _779448) ^ [_1741756, _1741758] : [-(c_List_Olist__all(_1741756, _1741758, c_List_Olist_ONil(_1741756)))], (47755 ^ _779448) ^ [_1741805, _1741807, _1741809, _1741811] : [c_List_Olist__all(_1741805, _1741807, hAPP(hAPP(c_List_Oappend(_1741805), _1741809), _1741811)), 47758 ^ _779448 : [(47759 ^ _779448) ^ [] : [-(c_List_Olist__all(_1741805, _1741807, _1741809))], (47761 ^ _779448) ^ [] : [-(c_List_Olist__all(_1741805, _1741807, _1741811))]]], (47763 ^ _779448) ^ [_1741930, _1741932, _1741934, _1741936] : [-(c_List_Olist__all(_1741930, _1741932, hAPP(hAPP(c_List_Oappend(_1741930), _1741934), _1741936))), c_List_Olist__all(_1741930, _1741932, _1741934), c_List_Olist__all(_1741930, _1741932, _1741936)], (47773 ^ _779448) ^ [_1742091] : [class_Nat_Osize(_1742091), -(c_FunDef_Ois__measure(_1742091, c_Nat_Osize__class_Osize(_1742091)))], (47779 ^ _779448) ^ [_1742168, _1742170] : [-(c_FunDef_Ois__measure(_1742168, _1742170))], (47781 ^ _779448) ^ [_1742193, _1742195] : [-(c_FunDef_Ois__measure(_1742193, _1742195))], (47783 ^ _779448) ^ [_1742218, _1742220] : [-(c_FunDef_Ois__measure(_1742218, _1742220))], (47795 ^ _779448) ^ [_1742451, _1742453, _1742455] : [47797 ^ _779448 : [(47798 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742451), 47796 ^ [_1742451, _1742453, _1742455]), hAPP(c_List_Oset(_1742451), _1742455))))], (47800 ^ _779448) ^ [] : [hBOOL(hAPP(_1742453, 47796 ^ [_1742451, _1742453, _1742455]))]], -(c_List_Olist__all(_1742451, _1742453, _1742455))], (47785 ^ _779448) ^ [_1742261, _1742263, _1742265] : [c_List_Olist__all(_1742261, _1742263, _1742265), 47788 ^ _779448 : [(47789 ^ _779448) ^ [_1742342] : [hBOOL(hAPP(hAPP(c_member(_1742261), _1742342), hAPP(c_List_Oset(_1742261), _1742265))), -(hBOOL(hAPP(_1742263, _1742342)))]]], (47804 ^ _779448) ^ [_1742633, _1742635, _1742637] : [c_FunDef_Ois__measure(_1742633, _1742635), -(c_FunDef_Ois__measure(tc_prod(_1742633, _1742637), hAPP(hAPP(c_COMBB(_1742633, tc_Nat_Onat, tc_prod(_1742633, _1742637)), _1742635), c_Product__Type_Ofst(_1742633, _1742637))))], (47810 ^ _779448) ^ [_1742750, _1742752, _1742754] : [c_FunDef_Ois__measure(_1742750, _1742752), -(c_FunDef_Ois__measure(tc_prod(_1742754, _1742750), hAPP(hAPP(c_COMBB(_1742750, tc_Nat_Onat, tc_prod(_1742754, _1742750)), _1742752), c_Product__Type_Osnd(_1742754, _1742750))))], (47816 ^ _779448) ^ [_1742885, _1742887, _1742889] : [c_List_Olist__all(_1742885, _1742887, hAPP(c_List_Orev(_1742885), _1742889)), -(c_List_Olist__all(_1742885, _1742887, _1742889))], (47822 ^ _779448) ^ [_1742974, _1742976, _1742978] : [c_List_Olist__all(_1742974, _1742976, _1742978), -(c_List_Olist__all(_1742974, _1742976, hAPP(c_List_Orev(_1742974), _1742978)))], (47828 ^ _779448) ^ [_1743090, _1743092, _1743094, _1743096] : [c_List_Olist__all(_1743090, _1743092, hAPP(hAPP(c_List_Olist_OCons(_1743090), _1743094), _1743096)), 47831 ^ _779448 : [(47832 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1743092, _1743094)))], (47834 ^ _779448) ^ [] : [-(c_List_Olist__all(_1743090, _1743092, _1743096))]]], (47836 ^ _779448) ^ [_1743217, _1743219, _1743221, _1743223] : [-(c_List_Olist__all(_1743217, _1743219, hAPP(hAPP(c_List_Olist_OCons(_1743217), _1743221), _1743223))), hBOOL(hAPP(_1743219, _1743221)), c_List_Olist__all(_1743217, _1743219, _1743223)], (47846 ^ _779448) ^ [_1743398, _1743400, _1743402] : [47848 ^ _779448 : [(47849 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743398), 47847 ^ [_1743398, _1743400, _1743402]), hAPP(c_List_Oset(_1743398), _1743400))))], (47851 ^ _779448) ^ [] : [hBOOL(hAPP(_1743402, 47847 ^ [_1743398, _1743400, _1743402]))]], -(c_List_Olist__all(_1743398, _1743402, _1743400))], (47855 ^ _779448) ^ [_1743574, _1743576, _1743578] : [c_List_Olist__all(_1743574, _1743578, _1743576), 47858 ^ _779448 : [(47859 ^ _779448) ^ [_1743655] : [hBOOL(hAPP(hAPP(c_member(_1743574), _1743655), hAPP(c_List_Oset(_1743574), _1743576))), -(hBOOL(hAPP(_1743578, _1743655)))]]], (47875 ^ _779448) ^ [_1743978, _1743980, _1743982] : [47877 ^ _779448 : [(47878 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743978), 47876 ^ [_1743978, _1743980, _1743982]), hAPP(c_List_Oset(_1743978), _1743982))))], (47880 ^ _779448) ^ [] : [hBOOL(hAPP(_1743980, 47876 ^ [_1743978, _1743980, _1743982]))]], -(c_List_Olist__all(_1743978, _1743980, _1743982))], (47865 ^ _779448) ^ [_1743788, _1743790, _1743792] : [c_List_Olist__all(_1743788, _1743790, _1743792), 47868 ^ _779448 : [(47869 ^ _779448) ^ [_1743869] : [hBOOL(hAPP(hAPP(c_member(_1743788), _1743869), hAPP(c_List_Oset(_1743788), _1743792))), -(hBOOL(hAPP(_1743790, _1743869)))]]], (47900 ^ _779448) ^ [_1744457, _1744459, _1744461, _1744463] : [-(c_List_Olist__ex1(_1744457, _1744459, hAPP(hAPP(c_List_Olist_OCons(_1744457), _1744461), _1744463))), 47903 ^ _779448 : [(47904 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1744459, _1744461)))], (47906 ^ _779448) ^ [] : [c_List_Olist__all(_1744457, hAPP(hAPP(c_COMBS(_1744457, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744457), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744457), c_fNot), _1744459))), hAPP(c_fequal, _1744461)), _1744463)]], 47907 ^ _779448 : [(47908 ^ _779448) ^ [] : [hBOOL(hAPP(_1744459, _1744461))], (47910 ^ _779448) ^ [] : [c_List_Olist__ex1(_1744457, _1744459, _1744463)]]], (47884 ^ _779448) ^ [_1744181, _1744183, _1744185, _1744187] : [c_List_Olist__ex1(_1744181, _1744183, hAPP(hAPP(c_List_Olist_OCons(_1744181), _1744185), _1744187)), 47887 ^ _779448 : [(47888 ^ _779448) ^ [] : [hBOOL(hAPP(_1744183, _1744185)), -(c_List_Olist__all(_1744181, hAPP(hAPP(c_COMBS(_1744181, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744181), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744181), c_fNot), _1744183))), hAPP(c_fequal, _1744185)), _1744187))], (47894 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1744183, _1744185))), -(c_List_Olist__ex1(_1744181, _1744183, _1744187))]]], (47914 ^ _779448) ^ [] : [-(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)))], (47916 ^ _779448) ^ [_1744795, _1744797] : [c_List_Olist__ex1(_1744795, _1744797, c_List_Olist_ONil(_1744795))], (47918 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47920 ^ _779448) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47922 ^ _779448) ^ [_1744877, _1744879, _1744881] : [c_List_Olist__ex1(_1744877, _1744879, _1744881), 47926 ^ _779448 : [(47927 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744877), 47925 ^ [_1744877, _1744879, _1744881]), hAPP(c_List_Oset(_1744877), _1744881))))], (47929 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1744879, 47925 ^ [_1744877, _1744879, _1744881])))], (47931 ^ _779448) ^ [_1745123] : [-(_1745123 = 47925 ^ [_1744877, _1744879, _1744881]), hBOOL(hAPP(hAPP(c_member(_1744877), _1745123), hAPP(c_List_Oset(_1744877), _1744881))), hBOOL(hAPP(_1744879, _1745123))]]], (47941 ^ _779448) ^ [_1745310, _1745312, _1745314] : [-(c_List_Olist__ex1(_1745310, _1745312, _1745314)), 47942 ^ _779448 : [(47943 ^ _779448) ^ [_1745404] : [hBOOL(hAPP(hAPP(c_member(_1745310), _1745404), hAPP(c_List_Oset(_1745310), _1745314))), hBOOL(hAPP(_1745312, _1745404)), 47951 ^ _779448 : [(47952 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745310), 47950 ^ [_1745310, _1745312, _1745314, _1745404]), hAPP(c_List_Oset(_1745310), _1745314))))], (47954 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1745312, 47950 ^ [_1745310, _1745312, _1745314, _1745404])))], (47956 ^ _779448) ^ [] : [47950 ^ [_1745310, _1745312, _1745314, _1745404] = _1745404]]]]], (47960 ^ _779448) ^ [_1745757, _1745759, _1745761, _1745763, _1745765] : [_1745757 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1745759, _1745761, _1745763, _1745765), _1745757) = c_Lazy__Sequence_Ohit__bound(_1745761))], (47966 ^ _779448) ^ [_1745854, _1745856, _1745858, _1745860, _1745862] : [-(_1745854 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1745856, _1745858, _1745860, _1745862), _1745854) = c_Lazy__Sequence_Ohb__bind(_1745856, _1745858, hAPP(_1745860, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1745854), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1745856, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1745858))), _1745862), _1745854)))], (47972 ^ _779448) ^ [_1745952, _1745954, _1745956, _1745958, _1745960] : [_1745952 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1745954, _1745956, _1745958, _1745960), _1745952) = c_Lazy__Sequence_Oempty(_1745956))], (47978 ^ _779448) ^ [_1746049, _1746051, _1746053, _1746055, _1746057] : [-(_1746049 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746051, _1746053, _1746055, _1746057), _1746049) = hAPP(c_Lazy__Sequence_Obind(_1746051, _1746053, hAPP(_1746055, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746049), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1746051, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746053)), _1746057), _1746049)))], (47984 ^ _779448) ^ [_1746129, _1746131, _1746133, _1746135, _1746137, _1746139, _1746141] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1746129, _1746131, _1746133, _1746135, _1746137, _1746139, _1746141) = c_New__DSequence_Oneg__decr__bind(_1746129, _1746131, hAPP(hAPP(hAPP(_1746133, _1746137), _1746139), _1746141), hAPP(hAPP(c_COMBC(_1746129, 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(_1746131)))), hAPP(hAPP(c_COMBC(_1746129, 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(_1746131))))), hAPP(hAPP(c_COMBC(_1746129, 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(_1746131)))))), _1746135), _1746137)), _1746139)), _1746141)))], (47986 ^ _779448) ^ [_1746246, _1746248, _1746250, _1746252, _1746254, _1746256, _1746258] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746246, _1746248, _1746250, _1746252, _1746254, _1746256, _1746258) = c_New__DSequence_Opos__decr__bind(_1746246, _1746248, hAPP(hAPP(hAPP(_1746250, _1746254), _1746256), _1746258), hAPP(hAPP(c_COMBC(_1746246, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746248))), hAPP(hAPP(c_COMBC(_1746246, 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(_1746248)))), hAPP(hAPP(c_COMBC(_1746246, 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(_1746248))))), _1746252), _1746254)), _1746256)), _1746258)))], (47988 ^ _779448) ^ [_1746357, _1746359, _1746361, _1746363, _1746365] : [-(hAPP(c_New__DSequence_Oneg__bind(_1746357, _1746359, _1746361, _1746363), _1746365) = c_Lazy__Sequence_Ohb__bind(_1746357, _1746359, hAPP(_1746361, _1746365), hAPP(hAPP(c_COMBC(_1746357, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746359))), _1746363), _1746365)))], (47990 ^ _779448) ^ [_1746418, _1746420] : [-(hAPP(c_New__DSequence_Opos__empty(_1746418), _1746420) = c_Lazy__Sequence_Oempty(_1746418))], (47992 ^ _779448) ^ [_1746450, _1746452, _1746454, _1746456] : [-(c_New__Random__Sequence_Opos__empty(_1746450, _1746452, _1746454, _1746456) = c_New__DSequence_Opos__empty(_1746450))], (47994 ^ _779448) ^ [_1746486, _1746488, _1746490, _1746492, _1746494, _1746496, _1746498] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1746486, _1746488, _1746490, _1746492), _1746494), _1746496), _1746498) = c_New__DSequence_Oneg__bind(_1746486, _1746488, hAPP(hAPP(hAPP(_1746490, _1746494), _1746496), _1746498), hAPP(hAPP(c_COMBC(_1746486, 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(_1746488)))), hAPP(hAPP(c_COMBC(_1746486, 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(_1746488))))), hAPP(hAPP(c_COMBC(_1746486, 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(_1746488)))))), _1746492), _1746494)), _1746496)), _1746498)))], (47996 ^ _779448) ^ [_1746609, _1746611, _1746613, _1746615, _1746617] : [-(hAPP(c_New__DSequence_Opos__bind(_1746609, _1746611, _1746613, _1746615), _1746617) = hAPP(c_Lazy__Sequence_Obind(_1746609, _1746611, hAPP(_1746613, _1746617)), hAPP(hAPP(c_COMBC(_1746609, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746611)), _1746615), _1746617)))], (47998 ^ _779448) ^ [_1746670, _1746672, _1746674, _1746676] : [-(c_New__Random__Sequence_Oneg__map(_1746670, _1746672, _1746674, _1746676) = c_New__Random__Sequence_Oneg__bind(_1746670, _1746672, _1746676, hAPP(c_Fun_Ocomp(_1746672, 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(_1746672)))))), _1746670, c_New__Random__Sequence_Oneg__single(_1746672)), _1746674)))], (48000 ^ _779448) ^ [_1746735, _1746737, _1746739, _1746741, _1746743] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1746735), _1746737), _1746739), _1746741), _1746743) = c_New__DSequence_Oneg__single(_1746735, _1746737))], (48002 ^ _779448) ^ [_1746783, _1746785, _1746787, _1746789, _1746791, _1746793, _1746795] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1746783, _1746785, _1746787, _1746789), _1746791), _1746793), _1746795) = c_New__DSequence_Opos__bind(_1746783, _1746785, hAPP(hAPP(hAPP(_1746787, _1746791), _1746793), _1746795), hAPP(hAPP(c_COMBC(_1746783, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746785))), hAPP(hAPP(c_COMBC(_1746783, 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(_1746785)))), hAPP(hAPP(c_COMBC(_1746783, 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(_1746785))))), _1746789), _1746791)), _1746793)), _1746795)))], (48004 ^ _779448) ^ [_1746900, _1746902, _1746904] : [-(hAPP(c_New__DSequence_Oneg__single(_1746900, _1746902), _1746904) = c_Lazy__Sequence_Ohb__single(_1746900, _1746902))], (48006 ^ _779448) ^ [_1746936, _1746938, _1746940, _1746942] : [-(c_New__Random__Sequence_Opos__map(_1746936, _1746938, _1746940, _1746942) = c_New__Random__Sequence_Opos__bind(_1746936, _1746938, _1746942, hAPP(c_Fun_Ocomp(_1746938, 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(_1746938))))), _1746936, c_New__Random__Sequence_Opos__single(_1746938)), _1746940)))], (48008 ^ _779448) ^ [_1746999, _1747001, _1747003, _1747005, _1747007] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1746999), _1747001), _1747003), _1747005), _1747007) = c_New__DSequence_Opos__single(_1746999, _1747001))], (48010 ^ _779448) ^ [_1747047, _1747049, _1747051] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747047)), c_List_Osplice(_1747047, _1747049, _1747051)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747047)), _1747049)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747047)), _1747051)))], (48012 ^ _779448) ^ [_1747105, _1747107, _1747109, _1747111, _1747113] : [-(c_List_Osplice(_1747105, hAPP(hAPP(c_List_Olist_OCons(_1747105), _1747107), _1747109), hAPP(hAPP(c_List_Olist_OCons(_1747105), _1747111), _1747113)) = hAPP(hAPP(c_List_Olist_OCons(_1747105), _1747107), hAPP(hAPP(c_List_Olist_OCons(_1747105), _1747111), c_List_Osplice(_1747105, _1747109, _1747113))))], (48014 ^ _779448) ^ [_1747176, _1747178] : [-(c_List_Osplice(_1747176, c_List_Olist_ONil(_1747176), _1747178) = _1747178)], (48016 ^ _779448) ^ [_1747207, _1747209] : [-(c_List_Osplice(_1747207, _1747209, c_List_Olist_ONil(_1747207)) = _1747209)], (48018 ^ _779448) ^ [_1747238, _1747240, _1747242] : [-(c_List_Osplice(_1747238, hAPP(hAPP(c_List_Olist_OCons(_1747238), _1747240), _1747242), c_List_Olist_ONil(_1747238)) = hAPP(hAPP(c_List_Olist_OCons(_1747238), _1747240), _1747242))], (48020 ^ _779448) ^ [_1747287, _1747289, _1747291] : [-(hAPP(c_New__DSequence_Opos__single(_1747287, _1747289), _1747291) = hAPP(c_Lazy__Sequence_Osingle(_1747287), _1747289))], (48022 ^ _779448) ^ [_1747340, _1747342] : [c_Wellfounded_Oacyclic(_1747340, hAPP(c_Set_OCollect(tc_prod(_1747340, _1747340)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747340, _1747340, tc_HOL_Obool), c_Predicate_Oconversep(_1747340, _1747340, _1747342)))), -(c_Wellfounded_Oacyclic(_1747340, hAPP(c_Set_OCollect(tc_prod(_1747340, _1747340)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747340, _1747340, tc_HOL_Obool), _1747342))))], (48028 ^ _779448) ^ [_1747481, _1747483] : [c_Wellfounded_Oacyclic(_1747481, hAPP(c_Set_OCollect(tc_prod(_1747481, _1747481)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747481, _1747481, tc_HOL_Obool), _1747483))), -(c_Wellfounded_Oacyclic(_1747481, hAPP(c_Set_OCollect(tc_prod(_1747481, _1747481)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747481, _1747481, tc_HOL_Obool), c_Predicate_Oconversep(_1747481, _1747481, _1747483)))))], (48034 ^ _779448) ^ [_1747628, _1747630, _1747632, _1747634] : [-(c_Predicate_Oconversep(_1747628, _1747630, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747628, tc_fun(_1747630, tc_HOL_Obool))), _1747632), _1747634)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747630, tc_fun(_1747628, tc_HOL_Obool))), c_Predicate_Oconversep(_1747628, _1747630, _1747632)), c_Predicate_Oconversep(_1747628, _1747630, _1747634)))], (48036 ^ _779448) ^ [_1747697, _1747699, _1747701, _1747703] : [-(c_Predicate_Oconversep(_1747697, _1747699, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747697, tc_fun(_1747699, tc_HOL_Obool))), _1747701), _1747703)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747699, tc_fun(_1747697, tc_HOL_Obool))), c_Predicate_Oconversep(_1747697, _1747699, _1747701)), c_Predicate_Oconversep(_1747697, _1747699, _1747703)))], (48038 ^ _779448) ^ [_1747784, _1747786, _1747788] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747784, _1747784, hAPP(hAPP(c_COMBB(tc_fun(_1747784, tc_HOL_Obool), tc_fun(_1747784, tc_HOL_Obool), _1747784), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1747784), c_fNot)), c_fequal)), _1747786), _1747788)), _1747786 = _1747788], (48044 ^ _779448) ^ [_1747922, _1747924, _1747926] : [-(_1747924 = _1747926), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747922, _1747922, hAPP(hAPP(c_COMBB(tc_fun(_1747922, tc_HOL_Obool), tc_fun(_1747922, tc_HOL_Obool), _1747922), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1747922), c_fNot)), c_fequal)), _1747924), _1747926)))], (48050 ^ _779448) ^ [_1747994, _1747996, _1747998, _1748000, _1748002] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747994, _1747996, _1747998), _1748000), _1748002)), -(hBOOL(hAPP(hAPP(_1747998, _1748002), _1748000)))], (48056 ^ _779448) ^ [_1748105, _1748107, _1748109, _1748111, _1748113] : [hBOOL(hAPP(hAPP(_1748105, _1748107), _1748109)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748111, _1748113, _1748105), _1748109), _1748107)))], (48062 ^ _779448) ^ [_1748240, _1748242, _1748244, _1748246, _1748248] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748240, _1748242, _1748244), _1748246), _1748248)), -(hBOOL(hAPP(hAPP(_1748244, _1748248), _1748246)))], (48068 ^ _779448) ^ [_1748347, _1748349, _1748351, _1748353, _1748355] : [hBOOL(hAPP(hAPP(_1748351, _1748355), _1748353)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748347, _1748349, _1748351), _1748353), _1748355)))], (48074 ^ _779448) ^ [_1748484, _1748486, _1748488, _1748490, _1748492] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748484, _1748486, _1748488), _1748490), _1748492)), -(hBOOL(hAPP(hAPP(_1748488, _1748492), _1748490)))], (48080 ^ _779448) ^ [_1748591, _1748593, _1748595, _1748597, _1748599] : [hBOOL(hAPP(hAPP(_1748595, _1748599), _1748597)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748591, _1748593, _1748595), _1748597), _1748599)))], (48086 ^ _779448) ^ [_1748704, _1748706, _1748708] : [-(c_Predicate_Oconversep(_1748704, _1748706, c_Predicate_Oconversep(_1748706, _1748704, _1748708)) = _1748708)], (48088 ^ _779448) ^ [_1748739] : [-(c_Predicate_Oconversep(_1748739, _1748739, c_fequal) = c_fequal)], (48090 ^ _779448) ^ [_1748766, _1748768, _1748770, _1748772, _1748774] : [-(c_Predicate_Oconversep(_1748766, _1748768, c_Predicate_Opred__comp(_1748766, _1748770, _1748768, _1748772, _1748774)) = c_Predicate_Opred__comp(_1748768, _1748770, _1748766, c_Predicate_Oconversep(_1748770, _1748768, _1748774), c_Predicate_Oconversep(_1748766, _1748770, _1748772)))], (48092 ^ _779448) ^ [_1748845, _1748847, _1748849, _1748851, _1748853] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748845, _1748847, hAPP(hAPP(c_COMBC(_1748845, tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_fun(_1748847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1748847, tc_fun(tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_fun(_1748847, tc_HOL_Obool)), _1748845), c_COMBC(_1748847, tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1748847, tc_prod(_1748845, _1748847)), tc_fun(_1748847, tc_fun(tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_HOL_Obool)), _1748845), hAPP(c_COMBB(tc_prod(_1748845, _1748847), tc_fun(tc_fun(tc_prod(_1748845, _1748847), tc_HOL_Obool), tc_HOL_Obool), _1748847), c_member(tc_prod(_1748845, _1748847)))), c_Product__Type_OPair(_1748845, _1748847)))), _1748849)), _1748851), _1748853)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748847, _1748845)), hAPP(hAPP(c_Product__Type_OPair(_1748847, _1748845), _1748851), _1748853)), hAPP(c_Relation_Oconverse(_1748845, _1748847), _1748849))))], (48098 ^ _779448) ^ [_1749228, _1749230, _1749232, _1749234, _1749236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749230, _1749228)), hAPP(hAPP(c_Product__Type_OPair(_1749230, _1749228), _1749234), _1749236)), hAPP(c_Relation_Oconverse(_1749228, _1749230), _1749232))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749228, _1749230, hAPP(hAPP(c_COMBC(_1749228, tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_fun(_1749230, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749230, tc_fun(tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_fun(_1749230, tc_HOL_Obool)), _1749228), c_COMBC(_1749230, tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749230, tc_prod(_1749228, _1749230)), tc_fun(_1749230, tc_fun(tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_HOL_Obool)), _1749228), hAPP(c_COMBB(tc_prod(_1749228, _1749230), tc_fun(tc_fun(tc_prod(_1749228, _1749230), tc_HOL_Obool), tc_HOL_Obool), _1749230), c_member(tc_prod(_1749228, _1749230)))), c_Product__Type_OPair(_1749228, _1749230)))), _1749232)), _1749234), _1749236)))], (48104 ^ _779448) ^ [_1749617, _1749619, _1749621, _1749623] : [-(c_Lazy__Sequence_Oproduct(_1749617, _1749619, _1749621, _1749623) = hAPP(c_Lazy__Sequence_Obind(_1749617, tc_prod(_1749617, _1749619), _1749621), hAPP(hAPP(c_COMBB(tc_fun(_1749619, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749617, _1749619))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749617, _1749619)), _1749617), c_Lazy__Sequence_Obind(_1749619, tc_prod(_1749617, _1749619), _1749623)), hAPP(hAPP(c_COMBB(tc_fun(_1749619, tc_prod(_1749617, _1749619)), tc_fun(_1749619, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749617, _1749619))), _1749617), hAPP(c_COMBB(tc_prod(_1749617, _1749619), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749617, _1749619)), _1749619), c_Lazy__Sequence_Osingle(tc_prod(_1749617, _1749619)))), c_Product__Type_OPair(_1749617, _1749619)))))], (48106 ^ _779448) ^ [_1749734, _1749736, _1749738] : [-(_1749734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1749736), c_List_Oreplicate(_1749736, _1749734, _1749738)) = c_List_Oreplicate(_1749736, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749734), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1749738))], (48112 ^ _779448) ^ [_1749791, _1749793, _1749795] : [-(c_List_Oreplicate(_1749791, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749791)), hAPP(c_List_Ofilter(_1749791, hAPP(c_fequal, _1749793)), _1749795)), _1749793) = hAPP(c_List_Ofilter(_1749791, hAPP(c_fequal, _1749793)), _1749795))], (48114 ^ _779448) ^ [_1749847, _1749849, _1749851] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749847)), c_List_Oreplicate(_1749847, _1749849, _1749851)) = _1749849)], (48116 ^ _779448) ^ [_1749885, _1749887, _1749889, _1749891] : [-(hAPP(hAPP(c_List_Omap(_1749885, _1749887), hAPP(c_COMBK(_1749887, _1749885), _1749889)), _1749891) = c_List_Oreplicate(_1749887, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749885)), _1749891), _1749889))], (48118 ^ _779448) ^ [_1749940, _1749942, _1749944, _1749946] : [-(hAPP(hAPP(c_List_Oappend(_1749940), c_List_Oreplicate(_1749940, _1749942, _1749944)), hAPP(hAPP(c_List_Olist_OCons(_1749940), _1749944), _1749946)) = hAPP(hAPP(c_List_Olist_OCons(_1749940), _1749944), hAPP(hAPP(c_List_Oappend(_1749940), c_List_Oreplicate(_1749940, _1749942, _1749944)), _1749946)))], (48120 ^ _779448) ^ [_1750009, _1750011, _1750013] : [-(c_List_Oreplicate(_1750009, hAPP(c_Nat_OSuc, _1750011), _1750013) = hAPP(hAPP(c_List_Olist_OCons(_1750009), _1750013), c_List_Oreplicate(_1750009, _1750011, _1750013)))], (48122 ^ _779448) ^ [_1750055, _1750057, _1750059] : [-(hAPP(c_List_Orev(_1750055), c_List_Oreplicate(_1750055, _1750057, _1750059)) = c_List_Oreplicate(_1750055, _1750057, _1750059))], (48124 ^ _779448) ^ [_1750095, _1750097, _1750099, _1750101] : [-(hAPP(hAPP(c_List_Odrop(_1750095), _1750097), c_List_Oreplicate(_1750095, _1750099, _1750101)) = c_List_Oreplicate(_1750095, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750099), _1750097), _1750101))], (48126 ^ _779448) ^ [_1750142, _1750144, _1750146] : [-(_1750142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750144), c_List_Oreplicate(_1750144, _1750142, _1750146)) = _1750146)], (48132 ^ _779448) ^ [_1750185, _1750187, _1750189] : [-(_1750185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750187, c_List_Oreplicate(_1750187, _1750185, _1750189)) = _1750189)], (48138 ^ _779448) ^ [_1750230, _1750232, _1750234, _1750236] : [-(hAPP(hAPP(c_List_Otake(_1750230), _1750232), c_List_Oreplicate(_1750230, _1750234, _1750236)) = c_List_Oreplicate(_1750230, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750232), _1750234), _1750236))], (48140 ^ _779448) ^ [_1750281, _1750283, _1750285, _1750287, _1750289, _1750291] : [-(hAPP(hAPP(c_List_Ozip(_1750281, _1750283), c_List_Oreplicate(_1750281, _1750285, _1750287)), c_List_Oreplicate(_1750283, _1750289, _1750291)) = c_List_Oreplicate(tc_prod(_1750281, _1750283), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750285), _1750289), hAPP(hAPP(c_Product__Type_OPair(_1750281, _1750283), _1750287), _1750291)))], (48142 ^ _779448) ^ [_1750374, _1750376, _1750378, _1750380] : [48149 ^ _779448 : [(48150 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1750380, _1750378)))], (48152 ^ _779448) ^ [] : [_1750376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48143 ^ _779448 : [(48144 ^ _779448) ^ [_1750446] : [hBOOL(hAPP(hAPP(c_member(_1750374), _1750446), hAPP(c_List_Oset(_1750374), c_List_Oreplicate(_1750374, _1750376, _1750378)))), hBOOL(hAPP(_1750380, _1750446))]]], (48154 ^ _779448) ^ [_1750616, _1750618, _1750620, _1750622] : [48162 ^ _779448 : [(48163 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750616), 48161 ^ [_1750616, _1750618, _1750620, _1750622]), hAPP(c_List_Oset(_1750616), c_List_Oreplicate(_1750616, _1750618, _1750620)))))], (48165 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1750622, 48161 ^ [_1750616, _1750618, _1750620, _1750622])))]], hBOOL(hAPP(_1750622, _1750620)), -(_1750618 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48167 ^ _779448) ^ [_1750872, _1750874, _1750876, _1750878] : [48169 ^ _779448 : [(48170 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750872), 48168 ^ [_1750872, _1750874, _1750876, _1750878]), hAPP(c_List_Oset(_1750872), c_List_Oreplicate(_1750872, _1750874, _1750876)))))], (48172 ^ _779448) ^ [] : [hBOOL(hAPP(_1750878, 48168 ^ [_1750872, _1750874, _1750876, _1750878]))]], -(hBOOL(hAPP(_1750878, _1750876))), -(_1750874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48180 ^ _779448) ^ [_1751079, _1751081, _1751083, _1751085] : [48181 ^ _779448 : [(48182 ^ _779448) ^ [] : [hBOOL(hAPP(_1751085, _1751083))], (48184 ^ _779448) ^ [] : [_1751081 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48185 ^ _779448 : [(48186 ^ _779448) ^ [_1751204] : [hBOOL(hAPP(hAPP(c_member(_1751079), _1751204), hAPP(c_List_Oset(_1751079), c_List_Oreplicate(_1751079, _1751081, _1751083)))), -(hBOOL(hAPP(_1751085, _1751204)))]]], (48192 ^ _779448) ^ [_1751355, _1751357, _1751359, _1751361, _1751363] : [c_List_Oreplicate(_1751355, _1751357, _1751359) = c_List_Oreplicate(_1751355, _1751361, _1751363), 48195 ^ _779448 : [(48196 ^ _779448) ^ [] : [-(_1751357 = _1751361)], (48198 ^ _779448) ^ [] : [-(_1751357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1751359 = _1751363)]]], (48204 ^ _779448) ^ [_1751491, _1751493, _1751495, _1751497, _1751499] : [-(c_List_Oreplicate(_1751491, _1751493, _1751495) = c_List_Oreplicate(_1751491, _1751497, _1751499)), _1751493 = _1751497, 48209 ^ _779448 : [(48210 ^ _779448) ^ [] : [_1751493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48212 ^ _779448) ^ [] : [_1751495 = _1751499]]], (48216 ^ _779448) ^ [_1751690, _1751692, _1751694, _1751696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751690), _1751692)), -(hAPP(hAPP(c_List_Onth(_1751694), c_List_Oreplicate(_1751694, _1751692, _1751696)), _1751690) = _1751696)], (48222 ^ _779448) ^ [_1751805, _1751807, _1751809, _1751811] : [-(c_List_Oreplicate(_1751805, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1751807), _1751809), _1751811) = hAPP(hAPP(c_List_Oappend(_1751805), c_List_Oreplicate(_1751805, _1751807, _1751811)), c_List_Oreplicate(_1751805, _1751809, _1751811)))], (48224 ^ _779448) ^ [_1751860, _1751862, _1751864, _1751866] : [-(hAPP(hAPP(c_List_Oappend(_1751860), c_List_Oreplicate(_1751860, _1751862, _1751864)), c_List_Oreplicate(_1751860, _1751866, _1751864)) = hAPP(hAPP(c_List_Oappend(_1751860), c_List_Oreplicate(_1751860, _1751866, _1751864)), c_List_Oreplicate(_1751860, _1751862, _1751864)))], (48226 ^ _779448) ^ [_1751936, _1751938, _1751940, _1751942] : [hBOOL(hAPP(_1751936, _1751938)), -(hAPP(c_List_Ofilter(_1751940, _1751936), c_List_Oreplicate(_1751940, _1751942, _1751938)) = c_List_Oreplicate(_1751940, _1751942, _1751938))], (48232 ^ _779448) ^ [_1752043, _1752045, _1752047, _1752049] : [-(hBOOL(hAPP(_1752043, _1752045))), -(hAPP(c_List_Ofilter(_1752047, _1752043), c_List_Oreplicate(_1752047, _1752049, _1752045)) = c_List_Olist_ONil(_1752047))], (48238 ^ _779448) ^ [_1752099, _1752101] : [-(c_List_Oconcat(_1752099, c_List_Oreplicate(tc_List_Olist(_1752099), _1752101, c_List_Olist_ONil(_1752099))) = c_List_Olist_ONil(_1752099))], (48240 ^ _779448) ^ [_1752137, _1752139] : [-(c_List_Oreplicate(_1752137, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1752139) = c_List_Olist_ONil(_1752137))], (48242 ^ _779448) ^ [_1752186, _1752188, _1752190] : [c_List_Olist_ONil(_1752186) = c_List_Oreplicate(_1752186, _1752188, _1752190), -(_1752188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48248 ^ _779448) ^ [_1752273, _1752275, _1752277] : [_1752275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1752273) = c_List_Oreplicate(_1752273, _1752275, _1752277))], (48254 ^ _779448) ^ [_1752384, _1752386, _1752388] : [c_List_Oreplicate(_1752384, _1752386, _1752388) = c_List_Olist_ONil(_1752384), -(_1752386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48260 ^ _779448) ^ [_1752471, _1752473, _1752475] : [_1752473 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1752471, _1752473, _1752475) = c_List_Olist_ONil(_1752471))], (48266 ^ _779448) ^ [_1752564, _1752566, _1752568, _1752570, _1752572] : [-(hAPP(hAPP(c_List_Omap(_1752564, _1752566), _1752568), c_List_Oreplicate(_1752564, _1752570, _1752572)) = c_List_Oreplicate(_1752566, _1752570, hAPP(_1752568, _1752572)))], (48268 ^ _779448) ^ [_1752636, _1752638, _1752640, _1752642] : [hBOOL(hAPP(hAPP(c_member(_1752636), _1752638), hAPP(c_List_Oset(_1752636), c_List_Oreplicate(_1752636, _1752640, _1752642)))), 48271 ^ _779448 : [(48272 ^ _779448) ^ [] : [-(_1752638 = _1752642)], (48274 ^ _779448) ^ [] : [_1752640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48276 ^ _779448) ^ [_1752779, _1752781, _1752783, _1752785] : [-(hBOOL(hAPP(hAPP(c_member(_1752779), _1752781), hAPP(c_List_Oset(_1752779), c_List_Oreplicate(_1752779, _1752783, _1752785))))), _1752781 = _1752785, -(_1752783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48286 ^ _779448) ^ [_1752953, _1752955, _1752957] : [-(hAPP(hAPP(c_List_Oappend(_1752953), c_List_Oreplicate(_1752953, _1752955, _1752957)), hAPP(hAPP(c_List_Olist_OCons(_1752953), _1752957), c_List_Olist_ONil(_1752953))) = hAPP(hAPP(c_List_Olist_OCons(_1752953), _1752957), c_List_Oreplicate(_1752953, _1752955, _1752957)))], (48288 ^ _779448) ^ [_1753014, _1753016, _1753018] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1753014), hAPP(c_COMBK(_1753014, tc_Nat_Onat), _1753016)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753018)) = c_List_Oreplicate(_1753014, _1753018, _1753016))], (48290 ^ _779448) ^ [_1753059, _1753061, _1753063] : [-(_1753059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753061), c_List_Oreplicate(_1753061, _1753059, _1753063)) = hAPP(hAPP(c_Set_Oinsert(_1753061), _1753063), c_Orderings_Obot__class_Obot(tc_fun(_1753061, tc_HOL_Obool))))], (48296 ^ _779448) ^ [_1753131, _1753133, _1753135] : [_1753131 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1753133), c_List_Oreplicate(_1753133, _1753131, _1753135)) = c_Orderings_Obot__class_Obot(tc_fun(_1753133, tc_HOL_Obool)))], (48302 ^ _779448) ^ [_1753232, _1753234, _1753236] : [-(_1753232 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753234), c_List_Oreplicate(_1753234, _1753232, _1753236)) = hAPP(hAPP(c_Set_Oinsert(_1753234), _1753236), c_Orderings_Obot__class_Obot(tc_fun(_1753234, tc_HOL_Obool))))], (48308 ^ _779448) ^ [_1753294, _1753296, _1753298] : [-(hAPP(c_List_Oset(_1753294), c_List_Oreplicate(_1753294, hAPP(c_Nat_OSuc, _1753296), _1753298)) = hAPP(hAPP(c_Set_Oinsert(_1753294), _1753298), c_Orderings_Obot__class_Obot(tc_fun(_1753294, tc_HOL_Obool))))], (48310 ^ _779448) ^ [_1753346, _1753348] : [class_Lazy__Sequence_Osmall__lazy(_1753346), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753346), _1753348) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1753346), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1753346)), c_List_Olist_ONil(_1753346)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753346))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1753348)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1753346, tc_List_Olist(_1753346)), tc_List_Olist(_1753346), c_Lazy__Sequence_Oproduct(_1753346, tc_List_Olist(_1753346), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753346, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753348), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753346), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753348), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1753346, tc_List_Olist(_1753346), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753346))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1753346), tc_List_Olist(_1753346)), tc_fun(tc_List_Olist(_1753346), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753346))), _1753346), hAPP(c_COMBB(tc_List_Olist(_1753346), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753346)), tc_List_Olist(_1753346)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1753346)))), c_List_Olist_OCons(_1753346))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1753346)))))], (48316 ^ _779448) ^ [_1753707, _1753709] : [-(c_Predicate_Opred__comp(_1753707, _1753707, _1753707, c_fequal, c_Predicate_Opred__comp(_1753707, _1753707, _1753707, _1753709, c_fequal)) = _1753709)], (48318 ^ _779448) ^ [_1753744, _1753746, _1753748] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1753744, _1753746), _1753748) = c_Lazy__Sequence_Oproduct(_1753744, _1753746, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753744, _1753748), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753746, _1753748))), class_Lazy__Sequence_Osmall__lazy(_1753744), class_Lazy__Sequence_Osmall__lazy(_1753746)], (48328 ^ _779448) ^ [_1753907, _1753909, _1753911, _1753913] : [-(hAPP(c_New__DSequence_Opos__union(_1753907, _1753909, _1753911), _1753913) = c_Lazy__Sequence_Oappend(_1753907, hAPP(_1753909, _1753913), hAPP(_1753911, _1753913)))], (48330 ^ _779448) ^ [_1753953, _1753955, _1753957] : [class_Fields_Olinordered__field(_1753953), 48336 ^ _779448 : [(48337 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1753953), c_Groups_Ozero__class_Ozero(_1753953)), 48335 ^ [_1753953, _1753955, _1753957])))], (48339 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753953), _1753955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1753953), _1753957), 48335 ^ [_1753953, _1753955, _1753957])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753953), _1753955), _1753957)))], (48343 ^ _779448) ^ [_1754231, _1754233, _1754235, _1754237, _1754239, _1754241] : [-(c_New__Random__Sequence_Opos__union(_1754231, _1754233, _1754235, _1754237, _1754239, _1754241) = c_New__DSequence_Opos__union(_1754231, hAPP(hAPP(hAPP(_1754233, _1754237), _1754239), _1754241), hAPP(hAPP(hAPP(_1754235, _1754237), _1754239), _1754241)))], (48345 ^ _779448) ^ [_1754302, _1754304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754302), _1754304)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754302, _1754304) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48351 ^ _779448) ^ [_1754389, _1754391] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754389), _1754391))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754389, _1754391) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754391), c_Lazy__Sequence_Osmall__lazy_H(_1754389, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754391), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48357 ^ _779448) ^ [_1754451] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1754451) = c_Lazy__Sequence_Osmall__lazy_H(_1754451, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1754451)))], (48359 ^ _779448) ^ [_1754483, _1754485] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1754483), _1754485))), 48362 ^ _779448 : [(48363 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754483), _1754485)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754483, _1754485) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48369 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754483), _1754485))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754483, _1754485) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754485), c_Lazy__Sequence_Osmall__lazy_H(_1754483, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754485), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48375 ^ _779448) ^ [_1754739, _1754741, _1754743] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754739)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754739, _1754741, _1754743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754739)), _1754743)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48377 ^ _779448) ^ [_1754790, _1754792, _1754794, _1754796] : [-(c_Lazy__Sequence_Oappend(_1754790, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754790, _1754792, _1754794), _1754796) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754790, _1754792, c_Lazy__Sequence_Oappend(_1754790, _1754794, _1754796)))], (48379 ^ _779448) ^ [_1754859, _1754861, _1754863, _1754865, _1754867] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1754859, _1754861, _1754863) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754859, _1754865, _1754867), 48382 ^ _779448 : [(48383 ^ _779448) ^ [] : [-(_1754861 = _1754865)], (48385 ^ _779448) ^ [] : [-(_1754863 = _1754867)]]], (48387 ^ _779448) ^ [_1754980, _1754982, _1754984, _1754986, _1754988] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1754980, _1754982, _1754984) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754980, _1754986, _1754988)), _1754982 = _1754986, _1754984 = _1754988], (48397 ^ _779448) ^ [_1755139, _1755141, _1755143, _1755145] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755139, _1755141), c_Lazy__Sequence_Olazy__sequence_OInsert(_1755139, _1755143, _1755145)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1755141, _1755143)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755139, _1755141), _1755145))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48399 ^ _779448) ^ [_1755199, _1755201, _1755203] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755199), _1755201))), -(hBOOL(hAPP(hAPP(_1755203, _1755199), _1755201))), 48406 ^ _779448 : [(48407 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 48404 ^ [_1755199, _1755201, _1755203]), 48405 ^ [_1755199, _1755201, _1755203]))))], (48415 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1755203, 48404 ^ [_1755199, _1755201, _1755203]), 48405 ^ [_1755199, _1755201, _1755203]))], (48409 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48404 ^ [_1755199, _1755201, _1755203]), 48405 ^ [_1755199, _1755201, _1755203]))), -(hBOOL(hAPP(hAPP(_1755203, 48404 ^ [_1755199, _1755201, _1755203]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48405 ^ [_1755199, _1755201, _1755203]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48419 ^ _779448) ^ [_1755651, _1755653] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755651)), _1755653) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755651, tc_Lazy__Sequence_Olazy__sequence(_1755651)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755651, tc_Lazy__Sequence_Olazy__sequence(_1755651), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755651), tc_Nat_Onat), _1755651), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755651), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755651)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755651)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1755651), _1755653)))], (48421 ^ _779448) ^ [_1755747, _1755749, _1755751] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755747, _1755749), _1755751) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755747, tc_Lazy__Sequence_Olazy__sequence(_1755747)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755747, tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1755747, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat)), _1755747), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1755747), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755747)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1755747, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755747), tc_Nat_Onat)), _1755747), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1755747))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1755747), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1755749))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755747, _1755749))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1755747), _1755751)))], (48423 ^ _779448) ^ [_1755940, _1755942, _1755944, _1755946, _1755948] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1755940, _1755942, _1755944, _1755946, _1755948) = c_Option_Ooption_Ooption__case(_1755940, tc_prod(_1755942, tc_Lazy__Sequence_Olazy__sequence(_1755942)), _1755944, hAPP(c_Product__Type_Oprod_Oprod__case(_1755942, tc_Lazy__Sequence_Olazy__sequence(_1755942), _1755940), _1755946), hAPP(c_Lazy__Sequence_Oyield(_1755942), _1755948)))], (48425 ^ _779448) ^ [_1756002] : [-(c_Lazy__Sequence_Oyieldn(_1756002) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1756002), _1756002, c_Lazy__Sequence_Oyield(_1756002)))], (48427 ^ _779448) ^ [_1756035, _1756037, _1756039, _1756041, _1756043, _1756045] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756035, _1756037, _1756039, _1756041, c_Lazy__Sequence_Olazy__sequence_OInsert(_1756037, _1756043, _1756045)) = hAPP(hAPP(_1756041, _1756043), _1756045))], (48429 ^ _779448) ^ [_1756084, _1756086, _1756088, _1756090, _1756092] : [48431 ^ _779448 : [(48432 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756084), 48430 ^ [_1756084, _1756086, _1756088, _1756090, _1756092]), _1756086)))], (48434 ^ _779448) ^ [] : [c_Relation_Orefl__on(_1756088, hAPP(_1756090, 48430 ^ [_1756084, _1756086, _1756088, _1756090, _1756092]), hAPP(_1756092, 48430 ^ [_1756084, _1756086, _1756088, _1756090, _1756092]))]], -(c_Relation_Orefl__on(_1756088, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756084, tc_fun(_1756088, tc_HOL_Obool)), _1756086), _1756090), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756084, tc_fun(tc_prod(_1756088, _1756088), tc_HOL_Obool)), _1756086), _1756092)))], (48438 ^ _779448) ^ [_1756370, _1756372, _1756374] : [hBOOL(hAPP(hAPP(c_member(_1756370), _1756372), hAPP(c_List_Oset(_1756370), _1756374))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756370), _1756374), _1756372)))], (48444 ^ _779448) ^ [_1756483, _1756485, _1756487] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756483), _1756487), _1756485)), -(hBOOL(hAPP(hAPP(c_member(_1756483), _1756485), hAPP(c_List_Oset(_1756483), _1756487))))], (48460 ^ _779448) ^ [_1756757, _1756759, _1756761, _1756763] : [48461 ^ _779448 : [(48462 ^ _779448) ^ [] : [_1756759 = _1756763], (48464 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756757), _1756761), _1756763))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1756757), hAPP(hAPP(c_List_Olist_OCons(_1756757), _1756759), _1756761)), _1756763)))], (48450 ^ _779448) ^ [_1756623, _1756625, _1756627, _1756629] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756623), hAPP(hAPP(c_List_Olist_OCons(_1756623), _1756625), _1756627)), _1756629)), -(_1756625 = _1756629), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756623), _1756627), _1756629)))], (48468 ^ _779448) ^ [_1756922] : [-(c_List_Omember(_1756922) = c_List_Oset(_1756922))], (48470 ^ _779448) ^ [_1756961, _1756963] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756961), c_List_Olist_ONil(_1756961)), _1756963))], (48472 ^ _779448) ^ [_1757013, _1757015, _1757017] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757013), _1757015), _1757017)), -(hBOOL(hAPP(hAPP(c_member(_1757013), _1757017), hAPP(c_List_Oset(_1757013), _1757015))))], (48478 ^ _779448) ^ [_1757126, _1757128, _1757130] : [hBOOL(hAPP(hAPP(c_member(_1757126), _1757130), hAPP(c_List_Oset(_1757126), _1757128))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757126), _1757128), _1757130)))], (48484 ^ _779448) ^ [_1757263, _1757265, _1757267] : [c_List_Olist__ex1(_1757263, _1757265, _1757267), 48488 ^ _779448 : [(48489 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757263), 48487 ^ [_1757263, _1757265, _1757267]), hAPP(c_List_Oset(_1757263), _1757267))))], (48491 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1757265, 48487 ^ [_1757263, _1757265, _1757267])))], (48493 ^ _779448) ^ [_1757509] : [-(_1757509 = 48487 ^ [_1757263, _1757265, _1757267]), hBOOL(hAPP(hAPP(c_member(_1757263), _1757509), hAPP(c_List_Oset(_1757263), _1757267))), hBOOL(hAPP(_1757265, _1757509))]]], (48503 ^ _779448) ^ [_1757696, _1757698, _1757700] : [-(c_List_Olist__ex1(_1757696, _1757698, _1757700)), 48504 ^ _779448 : [(48505 ^ _779448) ^ [_1757790] : [hBOOL(hAPP(hAPP(c_member(_1757696), _1757790), hAPP(c_List_Oset(_1757696), _1757700))), hBOOL(hAPP(_1757698, _1757790)), 48513 ^ _779448 : [(48514 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757696), 48512 ^ [_1757696, _1757698, _1757700, _1757790]), hAPP(c_List_Oset(_1757696), _1757700))))], (48516 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1757698, 48512 ^ [_1757696, _1757698, _1757700, _1757790])))], (48518 ^ _779448) ^ [] : [48512 ^ [_1757696, _1757698, _1757700, _1757790] = _1757790]]]]], (48522 ^ _779448) ^ [_1758125, _1758127, _1758129, _1758131] : [class_Groups_Ocomm__monoid__add(_1758125), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1758127, tc_HOL_Obool)), _1758129)), 48532 ^ _779448 : [(48533 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758127, tc_HOL_Obool)), 48531 ^ [_1758125, _1758127, _1758129, _1758131]), _1758129)))], (48535 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1758127), 48531 ^ [_1758125, _1758127, _1758129, _1758131]))]], 48539 ^ _779448 : [(48540 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758127, tc_HOL_Obool)), 48538 ^ [_1758125, _1758127, _1758129, _1758131]), _1758129)))], (48543 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758127, tc_HOL_Obool)), 48541 ^ [_1758125, _1758127, _1758129, _1758131]), _1758129)))], (48545 ^ _779448) ^ [] : [48538 ^ [_1758125, _1758127, _1758129, _1758131] = 48541 ^ [_1758125, _1758127, _1758129, _1758131]], (48548 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758127), 48546 ^ [_1758125, _1758127, _1758129, _1758131]), 48538 ^ [_1758125, _1758127, _1758129, _1758131])))], (48550 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758127), 48546 ^ [_1758125, _1758127, _1758129, _1758131]), 48541 ^ [_1758125, _1758127, _1758129, _1758131])))], (48552 ^ _779448) ^ [] : [hAPP(_1758131, 48546 ^ [_1758125, _1758127, _1758129, _1758131]) = c_Groups_Ozero__class_Ozero(_1758125)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758127, _1758125), _1758131), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1758127, tc_HOL_Obool), _1758129)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1758127, tc_HOL_Obool), _1758125), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758127, _1758125), _1758131)), _1758129))], (48556 ^ _779448) ^ [_1759134, _1759136, _1759138] : [-(c_FunDef_OTHE__default(_1759136, _1759138, _1759134) = c_HOL_OThe(_1759136, _1759134)), 48557 ^ _779448 : [(48558 ^ _779448) ^ [_1759198] : [hBOOL(hAPP(_1759134, _1759198)), 48562 ^ _779448 : [(48563 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1759134, 48561 ^ [_1759134, _1759136, _1759138, _1759198])))], (48565 ^ _779448) ^ [] : [48561 ^ [_1759134, _1759136, _1759138, _1759198] = _1759198]]]]], (48569 ^ _779448) ^ [_1759392, _1759394, _1759396] : [-(c_FunDef_OTHE__default(_1759394, _1759396, _1759392) = _1759396), 48571 ^ _779448 : [(48572 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1759392, 48570 ^ [_1759392, _1759394, _1759396])))], (48574 ^ _779448) ^ [_1759514] : [hBOOL(hAPP(_1759392, _1759514)), -(_1759514 = 48570 ^ [_1759392, _1759394, _1759396])]]], (48582 ^ _779448) ^ [_1759653, _1759655, _1759657, _1759659, _1759661, _1759663, _1759665] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1759653, tc_fun(_1759655, tc_fun(_1759657, tc_HOL_Obool))), _1759659), _1759661), _1759663), _1759665)), 48586 ^ _779448 : [(48587 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759653), 48585 ^ [_1759653, _1759655, _1759657, _1759659, _1759661, _1759663, _1759665]), _1759659)))], (48589 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1759661, 48585 ^ [_1759653, _1759655, _1759657, _1759659, _1759661, _1759663, _1759665]), _1759663), _1759665)))]]], (48591 ^ _779448) ^ [_1759879, _1759881, _1759883, _1759885, _1759887, _1759889, _1759891] : [48593 ^ _779448 : [(48594 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759879), 48592 ^ [_1759879, _1759881, _1759883, _1759885, _1759887, _1759889, _1759891]), _1759881)))], (48596 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1759883, 48592 ^ [_1759879, _1759881, _1759883, _1759885, _1759887, _1759889, _1759891]), _1759885), _1759887))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1759879, tc_fun(_1759889, tc_fun(_1759891, tc_HOL_Obool))), _1759881), _1759883), _1759885), _1759887)))], (48600 ^ _779448) ^ [_1760137, _1760139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760137)), _1760139)), 48604 ^ _779448 : [(48605 ^ _779448) ^ [_1760238] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760137)), _1760238), _1760139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760137)), _1760238)), 48603 ^ [_1760137, _1760139])))]]], (48611 ^ _779448) ^ [_1760377, _1760379] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760377, _1760379), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760377)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48613 ^ _779448) ^ [_1760410] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760410)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760410)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48615 ^ _779448) ^ [_1760442, _1760444] : [-(c_Lazy__Sequence_Oappend(_1760442, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760442), _1760444) = _1760444)], (48617 ^ _779448) ^ [_1760488, _1760490, _1760492] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760488, _1760490, _1760492) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760488)], (48619 ^ _779448) ^ [_1760536, _1760538, _1760540] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760536) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760536, _1760538, _1760540)], (48621 ^ _779448) ^ [_1760569, _1760571, _1760573, _1760575] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1760569, _1760571, _1760573, _1760575, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760571)) = _1760573)], (48623 ^ _779448) ^ [_1760624, _1760626, _1760628] : [c_List_Olist__ex(tc_Int_Oint, _1760624, c_List_Oupto(_1760626, _1760628)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760624), _1760626, _1760628)], (48629 ^ _779448) ^ [_1760714, _1760716, _1760718] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760714), _1760716, _1760718)), -(c_List_Olist__ex(tc_Int_Oint, _1760714, c_List_Oupto(_1760716, _1760718)))], (48635 ^ _779448) ^ [_1760780, _1760782, _1760784] : [c_List_Olist__all(tc_Int_Oint, _1760780, c_List_Oupto(_1760782, _1760784)), -(c_List_Oall__interval__int(_1760780, _1760782, _1760784))], (48641 ^ _779448) ^ [_1760865, _1760867, _1760869] : [c_List_Oall__interval__int(_1760865, _1760867, _1760869), -(c_List_Olist__all(tc_Int_Oint, _1760865, c_List_Oupto(_1760867, _1760869)))], (48657 ^ _779448) ^ [_1761155, _1761157, _1761159] : [48659 ^ _779448 : [(48660 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48658 ^ [_1761155, _1761157, _1761159]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761157, _1761159))))], (48662 ^ _779448) ^ [] : [hBOOL(hAPP(_1761155, 48658 ^ [_1761155, _1761157, _1761159]))]], -(c_List_Oall__interval__int(_1761155, _1761157, _1761159))], (48647 ^ _779448) ^ [_1760974, _1760976, _1760978] : [c_List_Oall__interval__int(_1760974, _1760976, _1760978), 48650 ^ _779448 : [(48651 ^ _779448) ^ [_1761052] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1761052), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1760976, _1760978))), -(hBOOL(hAPP(_1760974, _1761052)))]]], (48666 ^ _779448) ^ [_1761331, _1761333, _1761335, _1761337] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761331, _1761333, _1761335, c_Code__Numeral_OSuc__code__numeral(_1761337)) = hAPP(hAPP(_1761335, _1761337), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761331, _1761333, _1761335, _1761337)))], (48668 ^ _779448) ^ [_1761393, _1761395, _1761397, _1761399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761393), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761395, _1761397, _1761393, _1761399) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761395)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761395)))], (48674 ^ _779448) ^ [_1761524, _1761526, _1761528, _1761530] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761524), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1761526, _1761528, _1761524, _1761530) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1761528, _1761530)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1761526, _1761528, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761524), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761530))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526))))), tc_prod(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1761526)), hAPP(hAPP(c_COMBB(_1761526, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761526)))), tc_prod(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1761526)), c_Product__Type_Ofst(_1761526, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (48680 ^ _779448) ^ [_1761903, _1761905, _1761907] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761903, _1761905, _1761907, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1761905)], (48682 ^ _779448) ^ [_1761935, _1761937, _1761939] : [-(c_Random__Sequence_Oempty(_1761935, _1761937, _1761939) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761935)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761935)))], (48684 ^ _779448) ^ [_1761984, _1761986, _1761988, _1761990] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1761984), _1761986), _1761988), _1761990) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761984)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1761984), _1761986)))], (48686 ^ _779448) ^ [_1762045, _1762047, _1762049, _1762051] : [-(c_Random__Sequence_Omap(_1762045, _1762047, _1762049, _1762051) = c_Random__Sequence_Obind(_1762045, _1762047, _1762051, hAPP(c_Fun_Ocomp(_1762047, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762047)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1762045, c_Random__Sequence_Osingle(_1762047)), _1762049)))], (48688 ^ _779448) ^ [_1762116, _1762118, _1762120, _1762122, _1762124, _1762126, _1762128] : [hBOOL(hAPP(hAPP(_1762116, hAPP(c_Product__Type_Osnd(_1762118, _1762120), _1762122)), hAPP(c_Product__Type_Ofst(_1762118, _1762120), _1762122))), 48695 ^ _779448 : [(48696 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1762116, 48694 ^ [_1762116, _1762118, _1762120, _1762122, _1762124, _1762126, _1762128]), 48693 ^ [_1762116, _1762118, _1762120, _1762122, _1762124, _1762126, _1762128])))], (48698 ^ _779448) ^ [] : [hBOOL(hAPP(_1762124, hAPP(hAPP(_1762126, 48693 ^ [_1762116, _1762118, _1762120, _1762122, _1762124, _1762126, _1762128]), 48694 ^ [_1762116, _1762118, _1762120, _1762122, _1762124, _1762126, _1762128])))]], -(hBOOL(hAPP(_1762124, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1762118, _1762120, _1762128), _1762126), _1762122))))], (48702 ^ _779448) ^ [_1762513, _1762515, _1762517, _1762519] : [-(hAPP(c_Relation_OImage(_1762513, _1762515, hAPP(c_Set_OCollect(tc_prod(_1762513, _1762515)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762513, _1762515, tc_HOL_Obool), _1762517))), _1762519) = hAPP(c_Set_OCollect(_1762515), hAPP(hAPP(c_COMBB(tc_fun(_1762513, tc_HOL_Obool), tc_HOL_Obool, _1762515), c_HOL_OEx(_1762513)), hAPP(hAPP(c_COMBB(tc_fun(_1762513, tc_HOL_Obool), tc_fun(_1762513, tc_HOL_Obool), _1762515), hAPP(c_COMBS(_1762513, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762513), c_fconj), hAPP(hAPP(c_COMBC(_1762513, tc_fun(_1762513, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762513)), _1762519)))), hAPP(c_COMBC(_1762513, _1762515, tc_HOL_Obool), _1762517)))))], (48704 ^ _779448) ^ [_1762639, _1762641, _1762643, _1762645, _1762647] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762639), tc_List_Olist(_1762639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762639), tc_List_Olist(_1762639)), _1762641), _1762643)), c_List_Olexord(_1762639, _1762645))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762639), tc_List_Olist(_1762639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762639), tc_List_Olist(_1762639)), _1762643), _1762647)), c_List_Olexord(_1762639, _1762645))), c_Relation_Otrans(_1762639, _1762645), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762639), tc_List_Olist(_1762639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762639), tc_List_Olist(_1762639)), _1762641), _1762647)), c_List_Olexord(_1762639, _1762645))))], (48718 ^ _779448) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (48720 ^ _779448) ^ [_1763036, _1763038, _1763040, _1763042] : [c_Relation_Otrans(_1763036, _1763038), c_Relation_Otrans(_1763040, _1763042), -(c_Relation_Otrans(tc_prod(_1763036, _1763040), c_Wellfounded_Olex__prod(_1763036, _1763040, _1763038, _1763042)))], (48744 ^ _779448) ^ [_1763646, _1763648] : [48747 ^ _779448 : [(48748 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763646, _1763646)), hAPP(hAPP(c_Product__Type_OPair(_1763646, _1763646), 48745 ^ [_1763646, _1763648]), 48746 ^ [_1763646, _1763648])), _1763648)))], (48751 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763646, _1763646)), hAPP(hAPP(c_Product__Type_OPair(_1763646, _1763646), 48746 ^ [_1763646, _1763648]), 48749 ^ [_1763646, _1763648])), _1763648)))], (48753 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763646, _1763646)), hAPP(hAPP(c_Product__Type_OPair(_1763646, _1763646), 48745 ^ [_1763646, _1763648]), 48749 ^ [_1763646, _1763648])), _1763648))]], -(c_Relation_Otrans(_1763646, _1763648))], (48730 ^ _779448) ^ [_1763204, _1763206] : [c_Relation_Otrans(_1763204, _1763206), 48733 ^ _779448 : [(48734 ^ _779448) ^ [_1763340, _1763342] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763204, _1763204)), hAPP(hAPP(c_Product__Type_OPair(_1763204, _1763204), _1763342), _1763340)), _1763206)), 48737 ^ _779448 : [(48738 ^ _779448) ^ [_1763483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763204, _1763204)), hAPP(hAPP(c_Product__Type_OPair(_1763204, _1763204), _1763340), _1763483)), _1763206)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763204, _1763204)), hAPP(hAPP(c_Product__Type_OPair(_1763204, _1763204), _1763342), _1763483)), _1763206)))]]]]], (48757 ^ _779448) ^ [_1764066, _1764068, _1764070, _1764072, _1764074] : [c_Relation_Otrans(_1764066, _1764068), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764066, _1764066)), hAPP(hAPP(c_Product__Type_OPair(_1764066, _1764066), _1764070), _1764072)), _1764068)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764066, _1764066)), hAPP(hAPP(c_Product__Type_OPair(_1764066, _1764066), _1764072), _1764074)), _1764068)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764066, _1764066)), hAPP(hAPP(c_Product__Type_OPair(_1764066, _1764066), _1764070), _1764074)), _1764068)))], (48771 ^ _779448) ^ [_1764379, _1764381] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1764379, tc_HOL_Obool), _1764381) = hAPP(c_Set_OCollect(_1764379), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764379, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1764379), c_HOL_OEx(tc_fun(_1764379, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764379, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1764379, tc_HOL_Obool), tc_HOL_Obool), _1764379), hAPP(c_COMBS(tc_fun(_1764379, 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(_1764379, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1764379, tc_HOL_Obool), tc_fun(tc_fun(_1764379, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1764379, tc_HOL_Obool))), _1764381)))), c_member(_1764379)))))], (48773 ^ _779448) ^ [_1764507, _1764509] : [c_Relation_Otrans(_1764507, _1764509), -(c_Relation_Otrans(_1764507, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764507, _1764507), tc_HOL_Obool)), _1764509), c_Relation_OId(_1764507))))], (48779 ^ _779448) ^ [_1764616, _1764618, _1764620, _1764622] : [c_Relation_Otrans(_1764616, _1764618), -(c_Relation_Otrans(_1764620, hAPP(hAPP(c_Relation_Oinv__image(_1764616, _1764620), _1764618), _1764622)))], (48785 ^ _779448) ^ [_1764715, _1764717] : [c_Relation_Otrans(_1764715, _1764717), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1764715, _1764715), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1764715, _1764715, _1764715), _1764717), _1764717)), _1764717)))], (48791 ^ _779448) ^ [_1764838] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1764838, tc_HOL_Obool) = c_Set_OBex(_1764838))], (48793 ^ _779448) ^ [_1764866, _1764868, _1764870] : [c_Relation_Otrans(_1764866, _1764868), c_Relation_Otrans(_1764866, _1764870), -(c_Relation_Otrans(_1764866, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1764866, _1764866), tc_HOL_Obool)), _1764868), _1764870)))], (48814 ^ _779448) ^ [_1765242, _1765244] : [48815 ^ _779448 : [(48816 ^ _779448) ^ [_1765308] : [hBOOL(hAPP(_1765244, _1765308))]], 48818 ^ _779448 : [(48819 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765242), 48817 ^ [_1765242, _1765244]), c_Orderings_Otop__class_Otop(tc_fun(_1765242, tc_HOL_Obool)))))], (48821 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1765244, 48817 ^ [_1765242, _1765244])))]]], (48803 ^ _779448) ^ [_1765042, _1765044] : [-(hBOOL(hAPP(_1765044, 48810 ^ [_1765042, _1765044]))), 48804 ^ _779448 : [(48805 ^ _779448) ^ [_1765103] : [hBOOL(hAPP(hAPP(c_member(_1765042), _1765103), c_Orderings_Otop__class_Otop(tc_fun(_1765042, tc_HOL_Obool)))), hBOOL(hAPP(_1765044, _1765103))]]], (48823 ^ _779448) ^ [_1765411, _1765413, _1765415, _1765417] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765411), _1765413)), 48826 ^ _779448 : [(48837 ^ _779448) ^ [] : [48839 ^ _779448 : [(48840 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765411), 48838 ^ [_1765411, _1765413, _1765415, _1765417]), _1765413)))], (48842 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765415), hAPP(c_Set_OCollect(_1765415), hAPP(hAPP(c_COMBC(_1765415, _1765411, tc_HOL_Obool), _1765417), 48838 ^ [_1765411, _1765413, _1765415, _1765417]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765415), hAPP(c_Set_OCollect(_1765415), hAPP(hAPP(c_COMBB(tc_fun(_1765411, tc_HOL_Obool), tc_HOL_Obool, _1765415), c_HOL_OEx(_1765411)), hAPP(hAPP(c_COMBB(tc_fun(_1765411, tc_HOL_Obool), tc_fun(_1765411, tc_HOL_Obool), _1765415), hAPP(c_COMBS(_1765411, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765411), c_fconj), hAPP(hAPP(c_COMBC(_1765411, tc_fun(_1765411, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765411)), _1765413)))), _1765417))))))], (48827 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765415), hAPP(c_Set_OCollect(_1765415), hAPP(hAPP(c_COMBB(tc_fun(_1765411, tc_HOL_Obool), tc_HOL_Obool, _1765415), c_HOL_OEx(_1765411)), hAPP(hAPP(c_COMBB(tc_fun(_1765411, tc_HOL_Obool), tc_fun(_1765411, tc_HOL_Obool), _1765415), hAPP(c_COMBS(_1765411, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765411), c_fconj), hAPP(hAPP(c_COMBC(_1765411, tc_fun(_1765411, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765411)), _1765413)))), _1765417))))), 48830 ^ _779448 : [(48831 ^ _779448) ^ [_1765719] : [hBOOL(hAPP(hAPP(c_member(_1765411), _1765719), _1765413)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765415), hAPP(c_Set_OCollect(_1765415), hAPP(hAPP(c_COMBC(_1765415, _1765411, tc_HOL_Obool), _1765417), _1765719)))))]]]]], (48846 ^ _779448) ^ [_1766130, _1766132] : [c_Relation_Otrans(_1766130, hAPP(c_Relation_Oconverse(_1766130, _1766130), _1766132)), -(c_Relation_Otrans(_1766130, _1766132))], (48852 ^ _779448) ^ [_1766215, _1766217] : [c_Relation_Otrans(_1766215, _1766217), -(c_Relation_Otrans(_1766215, hAPP(c_Relation_Oconverse(_1766215, _1766215), _1766217)))], (48858 ^ _779448) ^ [_1766306, _1766308, _1766310] : [hBOOL(hAPP(hAPP(c_member(_1766308), _1766306), c_Orderings_Obot__class_Obot(tc_fun(_1766308, tc_HOL_Obool)))), hBOOL(hAPP(_1766310, _1766306))], (48864 ^ _779448) ^ [_1766412, _1766414] : [c_Relation_Otrans(_1766412, _1766414), -(c_Relation_Otrans(tc_List_Olist(_1766412), c_List_Olistrel(_1766412, _1766414)))], (48870 ^ _779448) ^ [_1766499, _1766501] : [c_Relation_Otrans(_1766499, _1766501), -(c_Relation_Otrans(tc_List_Olist(_1766499), c_List_Olexord(_1766499, _1766501)))], (48876 ^ _779448) ^ [_1766586] : [-(c_Relation_Otrans(tc_fun(_1766586, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1766586)))], (48878 ^ _779448) ^ [_1766614] : [-(c_Relation_Otrans(_1766614, c_Relation_OId(_1766614)))], (48880 ^ _779448) ^ [_1766639, _1766641] : [-(c_Relation_Otrans(_1766639, c_Transitive__Closure_Otrancl(_1766639, _1766641)))], (48882 ^ _779448) ^ [_1766667, _1766669] : [c_Relation_Otrans(_1766667, _1766669), -(c_Transitive__Closure_Otrancl(_1766667, _1766669) = _1766669)], (48888 ^ _779448) ^ [_1766750, _1766752] : [-(c_Relation_Otrans(_1766750, c_Relation_OId__on(_1766750, _1766752)))], (48890 ^ _779448) ^ [_1766778, _1766780] : [-(c_Relation_Otrans(_1766778, c_Transitive__Closure_Ortrancl(_1766778, _1766780)))], (48902 ^ _779448) ^ [_1767014, _1767016, _1767018] : [c_List_Olist__ex(_1767014, _1767018, _1767016), 48906 ^ _779448 : [(48907 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767014), 48905 ^ [_1767014, _1767016, _1767018]), hAPP(c_List_Oset(_1767014), _1767016))))], (48909 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1767018, 48905 ^ [_1767014, _1767016, _1767018])))]]], (48892 ^ _779448) ^ [_1766824, _1766826, _1766828] : [-(c_List_Olist__ex(_1766824, _1766828, _1766826)), 48893 ^ _779448 : [(48894 ^ _779448) ^ [_1766881] : [hBOOL(hAPP(hAPP(c_member(_1766824), _1766881), hAPP(c_List_Oset(_1766824), _1766826))), hBOOL(hAPP(_1766828, _1766881))]]], (48911 ^ _779448) ^ [_1767192, _1767194, _1767196] : [c_List_Olist__ex(_1767192, _1767194, _1767196), 48915 ^ _779448 : [(48916 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767192), 48914 ^ [_1767192, _1767194, _1767196]), hAPP(c_List_Oset(_1767192), _1767196))))], (48918 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1767194, 48914 ^ [_1767192, _1767194, _1767196])))]]], (48920 ^ _779448) ^ [_1767346, _1767348, _1767350] : [-(c_List_Olist__ex(_1767346, _1767348, _1767350)), 48921 ^ _779448 : [(48922 ^ _779448) ^ [_1767403] : [hBOOL(hAPP(hAPP(c_member(_1767346), _1767403), hAPP(c_List_Oset(_1767346), _1767350))), hBOOL(hAPP(_1767348, _1767403))]]], (48930 ^ _779448) ^ [_1767542, _1767544, _1767546, _1767548] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767542, tc_fun(_1767544, tc_HOL_Obool)), _1767546), _1767548) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767544, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767544, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767542, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767544, tc_HOL_Obool)), c_HOL_OEx(_1767542)), hAPP(hAPP(c_COMBB(tc_fun(_1767542, tc_HOL_Obool), tc_fun(_1767542, tc_HOL_Obool), tc_fun(_1767544, tc_HOL_Obool)), hAPP(c_COMBS(_1767542, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767542), c_fconj), hAPP(hAPP(c_COMBC(_1767542, tc_fun(_1767542, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767542)), _1767546)))), hAPP(hAPP(c_COMBC(tc_fun(_1767544, tc_HOL_Obool), tc_fun(_1767542, tc_fun(_1767544, tc_HOL_Obool)), tc_fun(_1767542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767544, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767542, tc_fun(_1767544, tc_HOL_Obool)), tc_fun(_1767542, tc_HOL_Obool)), tc_fun(_1767544, tc_HOL_Obool)), c_COMBB(tc_fun(_1767544, tc_HOL_Obool), tc_HOL_Obool, _1767542)), c_fequal)), _1767548))))))], (48932 ^ _779448) ^ [_1767726, _1767728, _1767730, _1767732] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1767726, tc_fun(_1767728, tc_HOL_Obool)), _1767730), _1767732) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1767728, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767728, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767726, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767728, tc_HOL_Obool)), c_HOL_OEx(_1767726)), hAPP(hAPP(c_COMBB(tc_fun(_1767726, tc_HOL_Obool), tc_fun(_1767726, tc_HOL_Obool), tc_fun(_1767728, tc_HOL_Obool)), hAPP(c_COMBS(_1767726, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767726), c_fconj), hAPP(hAPP(c_COMBC(_1767726, tc_fun(_1767726, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767726)), _1767730)))), hAPP(hAPP(c_COMBC(tc_fun(_1767728, tc_HOL_Obool), tc_fun(_1767726, tc_fun(_1767728, tc_HOL_Obool)), tc_fun(_1767726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767728, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767726, tc_fun(_1767728, tc_HOL_Obool)), tc_fun(_1767726, tc_HOL_Obool)), tc_fun(_1767728, tc_HOL_Obool)), c_COMBB(tc_fun(_1767728, tc_HOL_Obool), tc_HOL_Obool, _1767726)), c_fequal)), _1767732))))))], (48934 ^ _779448) ^ [_1767910, _1767912, _1767914, _1767916] : [class_Complete__Lattice_Ocomplete__lattice(_1767910), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767912, _1767910), _1767914), _1767916) = c_Complete__Lattice_OSup__class_OSup(_1767910, hAPP(c_Set_OCollect(_1767910), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool), tc_HOL_Obool, _1767910), c_HOL_OEx(tc_fun(_1767912, _1767910))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool), tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool), _1767910), hAPP(c_COMBS(tc_fun(_1767912, _1767910), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1767912, _1767910)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1767912, _1767910), tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1767912, _1767910))), _1767914)))), hAPP(hAPP(c_COMBC(_1767910, tc_fun(tc_fun(_1767912, _1767910), _1767910), tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767910, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1767912, _1767910), _1767910), tc_fun(tc_fun(_1767912, _1767910), tc_HOL_Obool)), _1767910), c_COMBB(_1767910, tc_HOL_Obool, tc_fun(_1767912, _1767910))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1767912, _1767910), _1767912, _1767910), c_COMBI(tc_fun(_1767912, _1767910))), _1767916)))))))], (48940 ^ _779448) ^ [_1768353, _1768355, _1768357, _1768359] : [class_Complete__Lattice_Ocomplete__lattice(_1768353), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768355, _1768353), _1768357), _1768359) = c_Complete__Lattice_OSup__class_OSup(_1768353, hAPP(c_Set_OCollect(_1768353), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool), tc_HOL_Obool, _1768353), c_HOL_OEx(tc_fun(_1768355, _1768353))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool), tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool), _1768353), hAPP(c_COMBS(tc_fun(_1768355, _1768353), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768355, _1768353)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768355, _1768353), tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768355, _1768353))), _1768357)))), hAPP(hAPP(c_COMBC(_1768353, tc_fun(tc_fun(_1768355, _1768353), _1768353), tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768353, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768355, _1768353), _1768353), tc_fun(tc_fun(_1768355, _1768353), tc_HOL_Obool)), _1768353), c_COMBB(_1768353, tc_HOL_Obool, tc_fun(_1768355, _1768353))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768355, _1768353), _1768355, _1768353), c_COMBI(tc_fun(_1768355, _1768353))), _1768359)))))))], (48946 ^ _779448) ^ [_1768796, _1768798, _1768800, _1768802] : [class_Complete__Lattice_Ocomplete__lattice(_1768796), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1768798, _1768796), _1768800), _1768802) = c_Complete__Lattice_OInf__class_OInf(_1768796, hAPP(c_Set_OCollect(_1768796), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool), tc_HOL_Obool, _1768796), c_HOL_OEx(tc_fun(_1768798, _1768796))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool), tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool), _1768796), hAPP(c_COMBS(tc_fun(_1768798, _1768796), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768798, _1768796)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768798, _1768796), tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768798, _1768796))), _1768800)))), hAPP(hAPP(c_COMBC(_1768796, tc_fun(tc_fun(_1768798, _1768796), _1768796), tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768796, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768798, _1768796), _1768796), tc_fun(tc_fun(_1768798, _1768796), tc_HOL_Obool)), _1768796), c_COMBB(_1768796, tc_HOL_Obool, tc_fun(_1768798, _1768796))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768798, _1768796), _1768798, _1768796), c_COMBI(tc_fun(_1768798, _1768796))), _1768802)))))))], (48952 ^ _779448) ^ [_1769239, _1769241, _1769243, _1769245] : [class_Complete__Lattice_Ocomplete__lattice(_1769239), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769241, _1769239), _1769243), _1769245) = c_Complete__Lattice_OInf__class_OInf(_1769239, hAPP(c_Set_OCollect(_1769239), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool), tc_HOL_Obool, _1769239), c_HOL_OEx(tc_fun(_1769241, _1769239))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool), tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool), _1769239), hAPP(c_COMBS(tc_fun(_1769241, _1769239), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769241, _1769239)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769241, _1769239), tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769241, _1769239))), _1769243)))), hAPP(hAPP(c_COMBC(_1769239, tc_fun(tc_fun(_1769241, _1769239), _1769239), tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769239, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769241, _1769239), _1769239), tc_fun(tc_fun(_1769241, _1769239), tc_HOL_Obool)), _1769239), c_COMBB(_1769239, tc_HOL_Obool, tc_fun(_1769241, _1769239))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769241, _1769239), _1769241, _1769239), c_COMBI(tc_fun(_1769241, _1769239))), _1769245)))))))], (48958 ^ _779448) ^ [_1769682, _1769684, _1769686, _1769688] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1769682), _1769684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1769682), _1769686)), -(_1769686 = c_Orderings_Obot__class_Obot(tc_fun(_1769682, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1769682, _1769688, _1769684, _1769686)), 48972 ^ _779448 : [(48973 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769682), 48971 ^ [_1769682, _1769684, _1769686, _1769688]), _1769684)))], (48975 ^ _779448) ^ [_1770027] : [hBOOL(hAPP(hAPP(c_member(_1769682), _1770027), _1769686)), hBOOL(hAPP(hAPP(_1769688, 48971 ^ [_1769682, _1769684, _1769686, _1769688]), _1770027))]]], (48983 ^ _779448) ^ [_1770208, _1770210] : [c_Predicate_Otransp(_1770208, _1770210), -(c_Relation_Otrans(_1770208, hAPP(c_Set_OCollect(tc_prod(_1770208, _1770208)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770208, _1770208, tc_HOL_Obool), _1770210))))], (48989 ^ _779448) ^ [_1770311, _1770313] : [c_Relation_Otrans(_1770311, hAPP(c_Set_OCollect(tc_prod(_1770311, _1770311)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770311, _1770311, tc_HOL_Obool), _1770313))), -(c_Predicate_Otransp(_1770311, _1770313))], (48995 ^ _779448) ^ [_1770420, _1770422, _1770424, _1770426, _1770428] : [c_Predicate_Otransp(_1770420, _1770422), hBOOL(hAPP(hAPP(_1770422, _1770424), _1770426)), hBOOL(hAPP(hAPP(_1770422, _1770426), _1770428)), -(hBOOL(hAPP(hAPP(_1770422, _1770424), _1770428)))], (49009 ^ _779448) ^ [_1770664, _1770666] : [c_Equiv__Relations_Oequivp(_1770664, _1770666), 49012 ^ _779448 : [(49013 ^ _779448) ^ [] : [-(c_Predicate_Oreflp(_1770664, _1770666))], (49015 ^ _779448) ^ [] : [-(c_Predicate_Osymp(_1770664, _1770666))], (49017 ^ _779448) ^ [] : [-(c_Predicate_Otransp(_1770664, _1770666))]]], (49019 ^ _779448) ^ [_1770787, _1770789] : [-(c_Equiv__Relations_Oequivp(_1770787, _1770789)), c_Predicate_Oreflp(_1770787, _1770789), c_Predicate_Osymp(_1770787, _1770789), c_Predicate_Otransp(_1770787, _1770789)], (49033 ^ _779448) ^ [_1770970, _1770972] : [c_Predicate_Oreflp(_1770970, _1770972), c_Predicate_Osymp(_1770970, _1770972), c_Predicate_Otransp(_1770970, _1770972), -(c_Equiv__Relations_Oequivp(_1770970, _1770972))], (49047 ^ _779448) ^ [_1771151, _1771153, _1771155, _1771157] : [c_Predicate_Osymp(_1771151, _1771153), hBOOL(hAPP(hAPP(_1771153, _1771155), _1771157)), -(hBOOL(hAPP(hAPP(_1771153, _1771157), _1771155)))], (49057 ^ _779448) ^ [_1771308, _1771310] : [c_Equiv__Relations_Oequivp(_1771308, _1771310), 49060 ^ _779448 : [(49061 ^ _779448) ^ [] : [-(c_Predicate_Oreflp(_1771308, _1771310))], (49063 ^ _779448) ^ [] : [-(c_Predicate_Osymp(_1771308, _1771310))], (49065 ^ _779448) ^ [] : [-(c_Predicate_Otransp(_1771308, _1771310))]]], (49067 ^ _779448) ^ [_1771460, _1771462, _1771464, _1771466] : [c_Wellfounded_Omax__extp(_1771460, _1771462, _1771464, _1771466), 49070 ^ _779448 : [(49071 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771460), _1771464)))], (49073 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771460), _1771466)))], (49075 ^ _779448) ^ [] : [_1771466 = c_Orderings_Obot__class_Obot(tc_fun(_1771460, tc_HOL_Obool))], (49077 ^ _779448) ^ [_1771676] : [hBOOL(hAPP(hAPP(c_member(_1771460), _1771676), _1771464)), 49081 ^ _779448 : [(49082 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771460), 49080 ^ [_1771460, _1771462, _1771464, _1771466, _1771676]), _1771466)))], (49084 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1771462, _1771676), 49080 ^ [_1771460, _1771462, _1771464, _1771466, _1771676])))]]]]], (49086 ^ _779448) ^ [_1771860, _1771862, _1771864, _1771866] : [-(c_Wellfounded_Omax__extp(_1771860, _1771862, _1771864, _1771866)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1771860), _1771864)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1771860), _1771866)), -(_1771866 = c_Orderings_Obot__class_Obot(tc_fun(_1771860, tc_HOL_Obool))), 49100 ^ _779448 : [(49101 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771860), 49099 ^ [_1771860, _1771862, _1771864, _1771866]), _1771864)))], (49103 ^ _779448) ^ [_1772205] : [hBOOL(hAPP(hAPP(c_member(_1771860), _1772205), _1771866)), hBOOL(hAPP(hAPP(_1771862, 49099 ^ [_1771860, _1771862, _1771864, _1771866]), _1772205))]]], (49111 ^ _779448) ^ [_1772373, _1772375] : [c_Relation_Otrans(_1772373, _1772375), c_Relation_Oantisym(_1772373, _1772375), -(c_Relation_Otrans(_1772373, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1772373, _1772373), tc_HOL_Obool)), _1772375), c_Relation_OId(_1772373))))], (49121 ^ _779448) ^ [_1772534, _1772536] : [-(c_Relation_Oantisym(_1772534, c_Relation_OId__on(_1772534, _1772536)))], (49123 ^ _779448) ^ [_1772562, _1772564, _1772566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1772562, _1772562), tc_HOL_Obool)), _1772564), _1772566)), c_Relation_Oantisym(_1772562, _1772566), -(c_Relation_Oantisym(_1772562, _1772564))], (49133 ^ _779448) ^ [_1772721] : [-(c_Relation_Oantisym(_1772721, c_Relation_OId(_1772721)))], (49135 ^ _779448) ^ [_1772746] : [-(c_Relation_Oantisym(_1772746, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1772746, _1772746), tc_HOL_Obool))))], (49137 ^ _779448) ^ [_1772792, _1772794] : [c_Relation_Oantisym(_1772792, hAPP(c_Relation_Oconverse(_1772792, _1772792), _1772794)), -(c_Relation_Oantisym(_1772792, _1772794))], (49143 ^ _779448) ^ [_1772877, _1772879] : [c_Relation_Oantisym(_1772877, _1772879), -(c_Relation_Oantisym(_1772877, hAPP(c_Relation_Oconverse(_1772877, _1772877), _1772879)))], (49163 ^ _779448) ^ [_1773308, _1773310] : [49166 ^ _779448 : [(49167 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773308, _1773308)), hAPP(hAPP(c_Product__Type_OPair(_1773308, _1773308), 49164 ^ [_1773308, _1773310]), 49165 ^ [_1773308, _1773310])), _1773310)))], (49169 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773308, _1773308)), hAPP(hAPP(c_Product__Type_OPair(_1773308, _1773308), 49165 ^ [_1773308, _1773310]), 49164 ^ [_1773308, _1773310])), _1773310)))], (49171 ^ _779448) ^ [] : [49164 ^ [_1773308, _1773310] = 49165 ^ [_1773308, _1773310]]], -(c_Relation_Oantisym(_1773308, _1773310))], (49149 ^ _779448) ^ [_1772983, _1772985] : [c_Relation_Oantisym(_1772983, _1772985), 49152 ^ _779448 : [(49153 ^ _779448) ^ [_1773095, _1773097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772983, _1772983)), hAPP(hAPP(c_Product__Type_OPair(_1772983, _1772983), _1773097), _1773095)), _1772985)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772983, _1772983)), hAPP(hAPP(c_Product__Type_OPair(_1772983, _1772983), _1773095), _1773097)), _1772985)), -(_1773097 = _1773095)]]], (49175 ^ _779448) ^ [_1773629, _1773631, _1773633, _1773635] : [c_Relation_Oantisym(_1773629, _1773631), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773629, _1773629)), hAPP(hAPP(c_Product__Type_OPair(_1773629, _1773629), _1773633), _1773635)), _1773631)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773629, _1773629)), hAPP(hAPP(c_Product__Type_OPair(_1773629, _1773629), _1773635), _1773633)), _1773631)), -(_1773633 = _1773635)], (49189 ^ _779448) ^ [_1773913, _1773915] : [c_Relation_Oantisym(_1773913, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773913, _1773913), tc_HOL_Obool)), _1773915), c_Relation_OId(_1773913))), -(c_Relation_Oantisym(_1773913, _1773915))], (49195 ^ _779448) ^ [_1774018, _1774020] : [c_Relation_Oantisym(_1774018, _1774020), -(c_Relation_Oantisym(_1774018, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774018, _1774018), tc_HOL_Obool)), _1774020), c_Relation_OId(_1774018))))], (49201 ^ _779448) ^ [_1774129, _1774131] : [c_Wellfounded_Oacyclic(_1774129, _1774131), -(c_Relation_Oantisym(_1774129, c_Transitive__Closure_Ortrancl(_1774129, _1774131)))], (49207 ^ _779448) ^ [_1774212, _1774214, _1774216, _1774218, _1774220, _1774222] : [-(c_Partial__Function_Ofun__lub(_1774212, _1774214, _1774216, _1774218, _1774220, _1774222) = hAPP(_1774218, hAPP(c_Set_OCollect(_1774212), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool), tc_HOL_Obool, _1774212), c_HOL_OEx(tc_fun(_1774216, _1774212))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool), tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool), _1774212), hAPP(c_COMBS(tc_fun(_1774216, _1774212), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774216, _1774212)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774216, _1774212), tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774216, _1774212))), _1774220)))), hAPP(hAPP(c_COMBC(_1774212, tc_fun(tc_fun(_1774216, _1774212), _1774212), tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774212, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774216, _1774212), _1774212), tc_fun(tc_fun(_1774216, _1774212), tc_HOL_Obool)), _1774212), c_COMBB(_1774212, tc_HOL_Obool, tc_fun(_1774216, _1774212))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774216, _1774212), _1774216, _1774212), c_COMBI(tc_fun(_1774216, _1774212))), _1774222)))))))], (49209 ^ _779448) ^ [_1774425, _1774427] : [c_Relation_Osym(_1774425, _1774427), c_Relation_Otrans(_1774425, _1774427), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774425, _1774425), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774425, _1774425, _1774425), hAPP(c_Relation_Oconverse(_1774425, _1774425), _1774427)), _1774427)), _1774427)))], (49229 ^ _779448) ^ [_1774890, _1774892] : [49232 ^ _779448 : [(49233 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774890, _1774890)), hAPP(hAPP(c_Product__Type_OPair(_1774890, _1774890), 49230 ^ [_1774890, _1774892]), 49231 ^ [_1774890, _1774892])), _1774892)))], (49235 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774890, _1774890)), hAPP(hAPP(c_Product__Type_OPair(_1774890, _1774890), 49231 ^ [_1774890, _1774892]), 49230 ^ [_1774890, _1774892])), _1774892))]], -(c_Relation_Osym(_1774890, _1774892))], (49219 ^ _779448) ^ [_1774627, _1774629] : [c_Relation_Osym(_1774627, _1774629), 49222 ^ _779448 : [(49223 ^ _779448) ^ [_1774733, _1774735] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774627, _1774627)), hAPP(hAPP(c_Product__Type_OPair(_1774627, _1774627), _1774735), _1774733)), _1774629)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774627, _1774627)), hAPP(hAPP(c_Product__Type_OPair(_1774627, _1774627), _1774733), _1774735)), _1774629)))]]], (49239 ^ _779448) ^ [_1775155, _1775157, _1775159, _1775161] : [c_Relation_Osym(_1775155, _1775157), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775155, _1775155)), hAPP(hAPP(c_Product__Type_OPair(_1775155, _1775155), _1775159), _1775161)), _1775157)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775155, _1775155)), hAPP(hAPP(c_Product__Type_OPair(_1775155, _1775155), _1775161), _1775159)), _1775157)))], (49249 ^ _779448) ^ [_1775368, _1775370, _1775372, _1775374] : [c_Relation_Osym(_1775368, _1775370), -(c_Relation_Osym(_1775372, hAPP(hAPP(c_Relation_Oinv__image(_1775368, _1775372), _1775370), _1775374)))], (49255 ^ _779448) ^ [_1775467, _1775469] : [-(c_Relation_Osym(_1775467, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775467, _1775467), tc_HOL_Obool)), _1775469), hAPP(c_Relation_Oconverse(_1775467, _1775467), _1775469))))], (49257 ^ _779448) ^ [_1775512, _1775514, _1775516] : [c_Relation_Osym(_1775512, _1775514), c_Relation_Osym(_1775512, _1775516), -(c_Relation_Osym(_1775512, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775512, _1775512), tc_HOL_Obool)), _1775514), _1775516)))], (49267 ^ _779448) ^ [_1775688, _1775690] : [c_Relation_Osym(_1775688, hAPP(c_Relation_Oconverse(_1775688, _1775688), _1775690)), -(c_Relation_Osym(_1775688, _1775690))], (49273 ^ _779448) ^ [_1775773, _1775775] : [c_Relation_Osym(_1775773, _1775775), -(c_Relation_Osym(_1775773, hAPP(c_Relation_Oconverse(_1775773, _1775773), _1775775)))], (49279 ^ _779448) ^ [_1775879, _1775881] : [c_Relation_Osym(_1775879, _1775881), -(hAPP(c_Relation_Oconverse(_1775879, _1775879), _1775881) = _1775881)], (49285 ^ _779448) ^ [_1775964, _1775966] : [hAPP(c_Relation_Oconverse(_1775964, _1775964), _1775966) = _1775966, -(c_Relation_Osym(_1775964, _1775966))], (49291 ^ _779448) ^ [_1776055, _1776057] : [c_Relation_Osym(_1776055, _1776057), -(c_Relation_Osym(tc_List_Olist(_1776055), c_List_Olistrel(_1776055, _1776057)))], (49297 ^ _779448) ^ [_1776142] : [-(c_Relation_Osym(_1776142, c_Relation_OId(_1776142)))], (49299 ^ _779448) ^ [_1776167, _1776169, _1776171] : [c_Relation_Osym(_1776167, _1776169), c_Relation_Osym(_1776167, _1776171), -(c_Relation_Osym(_1776167, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776167, _1776167), tc_HOL_Obool)), _1776169), _1776171)))], (49309 ^ _779448) ^ [_1776328, _1776330] : [c_Relation_Osym(_1776328, _1776330), -(c_Relation_Osym(_1776328, c_Transitive__Closure_Otrancl(_1776328, _1776330)))], (49315 ^ _779448) ^ [_1776411, _1776413] : [-(c_Relation_Osym(_1776411, c_Relation_OId__on(_1776411, _1776413)))], (49317 ^ _779448) ^ [_1776439, _1776441] : [c_Relation_Osym(_1776439, _1776441), -(c_Relation_Osym(_1776439, c_Transitive__Closure_Ortrancl(_1776439, _1776441)))], (49323 ^ _779448) ^ [_1776522, _1776524] : [-(c_Relation_Osym(_1776522, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1776522, _1776522), tc_HOL_Obool)), _1776524), hAPP(c_Relation_Oconverse(_1776522, _1776522), _1776524))))], (49325 ^ _779448) ^ [_1776567, _1776569, _1776571] : [c_Equiv__Relations_Oequiv(_1776567, _1776569, _1776571), 49328 ^ _779448 : [(49329 ^ _779448) ^ [] : [-(c_Relation_Orefl__on(_1776567, _1776569, _1776571))], (49331 ^ _779448) ^ [] : [-(c_Relation_Osym(_1776567, _1776571))], (49333 ^ _779448) ^ [] : [-(c_Relation_Otrans(_1776567, _1776571))]]], (49335 ^ _779448) ^ [_1776704, _1776706, _1776708] : [c_Relation_Orefl__on(_1776704, _1776706, _1776708), c_Relation_Osym(_1776704, _1776708), c_Relation_Otrans(_1776704, _1776708), -(c_Equiv__Relations_Oequiv(_1776704, _1776706, _1776708))], (49349 ^ _779448) ^ [_1776913, _1776915, _1776917] : [c_Equiv__Relations_Oequiv(_1776913, _1776915, _1776917), 49352 ^ _779448 : [(49353 ^ _779448) ^ [] : [-(c_Relation_Orefl__on(_1776913, _1776915, _1776917))], (49355 ^ _779448) ^ [] : [-(c_Relation_Osym(_1776913, _1776917))], (49357 ^ _779448) ^ [] : [-(c_Relation_Otrans(_1776913, _1776917))]]], (49359 ^ _779448) ^ [_1777042, _1777044, _1777046] : [-(c_Equiv__Relations_Oequiv(_1777042, _1777044, _1777046)), c_Relation_Orefl__on(_1777042, _1777044, _1777046), c_Relation_Osym(_1777042, _1777046), c_Relation_Otrans(_1777042, _1777046)], (49373 ^ _779448) ^ [_1777250, _1777252] : [c_Predicate_Osymp(_1777250, _1777252), -(c_Relation_Osym(_1777250, hAPP(c_Set_OCollect(tc_prod(_1777250, _1777250)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777250, _1777250, tc_HOL_Obool), _1777252))))], (49379 ^ _779448) ^ [_1777353, _1777355] : [c_Relation_Osym(_1777353, hAPP(c_Set_OCollect(tc_prod(_1777353, _1777353)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777353, _1777353, tc_HOL_Obool), _1777355))), -(c_Predicate_Osymp(_1777353, _1777355))], (49385 ^ _779448) ^ [_1777477, _1777479] : [c_Equiv__Relations_Opart__equivp(_1777477, _1777479), 49389 ^ _779448 : [(49390 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1777479, 49388 ^ [_1777477, _1777479]), 49388 ^ [_1777477, _1777479])))], (49392 ^ _779448) ^ [] : [-(c_Predicate_Osymp(_1777477, _1777479))], (49394 ^ _779448) ^ [] : [-(c_Predicate_Otransp(_1777477, _1777479))]]], (49396 ^ _779448) ^ [_1777629, _1777631] : [-(c_Equiv__Relations_Opart__equivp(_1777629, _1777631)), 49399 ^ _779448 : [(49400 ^ _779448) ^ [_1777706] : [hBOOL(hAPP(hAPP(_1777631, _1777706), _1777706))]], c_Predicate_Osymp(_1777629, _1777631), c_Predicate_Otransp(_1777629, _1777631)], (49410 ^ _779448) ^ [_1777835, _1777837] : [49411 ^ _779448 : [(49412 ^ _779448) ^ [_1777891] : [hBOOL(hAPP(hAPP(_1777835, _1777891), _1777891))]], c_Predicate_Osymp(_1777837, _1777835), c_Predicate_Otransp(_1777837, _1777835), -(c_Equiv__Relations_Opart__equivp(_1777837, _1777835))], (49424 ^ _779448) ^ [_1778039, _1778041] : [c_Equiv__Relations_Oequivp(_1778039, _1778041), -(c_Equiv__Relations_Opart__equivp(_1778039, _1778041))], (49461 ^ _779448) ^ [_1778712, _1778714] : [-(c_Equiv__Relations_Opart__equivp(_1778712, _1778714)), 49464 ^ _779448 : [(49465 ^ _779448) ^ [_1778832] : [hBOOL(hAPP(hAPP(_1778714, _1778832), _1778832))]], 49482 ^ _779448 : [(49483 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778714, 49466 ^ [_1778712, _1778714]), 49466 ^ [_1778712, _1778714])))], (49485 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778714, 49467 ^ [_1778712, _1778714]), 49467 ^ [_1778712, _1778714])))], (49487 ^ _779448) ^ [] : [-(hAPP(_1778714, 49466 ^ [_1778712, _1778714]) = hAPP(_1778714, 49467 ^ [_1778712, _1778714]))], (49489 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1778714, 49466 ^ [_1778712, _1778714]), 49467 ^ [_1778712, _1778714]))]], 49470 ^ _779448 : [(49471 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778714, 49466 ^ [_1778712, _1778714]), 49467 ^ [_1778712, _1778714])))], (49473 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1778714, 49466 ^ [_1778712, _1778714]), 49466 ^ [_1778712, _1778714])), hBOOL(hAPP(hAPP(_1778714, 49467 ^ [_1778712, _1778714]), 49467 ^ [_1778712, _1778714])), hAPP(_1778714, 49466 ^ [_1778712, _1778714]) = hAPP(_1778714, 49467 ^ [_1778712, _1778714])]]], (49430 ^ _779448) ^ [_1778131, _1778133] : [c_Equiv__Relations_Opart__equivp(_1778131, _1778133), 49434 ^ _779448 : [(49435 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778133, 49433 ^ [_1778131, _1778133]), 49433 ^ [_1778131, _1778133])))], (49437 ^ _779448) ^ [_1778304, _1778306] : [hBOOL(hAPP(hAPP(_1778133, _1778306), _1778304)), 49440 ^ _779448 : [(49441 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778133, _1778306), _1778306)))], (49443 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1778133, _1778304), _1778304)))], (49445 ^ _779448) ^ [] : [-(hAPP(_1778133, _1778306) = hAPP(_1778133, _1778304))]]], (49447 ^ _779448) ^ [_1778473, _1778475] : [-(hBOOL(hAPP(hAPP(_1778133, _1778475), _1778473))), hBOOL(hAPP(hAPP(_1778133, _1778475), _1778475)), hBOOL(hAPP(hAPP(_1778133, _1778473), _1778473)), hAPP(_1778133, _1778475) = hAPP(_1778133, _1778473)]]], (49493 ^ _779448) ^ [_1779380, _1779382, _1779384, _1779386] : [c_Equiv__Relations_Opart__equivp(_1779380, _1779382), hBOOL(hAPP(hAPP(_1779382, _1779384), _1779386)), -(hBOOL(hAPP(hAPP(_1779382, _1779386), _1779384)))], (49503 ^ _779448) ^ [_1779537, _1779539, _1779541, _1779543, _1779545] : [c_Equiv__Relations_Opart__equivp(_1779537, _1779539), hBOOL(hAPP(hAPP(_1779539, _1779541), _1779543)), hBOOL(hAPP(hAPP(_1779539, _1779543), _1779545)), -(hBOOL(hAPP(hAPP(_1779539, _1779541), _1779545)))], (49517 ^ _779448) ^ [_1779766, _1779768] : [c_Equiv__Relations_Opart__equivp(_1779766, _1779768), 49521 ^ _779448 : [(49522 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1779768, 49520 ^ [_1779766, _1779768]), 49520 ^ [_1779766, _1779768])))], (49524 ^ _779448) ^ [] : [-(c_Predicate_Osymp(_1779766, _1779768))], (49526 ^ _779448) ^ [] : [-(c_Predicate_Otransp(_1779766, _1779768))]]], (49528 ^ _779448) ^ [_1779926, _1779928] : [c_Equiv__Relations_Opart__equivp(_1779926, _1779928), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1779926, tc_HOL_Obool)), 49531 ^ [_1779926, _1779928]), hAPP(hAPP(c_COMBB(tc_fun(_1779926, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1779926, tc_HOL_Obool)), c_HOL_OEx(_1779926)), hAPP(hAPP(c_COMBB(tc_fun(_1779926, tc_HOL_Obool), tc_fun(_1779926, tc_HOL_Obool), tc_fun(_1779926, tc_HOL_Obool)), hAPP(c_COMBS(_1779926, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1779926), c_fconj), hAPP(hAPP(c_COMBS(_1779926, _1779926, tc_HOL_Obool), _1779928), c_COMBI(_1779926))))), hAPP(hAPP(c_COMBC(tc_fun(_1779926, tc_HOL_Obool), tc_fun(_1779926, tc_fun(_1779926, tc_HOL_Obool)), tc_fun(_1779926, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779926, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1779926, tc_fun(_1779926, tc_HOL_Obool)), tc_fun(_1779926, tc_HOL_Obool)), tc_fun(_1779926, tc_HOL_Obool)), c_COMBB(tc_fun(_1779926, tc_HOL_Obool), tc_HOL_Obool, _1779926)), c_fequal)), _1779928))))))], (49535 ^ _779448) ^ [_1780305, _1780307, _1780309] : [c_Fun_Oinj__on(_1780305, _1780307, _1780309, c_Orderings_Otop__class_Otop(tc_fun(_1780305, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780307, _1780305, _1780305, c_Hilbert__Choice_Oinv__into(_1780305, _1780307, c_Orderings_Otop__class_Otop(tc_fun(_1780305, tc_HOL_Obool)), _1780309)), _1780309) = c_Fun_Oid(_1780305))], (49541 ^ _779448) ^ [_1780434, _1780436, _1780438] : [hAPP(c_Fun_Ocomp(_1780436, _1780434, _1780434, c_Hilbert__Choice_Oinv__into(_1780434, _1780436, c_Orderings_Otop__class_Otop(tc_fun(_1780434, tc_HOL_Obool)), _1780438)), _1780438) = c_Fun_Oid(_1780434), -(c_Fun_Oinj__on(_1780434, _1780436, _1780438, c_Orderings_Otop__class_Otop(tc_fun(_1780434, tc_HOL_Obool))))], (49547 ^ _779448) ^ [_1780569, _1780571, _1780573] : [c_Fun_Oinj__on(_1780569, _1780571, _1780573, c_Orderings_Otop__class_Otop(tc_fun(_1780569, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780571, _1780569, _1780569, c_Hilbert__Choice_Oinv__into(_1780569, _1780571, c_Orderings_Otop__class_Otop(tc_fun(_1780569, tc_HOL_Obool)), _1780573)), _1780573) = c_Fun_Oid(_1780569))], (49553 ^ _779448) ^ [_1780702, _1780704, _1780706, _1780708, _1780710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780702, tc_HOL_Obool)), _1780704), hAPP(c_Set_Oimage(_1780706, _1780702, _1780708), _1780710))), -(c_Fun_Oinj__on(_1780702, _1780706, c_Hilbert__Choice_Oinv__into(_1780706, _1780702, _1780710, _1780708), _1780704))], (49559 ^ _779448) ^ [_1780833, _1780835, _1780837, _1780839, _1780841] : [c_Fun_Oinj__on(_1780833, _1780835, _1780837, _1780839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780833, tc_HOL_Obool)), _1780841), _1780839)), -(hAPP(c_Set_Oimage(_1780835, _1780833, c_Hilbert__Choice_Oinv__into(_1780833, _1780835, _1780839, _1780837)), hAPP(c_Set_Oimage(_1780833, _1780835, _1780837), _1780841)) = _1780841)], (49569 ^ _779448) ^ [_1781036, _1781038, _1781040] : [hAPP(c_Set_Oimage(_1781036, _1781038, _1781040), c_Orderings_Otop__class_Otop(tc_fun(_1781036, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781038, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1781038, _1781036, c_Hilbert__Choice_Oinv__into(_1781036, _1781038, c_Orderings_Otop__class_Otop(tc_fun(_1781036, tc_HOL_Obool)), _1781040), c_Orderings_Otop__class_Otop(tc_fun(_1781038, tc_HOL_Obool))))], (49575 ^ _779448) ^ [_1781183, _1781185, _1781187, _1781189] : [c_Fun_Oinj__on(_1781183, _1781185, _1781187, c_Orderings_Otop__class_Otop(tc_fun(_1781183, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781185, _1781183, c_Hilbert__Choice_Oinv__into(_1781183, _1781185, c_Orderings_Otop__class_Otop(tc_fun(_1781183, tc_HOL_Obool)), _1781187)), hAPP(c_Set_Oimage(_1781183, _1781185, _1781187), _1781189)) = _1781189)], (49581 ^ _779448) ^ [_1781326, _1781328, _1781330, _1781332] : [c_Fun_Oinj__on(_1781326, _1781328, _1781330, c_Orderings_Otop__class_Otop(tc_fun(_1781326, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781328, _1781326, c_Hilbert__Choice_Oinv__into(_1781326, _1781328, c_Orderings_Otop__class_Otop(tc_fun(_1781326, tc_HOL_Obool)), _1781330)), hAPP(c_Set_Oimage(_1781326, _1781328, _1781330), _1781332)) = _1781332)], (49587 ^ _779448) ^ [_1781469, _1781471, _1781473] : [c_Fun_Oinj__on(_1781469, _1781471, _1781473, c_Orderings_Otop__class_Otop(tc_fun(_1781469, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781471, _1781469, c_Hilbert__Choice_Oinv__into(_1781469, _1781471, c_Orderings_Otop__class_Otop(tc_fun(_1781469, tc_HOL_Obool)), _1781473)), c_Orderings_Otop__class_Otop(tc_fun(_1781471, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781469, tc_HOL_Obool)))], (49593 ^ _779448) ^ [_1781616, _1781618, _1781620, _1781622, _1781624, _1781626] : [hAPP(c_Set_Oimage(_1781616, _1781618, _1781620), _1781622) = _1781624, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781618, tc_HOL_Obool)), _1781626), _1781624)), -(hAPP(c_Set_Oimage(_1781616, _1781618, _1781620), hAPP(c_Set_Oimage(_1781618, _1781616, c_Hilbert__Choice_Oinv__into(_1781616, _1781618, _1781622, _1781620)), _1781626)) = _1781626)], (49603 ^ _779448) ^ [_1781851, _1781853, _1781855] : [hAPP(c_Set_Oimage(_1781851, _1781853, _1781855), c_Orderings_Otop__class_Otop(tc_fun(_1781851, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781853, tc_HOL_Obool)), 49606 ^ _779448 : [(49607 ^ _779448) ^ [_1781962] : [-(hAPP(_1781855, hAPP(c_Hilbert__Choice_Oinv__into(_1781851, _1781853, c_Orderings_Otop__class_Otop(tc_fun(_1781851, tc_HOL_Obool)), _1781855), _1781962)) = _1781962)]]], (49609 ^ _779448) ^ [_1782001, _1782003, _1782005] : [hAPP(_1782005, hAPP(c_Hilbert__Choice_Oinv__into(_1782001, _1782003, c_Orderings_Otop__class_Otop(tc_fun(_1782001, tc_HOL_Obool)), _1782005), 49610 ^ [_1782001, _1782003, _1782005])) = 49610 ^ [_1782001, _1782003, _1782005], -(hAPP(c_Set_Oimage(_1782001, _1782003, _1782005), c_Orderings_Otop__class_Otop(tc_fun(_1782001, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782003, tc_HOL_Obool)))], (49616 ^ _779448) ^ [_1782201, _1782203, _1782205, _1782207] : [hAPP(c_Set_Oimage(_1782201, _1782203, _1782205), c_Orderings_Otop__class_Otop(tc_fun(_1782201, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782203, tc_HOL_Obool)), -(hAPP(_1782205, hAPP(c_Hilbert__Choice_Oinv__into(_1782201, _1782203, c_Orderings_Otop__class_Otop(tc_fun(_1782201, tc_HOL_Obool)), _1782205), _1782207)) = _1782207)], (49622 ^ _779448) ^ [_1782348, _1782350, _1782352, _1782354] : [hAPP(c_Set_Oimage(_1782348, _1782350, _1782352), c_Orderings_Otop__class_Otop(tc_fun(_1782348, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782350, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782348, _1782350, _1782352), hAPP(c_Set_Oimage(_1782350, _1782348, c_Hilbert__Choice_Oinv__into(_1782348, _1782350, c_Orderings_Otop__class_Otop(tc_fun(_1782348, tc_HOL_Obool)), _1782352)), _1782354)) = _1782354)], (49628 ^ _779448) ^ [_1782511, _1782513, _1782515, _1782517, _1782519, _1782521] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782511, _1782513, _1782515, _1782517), _1782519) = hAPP(c_Hilbert__Choice_Oinv__into(_1782511, _1782513, _1782515, _1782517), _1782521), hBOOL(hAPP(hAPP(c_member(_1782513), _1782519), hAPP(c_Set_Oimage(_1782511, _1782513, _1782517), _1782515))), hBOOL(hAPP(hAPP(c_member(_1782513), _1782521), hAPP(c_Set_Oimage(_1782511, _1782513, _1782517), _1782515))), -(_1782519 = _1782521)], (49642 ^ _779448) ^ [_1782804, _1782806, _1782808, _1782810, _1782812] : [hBOOL(hAPP(hAPP(c_member(_1782804), _1782806), hAPP(c_Set_Oimage(_1782808, _1782804, _1782810), _1782812))), -(hBOOL(hAPP(hAPP(c_member(_1782808), hAPP(c_Hilbert__Choice_Oinv__into(_1782808, _1782804, _1782812, _1782810), _1782806)), _1782812)))], (49648 ^ _779448) ^ [_1782945, _1782947, _1782949, _1782951, _1782953] : [hBOOL(hAPP(hAPP(c_member(_1782945), _1782947), hAPP(c_Set_Oimage(_1782949, _1782945, _1782951), _1782953))), -(hAPP(_1782951, hAPP(c_Hilbert__Choice_Oinv__into(_1782949, _1782945, _1782953, _1782951), _1782947)) = _1782947)], (49654 ^ _779448) ^ [_1783078, _1783080, _1783082, _1783084, _1783086] : [c_Fun_Oinj__on(_1783078, _1783080, _1783082, _1783084), hBOOL(hAPP(hAPP(c_member(_1783078), _1783086), _1783084)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783078, _1783080, _1783084, _1783082), hAPP(_1783082, _1783086)) = _1783086)], (49664 ^ _779448) ^ [_1783259, _1783261, _1783263, _1783265, _1783267, _1783269] : [c_Fun_Oinj__on(_1783259, _1783261, _1783263, _1783265), hBOOL(hAPP(hAPP(c_member(_1783259), _1783267), _1783265)), hAPP(_1783263, _1783267) = _1783269, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783259, _1783261, _1783265, _1783263), _1783269) = _1783267)], (49678 ^ _779448) ^ [_1783504, _1783506, _1783508, _1783510, _1783512] : [c_Fun_Oinj__on(_1783504, _1783506, _1783508, c_Orderings_Otop__class_Otop(tc_fun(_1783504, tc_HOL_Obool))), hAPP(_1783508, _1783510) = _1783512, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783504, _1783506, c_Orderings_Otop__class_Otop(tc_fun(_1783504, tc_HOL_Obool)), _1783508), _1783512) = _1783510)], (49688 ^ _779448) ^ [_1783691, _1783693, _1783695, _1783697] : [c_Fun_Oinj__on(_1783691, _1783693, _1783695, c_Orderings_Otop__class_Otop(tc_fun(_1783691, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783691, _1783693, c_Orderings_Otop__class_Otop(tc_fun(_1783691, tc_HOL_Obool)), _1783695), hAPP(_1783695, _1783697)) = _1783697)], (49694 ^ _779448) ^ [_1783818] : [-(c_Hilbert__Choice_Oinv__into(_1783818, _1783818, c_Orderings_Otop__class_Otop(tc_fun(_1783818, tc_HOL_Obool)), c_Fun_Oid(_1783818)) = c_Fun_Oid(_1783818))], (49696 ^ _779448) ^ [_1783855, _1783857, _1783859, _1783861, _1783863] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783855, _1783857, _1783859, _1783861), _1783863) = c_Hilbert__Choice_OEps(_1783855, hAPP(hAPP(c_COMBS(_1783855, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1783855), c_fconj), hAPP(hAPP(c_COMBC(_1783855, tc_fun(_1783855, tc_HOL_Obool), tc_HOL_Obool), c_member(_1783855)), _1783859))), hAPP(hAPP(c_COMBC(_1783855, _1783857, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783857, tc_fun(_1783857, tc_HOL_Obool), _1783855), c_fequal), _1783861)), _1783863))))], (49698 ^ _779448) ^ [_1783955, _1783957, _1783959, _1783961] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783955, _1783957, c_Orderings_Otop__class_Otop(tc_fun(_1783955, tc_HOL_Obool)), _1783959), _1783961) = c_Hilbert__Choice_OEps(_1783955, hAPP(hAPP(c_COMBC(_1783955, _1783957, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783957, tc_fun(_1783957, tc_HOL_Obool), _1783955), c_fequal), _1783959)), _1783961)))], (49700 ^ _779448) ^ [_1784023, _1784025, _1784027, _1784029, _1784031] : [c_Fun_Oinj__on(_1784023, _1784025, _1784027, c_Orderings_Otop__class_Otop(tc_fun(_1784023, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784025, _1784029, _1784023, hAPP(c_Fun_Ocomp(_1784023, _1784029, _1784025, _1784031), c_Hilbert__Choice_Oinv__into(_1784023, _1784025, c_Orderings_Otop__class_Otop(tc_fun(_1784023, tc_HOL_Obool)), _1784027))), _1784027) = _1784031)], (49706 ^ _779448) ^ [_1784172, _1784174, _1784176, _1784178, _1784180, _1784182, _1784184] : [c_Fun_Oinj__on(_1784172, _1784174, _1784176, hAPP(c_Set_Oimage(_1784178, _1784172, _1784180), _1784182)), c_Fun_Oinj__on(_1784178, _1784172, _1784180, _1784182), hBOOL(hAPP(hAPP(c_member(_1784174), _1784184), hAPP(c_Set_Oimage(_1784172, _1784174, _1784176), hAPP(c_Set_Oimage(_1784178, _1784172, _1784180), _1784182)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784178, _1784174, _1784182, hAPP(c_Fun_Ocomp(_1784172, _1784174, _1784178, _1784176), _1784180)), _1784184) = hAPP(hAPP(c_Fun_Ocomp(_1784172, _1784178, _1784174, c_Hilbert__Choice_Oinv__into(_1784178, _1784172, _1784182, _1784180)), c_Hilbert__Choice_Oinv__into(_1784172, _1784174, hAPP(c_Set_Oimage(_1784178, _1784172, _1784180), _1784182), _1784176)), _1784184))], (49720 ^ _779448) ^ [_1784553, _1784555, _1784557] : [hAPP(c_Set_Oimage(_1784553, _1784555, _1784557), c_Orderings_Otop__class_Otop(tc_fun(_1784553, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784555, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1784553, _1784555, _1784555, _1784557), c_Hilbert__Choice_Oinv__into(_1784553, _1784555, c_Orderings_Otop__class_Otop(tc_fun(_1784553, tc_HOL_Obool)), _1784557)) = c_Fun_Oid(_1784555))], (49726 ^ _779448) ^ [_1784702, _1784704, _1784706] : [hAPP(c_Fun_Ocomp(_1784702, _1784704, _1784704, _1784706), c_Hilbert__Choice_Oinv__into(_1784702, _1784704, c_Orderings_Otop__class_Otop(tc_fun(_1784702, tc_HOL_Obool)), _1784706)) = c_Fun_Oid(_1784704), -(hAPP(c_Set_Oimage(_1784702, _1784704, _1784706), c_Orderings_Otop__class_Otop(tc_fun(_1784702, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784704, tc_HOL_Obool)))], (49732 ^ _779448) ^ [_1784857, _1784859, _1784861, _1784863, _1784865] : [c_Fun_Oinj__on(_1784857, _1784859, _1784861, c_Orderings_Otop__class_Otop(tc_fun(_1784857, tc_HOL_Obool))), 49738 ^ _779448 : [(49739 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784859), 49737 ^ [_1784857, _1784859, _1784861, _1784863, _1784865]), hAPP(c_Set_Oimage(_1784857, _1784859, _1784861), c_Orderings_Otop__class_Otop(tc_fun(_1784857, tc_HOL_Obool))))))], (49741 ^ _779448) ^ [] : [hBOOL(hAPP(_1784863, hAPP(c_Hilbert__Choice_Oinv__into(_1784857, _1784859, c_Orderings_Otop__class_Otop(tc_fun(_1784857, tc_HOL_Obool)), _1784861), 49737 ^ [_1784857, _1784859, _1784861, _1784863, _1784865])))]], -(hBOOL(hAPP(_1784863, _1784865)))], (49745 ^ _779448) ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193] : [class_Groups_Ocomm__monoid__mult(_1785183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785185), _1785187)), 49755 ^ _779448 : [(49756 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785185), 49754 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193]), _1785187)))], (49758 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785189), hAPP(_1785191, 49754 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193])))]], 49762 ^ _779448 : [(49763 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785185), 49761 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193]), _1785187)))], (49766 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785185), 49764 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193]), _1785187)))], (49768 ^ _779448) ^ [] : [49761 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193] = 49764 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193]], (49770 ^ _779448) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785189, tc_HOL_Obool)), hAPP(_1785191, 49761 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193])), hAPP(_1785191, 49764 ^ [_1785183, _1785185, _1785187, _1785189, _1785191, _1785193])) = c_Orderings_Obot__class_Obot(tc_fun(_1785189, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785183, _1785189, c_Groups_Otimes__class_Otimes(_1785183)), _1785193), c_Groups_Oone__class_Oone(_1785183)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785185, tc_fun(_1785189, tc_HOL_Obool)), _1785187), _1785191)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785183, _1785185, c_Groups_Otimes__class_Otimes(_1785183)), hAPP(hAPP(c_COMBB(tc_fun(_1785189, tc_HOL_Obool), _1785183, _1785185), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785183, _1785189, c_Groups_Otimes__class_Otimes(_1785183)), _1785193), c_Groups_Oone__class_Oone(_1785183))), _1785191)), c_Groups_Oone__class_Oone(_1785183)), _1785187))], (49774 ^ _779448) ^ [_1786143, _1786145] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786143), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786145, hAPP(c_Code__Numeral_Onat__of, 49779 ^ [_1786143, _1786145]))), -(hBOOL(hAPP(_1786145, _1786143)))], (49785 ^ _779448) ^ [_1786325] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786325), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786325 = hAPP(c_Code__Numeral_Onat__of, 49788 ^ [_1786325]))], (49792 ^ _779448) ^ [_1786430, _1786432] : [49794 ^ _779448 : [(49795 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49793 ^ [_1786430, _1786432]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49797 ^ _779448) ^ [] : [hBOOL(hAPP(_1786430, hAPP(c_Code__Numeral_Oof__nat, 49793 ^ [_1786430, _1786432])))]], -(hBOOL(hAPP(_1786430, _1786432)))], (49802 ^ _779448) ^ [_1786597] : [-(_1786597 = hAPP(c_Code__Numeral_Oof__nat, 49800 ^ [_1786597]))], (49804 ^ _779448) ^ [_1786625] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49800 ^ [_1786625]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49806 ^ _779448) ^ [_1786660, _1786662, _1786664, _1786666] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786660, _1786662, _1786664, _1786666, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1786662)) = _1786664)], (49808 ^ _779448) ^ [_1786706, _1786708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786706), _1786708)), -(c_Quickcheck_Obeyond(_1786706, _1786708) = _1786708)], (49814 ^ _779448) ^ [_1786793, _1786795] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786793), _1786795))), -(c_Quickcheck_Obeyond(_1786793, _1786795) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49820 ^ _779448) ^ [_1786839] : [-(c_Quickcheck_Obeyond(_1786839, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49822 ^ _779448) ^ [_1786865, _1786867, _1786869, _1786871, _1786873, _1786875] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786865, _1786867, _1786869, _1786871, c_Lazy__Sequence_Olazy__sequence_OInsert(_1786867, _1786873, _1786875)) = hAPP(hAPP(hAPP(_1786871, _1786873), _1786875), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786865, _1786867, _1786869, _1786871, _1786875)))], (49824 ^ _779448) ^ [_1786923, _1786925, _1786927, _1786929] : [c_Fun_Obij__betw(_1786923, _1786925, _1786927, c_Orderings_Otop__class_Otop(tc_fun(_1786923, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1786925, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1786923, _1786925, _1786927), hAPP(c_Set_OCollect(_1786923), _1786929)) = hAPP(c_Set_OCollect(_1786925), hAPP(hAPP(c_COMBB(_1786923, tc_HOL_Obool, _1786925), _1786929), c_Hilbert__Choice_Oinv__into(_1786923, _1786925, c_Orderings_Otop__class_Otop(tc_fun(_1786923, tc_HOL_Obool)), _1786927))))], (49830 ^ _779448) ^ [_1787104, _1787106, _1787108, _1787110, _1787112, _1787114] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1787104, _1787106, _1787108, _1787110), _1787112), _1787114) = hAPP(_1787110, hAPP(hAPP(c_Product__Type_OPair(_1787104, _1787106), _1787112), _1787114)))], (49832 ^ _779448) ^ [_1787160, _1787162, _1787164, _1787166, _1787168] : [hBOOL(hAPP(_1787160, hAPP(hAPP(c_Product__Type_OPair(_1787162, _1787164), _1787166), _1787168))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787162, _1787164, tc_HOL_Obool, _1787160), _1787166), _1787168)))], (49838 ^ _779448) ^ [_1787285, _1787287] : [-(c_Fun_Obij__betw(_1787285, _1787285, c_Fun_Oid(_1787285), _1787287, _1787287))], (49840 ^ _779448) ^ [_1787315, _1787317, _1787319] : [c_Fun_Obij__betw(_1787315, _1787317, _1787319, c_Orderings_Otop__class_Otop(tc_fun(_1787315, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787317, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1787317, _1787315, c_Hilbert__Choice_Oinv__into(_1787315, _1787317, c_Orderings_Otop__class_Otop(tc_fun(_1787315, tc_HOL_Obool)), _1787319), c_Orderings_Otop__class_Otop(tc_fun(_1787317, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787315, tc_HOL_Obool))))], (49846 ^ _779448) ^ [_1787466, _1787468, _1787470] : [c_Fun_Obij__betw(_1787466, _1787468, _1787470, c_Orderings_Otop__class_Otop(tc_fun(_1787466, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787468, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787468, _1787466, c_Orderings_Otop__class_Otop(tc_fun(_1787468, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1787466, _1787468, c_Orderings_Otop__class_Otop(tc_fun(_1787466, tc_HOL_Obool)), _1787470)) = _1787470)], (49852 ^ _779448) ^ [_1787611, _1787613, _1787615, _1787617, _1787619, _1787621] : [c_Fun_Obij__betw(_1787611, _1787613, _1787615, _1787617, _1787619), hBOOL(hAPP(hAPP(c_member(_1787611), _1787621), _1787617)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787613, _1787611, _1787619, c_Hilbert__Choice_Oinv__into(_1787611, _1787613, _1787617, _1787615)), _1787621) = hAPP(_1787615, _1787621))], (49862 ^ _779448) ^ [_1787808, _1787810, _1787812, _1787814, _1787816] : [c_Fun_Obij__betw(_1787808, _1787810, _1787812, _1787814, _1787816), -(c_Fun_Obij__betw(_1787810, _1787808, c_Hilbert__Choice_Oinv__into(_1787808, _1787810, _1787814, _1787812), _1787816, _1787814))], (49868 ^ _779448) ^ [_1787913, _1787915, _1787917, _1787919, _1787921] : [c_Fun_Obij__betw(_1787913, _1787915, _1787917, c_Orderings_Otop__class_Otop(tc_fun(_1787913, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787915, tc_HOL_Obool))), c_Fun_Obij__betw(_1787919, _1787913, _1787921, c_Orderings_Otop__class_Otop(tc_fun(_1787919, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787913, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787919, _1787915, c_Orderings_Otop__class_Otop(tc_fun(_1787919, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1787913, _1787915, _1787919, _1787917), _1787921)) = hAPP(c_Fun_Ocomp(_1787913, _1787919, _1787915, c_Hilbert__Choice_Oinv__into(_1787919, _1787913, c_Orderings_Otop__class_Otop(tc_fun(_1787919, tc_HOL_Obool)), _1787921)), c_Hilbert__Choice_Oinv__into(_1787913, _1787915, c_Orderings_Otop__class_Otop(tc_fun(_1787913, tc_HOL_Obool)), _1787917)))], (49878 ^ _779448) ^ [_1788198, _1788200, _1788202, _1788204, _1788206, _1788208, _1788210, _1788212] : [c_Fun_Obij__betw(_1788198, _1788200, _1788202, _1788204, _1788206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1788198, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1788208, _1788198, _1788210), _1788212)), _1788204)), 49885 ^ _779448 : [(49886 ^ _779448) ^ [] : [c_Fun_Obij__betw(_1788208, _1788198, _1788210, _1788212, _1788204), -(c_Fun_Obij__betw(_1788208, _1788200, hAPP(c_Fun_Ocomp(_1788198, _1788200, _1788208, _1788202), _1788210), _1788212, _1788206))], (49892 ^ _779448) ^ [] : [c_Fun_Obij__betw(_1788208, _1788200, hAPP(c_Fun_Ocomp(_1788198, _1788200, _1788208, _1788202), _1788210), _1788212, _1788206), -(c_Fun_Obij__betw(_1788208, _1788198, _1788210, _1788212, _1788204))]]], (49898 ^ _779448) ^ [_1788587, _1788589, _1788591, _1788593, _1788595] : [c_Fun_Obij__betw(_1788587, _1788589, _1788591, c_Orderings_Otop__class_Otop(tc_fun(_1788587, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788589, tc_HOL_Obool))), c_Fun_Obij__betw(_1788589, _1788593, _1788595, c_Orderings_Otop__class_Otop(tc_fun(_1788589, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788593, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1788587, _1788593, hAPP(c_Fun_Ocomp(_1788589, _1788593, _1788587, _1788595), _1788591), c_Orderings_Otop__class_Otop(tc_fun(_1788587, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788593, tc_HOL_Obool))))], (49908 ^ _779448) ^ [_1788822, _1788824, _1788826, _1788828, _1788830, _1788832, _1788834, _1788836] : [c_Fun_Obij__betw(_1788822, _1788824, _1788826, _1788828, _1788830), 49911 ^ _779448 : [(49912 ^ _779448) ^ [] : [c_Fun_Obij__betw(_1788824, _1788832, _1788834, _1788830, _1788836), -(c_Fun_Obij__betw(_1788822, _1788832, hAPP(c_Fun_Ocomp(_1788824, _1788832, _1788822, _1788834), _1788826), _1788828, _1788836))], (49918 ^ _779448) ^ [] : [c_Fun_Obij__betw(_1788822, _1788832, hAPP(c_Fun_Ocomp(_1788824, _1788832, _1788822, _1788834), _1788826), _1788828, _1788836), -(c_Fun_Obij__betw(_1788824, _1788832, _1788834, _1788830, _1788836))]]], (49924 ^ _779448) ^ [_1789113, _1789115, _1789117, _1789119, _1789121, _1789123, _1789125, _1789127] : [c_Fun_Obij__betw(_1789113, _1789115, _1789117, _1789119, _1789121), c_Fun_Obij__betw(_1789115, _1789123, _1789125, _1789121, _1789127), -(c_Fun_Obij__betw(_1789113, _1789123, hAPP(c_Fun_Ocomp(_1789115, _1789123, _1789113, _1789125), _1789117), _1789119, _1789127))], (49934 ^ _779448) ^ [_1789300, _1789302, _1789304, _1789306, _1789308] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789300, _1789302, tc_HOL_Obool, _1789304), _1789306), _1789308)), -(hBOOL(hAPP(_1789304, hAPP(hAPP(c_Product__Type_OPair(_1789300, _1789302), _1789306), _1789308))))], (49940 ^ _779448) ^ [_1789425, _1789427, _1789429, _1789431, _1789433] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789425, _1789427, tc_HOL_Obool, _1789429), _1789431), _1789433)), -(hBOOL(hAPP(_1789429, hAPP(hAPP(c_Product__Type_OPair(_1789425, _1789427), _1789431), _1789433))))], (49946 ^ _779448) ^ [_1789550, _1789552, _1789554, _1789556, _1789558, _1789560] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1789550, _1789552, _1789554, _1789556), _1789558), _1789560) = hAPP(_1789556, hAPP(hAPP(c_Product__Type_OPair(_1789550, _1789552), _1789558), _1789560)))], (49948 ^ _779448) ^ [_1789606, _1789608, _1789610, _1789612] : [c_Fun_Obij__betw(_1789606, _1789608, _1789610, c_Orderings_Otop__class_Otop(tc_fun(_1789606, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789608, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1789606, _1789608, _1789610), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789606, tc_HOL_Obool)), _1789612)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1789608, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1789606, _1789608, _1789610), _1789612)))], (49954 ^ _779448) ^ [_1789773, _1789775, _1789777, _1789779] : [c_Fun_Obij__betw(_1789773, _1789775, _1789777, c_Orderings_Otop__class_Otop(tc_fun(_1789773, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789775, tc_HOL_Obool))), 49957 ^ _779448 : [(49958 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1789773), hAPP(c_Set_Ovimage(_1789773, _1789775, _1789777), _1789779))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1789775), _1789779)))], (49964 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1789775), _1789779)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1789773), hAPP(c_Set_Ovimage(_1789773, _1789775, _1789777), _1789779))))]]], (49970 ^ _779448) ^ [_1790063, _1790065, _1790067, _1790069, _1790071, _1790073, _1790075] : [c_Fun_Obij__betw(_1790063, _1790065, _1790067, _1790069, _1790071), c_Fun_Obij__betw(_1790063, _1790065, _1790067, _1790073, _1790075), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1790065, tc_HOL_Obool)), _1790071), _1790075) = c_Orderings_Obot__class_Obot(tc_fun(_1790065, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1790063, _1790065, _1790067, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1790063, tc_HOL_Obool)), _1790069), _1790073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1790065, tc_HOL_Obool)), _1790071), _1790075)))], (49984 ^ _779448) ^ [_1790368, _1790370, _1790372, _1790374, _1790376, _1790378, _1790380] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1790368, tc_HOL_Obool)), _1790370), _1790372) = c_Orderings_Obot__class_Obot(tc_fun(_1790368, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1790374, tc_HOL_Obool)), _1790376), _1790378) = c_Orderings_Obot__class_Obot(tc_fun(_1790374, tc_HOL_Obool)), c_Fun_Obij__betw(_1790368, _1790374, _1790380, _1790370, _1790376), c_Fun_Obij__betw(_1790368, _1790374, _1790380, _1790372, _1790378), -(c_Fun_Obij__betw(_1790368, _1790374, _1790380, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1790368, tc_HOL_Obool)), _1790370), _1790372), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1790374, tc_HOL_Obool)), _1790376), _1790378)))], (50002 ^ _779448) ^ [_1790767] : [-(c_Fun_Obij__betw(_1790767, _1790767, c_Fun_Oid(_1790767), c_Orderings_Otop__class_Otop(tc_fun(_1790767, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790767, tc_HOL_Obool))))], (50004 ^ _779448) ^ [_1790823, _1790825, _1790827] : [c_Fun_Obij__betw(_1790823, _1790823, c_Fun_Oid(_1790823), _1790825, _1790827), -(_1790825 = _1790827)], (50010 ^ _779448) ^ [_1790908, _1790910, _1790912] : [_1790910 = _1790912, -(c_Fun_Obij__betw(_1790908, _1790908, c_Fun_Oid(_1790908), _1790910, _1790912))], (50016 ^ _779448) ^ [_1790999, _1791001, _1791003, _1791005, _1791007] : [c_Fun_Obij__betw(_1790999, _1791001, _1791003, _1791005, _1791007), 50019 ^ _779448 : [(50020 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1790999), _1791005)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1791001), _1791007)))], (50026 ^ _779448) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1791001), _1791007)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1790999), _1791005)))]]], (50032 ^ _779448) ^ [_1791254, _1791256, _1791258, _1791260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1791254), _1791256)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1791258), _1791260)), 50039 ^ _779448 : [(50040 ^ _779448) ^ [] : [50041 ^ _779448 : [(50042 ^ _779448) ^ [_1791443] : [c_Fun_Obij__betw(_1791254, _1791258, _1791443, _1791256, _1791260)]], -(hAPP(c_Finite__Set_Ocard(_1791254), _1791256) = hAPP(c_Finite__Set_Ocard(_1791258), _1791260))], (50046 ^ _779448) ^ [] : [hAPP(c_Finite__Set_Ocard(_1791254), _1791256) = hAPP(c_Finite__Set_Ocard(_1791258), _1791260), -(c_Fun_Obij__betw(_1791254, _1791258, 50049 ^ [_1791254, _1791256, _1791258, _1791260], _1791256, _1791260))]]], (50053 ^ _779448) ^ [_1791608, _1791610, _1791612, _1791614] : [c_Fun_Obij__betw(_1791608, _1791610, _1791612, c_Orderings_Obot__class_Obot(tc_fun(_1791608, tc_HOL_Obool)), _1791614), -(_1791614 = c_Orderings_Obot__class_Obot(tc_fun(_1791610, tc_HOL_Obool)))], (50059 ^ _779448) ^ [_1791715, _1791717, _1791719, _1791721] : [c_Fun_Obij__betw(_1791715, _1791717, _1791719, _1791721, c_Orderings_Obot__class_Obot(tc_fun(_1791717, tc_HOL_Obool))), -(_1791721 = c_Orderings_Obot__class_Obot(tc_fun(_1791715, tc_HOL_Obool)))], (50065 ^ _779448) ^ [_1791822, _1791824, _1791826, _1791828, _1791830] : [c_Fun_Obij__betw(_1791822, _1791824, _1791826, _1791828, _1791830), -(hAPP(c_Finite__Set_Ocard(_1791822), _1791828) = hAPP(c_Finite__Set_Ocard(_1791824), _1791830))], (50071 ^ _779448) ^ [_1791931, _1791933, _1791935, _1791937, _1791939] : [c_Fun_Obij__betw(_1791931, _1791933, _1791935, _1791937, _1791939), -(c_Fun_Obij__betw(_1791933, _1791931, c_Fun_Othe__inv__into(_1791931, _1791933, _1791937, _1791935), _1791939, _1791937))], (50077 ^ _779448) ^ [_1792036, _1792038, _1792040] : [c_Fun_Obij__betw(_1792036, _1792038, _1792040, c_Orderings_Otop__class_Otop(tc_fun(_1792036, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792038, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1792036, _1792038, _1792040, c_Orderings_Otop__class_Otop(tc_fun(_1792036, tc_HOL_Obool))))], (50083 ^ _779448) ^ [_1792155, _1792157, _1792159, _1792161, _1792163] : [c_Fun_Obij__betw(_1792155, _1792157, _1792159, _1792161, _1792163), -(c_Fun_Oinj__on(_1792155, _1792157, _1792159, _1792161))], (50089 ^ _779448) ^ [_1792248, _1792250, _1792252, _1792254] : [c_Fun_Oinj__on(_1792248, _1792250, _1792252, _1792254), -(c_Fun_Obij__betw(_1792248, _1792250, _1792252, _1792254, hAPP(c_Set_Oimage(_1792248, _1792250, _1792252), _1792254)))], (50095 ^ _779448) ^ [_1792377, _1792379, _1792381, _1792383, _1792385] : [c_Fun_Obij__betw(_1792377, _1792379, _1792381, _1792383, _1792385), 50098 ^ _779448 : [(50099 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_1792377, _1792379, _1792381, _1792383))], (50101 ^ _779448) ^ [] : [-(hAPP(c_Set_Oimage(_1792377, _1792379, _1792381), _1792383) = _1792385)]]], (50103 ^ _779448) ^ [_1792506, _1792508, _1792510, _1792512, _1792514] : [-(c_Fun_Obij__betw(_1792506, _1792508, _1792510, _1792512, _1792514)), c_Fun_Oinj__on(_1792506, _1792508, _1792510, _1792512), hAPP(c_Set_Oimage(_1792506, _1792508, _1792510), _1792512) = _1792514], (50113 ^ _779448) ^ [_1792673, _1792675, _1792677, _1792679] : [c_Fun_Obij__betw(_1792673, _1792675, _1792677, _1792679, c_Orderings_Otop__class_Otop(tc_fun(_1792675, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1792673, _1792675, _1792677), c_Orderings_Otop__class_Otop(tc_fun(_1792673, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792675, tc_HOL_Obool)))], (50119 ^ _779448) ^ [_1792804, _1792806, _1792808] : [c_Fun_Obij__betw(_1792804, _1792806, _1792808, c_Orderings_Otop__class_Otop(tc_fun(_1792804, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792806, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1792804, _1792806, _1792808), c_Orderings_Otop__class_Otop(tc_fun(_1792804, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792806, tc_HOL_Obool)))], (50125 ^ _779448) ^ [_1792943, _1792945, _1792947, _1792949, _1792951, _1792953, _1792955] : [c_Fun_Obij__betw(_1792943, _1792945, _1792947, _1792949, _1792951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1792943, tc_HOL_Obool)), _1792953), _1792949)), hAPP(c_Set_Oimage(_1792943, _1792945, _1792947), _1792953) = _1792955, -(c_Fun_Obij__betw(_1792943, _1792945, _1792947, _1792953, _1792955))], (50139 ^ _779448) ^ [_1793218, _1793220, _1793222] : [c_Fun_Obij__betw(_1793218, _1793220, _1793222, c_Orderings_Otop__class_Otop(tc_fun(_1793218, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793220, tc_HOL_Obool))), 50142 ^ _779448 : [(50143 ^ _779448) ^ [] : [-(c_Fun_Oinj__on(_1793218, _1793220, _1793222, c_Orderings_Otop__class_Otop(tc_fun(_1793218, tc_HOL_Obool))))], (50145 ^ _779448) ^ [] : [-(hAPP(c_Set_Oimage(_1793218, _1793220, _1793222), c_Orderings_Otop__class_Otop(tc_fun(_1793218, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793220, tc_HOL_Obool)))]]], (50147 ^ _779448) ^ [_1793393, _1793395, _1793397] : [-(c_Fun_Obij__betw(_1793393, _1793395, _1793397, c_Orderings_Otop__class_Otop(tc_fun(_1793393, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793395, tc_HOL_Obool)))), c_Fun_Oinj__on(_1793393, _1793395, _1793397, c_Orderings_Otop__class_Otop(tc_fun(_1793393, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1793393, _1793395, _1793397), c_Orderings_Otop__class_Otop(tc_fun(_1793393, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793395, tc_HOL_Obool))], (50157 ^ _779448) ^ [_1793602, _1793604, _1793606] : [c_Fun_Oinj__on(_1793602, _1793604, _1793606, c_Orderings_Otop__class_Otop(tc_fun(_1793602, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1793602, _1793604, _1793606), c_Orderings_Otop__class_Otop(tc_fun(_1793602, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793604, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1793602, _1793604, _1793606, c_Orderings_Otop__class_Otop(tc_fun(_1793602, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793604, tc_HOL_Obool))))], (50167 ^ _779448) ^ [_1793809, _1793811, _1793813, _1793815] : [-(c_Product__Type_Ocurry(_1793809, _1793811, _1793813, hAPP(c_Product__Type_Oprod_Oprod__case(_1793809, _1793811, _1793813), _1793815)) = _1793815)], (50169 ^ _779448) ^ [_1793850, _1793852, _1793854, _1793856] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1793850, _1793852, _1793854), c_Product__Type_Ocurry(_1793850, _1793852, _1793854, _1793856)) = _1793856)], (50171 ^ _779448) ^ [_1793891, _1793893, _1793895, _1793897, _1793899, _1793901] : [c_Fun_Obij__betw(_1793891, _1793893, _1793895, c_Orderings_Otop__class_Otop(tc_fun(_1793891, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793893, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793891, _1793893, _1793895), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793897, tc_fun(_1793891, tc_HOL_Obool)), _1793899), _1793901)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1793897, tc_fun(_1793893, tc_HOL_Obool)), _1793899), hAPP(hAPP(c_COMBB(tc_fun(_1793891, tc_HOL_Obool), tc_fun(_1793893, tc_HOL_Obool), _1793897), c_Set_Oimage(_1793891, _1793893, _1793895)), _1793901)))], (50177 ^ _779448) ^ [_1794104, _1794106, _1794108, _1794110, _1794112] : [c_Fun_Obij__betw(_1794104, _1794106, _1794108, c_Orderings_Otop__class_Otop(tc_fun(_1794104, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794106, tc_HOL_Obool))), 50180 ^ _779448 : [(50181 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794104, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794104, _1794106, _1794108), _1794110)), _1794112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794106, tc_HOL_Obool)), _1794110), hAPP(c_Set_Oimage(_1794104, _1794106, _1794108), _1794112))))], (50187 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794106, tc_HOL_Obool)), _1794110), hAPP(c_Set_Oimage(_1794104, _1794106, _1794108), _1794112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794104, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794104, _1794106, _1794108), _1794110)), _1794112)))]]], (50193 ^ _779448) ^ [_1794457, _1794459, _1794461, _1794463] : [c_Fun_Obij__betw(_1794457, _1794459, _1794461, c_Orderings_Otop__class_Otop(tc_fun(_1794457, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794459, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1794457, _1794459, _1794461), _1794463) = hAPP(c_Set_Oimage(_1794459, _1794457, c_Hilbert__Choice_Oinv__into(_1794457, _1794459, c_Orderings_Otop__class_Otop(tc_fun(_1794457, tc_HOL_Obool)), _1794461)), _1794463))], (50199 ^ _779448) ^ [_1794612, _1794614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1794612), _1794614)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1794612, 50202 ^ [_1794612, _1794614], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1794612), _1794614)), _1794614))], (50206 ^ _779448) ^ [_1794733, _1794735, _1794737, _1794739, _1794741, _1794743] : [c_Fun_Oinj__on(_1794733, _1794735, _1794737, _1794739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794735, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794733, _1794735, _1794737), _1794739)), _1794741)), c_Fun_Oinj__on(_1794735, _1794733, _1794743, _1794741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794733, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1794735, _1794733, _1794743), _1794741)), _1794739)), -(c_Fun_Obij__betw(_1794733, _1794735, 50221 ^ [_1794733, _1794735, _1794737, _1794739, _1794741, _1794743], _1794739, _1794741))], (50225 ^ _779448) ^ [_1795100, _1795102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795100), _1795102)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1795100, 50228 ^ [_1795100, _1795102], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795100), _1795102)), _1795102))], (50232 ^ _779448) ^ [_1795219, _1795221] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795219), _1795221)), -(c_Fun_Obij__betw(_1795219, tc_Nat_Onat, 50235 ^ [_1795219, _1795221], _1795221, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795219), _1795221))))], (50239 ^ _779448) ^ [_1795338, _1795340, _1795342, _1795344, _1795346] : [50241 ^ _779448 : [(50242 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795338), 50240 ^ [_1795338, _1795340, _1795342, _1795344, _1795346]), _1795340)))], (50244 ^ _779448) ^ [] : [c_Relation_Orefl__on(_1795342, hAPP(_1795344, 50240 ^ [_1795338, _1795340, _1795342, _1795344, _1795346]), hAPP(_1795346, 50240 ^ [_1795338, _1795340, _1795342, _1795344, _1795346]))]], -(c_Relation_Orefl__on(_1795342, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795338, tc_fun(_1795342, tc_HOL_Obool)), _1795340), _1795344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795338, tc_fun(tc_prod(_1795342, _1795342), tc_HOL_Obool)), _1795340), _1795346)))], (50248 ^ _779448) ^ [_1795606, _1795608, _1795610] : [c_Equiv__Relations_Oequivp(_1795606, _1795608), 50251 ^ _779448 : [(50263 ^ _779448) ^ [] : [50264 ^ _779448 : [(50265 ^ _779448) ^ [_1795895] : [hBOOL(hAPP(_1795610, _1795895))]], 50267 ^ _779448 : [(50268 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795606), 50266 ^ [_1795606, _1795608, _1795610]), c_Quotient_ORespects(_1795606, _1795608))))], (50270 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1795610, 50266 ^ [_1795606, _1795608, _1795610])))]]], (50252 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1795610, 50259 ^ [_1795606, _1795608, _1795610]))), 50253 ^ _779448 : [(50254 ^ _779448) ^ [_1795728] : [hBOOL(hAPP(hAPP(c_member(_1795606), _1795728), c_Quotient_ORespects(_1795606, _1795608))), hBOOL(hAPP(_1795610, _1795728))]]]]], (50272 ^ _779448) ^ [_1796022, _1796024, _1796026] : [hBOOL(hAPP(c_Quotient_ORespects(_1796022, _1796024), _1796026)), -(hBOOL(hAPP(hAPP(_1796024, _1796026), _1796026)))], (50278 ^ _779448) ^ [_1796117, _1796119, _1796121] : [hBOOL(hAPP(hAPP(_1796119, _1796121), _1796121)), -(hBOOL(hAPP(c_Quotient_ORespects(_1796117, _1796119), _1796121)))], (50284 ^ _779448) ^ [_1796236, _1796238, _1796240] : [hBOOL(hAPP(hAPP(c_member(_1796236), _1796238), c_Quotient_ORespects(_1796236, _1796240))), -(hBOOL(hAPP(hAPP(_1796240, _1796238), _1796238)))], (50290 ^ _779448) ^ [_1796341, _1796343, _1796345] : [hBOOL(hAPP(hAPP(_1796345, _1796343), _1796343)), -(hBOOL(hAPP(hAPP(c_member(_1796341), _1796343), c_Quotient_ORespects(_1796341, _1796345))))], (50296 ^ _779448) ^ [_1796452, _1796454, _1796456, _1796458] : [c_Equiv__Relations_Oequivp(_1796452, _1796454), 50302 ^ _779448 : [(50303 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1796456, 50301 ^ [_1796452, _1796454, _1796456, _1796458])))], (50305 ^ _779448) ^ [] : [hBOOL(hAPP(_1796458, 50301 ^ [_1796452, _1796454, _1796456, _1796458]))]], 50308 ^ _779448 : [(50309 ^ _779448) ^ [_1796711] : [hBOOL(hAPP(_1796456, _1796711))]], 50311 ^ _779448 : [(50312 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796452), 50310 ^ [_1796452, _1796454, _1796456, _1796458]), c_Quotient_ORespects(_1796452, _1796454))))], (50314 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1796458, 50310 ^ [_1796452, _1796454, _1796456, _1796458])))]]], (50316 ^ _779448) ^ [_1796824, _1796826, _1796828, _1796830] : [c_Equiv__Relations_Oequivp(_1796824, _1796826), -(c_Quotient_OBabs(_1796824, _1796828, c_Quotient_ORespects(_1796824, _1796826), _1796830) = _1796830)], (50322 ^ _779448) ^ [_1796921, _1796923, _1796925, _1796927, _1796929] : [hBOOL(hAPP(hAPP(c_member(_1796921), _1796923), _1796925)), -(hAPP(c_Quotient_OBabs(_1796921, _1796927, _1796925, _1796929), _1796923) = hAPP(_1796929, _1796923))], (50328 ^ _779448) ^ [_1797040, _1797042, _1797044] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797040, _1797040)), hAPP(hAPP(c_Product__Type_OPair(_1797040, _1797040), hAPP(_1797042, hAPP(c_Nat_OSuc, 50329 ^ [_1797040, _1797042, _1797044]))), hAPP(_1797042, 50329 ^ [_1797040, _1797042, _1797044]))), c_Transitive__Closure_Ortrancl(_1797040, _1797044))), c_Wellfounded_Owf(_1797040, c_Transitive__Closure_Otrancl(_1797040, _1797044)), 50337 ^ _779448 : [(50338 ^ _779448) ^ [_1797306] : [-(hAPP(_1797042, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50336 ^ [_1797040, _1797042, _1797044]), _1797306)) = hAPP(_1797042, 50336 ^ [_1797040, _1797042, _1797044]))]]], (50340 ^ _779448) ^ [_1797365, _1797367, _1797369, _1797371, _1797373, _1797375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797365, tc_HOL_Obool)), _1797367), _1797369)), 50346 ^ _779448 : [(50347 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797365), 50345 ^ [_1797365, _1797367, _1797369, _1797371, _1797373, _1797375]), _1797369)))], (50349 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797371, tc_HOL_Obool)), hAPP(_1797373, 50345 ^ [_1797365, _1797367, _1797369, _1797371, _1797373, _1797375])), hAPP(_1797375, 50345 ^ [_1797365, _1797367, _1797369, _1797371, _1797373, _1797375])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797371, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797365, tc_fun(_1797371, tc_HOL_Obool)), _1797369), _1797373)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797365, tc_fun(_1797371, tc_HOL_Obool)), _1797369), _1797375))))], (50353 ^ _779448) ^ [_1797762, _1797764, _1797766, _1797768, _1797770] : [50355 ^ _779448 : [(50356 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797762), 50354 ^ [_1797762, _1797764, _1797766, _1797768, _1797770]), _1797764)))], (50358 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797766, tc_HOL_Obool)), _1797768), hAPP(_1797770, 50354 ^ [_1797762, _1797764, _1797766, _1797768, _1797770])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797766, tc_HOL_Obool)), _1797768), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797762, tc_fun(_1797766, tc_HOL_Obool)), _1797764), _1797770))))], (50362 ^ _779448) ^ [_1798023, _1798025, _1798027, _1798029, _1798031, _1798033, _1798035] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025)), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798027), _1798029)), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798031), _1798033))), c_Transitive__Closure_Ortrancl(tc_prod(_1798023, _1798025), _1798035))), -(hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798027), _1798029) = hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798031), _1798033)), 50371 ^ _779448 : [(50372 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025)), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798027), _1798029)), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), 50369 ^ [_1798023, _1798025, _1798027, _1798029, _1798031, _1798033, _1798035]), 50370 ^ [_1798023, _1798025, _1798027, _1798029, _1798031, _1798033, _1798035]))), _1798035)))], (50374 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798023, _1798025), tc_prod(_1798023, _1798025)), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), 50369 ^ [_1798023, _1798025, _1798027, _1798029, _1798031, _1798033, _1798035]), 50370 ^ [_1798023, _1798025, _1798027, _1798029, _1798031, _1798033, _1798035])), hAPP(hAPP(c_Product__Type_OPair(_1798023, _1798025), _1798031), _1798033))), c_Transitive__Closure_Ortrancl(tc_prod(_1798023, _1798025), _1798035))))]]], (50376 ^ _779448) ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606)), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), _1798608), _1798610)), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), _1798612), _1798614))), c_Transitive__Closure_Ortrancl(tc_prod(_1798604, _1798606), _1798616))), hBOOL(hAPP(hAPP(_1798618, _1798608), _1798610)), 50387 ^ _779448 : [(50388 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606)), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), _1798608), _1798610)), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), 50385 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]), 50386 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]))), c_Transitive__Closure_Ortrancl(tc_prod(_1798604, _1798606), _1798616))))], (50392 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798604, _1798606), tc_prod(_1798604, _1798606)), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), 50385 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]), 50386 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618])), hAPP(hAPP(c_Product__Type_OPair(_1798604, _1798606), 50389 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]), 50390 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]))), _1798616)))], (50394 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1798618, 50385 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]), 50386 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618])))], (50396 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1798618, 50389 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]), 50390 ^ [_1798604, _1798606, _1798608, _1798610, _1798612, _1798614, _1798616, _1798618]))]], -(hBOOL(hAPP(hAPP(_1798618, _1798612), _1798614)))], (50400 ^ _779448) ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736)), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), _1799738), _1799740)), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), _1799742), _1799744))), c_Transitive__Closure_Ortrancl(tc_prod(_1799734, _1799736), _1799746))), hBOOL(hAPP(hAPP(_1799748, _1799742), _1799744)), 50413 ^ _779448 : [(50414 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736)), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), 50409 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]), 50410 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748])), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), 50411 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]), 50412 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]))), _1799746)))], (50416 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799734, _1799736), tc_prod(_1799734, _1799736)), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), 50411 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]), 50412 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748])), hAPP(hAPP(c_Product__Type_OPair(_1799734, _1799736), _1799742), _1799744))), c_Transitive__Closure_Ortrancl(tc_prod(_1799734, _1799736), _1799746))))], (50418 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(_1799748, 50411 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]), 50412 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748])))], (50420 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(_1799748, 50409 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]), 50410 ^ [_1799734, _1799736, _1799738, _1799740, _1799742, _1799744, _1799746, _1799748]))]], -(hBOOL(hAPP(hAPP(_1799748, _1799738), _1799740)))], (50424 ^ _779448) ^ [_1800794, _1800796, _1800798, _1800800] : [50427 ^ _779448 : [(50428 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800794, _1800794)), hAPP(hAPP(c_Product__Type_OPair(_1800794, _1800794), 50425 ^ [_1800794, _1800796, _1800798, _1800800]), 50426 ^ [_1800794, _1800796, _1800798, _1800800])), _1800796)))], (50430 ^ _779448) ^ [] : [hAPP(_1800798, 50425 ^ [_1800794, _1800796, _1800798, _1800800]) = hAPP(_1800798, 50426 ^ [_1800794, _1800796, _1800798, _1800800])]], -(c_Equiv__Relations_Ocongruent(_1800794, _1800800, _1800796, _1800798))], (50434 ^ _779448) ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062] : [50437 ^ _779448 : [(50438 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801052, _1801052)), hAPP(hAPP(c_Product__Type_OPair(_1801052, _1801052), 50435 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062]), 50436 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062])), _1801054)))], (50442 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801056, _1801056)), hAPP(hAPP(c_Product__Type_OPair(_1801056, _1801056), 50439 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062]), 50440 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062])), _1801058)))], (50444 ^ _779448) ^ [] : [hAPP(hAPP(_1801060, 50435 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062]), 50439 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062]) = hAPP(hAPP(_1801060, 50436 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062]), 50440 ^ [_1801052, _1801054, _1801056, _1801058, _1801060, _1801062])]], -(c_Equiv__Relations_Ocongruent2(_1801052, _1801056, _1801062, _1801054, _1801058, _1801060))], (50448 ^ _779448) ^ [_1801616, _1801618, _1801620] : [-(c_Lazy__Sequence_Oflat(_1801616, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1801616), _1801618, _1801620)) = c_Lazy__Sequence_Oappend(_1801616, _1801618, c_Lazy__Sequence_Oflat(_1801616, _1801620)))], (50450 ^ _779448) ^ [_1801677, _1801679, _1801681] : [c_List_Olist__all(tc_Nat_Onat, _1801677, c_List_Oupt(_1801679, _1801681)), -(c_List_Oall__interval__nat(_1801677, _1801679, _1801681))], (50456 ^ _779448) ^ [_1801762, _1801764, _1801766] : [c_List_Oall__interval__nat(_1801762, _1801764, _1801766), -(c_List_Olist__all(tc_Nat_Onat, _1801762, c_List_Oupt(_1801764, _1801766)))], (50462 ^ _779448) ^ [_1801853] : [-(c_Lazy__Sequence_Oflat(_1801853, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1801853))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1801853))], (50474 ^ _779448) ^ [_1802090, _1802092, _1802094] : [50476 ^ _779448 : [(50477 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50475 ^ [_1802090, _1802092, _1802094]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802092), _1802094))))], (50479 ^ _779448) ^ [] : [hBOOL(hAPP(_1802090, 50475 ^ [_1802090, _1802092, _1802094]))]], -(c_List_Oall__interval__nat(_1802090, _1802092, _1802094))], (50464 ^ _779448) ^ [_1801903, _1801905, _1801907] : [c_List_Oall__interval__nat(_1801903, _1801905, _1801907), 50467 ^ _779448 : [(50468 ^ _779448) ^ [_1801983] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1801983), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1801905), _1801907))), -(hBOOL(hAPP(_1801903, _1801983)))]]], (50483 ^ _779448) ^ [_1802288, _1802290, _1802292] : [c_List_Olist__ex(tc_Nat_Onat, _1802288, c_List_Oupt(_1802290, _1802292)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802288), _1802290, _1802292)], (50489 ^ _779448) ^ [_1802378, _1802380, _1802382] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802378), _1802380, _1802382)), -(c_List_Olist__ex(tc_Nat_Onat, _1802378, c_List_Oupt(_1802380, _1802382)))], (50495 ^ _779448) ^ [_1802426, _1802428, _1802430, _1802432] : [-(hAPP(c_Lazy__Sequence_Obind(_1802426, _1802428, _1802430), _1802432) = c_Lazy__Sequence_Oflat(_1802428, c_Lazy__Sequence_Omap(_1802426, tc_Lazy__Sequence_Olazy__sequence(_1802428), _1802432, _1802430)))], (50497 ^ _779448) ^ [_1802472, _1802474, _1802476, _1802478, _1802480, _1802482, _1802484, _1802486] : [c_Finite__Set_Ofolding__image(_1802472, _1802474, _1802476, _1802478, _1802480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802474), _1802482)), 50507 ^ _779448 : [(50508 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802474), 50506 ^ [_1802472, _1802474, _1802476, _1802478, _1802480, _1802482, _1802484, _1802486]), _1802482)))], (50510 ^ _779448) ^ [] : [hAPP(_1802484, 50506 ^ [_1802472, _1802474, _1802476, _1802478, _1802480, _1802482, _1802484, _1802486]) = hAPP(_1802486, 50506 ^ [_1802472, _1802474, _1802476, _1802478, _1802480, _1802482, _1802484, _1802486])]], -(hAPP(hAPP(_1802480, _1802484), _1802482) = hAPP(hAPP(_1802480, _1802486), _1802482))], (50514 ^ _779448) ^ [_1802877, _1802879, _1802881, _1802883, _1802885] : [-(c_Lazy__Sequence_Omap(_1802877, _1802879, _1802881, c_Lazy__Sequence_Olazy__sequence_OInsert(_1802877, _1802883, _1802885)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1802879, hAPP(_1802881, _1802883), c_Lazy__Sequence_Omap(_1802877, _1802879, _1802881, _1802885)))], (50516 ^ _779448) ^ [_1802929, _1802931, _1802933] : [-(c_Lazy__Sequence_Omap(_1802929, _1802931, _1802933, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802929)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802931))], (50518 ^ _779448) ^ [_1802965, _1802967, _1802969, _1802971, _1802973] : [-(c_New__DSequence_Opos__map(_1802965, _1802967, _1802969, _1802971, _1802973) = c_Lazy__Sequence_Omap(_1802965, _1802967, _1802969, hAPP(_1802971, _1802973)))], (50520 ^ _779448) ^ [_1803010, _1803012, _1803014] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803010), _1803012)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803010), _1803014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1803010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803012), _1803014)))], (50530 ^ _779448) ^ [_1803191] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803191), _1803191)))], (50532 ^ _779448) ^ [_1803219, _1803221] : [class_Rings_Ocomm__semiring__1(_1803219), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803219), _1803221), c_Groups_Ozero__class_Ozero(_1803219))))], (50538 ^ _779448) ^ [_1803312] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1803312)))], (50540 ^ _779448) ^ [_1803337, _1803339] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803337), _1803339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803337), _1803339)))], (50550 ^ _779448) ^ [_1803490, _1803492, _1803494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803490)), 50553 ^ _779448 : [(50554 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803490), _1803492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803490), _1803494))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803492), _1803494)))], (50560 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803492), _1803494)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803490), _1803492)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803490), _1803494))))]]], (50566 ^ _779448) ^ [_1803773, _1803775, _1803777] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803773), _1803775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1803773), _1803777))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1803773)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803775), _1803777)))], (50576 ^ _779448) ^ [_1803954, _1803956, _1803958, _1803960, _1803962] : [class_Groups_Ocomm__monoid__mult(_1803954), class_Rings_Odvd(_1803954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803956), _1803958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803956, tc_HOL_Obool)), _1803960), _1803958)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803954), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1803956, _1803954), _1803962), _1803960)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1803956, _1803954), _1803962), _1803958))))], (50594 ^ _779448) ^ [_1804287, _1804289, _1804291] : [class_Divides_Osemiring__div(_1804287), class_Int_Onumber(_1804287), 50601 ^ _779448 : [(50602 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804287), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804289)), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804291))), -(c_Divides_Odiv__class_Omod(_1804287, hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804291), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804289)) = c_Groups_Ozero__class_Ozero(_1804287))], (50608 ^ _779448) ^ [] : [c_Divides_Odiv__class_Omod(_1804287, hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804291), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804289)) = c_Groups_Ozero__class_Ozero(_1804287), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804287), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804289)), hAPP(c_Int_Onumber__class_Onumber__of(_1804287), _1804291))))]]], (50614 ^ _779448) ^ [_1804651, _1804653, _1804655, _1804657] : [class_Divides_Osemiring__div(_1804651), -(_1804653 = c_Groups_Ozero__class_Ozero(_1804651)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804651), _1804653), _1804655)), 50625 ^ _779448 : [(50626 ^ _779448) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804651), _1804655), _1804653) = _1804657, -(_1804655 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804651), _1804657), _1804653))], (50632 ^ _779448) ^ [] : [_1804655 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804651), _1804657), _1804653), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1804651), _1804655), _1804653) = _1804657)]]], (50638 ^ _779448) ^ [_1805049, _1805051, _1805053, _1805055, _1805057] : [class_Divides_Osemiring__div(_1805049), -(_1805051 = c_Groups_Ozero__class_Ozero(_1805049)), -(_1805053 = c_Groups_Ozero__class_Ozero(_1805049)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805049), _1805051), _1805055)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805049), _1805053), _1805057)), 50657 ^ _779448 : [(50658 ^ _779448) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1805049), _1805055), _1805051) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1805049), _1805057), _1805053), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805049), _1805055), _1805053) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805049), _1805051), _1805057))], (50664 ^ _779448) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805049), _1805055), _1805053) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805049), _1805051), _1805057), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1805049), _1805055), _1805051) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1805049), _1805057), _1805053))]]], (50670 ^ _779448) ^ [_1805642, _1805644, _1805646, _1805648] : [class_Rings_Ocomm__semiring__1(_1805642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805644), _1805646)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805642), hAPP(hAPP(c_Power_Opower__class_Opower(_1805642), _1805648), _1805644)), hAPP(hAPP(c_Power_Opower__class_Opower(_1805642), _1805648), _1805646))))], (50680 ^ _779448) ^ [_1805833, _1805835, _1805837, _1805839, _1805841] : [class_Rings_Ocomm__semiring__1(_1805833), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805833), _1805835), _1805837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1805839), _1805841)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805833), hAPP(hAPP(c_Power_Opower__class_Opower(_1805833), _1805835), _1805839)), hAPP(hAPP(c_Power_Opower__class_Opower(_1805833), _1805837), _1805841))))], (50694 ^ _779448) ^ [_1806100, _1806102, _1806104, _1806106, _1806108] : [class_Rings_Ocomm__semiring__1(_1806100), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806100), hAPP(hAPP(c_Power_Opower__class_Opower(_1806100), _1806102), _1806104)), _1806106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1806108), _1806104)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806100), hAPP(hAPP(c_Power_Opower__class_Opower(_1806100), _1806102), _1806108)), _1806106)))], (50708 ^ _779448) ^ [_1806388, _1806390, _1806392, _1806394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806388, _1806390)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806392, _1806394))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806388), _1806390)), 50715 ^ _779448 : [(50716 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806392), _1806388)))], (50718 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806390), _1806394)))]]], (50720 ^ _779448) ^ [_1806609, _1806611, _1806613, _1806615] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806609, _1806611)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806613, _1806615)))), 50721 ^ _779448 : [(50722 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806609), _1806611)))], (50724 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806613), _1806609)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806611), _1806615))]]], (50732 ^ _779448) ^ [_1806841, _1806843, _1806845] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806841), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1806843), _1806845))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806841), _1806843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1806845), _1806843)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1806841), _1806845)))], (50746 ^ _779448) ^ [_1807080, _1807082, _1807084] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807080), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1807082), _1807084))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807080), _1807084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1807084), _1807082)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807080), _1807082)))], (50760 ^ _779448) ^ [_1807334, _1807336] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807334), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807336))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807336), _1807334)))], (50766 ^ _779448) ^ [_1807435, _1807437] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807437), _1807435)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807435), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807437))))], (50772 ^ _779448) ^ [_1807557, _1807559] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807557), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807559))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807557), _1807559)))], (50778 ^ _779448) ^ [_1807658, _1807660] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807658), _1807660)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807658), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807660))))], (50784 ^ _779448) ^ [_1807780, _1807782] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807780), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1807782))), 50787 ^ _779448 : [(50788 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807780), _1807782)))], (50790 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807782), _1807780))]]], (50792 ^ _779448) ^ [_1807925, _1807927] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1807925), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1807927)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807925), _1807927)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1807927), _1807925)))], (50802 ^ _779448) ^ [_1808112, _1808114] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1808112), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1808114))), 50805 ^ _779448 : [(50806 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808114), _1808112)))], (50808 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808112), _1808114))]]], (50810 ^ _779448) ^ [_1808257, _1808259] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1808257), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1808259)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808259), _1808257)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1808257), _1808259)))], (50820 ^ _779448) ^ [_1808429, _1808431, _1808433] : [class_Divides_Osemiring__div(_1808429), 50823 ^ _779448 : [(50824 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808429), _1808431), _1808433)), -(c_Divides_Odiv__class_Omod(_1808429, _1808433, _1808431) = c_Groups_Ozero__class_Ozero(_1808429))], (50830 ^ _779448) ^ [] : [c_Divides_Odiv__class_Omod(_1808429, _1808433, _1808431) = c_Groups_Ozero__class_Ozero(_1808429), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808429), _1808431), _1808433)))]]], (50836 ^ _779448) ^ [_1808679, _1808681, _1808683] : [class_Divides_Osemiring__div(_1808679), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808679), _1808681), _1808683)), -(c_Divides_Odiv__class_Omod(_1808679, _1808683, _1808681) = c_Groups_Ozero__class_Ozero(_1808679))], (50846 ^ _779448) ^ [_1808836, _1808838, _1808840] : [class_Rings_Olinordered__idom(_1808836), 50849 ^ _779448 : [(50850 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808836), _1808838), hAPP(c_Groups_Oabs__class_Oabs(_1808836), _1808840))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808836), _1808838), _1808840)))], (50856 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808836), _1808838), _1808840)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808836), _1808838), hAPP(c_Groups_Oabs__class_Oabs(_1808836), _1808840))))]]], (50862 ^ _779448) ^ [_1809104, _1809106, _1809108] : [class_Rings_Olinordered__idom(_1809104), 50865 ^ _779448 : [(50866 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809104), hAPP(c_Groups_Oabs__class_Oabs(_1809104), _1809106)), _1809108)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809104), _1809106), _1809108)))], (50872 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809104), _1809106), _1809108)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809104), hAPP(c_Groups_Oabs__class_Oabs(_1809104), _1809106)), _1809108)))]]], (50878 ^ _779448) ^ [_1809372, _1809374, _1809376] : [class_Rings_Olinordered__idom(_1809372), hAPP(c_Groups_Oabs__class_Oabs(_1809372), _1809374) = hAPP(c_Groups_Oabs__class_Oabs(_1809372), _1809376), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809372), _1809374), _1809376)))], (50888 ^ _779448) ^ [_1809537, _1809539] : [class_Rings_Ocomm__semiring__1(_1809537), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1809537), c_Groups_Oone__class_Oone(_1809537)), _1809539)))], (50894 ^ _779448) ^ [_1809645, _1809647] : [_1809645 = _1809647, 50897 ^ _779448 : [(50898 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809645), _1809647)))], (50900 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809647), _1809645)))]]], (50902 ^ _779448) ^ [_1809764, _1809766] : [-(_1809764 = _1809766), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809764), _1809766)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809766), _1809764))], (50912 ^ _779448) ^ [_1809930, _1809932] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809930), _1809932)), 50917 ^ _779448 : [(50918 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809930), _1809932)))], (50920 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809932), _1809930))]], -(_1809930 = _1809932)], (50924 ^ _779448) ^ [_1810120, _1810122] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810120), _1810122))), 50925 ^ _779448 : [(50932 ^ _779448) ^ [] : [_1810120 = _1810122], (50926 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810120), _1810122)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810122), _1810120)))]]], (50936 ^ _779448) ^ [_1810330, _1810332] : [50943 ^ _779448 : [(50944 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810330), _1810332)))], (50946 ^ _779448) ^ [] : [_1810330 = _1810332]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810330), _1810332)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810332), _1810330)))], (50948 ^ _779448) ^ [_1810522, _1810524] : [50955 ^ _779448 : [(50956 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810522), _1810524)))], (50958 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810524), _1810522))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810522), _1810524)), -(_1810522 = _1810524)], (50960 ^ _779448) ^ [_1810719, _1810721] : [-(_1810719 = _1810721), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810719), _1810721)), 50967 ^ _779448 : [(50968 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810719), _1810721)))], (50970 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810721), _1810719))]]], (50972 ^ _779448) ^ [_1810910, _1810912] : [_1810910 = _1810912, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810910), _1810912)))], (50978 ^ _779448) ^ [_1810997, _1810999] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810997), _1810999)), 50981 ^ _779448 : [(50982 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810999), _1810997)), -(_1810999 = _1810997)], (50988 ^ _779448) ^ [] : [_1810999 = _1810997, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810999), _1810997)))]]], (50994 ^ _779448) ^ [_1811229, _1811231] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811229), _1811231)), 50999 ^ _779448 : [(51000 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811229), _1811231)))], (51002 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811231), _1811229))]], -(_1811229 = _1811231)], (51006 ^ _779448) ^ [_1811423, _1811425] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811423), _1811425)), -(_1811423 = _1811425), 51013 ^ _779448 : [(51014 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811423), _1811425)))], (51016 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811425), _1811423))]]], (51018 ^ _779448) ^ [_1811619, _1811621, _1811623] : [_1811619 = _1811621, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811621), _1811623)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811619), _1811623)))], (51028 ^ _779448) ^ [_1811772, _1811774, _1811776] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811772), _1811774)), _1811774 = _1811776, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811772), _1811776)))], (51038 ^ _779448) ^ [_1811925, _1811927] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811925), _1811927)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811927), _1811925)), -(_1811925 = _1811927)], (51048 ^ _779448) ^ [_1812074, _1812076] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812074), _1812076)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812076), _1812074)), -(_1812074 = _1812076)], (51058 ^ _779448) ^ [_1812223, _1812225, _1812227] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812223), _1812225)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812225), _1812227)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812223), _1812227)))], (51068 ^ _779448) ^ [_1812386, _1812388, _1812390] : [_1812386 = _1812388, 51079 ^ _779448 : [(51080 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812386), _1812390)))], (51082 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812390), _1812386))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812388), _1812390)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812390), _1812388)))], (51084 ^ _779448) ^ [_1812650, _1812652, _1812654] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812650), _1812652)), 51095 ^ _779448 : [(51096 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812650), _1812654)))], (51098 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812654), _1812650))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812652), _1812654)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812654), _1812652)))], (51100 ^ _779448) ^ [_1812924, _1812926] : [_1812924 = _1812926, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812924), _1812926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812926), _1812924)))], (51110 ^ _779448) ^ [_1813077, _1813079] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813077), _1813079)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813079), _1813077))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813079), _1813077)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813077), _1813079)))], (51124 ^ _779448) ^ [_1813307, _1813309] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813307), _1813309))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813307), _1813309)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813309), _1813307)))], (51134 ^ _779448) ^ [_1813469, _1813471] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813469), _1813471)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813471), _1813469))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813471), _1813469)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813469), _1813471)))], (51148 ^ _779448) ^ [_1813699, _1813701] : [_1813699 = _1813701, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813699), _1813701)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813701), _1813699)))], (51158 ^ _779448) ^ [_1813852, _1813854] : [_1813854 = _1813852, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813852), _1813854)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813854), _1813852)))], (51168 ^ _779448) ^ [_1814005, _1814007, _1814009] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814005), _1814007)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814007), _1814005))), _1814007 = _1814009, 51179 ^ _779448 : [(51180 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814005), _1814009)))], (51182 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814009), _1814005))]]], (51184 ^ _779448) ^ [_1814271, _1814273, _1814275] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814271), _1814273)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814273), _1814271))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814273), _1814275)), 51195 ^ _779448 : [(51196 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814271), _1814275)))], (51198 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814275), _1814271))]]], (51200 ^ _779448) ^ [_1814547, _1814549] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814547), _1814549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814549), _1814547))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814549), _1814547)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814547), _1814549)))], (51214 ^ _779448) ^ [_1814777, _1814779, _1814781] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814777), _1814779)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814779), _1814777))), 51229 ^ _779448 : [(51230 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814777), _1814781)))], (51232 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814781), _1814777))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814779), _1814781)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814781), _1814779)))], (51234 ^ _779448) ^ [_1815120, _1815122] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815120), _1815122)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815122), _1815120))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815122), _1815120)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815120), _1815122)))], (51248 ^ _779448) ^ [_1815350, _1815352] : [class_Rings_Ocomm__semiring__1(_1815350), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815350), _1815352), _1815352)))], (51254 ^ _779448) ^ [_1815439, _1815441, _1815443, _1815445] : [class_Rings_Ocomm__semiring__1(_1815439), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815439), _1815441), _1815443)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815439), _1815443), _1815445)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815439), _1815441), _1815445)))], (51268 ^ _779448) ^ [_1815672, _1815674] : [class_Rings_Ocomm__semiring__1(_1815672), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815672), c_Groups_Ozero__class_Ozero(_1815672)), _1815674)), -(_1815674 = c_Groups_Ozero__class_Ozero(_1815672))], (51278 ^ _779448) ^ [_1815821, _1815823, _1815825, _1815827] : [class_Divides_Osemiring__div(_1815821), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), _1815823), _1815825)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), _1815823), _1815827)), 51289 ^ _779448 : [(51290 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815821), _1815825), _1815823)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815821), _1815827), _1815823))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), _1815825), _1815827)))], (51296 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), _1815825), _1815827)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815821), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815821), _1815825), _1815823)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815821), _1815827), _1815823))))]]], (51302 ^ _779448) ^ [_1816268, _1816270, _1816272, _1816274] : [class_Rings_Ocomm__semiring__1(_1816268), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816268), _1816270), _1816272)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816268), hAPP(hAPP(c_Power_Opower__class_Opower(_1816268), _1816270), _1816274)), hAPP(hAPP(c_Power_Opower__class_Opower(_1816268), _1816272), _1816274))))], (51312 ^ _779448) ^ [_1816463, _1816465, _1816467, _1816469] : [class_Divides_Osemiring__div(_1816463), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816463), _1816465), c_Divides_Odiv__class_Omod(_1816463, _1816467, _1816469))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816463), _1816465), _1816469)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816463), _1816465), _1816467)))], (51326 ^ _779448) ^ [_1816704, _1816706, _1816708, _1816710] : [class_Divides_Osemiring__div(_1816704), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816704), _1816706), _1816708)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816704), _1816706), _1816710)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816704), _1816706), c_Divides_Odiv__class_Omod(_1816704, _1816708, _1816710))))], (51340 ^ _779448) ^ [_1816945, _1816947, _1816949, _1816951] : [class_Divides_Osemiring__div(_1816945), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816945), _1816947), _1816949)), -(c_Divides_Odiv__class_Omod(_1816945, c_Divides_Odiv__class_Omod(_1816945, _1816951, _1816949), _1816947) = c_Divides_Odiv__class_Omod(_1816945, _1816951, _1816947))], (51350 ^ _779448) ^ [_1817118, _1817120, _1817122, _1817124] : [class_Divides_Osemiring__div(_1817118), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817118), _1817120), _1817122)), 51357 ^ _779448 : [(51358 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817118), _1817120), c_Divides_Odiv__class_Omod(_1817118, _1817124, _1817122))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817118), _1817120), _1817124)))], (51364 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817118), _1817120), _1817124)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817118), _1817120), c_Divides_Odiv__class_Omod(_1817118, _1817124, _1817122))))]]], (51370 ^ _779448) ^ [_1817471] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817471), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1817471 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51376 ^ _779448) ^ [_1817552] : [_1817552 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817552), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (51382 ^ _779448) ^ [_1817639, _1817641, _1817643] : [class_Divides_Oring__div(_1817639), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817639), _1817641), _1817643)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817639), hAPP(c_Groups_Ouminus__class_Ouminus(_1817639), _1817643)), _1817641) = hAPP(c_Groups_Ouminus__class_Ouminus(_1817639), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817639), _1817643), _1817641)))], (51392 ^ _779448) ^ [_1817836, _1817838, _1817840] : [class_Divides_Oring__div(_1817836), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817836), _1817838), _1817840)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817836), _1817840), hAPP(c_Groups_Ouminus__class_Ouminus(_1817836), _1817838)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1817836), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817836), _1817840), _1817838)))], (51402 ^ _779448) ^ [_1818033, _1818035, _1818037] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818033), _1818035)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818033), _1818037)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1818035), _1818037))))], (51412 ^ _779448) ^ [_1818208, _1818210, _1818212, _1818214] : [class_Rings_Ocomm__ring__1(_1818208), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818208), _1818210), _1818212)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818208), _1818210), _1818214)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818208), _1818210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1818208), _1818212), _1818214))))], (51426 ^ _779448) ^ [_1818457, _1818459, _1818461] : [class_Rings_Ocomm__ring__1(_1818457), 51429 ^ _779448 : [(51430 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818457), _1818459), hAPP(c_Groups_Ouminus__class_Ouminus(_1818457), _1818461))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818457), _1818459), _1818461)))], (51436 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818457), _1818459), _1818461)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818457), _1818459), hAPP(c_Groups_Ouminus__class_Ouminus(_1818457), _1818461))))]]], (51442 ^ _779448) ^ [_1818725, _1818727, _1818729] : [class_Rings_Ocomm__ring__1(_1818725), 51445 ^ _779448 : [(51446 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818725), hAPP(c_Groups_Ouminus__class_Ouminus(_1818725), _1818727)), _1818729)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818725), _1818727), _1818729)))], (51452 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818725), _1818727), _1818729)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818725), hAPP(c_Groups_Ouminus__class_Ouminus(_1818725), _1818727)), _1818729)))]]], (51458 ^ _779448) ^ [_1818993, _1818995, _1818997, _1818999] : [class_Divides_Osemiring__div(_1818993), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818993), _1818995), _1818997)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1818993), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818993), _1818997), _1818995)), _1818999) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1818993), hAPP(hAPP(c_Power_Opower__class_Opower(_1818993), _1818997), _1818999)), hAPP(hAPP(c_Power_Opower__class_Opower(_1818993), _1818995), _1818999)))], (51468 ^ _779448) ^ [_1819234] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819234), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1819234 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51474 ^ _779448) ^ [_1819315] : [_1819315 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819315), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51480 ^ _779448) ^ [_1819402, _1819404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1819402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1819402), _1819404)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819404), _1819402))], (51490 ^ _779448) ^ [_1819556, _1819558, _1819560, _1819562] : [class_Divides_Osemiring__div(_1819556), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819556), _1819558), _1819560)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819556), _1819558), _1819562)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1819556), _1819560), _1819562)), _1819558) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1819556), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819556), _1819560), _1819558)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1819556), _1819562), _1819558)))], (51504 ^ _779448) ^ [_1819870, _1819872] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819870), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1819872), _1819870))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819870), _1819872)))], (51510 ^ _779448) ^ [_1819975, _1819977] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819975), _1819977)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819975), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1819977), _1819975))))], (51516 ^ _779448) ^ [_1820086, _1820088, _1820090, _1820092] : [class_Rings_Ocomm__semiring__1(_1820086), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820086), _1820088), _1820090)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820086), _1820088), _1820092)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820086), _1820088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1820086), _1820090), _1820092))))], (51530 ^ _779448) ^ [_1820356, _1820358, _1820360, _1820362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820356, _1820358)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820360, _1820362))), 51533 ^ _779448 : [(51552 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820360), _1820362)))], (51534 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820356), _1820358)), 51537 ^ _779448 : [(51538 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820360), _1820356)))], (51540 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820358), _1820362)))], (51542 ^ _779448) ^ [] : [51543 ^ _779448 : [(51544 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820360), _1820356)))], (51546 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820356), _1820360))]], 51547 ^ _779448 : [(51548 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820358), _1820362)))], (51550 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820362), _1820358))]]]]]]], (51554 ^ _779448) ^ [_1820818, _1820820, _1820822, _1820824] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820818, _1820820)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820822, _1820824)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820822), _1820824)), 51557 ^ _779448 : [(51558 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820818), _1820820)))], (51560 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820822), _1820818)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820820), _1820824)), 51567 ^ _779448 : [(51568 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820822), _1820818)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820818), _1820822)))], (51574 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820820), _1820824)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820824), _1820820)))]]]]], (51584 ^ _779448) ^ [_1821361, _1821363] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821361), _1821363)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821363, _1821361) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51590 ^ _779448) ^ [_1821458, _1821460] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821458), _1821460)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821460, _1821458) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51596 ^ _779448) ^ [_1821557, _1821559] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821557), _1821559)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821559, _1821557) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51612 ^ _779448) ^ [_1821832, _1821834] : [51613 ^ _779448 : [(51614 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821832), _1821834)))], (51616 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821834), _1821832))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821832, _1821834) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51602 ^ _779448) ^ [_1821671, _1821673] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821671, _1821673) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821671), _1821673)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821673), _1821671)))], (51630 ^ _779448) ^ [_1822156, _1822158] : [51631 ^ _779448 : [(51632 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822156), _1822158)))], (51634 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822158), _1822156))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822156, _1822158) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51620 ^ _779448) ^ [_1821995, _1821997] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821995, _1821997) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821995), _1821997)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821997), _1821995)))], (51648 ^ _779448) ^ [_1822480, _1822482] : [51649 ^ _779448 : [(51650 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822480), _1822482)))], (51652 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822482), _1822480))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822480, _1822482))], (51638 ^ _779448) ^ [_1822319, _1822321] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822319, _1822321), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822319), _1822321)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822321), _1822319)))], (51666 ^ _779448) ^ [_1822804, _1822806] : [51667 ^ _779448 : [(51668 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822804), _1822806)))], (51670 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822806), _1822804))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822804, _1822806))], (51656 ^ _779448) ^ [_1822643, _1822645] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822643, _1822645), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822643), _1822645)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822645), _1822643)))], (51674 ^ _779448) ^ [_1822952, _1822954] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822954, _1822952) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822952), _1822954)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822954), _1822952)))], (51684 ^ _779448) ^ [_1823129, _1823131] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823129, _1823131) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823129), _1823131))], (51690 ^ _779448) ^ [_1823221, _1823223] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823221), _1823223))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823221, _1823223) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51696 ^ _779448) ^ [_1823284, _1823286] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823284, _1823286), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823284), _1823286))], (51702 ^ _779448) ^ [_1823376, _1823378] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823376), _1823378))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823376, _1823378))], (51708 ^ _779448) ^ [_1823424, _1823426] : [_1823424 = _1823426, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823424, _1823426) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823424), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51714 ^ _779448) ^ [_1823523] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823523, _1823523) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823523), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51716 ^ _779448) ^ [_1823575, _1823577, _1823579] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823575, _1823577) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823579), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51719 ^ _779448 : [(51720 ^ _779448) ^ [] : [-(_1823575 = _1823577)], (51722 ^ _779448) ^ [] : [-(_1823577 = _1823579)]]], (51724 ^ _779448) ^ [_1823698, _1823700, _1823702] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823698, _1823700) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1823702), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1823698 = _1823700, _1823700 = _1823702], (51734 ^ _779448) ^ [_1823855, _1823857, _1823859, _1823861] : [class_Rings_Ocomm__ring(_1823855), class_Rings_Odvd(_1823855), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823855), _1823857), _1823859)), 51745 ^ _779448 : [(51746 ^ _779448) ^ [_1824108, _1824110] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823855), _1823857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823855), _1824110), _1823861))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823855), _1823857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1823855), _1824110), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823855), _1824108), _1823859))), _1823861))))], (51752 ^ _779448) ^ [_1824281, _1824283] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823855), _1823857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1823855), _1824283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1823855), _1824281), _1823859))), _1823861))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823855), _1823857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823855), _1824283), _1823861))))]]], (51758 ^ _779448) ^ [_1824468, _1824470, _1824472, _1824474] : [class_Rings_Ocomm__ring(_1824468), class_Rings_Odvd(_1824468), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824468), _1824470), _1824472)), 51769 ^ _779448 : [(51770 ^ _779448) ^ [_1824721, _1824723] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824468), _1824470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824468), _1824723), _1824474))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824468), _1824470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824468), _1824723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824468), _1824721), _1824472))), _1824474))))], (51776 ^ _779448) ^ [_1824894, _1824896] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824468), _1824470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1824468), _1824896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1824468), _1824894), _1824472))), _1824474))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824468), _1824470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1824468), _1824896), _1824474))))]]], (51792 ^ _779448) ^ [_1825231, _1825233, _1825235] : [51793 ^ _779448 : [(51794 ^ _779448) ^ [] : [_1825231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51796 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825233), _1825235))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825231), _1825233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825231), _1825235))))], (51782 ^ _779448) ^ [_1825099, _1825101, _1825103] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825099), _1825101)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1825099), _1825103))), -(_1825099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825101), _1825103)))], (51800 ^ _779448) ^ [_1825394, _1825396, _1825398, _1825400, _1825402] : [class_Divides_Osemiring__div(_1825394), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825394), _1825396), _1825398)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825394), _1825400), _1825402)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825394), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825394), _1825398), _1825396)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825394), _1825402), _1825400)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825394), _1825398), _1825402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825394), _1825396), _1825400)))], (51814 ^ _779448) ^ [_1825715, _1825717, _1825719, _1825721] : [class_Divides_Osemiring__div(_1825715), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825715), _1825717), _1825719)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825715), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825715), _1825719), _1825717)), _1825721) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825715), _1825719), _1825721)), _1825717))], (51824 ^ _779448) ^ [_1825928, _1825930, _1825932] : [class_Divides_Osemiring__div(_1825928), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825928), _1825930), _1825932)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825928), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825928), _1825932), _1825930)), _1825930) = _1825932)], (51834 ^ _779448) ^ [_1826105, _1826107, _1826109, _1826111] : [class_Divides_Osemiring__div(_1826105), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826105), _1826107), _1826109)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826105), _1826111), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826105), _1826109), _1826107)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826105), _1826111), _1826109)), _1826107))], (51844 ^ _779448) ^ [_1826318, _1826320, _1826322] : [class_Divides_Osemiring__div(_1826318), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826318), _1826320), _1826322)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826318), _1826320), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826318), _1826322), _1826320)) = _1826322)], (51854 ^ _779448) ^ [_1826495, _1826497, _1826499, _1826501] : [class_Rings_Oidom(_1826495), 51857 ^ _779448 : [(51868 ^ _779448) ^ [] : [51869 ^ _779448 : [(51870 ^ _779448) ^ [] : [_1826497 = c_Groups_Ozero__class_Ozero(_1826495)], (51872 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826495), _1826499), _1826501))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826495), _1826497), _1826499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826495), _1826497), _1826501))))], (51858 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826495), _1826497), _1826499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826495), _1826497), _1826501))), -(_1826497 = c_Groups_Ozero__class_Ozero(_1826495)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826495), _1826499), _1826501)))]]], (51876 ^ _779448) ^ [_1826853, _1826855, _1826857, _1826859] : [class_Rings_Oidom(_1826853), 51879 ^ _779448 : [(51890 ^ _779448) ^ [] : [51891 ^ _779448 : [(51892 ^ _779448) ^ [] : [_1826857 = c_Groups_Ozero__class_Ozero(_1826853)], (51894 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826853), _1826855), _1826859))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826853), _1826855), _1826857)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826853), _1826859), _1826857))))], (51880 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826853), _1826855), _1826857)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826853), _1826859), _1826857))), -(_1826857 = c_Groups_Ozero__class_Ozero(_1826853)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826853), _1826855), _1826859)))]]], (51898 ^ _779448) ^ [_1827211, _1827213, _1827215, _1827217] : [class_Rings_Ocomm__semiring__1(_1827211), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827211), _1827213), _1827215)), _1827217)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827211), _1827215), _1827217)))], (51908 ^ _779448) ^ [_1827390, _1827392, _1827394, _1827396] : [class_Rings_Ocomm__semiring__1(_1827390), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827390), _1827392), _1827394)), _1827396)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827390), _1827392), _1827396)))], (51918 ^ _779448) ^ [_1827569, _1827571, _1827573, _1827575] : [class_Rings_Odvd(_1827569), _1827571 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827569), _1827573), _1827575), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827569), _1827573), _1827571)))], (51928 ^ _779448) ^ [_1827734, _1827736, _1827738, _1827740, _1827742] : [class_Rings_Ocomm__semiring__1(_1827734), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827734), _1827736), _1827738)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827734), _1827740), _1827742)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827734), _1827736), _1827740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827734), _1827738), _1827742))))], (51942 ^ _779448) ^ [_1828005, _1828007, _1828009, _1828011] : [class_Rings_Ocomm__semiring__1(_1828005), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828005), _1828007), _1828009)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828005), _1828007), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828005), _1828011), _1828009))))], (51952 ^ _779448) ^ [_1828184, _1828186, _1828188, _1828190] : [class_Rings_Ocomm__semiring__1(_1828184), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828184), _1828186), _1828188)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828184), _1828186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828184), _1828188), _1828190))))], (51962 ^ _779448) ^ [_1828363, _1828365, _1828367] : [class_Rings_Ocomm__semiring__1(_1828363), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828363), _1828365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828363), _1828367), _1828365))))], (51968 ^ _779448) ^ [_1828470, _1828472, _1828474] : [class_Rings_Ocomm__semiring__1(_1828470), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828470), _1828472), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828470), _1828472), _1828474))))], (51974 ^ _779448) ^ [_1828577, _1828579, _1828581] : [class_Rings_Odvd(_1828577), class_Rings_Osemiring__0(_1828577), 51981 ^ _779448 : [(51982 ^ _779448) ^ [] : [51983 ^ _779448 : [(51984 ^ _779448) ^ [_1828769] : [hBOOL(hAPP(_1828579, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828577), _1828581), _1828769)))]], 51986 ^ _779448 : [(51987 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828577), _1828581), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828577), 51985 ^ [_1828577, _1828579, _1828581]), c_Groups_Ozero__class_Ozero(_1828577)))))], (51989 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1828579, 51985 ^ [_1828577, _1828579, _1828581])))]]], (51991 ^ _779448) ^ [] : [-(hBOOL(hAPP(_1828579, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828577), _1828581), 51998 ^ [_1828577, _1828579, _1828581])))), 51992 ^ _779448 : [(51993 ^ _779448) ^ [_1828906] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828577), _1828581), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1828577), _1828906), c_Groups_Ozero__class_Ozero(_1828577)))), hBOOL(hAPP(_1828579, _1828906))]]]]], (52002 ^ _779448) ^ [_1829079, _1829081, _1829083, _1829085, _1829087] : [class_Rings_Ocomm__semiring__1(_1829079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1829081), _1829083)), hBOOL(hAPP(hAPP(c_member(_1829081), _1829085), _1829083)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829079), hAPP(_1829087, _1829085)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1829081, _1829079), _1829087), _1829083))))], (52016 ^ _779448) ^ [_1829336, _1829338, _1829340] : [class_Rings_Ocomm__semiring__1(_1829336), 52021 ^ _779448 : [(52022 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829338))], (52024 ^ _779448) ^ [] : [_1829340 = c_Groups_Oone__class_Oone(_1829336)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829336), _1829340), hAPP(hAPP(c_Power_Opower__class_Opower(_1829336), _1829340), _1829338))))], (52028 ^ _779448) ^ [_1829543, _1829545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829543)), 52031 ^ _779448 : [(52032 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829543), _1829545)), _1829543)), -(_1829545 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52038 ^ _779448) ^ [] : [_1829545 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829543), _1829545)), _1829543)))]]], (52044 ^ _779448) ^ [_1829787, _1829789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829787)), 52047 ^ _779448 : [(52048 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829789), _1829787)), _1829787)), -(_1829789 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52054 ^ _779448) ^ [] : [_1829789 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829789), _1829787)), _1829787)))]]], (52060 ^ _779448) ^ [_1830031, _1830033, _1830035, _1830037] : [class_Orderings_Oorder(_1830031), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1830031, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1830033), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1830031), hAPP(_1830033, _1830035)), hAPP(_1830033, _1830037)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830035), _1830037)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830037), _1830035)))], (52078 ^ _779448) ^ [_1830331, _1830333, _1830335, _1830337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1830331), _1830333)), c_Equiv__Relations_Oequiv(_1830331, _1830333, _1830335), 52088 ^ _779448 : [(52089 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1830331, tc_HOL_Obool)), 52087 ^ [_1830331, _1830333, _1830335, _1830337]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1830331), _1830333), _1830335))))], (52091 ^ _779448) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830337), hAPP(c_Finite__Set_Ocard(_1830331), 52087 ^ [_1830331, _1830333, _1830335, _1830337])))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830337), hAPP(c_Finite__Set_Ocard(_1830331), _1830333))))], (52095 ^ _779448) ^ [_1830696, _1830698] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1830696), _1830698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1830698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1830696), _1830698)))], (52105 ^ _779448) ^ [_1830849, _1830851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1830849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1830851)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1830849), _1830851)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1830851), _1830849)), -(_1830849 = _1830851)], (52123 ^ _779448) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (52125 ^ _779448) ^ [_1831128, _1831130] : [class_Lattices_Obounded__lattice(_1831128), -(class_Lattices_Obounded__lattice(tc_fun(_1831130, _1831128)))], (52131 ^ _779448) ^ [_1831207, _1831209] : [class_Complete__Lattice_Ocomplete__lattice(_1831207), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1831209, _1831207)))], (52137 ^ _779448) ^ [_1831286, _1831288] : [class_Lattices_Obounded__lattice(_1831286), -(class_Lattices_Obounded__lattice__top(tc_fun(_1831288, _1831286)))], (52143 ^ _779448) ^ [_1831365, _1831367] : [class_Lattices_Obounded__lattice(_1831365), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1831367, _1831365)))], (52149 ^ _779448) ^ [_1831444, _1831446] : [class_Lattices_Olattice(_1831444), -(class_Lattices_Osemilattice__sup(tc_fun(_1831446, _1831444)))], (52155 ^ _779448) ^ [_1831523, _1831525] : [class_Lattices_Olattice(_1831523), -(class_Lattices_Osemilattice__inf(tc_fun(_1831525, _1831523)))], (52161 ^ _779448) ^ [_1831602, _1831604] : [class_Lattices_Odistrib__lattice(_1831602), -(class_Lattices_Odistrib__lattice(tc_fun(_1831604, _1831602)))], (52167 ^ _779448) ^ [_1831681, _1831683] : [class_Lattices_Oboolean__algebra(_1831681), -(class_Lattices_Oboolean__algebra(tc_fun(_1831683, _1831681)))], (52173 ^ _779448) ^ [_1831760, _1831762] : [class_Orderings_Opreorder(_1831760), -(class_Orderings_Opreorder(tc_fun(_1831762, _1831760)))], (52179 ^ _779448) ^ [_1831839, _1831841] : [-(class_Finite__Set_Ofinite(tc_fun(_1831839, _1831841))), class_Finite__Set_Ofinite(_1831839), class_Finite__Set_Ofinite(_1831841)], (52189 ^ _779448) ^ [_1831968, _1831970] : [class_Lattices_Olattice(_1831968), -(class_Lattices_Olattice(tc_fun(_1831970, _1831968)))], (52195 ^ _779448) ^ [_1832047, _1832049] : [class_Orderings_Oorder(_1832047), -(class_Orderings_Oorder(tc_fun(_1832049, _1832047)))], (52201 ^ _779448) ^ [_1832126, _1832128] : [class_Orderings_Otop(_1832126), -(class_Orderings_Otop(tc_fun(_1832128, _1832126)))], (52207 ^ _779448) ^ [_1832205, _1832207] : [class_Orderings_Oord(_1832205), -(class_Orderings_Oord(tc_fun(_1832207, _1832205)))], (52213 ^ _779448) ^ [_1832284, _1832286] : [class_Orderings_Obot(_1832284), -(class_Orderings_Obot(tc_fun(_1832286, _1832284)))], (52219 ^ _779448) ^ [_1832363, _1832365] : [class_Groups_Ouminus(_1832363), -(class_Groups_Ouminus(tc_fun(_1832365, _1832363)))], (52225 ^ _779448) ^ [_1832442, _1832444] : [class_Groups_Ominus(_1832442), -(class_Groups_Ominus(tc_fun(_1832444, _1832442)))], (52231 ^ _779448) ^ [_1832521, _1832523] : [-(class_Enum_Oenum(tc_fun(_1832521, _1832523))), class_Enum_Oenum(_1832521), class_Enum_Oenum(_1832523)], (52241 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (52243 ^ _779448) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (52245 ^ _779448) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (52247 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (52249 ^ _779448) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52251 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (52253 ^ _779448) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52255 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (52257 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (52259 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (52261 ^ _779448) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (52263 ^ _779448) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (52265 ^ _779448) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52267 ^ _779448) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (52269 ^ _779448) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52271 ^ _779448) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52273 ^ _779448) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (52275 ^ _779448) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (52277 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (52279 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52281 ^ _779448) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (52283 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (52285 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (52287 ^ _779448) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52289 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (52291 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (52293 ^ _779448) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (52295 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52297 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (52299 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52301 ^ _779448) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52303 ^ _779448) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52305 ^ _779448) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (52307 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (52309 ^ _779448) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (52311 ^ _779448) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (52313 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52315 ^ _779448) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52317 ^ _779448) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52319 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52321 ^ _779448) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52323 ^ _779448) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52325 ^ _779448) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52327 ^ _779448) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52329 ^ _779448) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52331 ^ _779448) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52333 ^ _779448) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52335 ^ _779448) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52337 ^ _779448) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52339 ^ _779448) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52341 ^ _779448) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52343 ^ _779448) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52345 ^ _779448) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52347 ^ _779448) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52349 ^ _779448) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52351 ^ _779448) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52353 ^ _779448) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52355 ^ _779448) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52357 ^ _779448) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52359 ^ _779448) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52361 ^ _779448) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52363 ^ _779448) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52365 ^ _779448) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52367 ^ _779448) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52369 ^ _779448) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52371 ^ _779448) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52373 ^ _779448) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52375 ^ _779448) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52377 ^ _779448) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52379 ^ _779448) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52381 ^ _779448) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52383 ^ _779448) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52385 ^ _779448) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52387 ^ _779448) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52389 ^ _779448) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52391 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52393 ^ _779448) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52395 ^ _779448) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52397 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52399 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52401 ^ _779448) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52403 ^ _779448) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52405 ^ _779448) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52407 ^ _779448) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52409 ^ _779448) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52411 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52413 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52415 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52417 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52419 ^ _779448) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52421 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52423 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52425 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52427 ^ _779448) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52429 ^ _779448) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52431 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52433 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52435 ^ _779448) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52437 ^ _779448) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52439 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52441 ^ _779448) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52443 ^ _779448) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52445 ^ _779448) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52447 ^ _779448) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52449 ^ _779448) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52451 ^ _779448) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52453 ^ _779448) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52455 ^ _779448) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52457 ^ _779448) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52459 ^ _779448) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52461 ^ _779448) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52463 ^ _779448) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52465 ^ _779448) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52467 ^ _779448) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52469 ^ _779448) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52471 ^ _779448) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52473 ^ _779448) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52475 ^ _779448) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52477 ^ _779448) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52479 ^ _779448) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52481 ^ _779448) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52483 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52485 ^ _779448) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52487 ^ _779448) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52489 ^ _779448) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52491 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52493 ^ _779448) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52495 ^ _779448) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52497 ^ _779448) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52499 ^ _779448) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52501 ^ _779448) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52503 ^ _779448) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52505 ^ _779448) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52507 ^ _779448) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52509 ^ _779448) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52511 ^ _779448) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52513 ^ _779448) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52515 ^ _779448) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52517 ^ _779448) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52519 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52521 ^ _779448) ^ [_1835170] : [class_Lazy__Sequence_Osmall__lazy(_1835170), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1835170)))], (52527 ^ _779448) ^ [_1835245] : [-(class_Nat_Osize(tc_List_Olist(_1835245)))], (52529 ^ _779448) ^ [_1835269, _1835271] : [-(class_Finite__Set_Ofinite(tc_sum(_1835269, _1835271))), class_Finite__Set_Ofinite(_1835269), class_Finite__Set_Ofinite(_1835271)], (52539 ^ _779448) ^ [_1835398, _1835400] : [-(class_Enum_Oenum(tc_sum(_1835398, _1835400))), class_Enum_Oenum(_1835398), class_Enum_Oenum(_1835400)], (52549 ^ _779448) ^ [_1835527, _1835529] : [-(class_Nat_Osize(tc_sum(_1835527, _1835529)))], (52551 ^ _779448) ^ [_1835554] : [class_Finite__Set_Ofinite(_1835554), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1835554)))], (52557 ^ _779448) ^ [_1835629] : [class_Enum_Oenum(_1835629), -(class_Enum_Oenum(tc_Option_Ooption(_1835629)))], (52563 ^ _779448) ^ [_1835704] : [-(class_Nat_Osize(tc_Option_Ooption(_1835704)))], (52565 ^ _779448) ^ [_1835728, _1835730] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1835728, _1835730)))], (52567 ^ _779448) ^ [_1835755, _1835757] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1835755, _1835757))), class_Lazy__Sequence_Osmall__lazy(_1835755), class_Lazy__Sequence_Osmall__lazy(_1835757)], (52577 ^ _779448) ^ [_1835884, _1835886] : [-(class_Finite__Set_Ofinite(tc_prod(_1835884, _1835886))), class_Finite__Set_Ofinite(_1835884), class_Finite__Set_Ofinite(_1835886)], (52587 ^ _779448) ^ [_1836013, _1836015] : [-(class_Enum_Oenum(tc_prod(_1836013, _1836015))), class_Enum_Oenum(_1836013), class_Enum_Oenum(_1836015)], (52597 ^ _779448) ^ [_1836142, _1836144] : [-(class_Nat_Osize(tc_prod(_1836142, _1836144)))], (52599 ^ _779448) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52601 ^ _779448) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52603 ^ _779448) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52605 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52607 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52609 ^ _779448) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52611 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52613 ^ _779448) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52615 ^ _779448) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52617 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52619 ^ _779448) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52621 ^ _779448) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52623 ^ _779448) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52625 ^ _779448) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52627 ^ _779448) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52629 ^ _779448) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52631 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52633 ^ _779448) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52635 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52637 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52639 ^ _779448) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52641 ^ _779448) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52643 ^ _779448) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52645 ^ _779448) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52647 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52649 ^ _779448) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52651 ^ _779448) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52653 ^ _779448) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52655 ^ _779448) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52657 ^ _779448) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52659 ^ _779448) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52661 ^ _779448) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52663 ^ _779448) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52665 ^ _779448) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52667 ^ _779448) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52669 ^ _779448) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52671 ^ _779448) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52673 ^ _779448) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52675 ^ _779448) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52677 ^ _779448) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52679 ^ _779448) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52681 ^ _779448) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52683 ^ _779448) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52685 ^ _779448) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52687 ^ _779448) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52689 ^ _779448) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52691 ^ _779448) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52693 ^ _779448) ^ [_1837015] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1837015)))], (52695 ^ _779448) ^ [_1837039, _1837041] : [-(hAPP(c_COMBI(_1837039), _1837041) = _1837041)], (52697 ^ _779448) ^ [_1837069, _1837071, _1837073, _1837075] : [-(hAPP(hAPP(c_COMBK(_1837069, _1837071), _1837073), _1837075) = _1837073)], (52699 ^ _779448) ^ [_1837107, _1837109, _1837111, _1837113, _1837115, _1837117] : [-(hAPP(hAPP(hAPP(c_COMBB(_1837107, _1837109, _1837111), _1837113), _1837115), _1837117) = hAPP(_1837113, hAPP(_1837115, _1837117)))], (52701 ^ _779448) ^ [_1837159, _1837161, _1837163, _1837165, _1837167, _1837169] : [-(hAPP(hAPP(hAPP(c_COMBC(_1837159, _1837161, _1837163), _1837165), _1837167), _1837169) = hAPP(hAPP(_1837165, _1837169), _1837167))], (52703 ^ _779448) ^ [_1837211, _1837213, _1837215, _1837217, _1837219, _1837221] : [-(hAPP(hAPP(hAPP(c_COMBS(_1837211, _1837213, _1837215), _1837217), _1837219), _1837221) = hAPP(hAPP(_1837217, _1837221), hAPP(_1837219, _1837221)))], (52705 ^ _779448) ^ [_1837266, _1837268] : [hBOOL(hAPP(hAPP(c_fequal, _1837266), _1837268)), -(_1837266 = _1837268)], (52711 ^ _779448) ^ [_1837355, _1837357] : [_1837355 = _1837357, -(hBOOL(hAPP(hAPP(c_fequal, _1837355), _1837357)))], (52717 ^ _779448) ^ [] : [hBOOL(c_fFalse)], (52719 ^ _779448) ^ [] : [-(hBOOL(c_fTrue))], (52721 ^ _779448) ^ [_1837486] : [hBOOL(hAPP(c_fNot, _1837486)), hBOOL(_1837486)], (52727 ^ _779448) ^ [_1837562] : [-(hBOOL(_1837562)), -(hBOOL(hAPP(c_fNot, _1837562)))], (52733 ^ _779448) ^ [_1837597, _1837599] : [hBOOL(_1837597), hBOOL(_1837599), -(hBOOL(hAPP(hAPP(c_fconj, _1837597), _1837599)))], (52743 ^ _779448) ^ [_1837736, _1837738] : [hBOOL(hAPP(hAPP(c_fconj, _1837736), _1837738)), -(hBOOL(_1837736))], (52749 ^ _779448) ^ [_1837823, _1837825] : [hBOOL(hAPP(hAPP(c_fconj, _1837823), _1837825)), -(hBOOL(_1837825))], (52755 ^ _779448) ^ [_1837910, _1837912] : [hBOOL(_1837910), -(hBOOL(hAPP(hAPP(c_fdisj, _1837910), _1837912)))], (52761 ^ _779448) ^ [_1837997, _1837999] : [hBOOL(_1837997), -(hBOOL(hAPP(hAPP(c_fdisj, _1837999), _1837997)))], (52767 ^ _779448) ^ [_1838084, _1838086] : [hBOOL(hAPP(hAPP(c_fdisj, _1838084), _1838086)), -(hBOOL(_1838084)), -(hBOOL(_1838086))], (52777 ^ _779448) ^ [_1838178, _1838180] : [-(hBOOL(_1838178)), -(hBOOL(hAPP(hAPP(c_fimplies, _1838178), _1838180)))], (52783 ^ _779448) ^ [_1838218, _1838220] : [hBOOL(_1838218), -(hBOOL(hAPP(hAPP(c_fimplies, _1838220), _1838218)))], (52789 ^ _779448) ^ [_1838305, _1838307] : [hBOOL(hAPP(hAPP(c_fimplies, _1838305), _1838307)), hBOOL(_1838305), -(hBOOL(_1838307))], (52799 ^ _779448) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))], (52815 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))], (52817 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, v_n)), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))))], (52819 ^ _779448) ^ [] : [-(hAPP(c_Finite__Set_Ocard(t_a), v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hAPP(c_Nat_OSuc, v_n)))], (52821 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))], (52823 ^ _779448) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), v_G)))], (52801 ^ _779448) ^ [_1838462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _1838462), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hAPP(c_Finite__Set_Ocard(t_a), _1838462) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), v_n), 52808 ^ _779448 : [(52809 ^ _779448) ^ [_1838594] : [v_wt(_1838594), -(v_P(_1838462, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_1838594)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))]]]], input).
% 142.73/137.45  ncf('1',plain,[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), v_G))],start(52825 ^ 0)).
% 142.73/137.45  ncf('1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), v_G))), hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), v_G)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), v_G))],extension(6266 ^ 1,bind([[_880215, _880217, _880219, _880221], [t_a, hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)), v_G]]))).
% 142.73/137.45  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), v_G)))],extension(52823 ^ 2)).
% 142.73/137.45  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), v_G)))],extension(5706 ^ 2,bind([[_869540, _869542], [t_a, v_G]]))).
% 142.73/137.45  %-----------------------------------------------------
% 142.73/137.45  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------